chapter 11. statistical analysis and...
TRANSCRIPT
Statistical analysis of relevés tatbles 2020
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Chapter 11. Statistical analysis and
phytosociology
by Guy BOUXIN°
Contents
Introduction ............................................................................................................................................................. 2
The data .............................................................................................................................................................. 2
The phytosociological analysis .......................................................................................................................... 3
The character-species of the associations ...................................................................................................... 3
Data analysis ...................................................................................................................................................... 6
The covariance matrices and the choice of a technique ................................................................................. 6
Correspondence analysis of presence data..................................................................................................... 8
Non-symmetric analysis of presence data ................................................................................................... 11
Non-symmetric correspondence analysis of the simple disjunctive table ................................................... 15
Non-symmetric correspondence analysis of the simplified disjunctive table .............................................. 20
Conclusions about the analysis of the ROYER’s table .................................................................................... 21
The BAILLY’s file................................................................................................................................................ 21
The data ............................................................................................................................................................ 21
The phytosociological analysis ........................................................................................................................ 22
The character-species of the associations .................................................................................................... 23
Data analysis of the complete file .................................................................................................................... 34
Covariance matrix and the choice of a technique ........................................................................................ 34
Multiple factor analysis based on non-symmetric correspondence analysis of the presence table .............. 36
Classification and ranking of the relevés set ............................................................................................... 39
Data analysis of the fern Alder file................................................................................................................... 42
Multiple factor analysis of the simplified disjunctive table ......................................................................... 42
Classification and ranking of the fern Alders .............................................................................................. 45
Data analysis of the sedge Alder file ................................................................................................................ 51
Multiple factor analysis of the simplified disjunctive table ......................................................................... 51
Classification and ranking of the Alders with Sedge ................................................................................... 55
Conclusions on the analysis of the BAILLY’s table ........................................................................................ 60
General conclusions .............................................................................................................................................. 61
References ............................................................................................................................................................. 61
2
Introduction
The statistical analysis of the tables of phytosociological relevés has long raised a lot of skepticism among
the proponents of the sigmatist school. However, increasingly, relevé tables are submitted to multivariate
analyses, usually on the basis of abundance-dominance coefficients or on presences. Among the many examples,
GUYONNEAU (2005) uses correspondence analysis alone, BAILLY (2012) correspondence analysis and the
hierarchical ascending classification with presence-absence data (agglomerative grouping with complete links
with the Bray-Curtis distance) or abundance-dominance (Ward method with chord distance), COLLAUD and
collaborators (2010) correspondence analysis and hierarchical ascending classification in abundance-dominance
(Ward method with the chord distance) and FERREY (2007, 2009 and 2011) the hierarchical ascending
classification in abundance-dominance (Ward's method on the chord distance). As we have already explained in
Chapter 5, abundance-dominance data are poorly adapted to multivariate analyses. The objective of this chapter
is to compare the results provided by phytosociologists and those proposed by multivariate analyses used in a
biometrician approach, in a spirit of data analysis. Do these two approaches produce consistent results? To what
extent can data analysis help the phytosociologist?
To develop our argument, we first chose two files published and analysed by phytosociologists: the file
ROYER (2009) and the file BAILLY (2012). In order to ensure an easy comparison between the two texts and
ours, we have reproduced the botanical nomenclature adopted by the authors.
The data
These are relevés of limestone walls (table 1).
Species/Relevés 1 2 3 4 5 6 7 8 9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
2
1
2
2
2
3
2
4
2
5
2
6
2
7
Asplenium trichomanes subsp.
quadrivalens + . 1 . 2 + 1 + 1 + 3 . 1 + . . + . 1 1 + 1 . . 1 1 .
Potentilla neumanniana 1 . . . . . . . . . . . . . + . . . . . . + . . . . +
Ceterach officinarum 2 . . . . . . . . . . . . . . . . . . . . 1 . . . . .
Helleborus foetidus + . . . . . . . . . . . . . . . . . . . . . . . . . .
Sanguisorba minor + . . . . . . . . . . . . . . . . . . . . . . . . . .
Bromus erectus 1 . . . . . . . . . . . . . . . . . . . . . . . . . .
Asplenium trichomanes subsp. hastatum . 2 . . . 2 + . . . . 1 . . . 1 . 1 . . . . 1 . . . .
Poa nemoralis . + . . + + 1 . + . 2 . 1 . . . . . . . . . . + . . .
Geranium robertianum . + + . . . . + . 1 1 . 1 + . + . . . 1 1 . . . . . .
Phyllitis scolopendrium . . 2 . . . . 1 . 2 . . 1 1 . . . . . . 1 . . + 1 . .
Cystopteris fragilis . . 1 . . + . + . . . . 1 2 . + . + . + + . . 1 + . .
Cardamine impatiens . . + . . . . . . + . . 1 . . . . . . . . . . . + . .
Hedera helix . . + . . . 1 + . + . 1 . . . . . + . . . + 1 . . + .
Moehringia trinervia . . + . . . . . . . . . + . . . . . . . + . . . + . .
Vinca minor . . + . . . . . . . . . . . . . . . . . . . . . . . .
Asplenium trichomanes subsp.
pachyrachis . . . 1 . . . . . . . . . . 1 . . . . . . . . . . . 1
Asplenium ruta-muraria . . . + 1 . + . . . + + . . + . + . + 1 . 1 + 1 . 1 +
Mycelis muralis . . . . + . . . 1 . . . + . . . . . . . . . . . . . .
Cardaminopsis arenosa subsp. borbasii . . . . 1 . 2 . . . . . . . . . . . + + 1 . . 1 + . .
3
Campanula rotundifolia . . . . + . + . . . . . . . + . + . + . 1 . . . . + .
Sesleria caerulea . . . . + . . . . . . . . . . . + . . . . . . . . . .
Lamium galeobdolon . . . . . . . 1 . 1 . . . . . . . . . . . . . + . . .
Mercurialis perennis . . . . . . . 2 . . . . . . . . . . . . . . . . . . .
Oxalis acetosella . . . . . . . 1 . . . . . . . . . . . . 1 . . + + . .
Campanula trachelium . . . . . . . + . . . . . . . . . . . . . . . . . . .
Galium aparine . . . . . . . . . + . . . . . . . . . . . . . . . . .
Chrysosplenium alternifolium . . . . . . . . . + . . . . . . . . . . . . . . . . .
Arabis hirsuta . . . . . . . . . . + . . . . . . . . . . . . . . . .
Origanum vulgare . . . . . . . . . . + . . . . . . . . . . . . . . . .
Thymus praecox . . . . . . . . . . + . . . . . . . . . . . . . . . .
Ribes uva-crispa . . . . . . . . . . + . . . . . . . . . . . . . . + .
Polypodium interjectum . . . . . . . . . . . . 1 . . . . . . 1 + . . . . . .
Fragaria vesca . . . . . . . . . . . . . . . . + . . . . . . . . . .
Viola alba . . . . . . . . . . . . . . . . . . 1 . . . . . . . .
Silene nutans . . . . . . . . . . . . . . . . . . + . . . . . . . .
Potentilla micrantha . . . . . . . . . . . . . . . . . . + . . . . . . . .
Poa compressa . . . . . . . . . . . . . . . . . . . + . . . . . . .
Melica uniflora . . . . . . . . . . . . . . . . . . . . . . + . . . .
Clematis vitalba . . . . . . . . . . . . . . . . . . . . . . + . . . .
Sedum spurium . . . . . . . . . . . . . . . . . . . . . . . + . . .
Ribes alpinum . . . . . . . . . . . . . . . . . . . . . . . . + . .
Sedum album . . . . . . . . . . . . . . . . . . . . . . . . . + .
Table 1. Table of the 27 phytosociological relevés with the abundance-dominance coefficients +, 1, 2, 3. « . » =
absent species.
.
This table is relatively simple, with a majority of empty cells and mainly coefficients +, 1, 2 and 3.
The phytosociological analysis
The character-species of the associations
The methodological approach is based on the concept of elementary syntaxon (Sy-E) developed by de
FOUCAULT (1982). The elementary syntaxon groups together a set of relevés in a homotone table. The
elementary syntaxa constitute the elementary element for the elaboration of the phytosociological typology and
must not be confused with the associations. SY-E often correspond to syntaxons of sub-association rank
(variants, sub-associations).
Five elementary syntaxa (A to K) have been identified. The constant species of the syntaxon Asplenietum
pachyrachidis (relevés 4, 15, 27) are Asplenium trichomanes subsp. pachyrachis and Asplenium ruta-muraria,
the positive differential species are Asplenium trichomanes subsp. pachyrachis, Potentilla neumanniana (the
latter only with respect to the syntaxa C, D and E) and the negative differential species Asplenium trichomanes
subsp. quadrivalens and Hedera helix. Syntaxon D has more constant species : Phyllitis scolopendrium,
Cystopteris fragilis, Geranium robertianum, Asplenium trichomanes subsp. quadrivalens. Its positive differential
species are Cardamine impatiens, Polypodium interjectum, Moehringia trinervia, Lamium galeobdolon, Oxalis
4
acetosella, Cystopteris fragilis (the latter with respect to A-B-C but not with respect to E), its negative
differential, Asplenium trichomanes subsp. pachyrachys (with respect to A), Asplenium trichomanes subsp.
hastatum (with respect to E)… The syntaxon B corresponds to the Asplenietum trichomano-rutae-murariae
ceterachetosum officinarum (relevés 1, 22), the syntaxon C to the Asplenietum trichomano-rutae-murariae
cardaminopsietosum borbasii (relevés 5, 7, 9, 11, 17, 19, 26), the syntaxon D to the Cystopterido fragilis-
Phyllitidetum scolopendrii (relevés 3, 8, 10, 13, 14, 20, 21, 24, 25) and the syntaxon E to the Asplenietum
hastati (relevés 2, 6, 12, 16, 18, 23).
In each defined grouping, we subject the frequency of the floristic variables to a test by permutation. Let us
recall the technique. The frequency of a variable in a group is compared with those obtained in the same set of
relevés when all the columns in the table are randomly permuted. The tests are built with 100,000 permutations.
There is thus a statistical basis for defining character-species. Each grouping is characterized by all the character-
species (exclusive, preferential), companions or accidental. Character-species are frequent species whose
frequency is statistically greater than that of all relevés; exclusive species are rare. It is necessary to specify that
it is sometimes either the presence of the species that is characteristic or the abundance, starting from a certain
threshold. Companions are frequent species but whose frequency is not greater than that of all the relevés.
Within a species, it happens that it is a simple companion by its presence and a characteristic by its local
abundance. The so-called accidental species are infrequent in relevés. A species may be characteristic only a the
scale of a table and have another status at another scale.
The results of the phytosociological study are the references for evaluating the statistical analyses.
The character-species of the Asplenietum pachyrachidis
Species/Relevés 4 15 27 Fr Pr
Potentilla neumanniana 0 1 1 2 0,67 0,04889
Asplenium trichomanes subsp. pachyrachis 1 1 1 3 1 0,00031
Table2. Character-species of the Asplenietum pachyrachidis. = frequence, Fr = relative frequence, Pr =
probability computed with the test.
With the permutation test, we find (table 2) as character-species, the two ones cited as positive differentials
by ROYER (2009)
The character-species of the Asplenietum trichomanes-rutae-murariae ceterachetosum
officinarum
Species/Relevés 1 22 Fr Pr
Potentilla neumanniana 1 1 2 1 0,01754
Ceterach officinarum 1 1 2 1 0,00306
Table 3. Character-species of the Asplenietum trichomanes-rutae-murariae ceterachetosum officinarum. =
frequence, Fr = relative frequence, Pr = probability computed with the test.
5
The two species highlighted in the final table of ROYER (2009) are found here as character-species (Table
3).
The character-species of the Asplenietum trichomano-rutae-murariae cardaminopsietosum
borbasii
Here, the differences are notorious since only Campanula rotundifolia is common to statistical analysis
(table 4) and to that of ROYER (2009), which also highlights Seseleria caerulea and Cardaminopsis arenosa
subsp. borbasii.
Species/Relevés 19 26 5 17 7 9 11 Fr Pr
Asplenium trichomanes subsp. quadrivalens 1 1 1 1 1 1 1 7 1 0,03507
Asplenium ruta-muraria 1 1 1 1 1 0 1 6 0,86 0,04802
Campanula rotundifolia 1 1 1 1 1 0 0 5 0,71 0,00471
Table 4. Character-species of the Asplenietum trichomano-rutae-murariae cardaminopsietosum borbasii. =
frequence, Fr = relative frequence, Pr = probability computed with the test.
The character-species of the Cystopterido fragilis-Phyllitidetum scolopendrii
Almost all positive differentiated species differentiated from the ROYER’s table, with the exception of
Cardaminopsis arenosa subsp. borbasii, are considered with significant frequency by statistical analysis (table
5).
Species/Relevés 21 14 8 24 25 13 20 10 3 Fr Pr
Geranium robertianum 1 1 1 0 0 1 1 1 1 7 0,78 0,00349
Phyllitis scolopendrium 1 1 1 1 1 1 0 1 1 8 0,89 0
Cystopteris fragilis 1 1 1 1 1 1 1 0 1 8 0,89 0,00058
Cardamine impatiens 0 0 0 0 1 1 0 1 1 4 0,44 0,00722
Moehringia trinervia 1 0 0 0 1 1 0 0 1 4 0,44 0,00726
Lamium galeobdolon 0 0 1 1 0 0 0 1 0 3 0,33 0,02872
Oxalis acetosella 1 0 1 1 1 0 0 0 0 4 0,44 0,00694
Polypodium interjectum 1 0 0 0 0 1 1 0 0 3 0,33 0,02853
Table 5. Character-species of the Cystopterido fragilis-Phyllitidetum scolopendrii. = frequence, Fr = relative
frequence, Pr = probability computed with the test.
The character-species of the Asplenietum hastati
Espèces/Relevés 6 16 18 2 12 23 Fr Pr
Asplenium trichomanes subsp. hastatum 1 1 1 1 1 1 6 1 0,00003
Table 6. Character-species of the Asplenietum hastati. = frequence, Fr = relative frequence, Pr = probability
computed with the test.
A single species is characteristic here (table 6) versus three by ROYER (2009).
6
Data analysis
This analysis of the data is a consequence of numerous studies presented in this website in chapters 5 to 10.
The techniques are therefore presented succinctly.
The phytosociologists' files include coefficients that can not be used as they are in calculations (+, r, i, s)
and that it is impossible to add to the other coefficients 1, 2, 3, 4 and 5 of the same row or column; these latter
coefficients also belong to an ordinal variable. It is possible to replace each + or r or i or s by a coefficient 1 or
0.1 for example but this choice retains a large part of arbitrary and this does not change the fact that the variable
is ordinal. Mathematical operations such as additions or averaging are illicit. It is therefore necessary to adapt the
original file and several transformations are possible by:
- a presence table, with a single line per species, with 0 and 1,
- a complete disjunctive table with, for each species, a line for absences with 1 for absence and 0 for presence,
regardless of the abundance coefficients and as many lines as there are different coefficients of abundance -
dominance,
- a simple disjunctive table with as many lines as there are different coefficients of abundance-dominance,
without line for absences,
- a "simplified" disjunctive table obtained by grouping, for example, the lines +, r, i or s and 1 into one,
abundances> 1 in a single line (there are a few abundance-dominances '3' and no higher than 3).
The latter kind of table is purely empirical but it has been the basis of interesting results on several
occasions. So we continue to evaluate it.
The relevance of the analyses and the final choice is made after examining the covariance matrices of the
correspondence analyses and the non-symmetric correspondence analyses, single or in a multiple factor analysis.
This greatly reduces the arbitrariness of the transformations.Either simplification is still possible by applying
multivariate analyses only to some of the columns in the table when a group of relevés is readily isolated from
view. Classification and ranking techniques (see chapter 12) are then calculated on the basis of the variables
transformed by correspondence analyses.
The covariance matrices and the choice of a technique
The covariance matrices of six analyses are compared (figure 1). The non-symmetric correspondence
analysis of the complete disjunctive table is not presented, as it focuses on absences that are more numerous than
presences. There are 61.11% empty cells in the presence table.
7
Figure 1. Covariance distributions in the multivariate analyses of the ROYER’s file, in three transformed tables
and two correspondence analyses.
From the six analyzes, it appears that, in correspondence analysis of the three types of tables, the spread of
the covariances is much less than in the non-symmetric analyzes. We deduce once again that the correspondence
analyzes misuse the significant variability of this type of table. Non-symmetric analyzes provide a better basis
for interpretation. In this specific case, the presence data and the disjunctive table with the presence and
abundance lines > 1 are a good basis for analysis.
8
Correspondence analysis of presence data
Certain phytosociologists attach great importance to the presence data alone. This is why it is important to
compare the previous results with those obtained with the presence data only, regardless of the abundance-
dominance coefficients.
The decrease in the eigenvalues is progressive (figure 2) and none of the eigenvalues of the axes is
significant.
Figure 2. The firdt twelve eigenvalues of correspondence analysis of the presence table.
On the first two axes, only two species have a significant relative contributions: Potentilla neumanniana for
the first axis and Asplenium ruta-muraria for the second. The main results appear in table 7 and figures 3 and 4.
coord 1 Cr% 1 P 1 coord 2 Cr% 2 P 2
Vp.Vp% et P 0.717008468 12.37844497 8.837113825 0.597730061 10.31922076 6.343015498
Asplenium trichomanes subsp. quadrivalens 0.015173238 0.003753047 97.03376783 0.120783744 0.285274966 64.3538951
Potentilla neumanniana 2.225138464 17.93614341 1.108488145 0.010974809 0.000523393 98.70676383
Ceterach officinarum 2.580943347 12.06540581 6.014574566 1.444740688 4.535069898 16.53494817
Helleborus foetidus 3.702816373 12.41707617 8.139176845 2.68852666 7.85240835 9.801909063
Sanguisorba minor 3.702816373 12.41707617 8.07759417 2.68852666 7.85240835 9.411885456
Bromus erectus 3.702816373 12.41707617 8.241814636 2.68852666 7.85240835 10.03797598
Asplenium trichomanes subsp. hastatum -0.265642707 0.447351429 51.56522632 -0.33093055 0.832810022 50.77491532
Poa nemoralis -0.317207514 0.729007361 42.12254952 -0.150722902 0.197434327 75.70563481
Geranium robertianum -0.54867835 2.726406709 15.84727497 0.389726184 1.650035741 32.9877861
Phyllitis scolopendrium -0.640465952 2.971919732 16.13466078 0.69695132 4.221522016 14.34876321
Cystopteris fragilis -0.567929466 3.213190562 12.13178692 0.461392824 2.543949805 21.64631017
Cardamine impatiens -0.682160702 1.68573141 24.60227856 0.809597182 2.848210925 24.46884943
Hedera helix -0.072229824 0.042523658 87.14974854 -0.08873732 0.076989112 84.21430771
Moehringia trinervia -0.647046031 1.5166499 25.61839269 0.678586709 2.000989786 31.19162476
0
2
4
6
8
10
12
14
1 2 3 4 5 6 7 8 9 10 11 12
9
Vinca minor -0.663701884 0.398934041 39.45396695 0.811324712 0.715094751 41.8864826
Asplenium trichomanes subsp. pachyrachis 1.769541422 8.507416896 7.667043005 -1.658286065 8.962193964 8.098121728
Asplenium ruta-muraria 0.481803655 2.943223281 9.996920866 -0.887178547 11.97083046 0
Mycelis muralis -0.307795491 0.257395384 55.16781279 -0.052765384 0.009073893 93.59540183
Cardaminopsis arenosa subsp. borbasii -0.277593521 0.488508007 50.51832085 -0.15849306 0.191026107 75.62352458
Campanula rotundifolia 0.277495792 0.488164101 50.49779329 -0.889750401 6.020167934 8.950015396
Sesleria caerulea 0.193837336 0.068054971 73.84789079 -1.04529101 2.373988481 25.89551473
Lamium galeobdolon -0.642731146 1.122367133 28.95412091 0.721089059 1.694623592 33.88073489
Mercurialis perennis -0.692721551 0.434582659 39.28974648 0.86540119 0.81359666 40.23401416
Oxalis acetosella -0.627880361 1.428133427 26.08026275 0.62347856 1.689185015 34.19891204
Campanula trachelium -0.692721551 0.434582659 38.66365596 0.86540119 0.81359666 40.53166376
Galium aparine -0.688181508 0.428904884 39.24869137 0.952394712 0.985389959 37.23699066
Chrysosplenium alternifolium -0.688181508 0.428904884 39.17684491 0.952394712 0.985389959 36.95986862
Arabis hirsuta -0.113468821 0.011660256 87.10869342 -0.813716807 0.719317712 42.6254747
Origanum vulgare -0.113468821 0.011660256 87.5602997 -0.813716807 0.719317712 42.10202196
Thymus praecox -0.113468821 0.011660256 86.86236272 -0.813716807 0.719317712 41.2501283
Ribes uva-crispa 0.058450591 0.006188178 93.40039002 -0.922522029 1.849088376 29.95997126
Polypodium interjectum -0.517572487 0.727810998 36.25166786 0.381678355 0.474777906 57.14872216
Fragaria vesca 0.37458188 0.127071608 59.67361182 -1.358426974 2.004687925 25.70050293
Viola alba 0.246094391 0.054847701 73.1088987 -1.532490742 2.551349181 22.36477471
Silene nutans 0.246094391 0.054847701 73.32443806 -1.532490742 2.551349181 21.34866058
Potentilla micrantha 0.246094391 0.054847701 72.21594991 -1.532490742 2.551349181 21.56419994
Poa compressa -0.352021912 0.112226234 61.91111567 0.096701891 0.01015884 90.91655548
Melica uniflora 0.090805854 0.007467628 89.81833111 -1.321849001 1.898182111 25.87498717
Clematis vitalba 0.090805854 0.007467628 90.32125629 -1.321849001 1.898182111 26.6960895
Sedum spurium -0.547290378 0.271263037 46.70019501 0.345471275 0.129657626 69.99897362
Ribes alpinum -0.72378669 0.474434409 36.85723083 0.854688951 0.793579355 40.09032126
Sedum album 0.230370002 0.048062554 74.26870574 -1.031327252 1.155492601 34.31181361
X1 3.135409846 53.41889256 2.22724007 2.078580727 28.16172312 3.212562866
X2 -0.445432732 0.539064216 42.88206918 -0.039634241 0.005119606 94.99127579
X3 -0.561998547 2.288312682 18.74166068 0.627259508 3.419469031 19.77830237
X4 1.329382413 3.200993909 13.70214513 -1.646207285 5.888073404 12.78866879
X5 0.011086498 0.000779187 98.20383865 -0.566051061 2.436595504 24.40726676
X6 -0.335278509 0.407217486 48.37319101 0.032505242 0.004591356 95.22734271
X7 -0.026690009 0.004515964 95.01180335 -0.440700032 1.476924806 33.20332546
X8 -0.586571343 2.804395016 15.01590886 0.669067657 4.37680063 16.11413322
X9 -0.240062996 0.15657654 68.40808786 -0.035657883 0.004143874 95.66868521
X10 -0.582727 2.460227471 17.24314893 0.736324963 4.711977599 15.59068049
X11 -0.096081259 0.066884017 78.51791029 -0.629108908 3.439662555 18.9777276
X12 0.056659315 0.008722056 93.59540183 -0.563443986 1.034658266 41.08590783
X13 -0.552913486 2.491792473 17.3560505 0.479325434 2.246351113 25.85445961
X14 -0.514281874 0.958114517 31.23267987 0.539642099 1.265452412 35.42030176
X15 1.403573486 7.136500442 8.026275275 -1.107265279 5.327672699 14.03058606
X16 -0.54413087 0.804420223 35.23555373 0.224278121 0.163934082 72.35964282
X17 0.317182274 0.455557095 46.51544699 -1.050240702 5.991311177 12.47049164
X18 -0.356574167 0.345442686 51.5754901 0.017989623 0.001054726 97.8343426
10
X19 0.208383754 0.275283861 56.9331828 -1.184814631 10.67512671 8.016011495
X20 -0.298079315 0.563270121 42.07123063 0.074763137 0.042505708 85.70255568
X21 -0.463791711 1.753248471 21.48208971 0.331172436 1.072321608 40.30586062
X22 1.235487529 6.911968194 8.344452427 0.155364128 0.131112981 75.32587499
X23 0.076891085 0.026771764 87.18053987 -1.021961173 5.673002541 13.77399158
X24 -0.46342553 1.555983157 23.2064046 0.267094221 0.620002087 51.00071846
X25 -0.612876169 2.721387908 15.69331828 0.660785704 3.794769889 18.20794417
X26 0.195068915 0.20676755 62.4858873 -0.797350081 4.144035975 17.43816073
X27 1.7621935 8.436910437 7.513086318 -1.092739758 3.891606549 17.75633788
Table 7. Complete results, for the first two axes of the correspondence analysis of the ROYER presence file. Vp,
Vp% and P = eigenvalues, percentages of contribution and associated probabilities, coordi. = coordinates of the
floristic variables or relevés on the axes, CR% = relative contributions of the species or relevés on the axes, Pi:
probabilities associated with the relative contributions on the axes. Signicicant eigenvalues and relative
contributions are in bold red.
Figure 3. Correspondence analysis of the presence table. Distribution of species in the in the plane of axes 1 and
2. In red, the species with a significant relative contribution.
The three species Bromus erectus, Helleborus foetidus and Sanguisorba minor are present only once in the
same relevé 1. Ceterach officinarum is present in relevés 1 and 22, Potentilla neumanniana in relevés 1,15,22,27
and Asplenium trichomanes subsp. pachyrachis in relevés 4, 15 and 27. These relevés 1, 4, 15, 22 and 27 are
highlighted in figure 4.
-2
-1,5
-1
-0,5
0
0,5
1
1,5
2
2,5
3
-1 -0,5 0 0,5 1 1,5 2 2,5 3 3,5 4
Royerpres-ca Bromus erectus, Helleborus
foetidus & Sanguisorba
minor
Ceterach officinarum
Potentilla neumanniana
Asplenium trichomanes subsp.
pachyrachis
axe 1
axe
2
11
Figure 4. Correspondence analysis of the presence table. Distribution of relevés in the in the plane of axes 1 and
2. In red, the relevés with a significant relative contribution.
It appears once again that dual correspondence analysis is not suitable for the analysis of this kind of table,
since only a small part of the variability of the relevé table is highlighted. Only relevés with a rare species
combination are revealed. The results obtained for simple or simplified disjunctive tables suffer from the same
characteristics and are not presented here. This kind of analysis is not useful for phytosociology.
Only the non-symmetric analyzes are now used.
Non-symmetric analysis of presence data
Only the first two eigenvalues are significant (in red in table 8). The decrease of the eigenvalues is rapid.
However, there are still relative contributions of relevés and significant floristic variables in several other axes,
which is a result of local variations.
Figure 5. The firt twelve eigenvalues of non-symmetric analysis of the presence table.
-2
-1,5
-1
-0,5
0
0,5
1
1,5
2
2,5
-1 -0,5 0 0,5 1 1,5 2 2,5 3 3,5
Royerpres-ca 1
4
15
22
27
axe 1
axe
2
0
5
10
15
20
25
1 2 3 4 5 6 7 8 9 10 11 12
12
coord 1 Cr% 1 P 1 coord 2 Cr% 2 P 2
Vp.Vp% et P 1.09144854 21.0486547 0 0.72758032 14.0314328 0.64661808
Asplenium trichomanes subsp.
quadrivalens 0.08914813 0.7947389 89.7567484 -0.27979555 7.82855511 47.2647029
Potentilla neumanniana -0.24211429 5.86193297 4.38263369 -0.06209137 0.38553387 66.8069383
Ceterach officinarum -0.05849024 0.34211078 41.3835574 -0.03449984 0.11902391 66.6735092
Helleborus foetidus -0.01197869 0.01434891 79.8624654 -0.03844786 0.14782377 46.6591399
Sanguisorba minor -0.01197869 0.01434891 80.0369496 -0.03844786 0.14782377 46.7823052
Bromus erectus -0.01197869 0.01434891 80.1395874 -0.03844786 0.14782377 47.2236477
Asplenium trichomanes subsp.
hastatum 0.03103875 0.0963404 88.8843272 0.71646164 51.3317279 0.03079134
Poa nemoralis 0.06773469 0.45879885 80.3653905 0.04305575 0.18537972 88.1453351
Geranium robertianum 0.32982986 10.8787738 32.669609 0.11197835 1.25391499 75.4798317
Phyllitis scolopendrium 0.27727817 7.68831832 27.4658729 -0.13332445 1.77754081 64.6002258
Cystopteris fragilis 0.37938207 14.3930754 29.1491327 0.19456748 3.78565026 61.2850251
Cardamine impatiens 0.14074062 1.98079223 25.5773376 -0.07104359 0.50471919 61.0900133
Hedera helix -0.0855527 0.73192642 79.1850559 0.43665265 19.0665539 11.7930822
Moehringia trinervia 0.14631812 2.14089909 23.3808888 -0.10109397 1.02199918 48.8453248
Vinca minor 0.03944738 0.15560961 39.7516165 -0.00034345 1.18E-05 99.4662835
Asplenium trichomanes subsp.
pachyrachis -0.29744353 8.84726548 0.28738582 -0.02144408 0.04598485 84.8096069
Asplenium ruta-muraria -0.60014978 36.0179759 9.01159807 0.09547621 0.91157067 82.5926306
Mycelis muralis 0.02737224 0.07492393 78.8874063 -0.12130007 1.47137082 26.9424202
Cardaminopsis arenosa subsp. borbasii -0.00468343 0.00219345 98.4296418 -0.15407184 2.37381318 53.8437853
Campanula rotundifolia -0.2264688 5.1288116 30.1549831 -0.15736851 2.47648487 53.3100688
Sesleria caerulea -0.07165865 0.51349619 31.7048137 -0.08609897 0.74130323 28.8001642
Lamium galeobdolon 0.06544166 0.42826111 50.5388484 -0.01451566 0.02107045 89.9414965
Mercurialis perennis 0.03236606 0.10475617 48.7016319 0.00211077 0.00044554 96.838756
Oxalis acetosella 0.10585251 1.12047529 39.0844709 -0.08356106 0.69824503 56.5123679
Campanula trachelium 0.03236606 0.10475617 49.4508878 0.00211077 0.00044554 96.46926
Galium aparine 0.02542774 0.064657 59.2117418 -0.00594424 0.0035334 91.2142051
Chrysosplenium alternifolium 0.02542774 0.064657 59.1296315 -0.00594424 0.0035334 90.7420712
Arabis hirsuta -0.00737588 0.00544036 88.0324335 -0.01136381 0.01291361 83.2187211
Origanum vulgare -0.00737588 0.00544036 87.2318588 -0.01136381 0.01291361 83.3726778
Thymus praecox -0.00737588 0.00544036 88.0734887 -0.01136381 0.01291361 82.6747408
Ribes uva-crispa -0.04692897 0.22023281 52.0886791 -0.01422632 0.02023882 86.8110438
Polypodium interjectum 0.08044135 0.64708104 39.6181874 -0.0760235 0.57795728 49.0300729
Fragaria vesca -0.04432751 0.1964928 34.6094632 -0.04302355 0.18510262 40.7779945
Viola alba -0.03154647 0.099518 50.4156831 -0.04083503 0.16674996 43.3336755
Silene nutans -0.03154647 0.099518 49.2866674 -0.04083503 0.16674996 42.3175613
Potentilla micrantha -0.03154647 0.099518 50.5901673 -0.04083503 0.16674996 42.9025967
Poa compressa 0.00840397 0.00706266 86.2362722 -0.01426798 0.02035753 78.4255363
Melica uniflora -0.0382121 0.14601645 41.773581 0.10102422 1.02058935 4.75212973
Clematis vitalba -0.0382121 0.14601645 41.3732936 0.10102422 1.02058935 4.76239351
Sedum spurium 0.00764786 0.00584898 87.7758391 -0.01068219 0.01141093 84.2861542
Ribes alpinum 0.03483335 0.12133622 46.094632 -0.03899501 0.15206109 45.2427384
Sedum album -0.03955309 0.15644469 39.7105614 -0.00286251 0.0008194 95.5044647
X1 -0.29737689 0.34454421 80.8785795 -0.7793072 2.36618068 46.0433131
13
X2 0.8446503 1.38980675 60.9155291 2.05049702 8.19065851 14.2769168
X3 0.97930037 4.98196994 28.5846249 -0.00696137 0.00025174 99.4457559
X4 -2.82562355 10.3690239 7.99548394 0.12460393 0.02016382 95.1144411
X5 -0.67850876 2.09260969 50.7954429 -0.87310406 3.46504864 37.6167505
X6 0.83818734 1.82482602 53.8848404 1.12413362 3.28227633 38.8586678
X7 -0.68757226 2.14888913 50.3643642 0.60358459 1.65597436 54.9317459
X8 0.80350303 3.7730871 37.45253 0.04278367 0.01069739 96.2434568
X9 0.33939488 0.22439393 83.7934928 -1.06339846 2.20288888 47.8292107
X10 0.63125596 2.07004719 51.9449861 -0.12048503 0.07541112 89.9414965
X11 -0.18310976 0.17417758 85.4664888 -0.23033522 0.27560683 81.1967566
X12 -1.39529433 3.79255769 36.5185261 3.00551914 17.5970363 1.36508262
X13 1.01864284 6.06409039 22.724007 -0.52215261 1.59337019 55.9273324
X14 1.62652574 6.87165193 19.4395977 -0.35906495 0.33487699 79.369804
X15 -2.16030342 12.1218464 5.3576927 -0.43286476 0.48668025 75.2848199
X16 1.4890647 4.31944221 33.2033255 2.43421237 11.5429673 6.75356666
X17 -1.10045182 3.93179935 35.4716207 -0.8720529 2.46907876 46.1151596
X18 0.63015003 0.77355013 70.0913476 3.25647555 20.658376 0.57477163
X19 -0.78315644 2.78788189 44.7090219 -0.82769325 3.11398236 40.0184748
X20 0.20863252 0.1978524 85.03541 -0.28920056 0.38016801 77.6762804
X21 0.76971995 3.46248003 39.5873961 -0.72958217 3.11078659 40.6035102
X22 -1.1546715 4.32878664 32.6798727 0.0800231 0.02079122 94.7141538
X23 -0.94863381 2.92177308 43.4055219 2.04767988 13.6136132 4.21841322
X24 0.18986187 0.1872599 84.9122447 -0.21651948 0.24353603 82.0281228
X25 0.86475473 3.88467919 35.6050498 -0.79039756 3.24534183 38.7252386
X26 -0.98192455 3.75652921 36.8367033 -0.05802085 0.01311592 95.6892128
X27 -2.39825242 11.2044441 6.37380684 -0.12639344 0.03112072 93.7596223
Tableau 8. Complete results, for the first three axes of non-symmetric correspondence analysis of the ROYER’s
presence file. Vp, V% and P== : eigenvalues, contribution percentages, and associated probabimities, coordi. =
coordinates of the floristic variables or the relevés on axes, Cr% = relative contributions of species or relevés on
the respective axes, Pi : probabilities associated to relative contributions on the respective axes. The eigenvalues
and the significant relative contributions are in bold red.
On the first axis (figures 6 and 7), no relevé has a significant relative contribution. Two species have
significant contributions : Potentilla tabernaemontani and Asplenium trichomanes subsp. pachyrachis.
On the second axis, three relevés have significant relative contributions: 12, 18 and 23 as well as two
species: Asplenium trichomanes subsp. hastatum and Melica uniflora.
On the third axis, only the relevé 9 has a significant relative contribution, but on the other hand three
species are highlighted: Poa nemoralis, Asplenium trichomanes subsp. pachyrachis and Mycelis muralis.
14
Figure 6. Non-symmetric correspondence analysis of the simple disjunctive table. Distribution of species in the
plans of axes 1 and 2. The species with a significant relative contribution are in red.
Figure 7 is instructive because it is easy to find the phytosociological classification of ROYER (2009), with
the exception of relevés 1 and 2 of the Asplenietum trichomanes-rutae-murariae ceterachetosum officinarum.
At this step of the analysis, it is not necessary to go further, because the utility of a multivariate analysis is well
demonstrated, provided that the data are adapted to the statistical technique. As for the difficulty of
discriminating an association represented by only two relevés, this is easily understandable because a small
number of relevés are certainly not favorable to statistical analysis.
-0,4
-0,2
0
0,2
0,4
0,6
0,8
-0,8 -0,6 -0,4 -0,2 0 0,2 0,4
Royerpres-nscaAsplenium trichomanes subsp,
hastatum
Hedera helix
Asplenium trichomanes subsp. quadrivalens
Phyllitis scolopendrium
Cardaminopsis arenosa subsp. borbasiiCampanula rotundifolia
Asplenium ruta-muraria
Asplenium trichomanes subsp. pachyrachis
Potentilla neumanniana
Cystopteris fragilis
Geranium robertianum
axe 1
axe
2
15
Figure 7. Non-symmetric correspondence analysis of the simple disjunctif table. Distribution of relevés in the
plane of axes 1 and 2. Relevés 4, 15, 27 : Asplenietum pachyrachidis ; Relevés 1, 22 : Asplenietum
trichomano-rutae-murariae ceterachetosum officinarum ; Relevés 5, 7, 9, 11, 17, 19, 26 : Asplenietum
trichomano-rutae-murariae cardaminopsietosum borbasii ; Relevés 3, 8, 10, 13, 14, 20, 21, 24, 25 :
Cystopterido fragilis-Phyllitidetum scolopendrii et les relevés 2, 6, 12, 16, 18, 23 : Asplenietum hastati .
No classification attempt is made in this paragraph because the results are sufficiently explicit. In addition,
the environmental data provided are very general.
Non-symmetric correspondence analysis of the simple disjunctive table
Only the first two eigenvalues are significant (figure 10 and table 11). However, on the other axes, several
floristic variables and relevés have significant relative contributions.
-1,5
-1
-0,5
0
0,5
1
1,5
2
2,5
3
3,5
-3 -2,5 -2 -1,5 -1 -0,5 0 0,5 1 1,5 2
Royerpres-nsca
axe 1
axe
2
14
16
13
3
252
2
6
8
10
18
9
20
24
12
23
4
27
15
22
1
11
7
519
26
17
16
Figure 8. The first twelve eigenvalues of non-symmetric correspondence analysis of the simple disjunctive table.
coord 1 Cr% 1 P 1 coord 2 Cr% 2 P 2
Vp.Vp% et P 1.477602818 15.04113161 0.021074816 1.021554466 10.39882639 1.412012645
Asplenium trichomanes subsp. quadrivalens+ 0.151665837 2.300252609 65.45837724
-
0.288959192 8.349741447 33.84615385
Asplenium trichomanes subsp. quadrivalens1 0.04425427 0.195844042 94.49947313 0.449350775 20.19161188 18.1032666
Asplenium trichomanes subsp. quadrivalens2 0.002195412 0.000481983 96.6280295 0.049401349 0.244049331 35.08956797
Asplenium trichomanes subsp. quadrivalens3 -0.023650463 0.055934442 64.23603793 0.000524841 2.75E-05 99.34668072
Potentilla neumanniana+ -0.222092707 4.932517046 3.371970495 0.058438387 0.341504508 63.19283456
Potentilla neumanniana1 0.013629061 0.018575131 78.83034773
-
0.026435708 0.069884664 62.62381454
Ceterach officinarum1 0.002705703 0.000732083 95.93256059 0.078057935 0.609304125 12.20231823
Ceterach officinarum2 0.013629061 0.018575131 79.11485774
-
0.026435708 0.069884664 61.94942044
Helleborus foetidus+ 0.013629061 0.018575131 79.03055848 -
0.026435708 0.069884664 62.14963119
Sanguisorba minor+ 0.013629061 0.018575131 79.71548999
-
0.026435708 0.069884664 63.20337197
Bromus erectus1 0.013629061 0.018575131 79.4625922 -
0.026435708 0.069884664 62.58166491
Asplenium trichomanes subsp. hastatum+ -0.045210431 0.204398308 34.03582719 0.030673827 0.094088366 57.20758693
Asplenium trichomanes subsp. hastatum1 -0.081377255 0.66222577 59.22023182
-
0.405896044 16.47515983 1.138040042
Asplenium trichomanes subsp. hastatum2 0.08905569 0.793091599 24.3308746 -0.11334328 1.284669914 17.79768177
Poa nemoralis+ 0.130481091 1.702531519 50.03161222 0.062018131 0.384624861 77.71338251
Poa nemoralis1 -0.02565586 0.065822315 74.56269758 0.072951791 0.532196384 39.50474183
Poa nemoralis2 -0.023650463 0.055934442 64.07797682 0.000524841 2.75E-05 99.09378293
Geranium robertianum+ 0.185228218 3.430949287 32.21285564
-
0.298300787 8.898335967 14.09905163
Geranium robertianum1 0.076205814 0.580732603 69.85247629 0.045639893 0.208299987 83.42465753
Phyllitis scolopendrium+ 0.017203517 0.0295961 73.5194942 0.039322206 0.15462359 45.93256059
Phyllitis scolopendrium1 0.160750362 2.584067878 40.01053741
-
0.104570659 1.093502271 61.79135933
Phyllitis scolopendrium2 0.052667819 0.27738992 50.28451001 0.012057468 0.014538253 89.28345627
Cystopteris fragilis+ 0.234440006 5.496211663 46.22760801 -
0.331634219 10.9981255 25.58482613
Cystopteris fragilis1 0.064770556 0.419522496 55.10010537 0.105112112 1.104855611 38.96733404
Cystopteris fragilis2 0.042143944 0.177611202 38.9251844
-
0.077699101 0.603715029 12.51844046
Cardamine impatiens+ 0.081853432 0.669998427 45.06849315 0.029640176 0.087854006 80.85353003
Cardamine impatiens1 0.019554571 0.038238126 70.05268704 0.042277964 0.178742626 42.82402529
Hedera helix+ 0.123623329 1.528272745 62.32876712 0.016534508 0.027338995 95.17386723
Hedera helix1 -0.192051118 3.688363186 5.974710221
-
0.135564163 1.837764228 25.90094837
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9 10 11 12
17
Moehringia trinervia+ 0.109393397 1.196691541 45.32139094 0.053029392 0.281211638 74.93150685
Vinca minor+ 0.028012468 0.078469836 57.00737619 0.023511942 0.05528114 65.75342466
Asplenium trichomanes subsp. pachyrachis1 -0.373187156 13.92686535 0.052687039
-0.067952949 0.461760325 57.57639621
Asplenium ruta-muraria+ -0.67073298 44.98827304 4.004214963
-
0.176818163 3.126466288 63.93045311
Asplenium ruta-muraria1 0.046380876 0.215118565 81.35932561 0.292039675 8.528717148 14.25711275
Mycelis muralis+ 0.021749983 0.047306178 78.57744995 0.091679313 0.840509652 27.26027397
Mycelis muralis1 0.022026472 0.048516545 66.80716544 0.086637856 0.750611808 8.682824025
Cardaminopsis arenosa subsp. borbasii+ 0.015894852 0.025264632 88.67228662 0.107567852 1.157084282 37.49209694
Cardaminopsis arenosa subsp. borbasii1 0.052039675 0.270812781 64.29926238 0.058380333 0.340826323 63.75131718
Cardaminopsis arenosa subsp. borbasii2 -0.045210431 0.204398308 34.67860906 0.030673827 0.094088366 57.67123288
Campanula rotundifolia+ -0.228989976 5.243640894 34.1938883 0.19029959 3.621393393 47.2918862
Campanula rotundifolia1 0.032640746 0.10654183 51.60168599
-
0.030343223 0.092071118 57.8398314
Seseleria caerulea+ -0.043352462 0.187943595 58.12434141 0.030225099 0.091355658 73.14014752
Lamium galeobdolon+ 0.017203517 0.0295961 74.01475237 0.039322206 0.15462359 46.29083246
Lamium galeobdolon1 0.06188084 0.38292383 43.29820864 -
0.067843482 0.460273801 43.16122234
Mercurialis perennis2 0.037225488 0.138573697 45.04741834
-
0.056389008 0.317972021 28.59852476
Oxalis acetosella+ 0.046389129 0.215195132 55.30031612 0.056904915 0.323816933 51.67544784
Oxalis acetosella1 0.069866234 0.488129068 36.38566913
-
0.086732231 0.752247986 31.14857745
Campanula trachelium+ 0.037225488 0.138573697 44.83667018
-
0.056389008 0.317972021 28.19810327
Galium aparine+ 0.024655351 0.060788635 62.93993678
-
0.011454474 0.013120497 83.53003161
Chrysosplenium alternifolium+ 0.024655351 0.060788635 63.27713383
-
0.011454474 0.013120497 83.57218124
Arabis hirsuta+ -0.023650463 0.055934442 64.29926238 0.000524841 2.75E-05 99.27291886
Origanum vulgare+ -0.023650463 0.055934442 63.45626976 0.000524841 2.75E-05 99.34668072
Thymus praecox+ -0.023650463 0.055934442 64.51001054 0.000524841 2.75E-05 99.07270811
Ribes uva-crispa+ -0.022379829 0.050085673 78.47207587 0.081148239 0.658503676 33.44573235
Polypodium interjectum+ 0.032640746 0.10654183 51.87565859 -
0.030343223 0.092071118 57.44994731
Polypodium interjectum1 0.04256018 0.181136889 58.60906217 0.086912749 0.755382601 31.11696523
Fragaria vesca+ -0.045547874 0.207460884 34.61538462
-
0.019176251 0.036772859 72.10748156
Viola alba1 -0.036296368 0.131742636 46.4910432 0.045350358 0.205665501 39.65226554
Silene nutans+ -0.036296368 0.131742636 46.50158061 0.045350358 0.205665501 39.83140148
Potentilla micrantha+ -0.036296368 0.131742636 46.10115911 0.045350358 0.205665501 38.56691254
Poa compressa+ 0.023005608 0.052925802 64.81559536 0.044634785 0.199226405 40.4004215
Melica uniflora+ -0.058560772 0.342936407 20.72708114
-
0.068802711 0.473381303 17.86090622
Clematis vitalba+ -0.058560772 0.342936407 20.65331928 -
0.068802711 0.473381303 18.08219178
Sedum spurium+ 0.017203517 0.0295961 73.56164384 0.039322206 0.15462359 45.48998946
Ribes alpinum+ 0.029185612 0.085179996 55.52160169 0.017582709 0.030915164 74.84720759
Sedum album+ 0.001270635 0.000161451 98.13487882 0.080623399 0.650013242 11.19072708
X1 0.314046203 0.384253315 78.69336143 -
0.506489511 0.999473863 64.38356164
X2 0.970927471 1.836428872 55.25816649
-
0.879063926 1.505363738 56.93361433
X3 0.645474339 2.164348684 51.06427819 0.450472218 1.054156983 64.04636459
X4 -3.419232023 15.18330861 1.907270811
-
0.926033865 1.113686649 61.91780822
18
X5 0.050587555 0.011632276 95.99578504 0.946495006 4.072058169 33.29820864
X6 1.081128883 3.03594717 43.54056902 -
1.292513374 4.339196942 31.66491043
X7 -1.041756591 4.932985428 27.63962065 0.587688889 1.569901045 55.92202318
X8 0.857764384 4.299894578 33.16122234
-
1.080373618 6.821340514 18.90410959
X9 0.507542648 0.501817285 76.17492097 1.659920209 5.367535913 25.11064278
X10 0.568118335 1.676667234 56.76501581
-
0.219459639 0.250194976 81.68598525
X11 -0.544963309 1.542779262 58.07165437 0.010055578 0.000525271 98.93572181
X12 -2.034180615 8.06082618 14.08851423 -1.86679122 6.788784662 19.11485774
X13 0.450584145 1.186516005 64.41517387 0.810015974 3.834501889 34.82613277
X14 0.971097385 2.449428914 48.36670179 -1.48865997 5.756125989 24.96311907
X15 -2.428699467 15.32098987 1.780821918 0.065657127 0.011197035 96.03793467
X16 0.822838106 1.318953018 62.20231823
-
2.717607383 14.38712316 3.20337197
X17 -1.049532087 3.576355847 38.66174921 -
0.367403437 0.438263914 75.71127503
X18 0.685596106 0.915666273 68.00842993
-
1.874071885 6.841841748 19.51527924
X19 -0.836355242 3.179500416 41.12750263 0.868880879 3.431609008 38.29293994
X20 0.530104304 1.277320788 62.23393045 0.855171001 3.324170185 38.81981033
X21 0.752120948 3.305956679 39.51527924
-
0.581354748 1.975168888 51.68598525
X22 0.062345886 0.012620161 96.16438356 1.49553498 7.261769083 17.34457323
X23 -1.349380422 5.911777677 23.71970495 -
1.318211411 5.641822481 24.27818757
X24 0.396410228 0.81631724 69.56796628 0.753385735 2.948519822 41.2223393
X25 0.672506392 2.349427778 48.47207587 0.336872295 0.589521782 72.48682824
X26 0.029278469 0.003339852 98.06111697 1.544687452 9.296335026 11.53846154
X27 -2.751194195 14.74494058 2.307692308 -0.44155383 0.37981127 77.76606955
Table 9. Results for the first two axes of the non-symmetric correspondence analysis of the simple disjunctive
ROYER file. Eigenvalues and significant relative contributions are in bold red.
Axis 1 (figure 10) is dominated by three variables: Asplenium ruta-muraria (abundance +), Asplenium
trichomanes subsp. pachyrachis (abundance 1) and Potentilla tabernaemontani (abundance +). These three
variables form the characteristic combination of relevés 4, 15 and 27 (figure 11), all three with significant
relative contributions, which corresponds to the association Asplenietum pachyrachidis.
Axis 2 is strongly influenced by Asplenium trichomanes subsp. hastatum (abundance1) and to a lesser
extent by Cystopteris fragilis (abundance +) and Geranium robertianum (abundance +).
Axis 3 opposes Asplenium trichomanes subsp. hastatum (abundance 1) and Asplenium trichomanes subsp.
hastatum (abundance 2).
By examining the dispersion of the relevés (figure 11) in the plans of axes 1 and 2, then 2 and 3, we note
that only one of the associations is clearly discriminated, it is the Asplenietum pachyrachidis (relevés 4, 15, 27).
The other syntaxons mix. For example, on axis 3, the Asplenietum hastati is cut in half based on the abundance
of Asplenium trichomanes subsp. hastatum., abundance 1 on one side, abundance 2 on the other.
19
Figure 10. Non-symmetric correspondence analysis of the simple disjunctive table. Distribution of species in the
planes of axes 1 and 2. In red, the floristic variables with significant relative contributions.
-0,5
-0,4
-0,3
-0,2
-0,1
0
0,1
0,2
0,3
0,4
0,5
-0,8 -0,7 -0,6 -0,5 -0,4 -0,3 -0,2 -0,1 0 0,1 0,2 0,3
Royer-disjsimple-nsca
Asplenium ruta-muraria+
Asplenium trichomanes
subsp. pachyrachis1
Campanula rotundifolia+
Potentilla neumanniana+
Hedera helix1
Asplenium trichomanes
subsp. quadrivalens1
Asplenium ruta-muraria1
Asplenium trichomanes subsp. quadrivalens+
Cystopteris fragilis+
Geranium robertianum+
Asplenium trichomanes subsp. hastatum1
20
Figure 11. Non-symmetric analysis of the simple disjunctive table. Distribution of relevés in the plane of axes 1
and 2. Relevés 4, 15, 27 : Asplenietum pachyrachidis ; Relevés 1, 22 : Asplenietum trichomano-rutae-
murariae ceterachetosum officinarum ; Relevés 5, 7, 9, 11, 17, 19, 26 : Asplenietum trichomano-rutae-
murariae cardaminopsietosum borbasii ; Relevés 3, 8, 10, 13, 14, 20, 21, 24, 25 : Cystopterido fragilis-
Phyllitidetum scolopendrii et les relevés 2, 6, 12, 16, 18, 23 : Asplenietum hastati.
Only one association is clearly separated from the other relevés (Asplenietum pachyrachidis). The others
mix. This analysis does not lead to a clear phytosociological interpretation of the data table.
Non-symmetric correspondence analysis of the simplified disjunctive table
This type of analysis brings practically the same results as with the presence file and is not detailed.
-3
-2,5
-2
-1,5
-1
-0,5
0
0,5
1
1,5
2
-4 -3,5 -3 -2,5 -2 -1,5 -1 -0,5 0 0,5 1 1,5
Royerdisjsimple-nsca
1
22
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19 20
21
23
24
25
26
27
21
The representation of the relevés again intermixes the associations. The first three axes are therefore
strongly influenced by local variations. The synthetic power of the technique is low.
Conclusions about the analysis of the ROYER’s table
We thus arrive at a good agreement between the analysis of the phytosociologist and the statistical analysis,
provided that we analyse a presence table with non-symmetric correspondence. Only the association defined by
only two relevés can not be clearly discriminated against by the others.
The BAILLY’s file
After a small file, the analysis of an important file was necessary. We have selected a pluristratal ligneous
vegetation file to better compare the robustness of the various statistical techniques.
The data
This file is the result of a study of the Franche-Comté swampy Alder woodlands (BAILLY 2012). Many
relevés (190 originally) have been described using the phytosociological method. The species are divided into
six strata called a1, b1 (woody strata), ep1 (epiphytes), h1 (herbaceous plants), hylf (hydrophyte, single species)
and m1 (mosses and liverworts). The strata were recorded separately and some species are present in two or
more strata; the latter are therefore present in two or more rows of the data table. Abundance-dominance is
expressed using the coefficients +, s, r, i, 1, 2, 3, 4 and 5. No explicit environmental or pedological data has been
published.
The tables have already been analysed by various multivariate analysis techniques such as ascending
hierarchical classification of presence data (agglomerative clustering of complete links by BRAY-CURTIS
distance) or abundance-dominance (WARD method with chord distance) and finally, a table of 112 relevés was
used to establish the typology. The correspondence analysis was also used, with no particular precision on the
type of numerical data.
The approach by elementary syntaxa was used as in the ROYER’s file.
Sufficiently discriminable syntaxa have been recognized from column reassignments and basing on syntaxa
already known in the literature and creating new ones.
Two relevés sufficiently individualized of all the others, located at the articulation of Betulion pubescentis
and Sphagno-Alnion glutinosae, do not appear in the typology.
22
The phytosociological analysis
The typology includes three associations of alder woodland with ferns and four of the alder woodlands with
sedges.
- Mesohygrophilous Alder woodlands with ferns and Carex brizoides: Dryopterido carthusianae - Alnetum
glutinosae, ass. nov. hoc. loco. with two sub-associations, the subass. typicum (17 relevés named DA1 to 17) and
the subass. circaetosum (6 relevés designated DA18 to 23).
- Peaty Alder woodlands with Sphagnum : Sphagno flexuosi - Alnetum glutinosae Malcuit ex Bœuf, Cartier &
Ritz 2013 with two sub-associations, the subass. Polytrichastretosum formosi (6 relevés named SA1 to 6) and
subass. typicum (7 relevés named SA7 to 13).
- Hygrophilous Alder woodlands with Lady-fern, Club-rush and Carex brizoides : Athyrio filicis-feminae -
Alnetum glutinosae Passarge 1968 caricetosum brizoidis subass. nov. hoc. loco., with the mesoacidiphilic variant
with Molinia caerulea and Sphagnum palustre (12 relevés named Ata1 to 12), the acidicline to neutroacidicline
variant with Caltha palustris and Filipendula ulmaria (10 relevés named AtA 13-22) and the transition variant
towards Peucedano - Alnetum, Filipendula ulmaria and Iris pseudacorus (5 relevés designated AtA23-27).
- Paludal acidicline Alder woodlands with Carex elongata : Peudedano palustris – Alnetum glutinosae Noirfalise
& Sougnez 1961, with three variants and a subgroup, the typical variant with Dryopteris cristata (1 relevés
named PA1), the variant with Carex acutiformis and Phalaris arundinacea (5 relevés named PA2 to 6), the
Carex vesicaria variant (5 relevés named PA7 to 11), and the subass. Agrostietosum caninae (6 relevés named
PA12 to 17).
- Hygrophilous neutroacidiclinous Alder woodlands with Enchanter’s nightshade and Lesser Pond-sedge :
Carici acutiformis - Alnetum glutinosae Scamoni 1933, with the typical variant (12 relevés named CA1 to 12)
and the variant with Poa trivialis (4 relevés named CA13 to 16).
- Mountaineer Alder woodlands with Monk’s wood: Aconito napelli - Alnetum glutinosae ass. nov. hoc. loco.
with the alluvial sub-unit (2 relevés named AcA1 and 2), the fontinal sub-unit (2 relevés named AcA3 and 4),
and the peri-lacustrine sub-unit with Carex appropinquata (3 relevés referred to as AcA5 to 7).
- Amphibious Alder woodlands with Water Violet : Hottonio palustris - Alnetum glutinosae Hueck 1929 with a
sub-unit to Hottonia palustris (1 relevé named HA1), and a sub-unit with Glyceria fluitans and Lemna minor (4
relevés named HA2 to 5).
Finally, 108 relevés are completely described completely, which were included in our study.
23
The character-species of the associations
As in the previous file, the operation consists in comparing the list of character- and differential species given by BAILLY (2012) with that provided by the permutation
technique based on the frequency of species in the phytosociological units or the elementary syntaxons obtained at multivariate analyses.
Mesohygrophilous Alder woodlands with ferns and Carex brizoides : Dryopterido carthusianae – Alnetum glutinosae
The association is represented by 23 relevés. Character- or differential species, from a statistical point of view, are shown in table 10. Only common species are
presented.
Species/relevés
DA
1
DA
2
DA
3
DA
4
DA
5
DA
6
DA
7
DA
8
DA
9
DA
10
DA
11
DA
12
DA
13
DA
14
DA
15
DA
16
DA
17
DA
18
DA
19
DA
20
DA
21
DA
22
DA
23
Fr Pr
Athyrium filix femina-h1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 23 1 0,0002
Rubus fruticosus-h1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 21 0,91 0,0250
Alnus glutinosa-b1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 0 0 1 1 1 1 1 1 1 18 0,78 0,0185
Lonicera periclymenum-h1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 0 18 0,78 0,0038
Thuidium tamariscinum 0 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 17 0,74 0,0032
Corylus avellana-b1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 0 16 0,70 0,0047
Viburnum opulus-h1 1 0 1 1 1 0 0 1 0 1 1 1 1 1 0 1 1 0 0 1 1 1 1 16 0,70 0,0229
Eurhynchium striatum 0 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 15 0,65 0,0022
Carex brizoides-h1 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 14 0,61 0,0155
Quercus robur-a1 1 1 1 0 0 1 0 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 11 0,48 0,0007
Dryopteris dilatata-h1 1 0 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 0 0 0 1 0 1 10 0,43 0,0425
Betula pendula-a1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 9 0,39 0,0015
Polytrichastrum formosum 0 1 1 1 0 1 0 0 0 1 0 1 1 1 0 0 0 0 1 0 0 0 0 9 0,39 0,0047
24
Lonicera periclymenum-a1 0 0 1 0 0 0 0 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 7 0,30 0,0253
Carpinus betulus-h1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 0 7 0,30 0,0058
Quercus robur-b1 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 6 0,26 0,0454
Atrichum undulatum 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 1 6 0,26 0,0306
Corylus avellana-h1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 0 0 0 0 4 0,17 0,0178
Stellaria holostea-h1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 3 0,13 0,0303
Calypogeia fissa 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 3 0,13 0,0286
Quercus palustris-a1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 2 0,09 0,0450
Chiloscyphus pallescens 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0,09 0,0429
Table 10. Species of the Alder woodlands with ferns and Carex brizoides with a relative frequency statistically higher than in the whole of relevés. The species names are
followed by their membership to a layer. = frequency, Fr = relative frequency, Pr = probability calculated by the test.
The four species with the lowest probabilities obtained with the permutation test are also fairly common species in all 108 records of the Alder woodlands. They are
Athyrium filix-femina (79 presences in the whole), Lonicera periclymenum-h1 (56 presences), Eurhynchium striatum (40 presences) and Thuidium tamariscinum (50
presences). As for Dryopteris carthusiana (75 presences), which is included in the name of the association, its frequency in relevés of mesohyrophrophilous Alder woodlands
with ferns and Carex brizoides is not statistically more frequent than in all relevés. Carex brizoides is considered to be a character-species of the association, but with a
relative frequency of only 0.61. From BAILLY’s character-species set, the test retained Athyrium filix-femina, Rubus fruticosus-h1, Carex brizoides, Dryopteris dilatata but
failed on Dryopteris carthusiana, Lysimachia vulgaris and Juncus effusus.
The typical sub-association is characterized by the combination of woody species: Corylus avellana (shrub layer), Betula pendula and Quercus robur (tree layer) and
Lonicera periclymenum (both in shrub and herbaceous layers). Next are Athyrium filix-femina, Rubus fruticosus (herbaceous layer), Thuidium tamariscinum and Molinia
caerulea. Besides Betula pendula (17 presences in the whole) and Quercus robur (22 presences in the whole), the other species are common in Alder woodlands. As for Salix
aurita, its frequency is not statistically higher in this sub-association than in the Alder woodlands, whereas it is considered as such by BAILLY (2012). With Molinia caerulea
and Lonicera periclymenum, statistical analysis confirms the differential status of sub-association of these two species.
25
In the sub-association circaetosum, the combination of BAILLY (2012), we find, among the character-
species, the combination cited by BAILLY (2012), with Circaea lutetiana, Lamium galeobdolon, Stachys
sylvatica, but without Urtica dioica, the frequency of which is not significant.
Peaty Alder woodlands with Sphagnum : Sphagno flexuosi – Alnetum glutinosae and two
sub-associations
Species/relevés SA1 SA2 SA3 SA4 SA5 SA6 SA7 SA8 SA9 SA10 SA11 SA12 SA13 Fr Pr
Athyrium filix femina-h1 1 1 1 1 1 1 1 1 1 1 1 1 1 13 1 0,01246
Lonicera periclymenum-h1 1 1 1 1 1 1 1 1 1 1 1 1 1 13 1 0,0001
Rubus fruticosus-h1 1 1 1 1 1 1 1 1 1 1 1 1 1 13 1 0,01517
Salix aurita-b1 1 1 1 0 1 1 1 1 1 1 1 1 1 12 0,92 0,00312
Sphagnum palustre 1 1 1 1 1 1 0 1 1 1 1 1 1 12 0,92 0
Molinia caerulea-h1 1 1 1 0 1 1 1 1 0 1 1 1 1 11 0,85 0,00005
Thuidium tamariscinum 1 1 1 1 1 1 1 1 1 1 0 0 0 10 0,77 0,01898
Lonicera periclymenum-b1 0 1 1 1 1 1 1 1 0 1 1 0 0 9 0,69 0,01627
Rubus fruticosus-b1 0 1 0 1 1 1 1 1 0 0 1 0 0 7 0,54 0,01038
Dryopteris dilatata-h1 1 1 0 0 1 0 0 0 1 1 0 1 1 7 0,54 0,02693
Osmunda regalis-h1 0 1 0 0 0 0 1 0 1 1 0 1 0 5 0,38 0,00006
Trichocolea tomentella 0 0 0 0 0 0 1 1 1 0 1 0 1 5 0,38 0,00357
Carex echinata-h1 0 0 0 0 0 0 1 1 1 0 1 0 0 4 0,31 0,00724
Pteridium aquilinum-h1 0 1 0 0 1 0 1 0 0 0 0 0 1 4 0,31 0,01133
Teucrium scorodonia-h1 0 0 0 0 0 1 0 1 1 0 0 1 0 4 0,31 0,0018
Sorbus aucuparia-b1 0 0 1 0 1 0 0 0 0 0 0 1 0 3 0,23 0,03811
Sphagnum flexuosum 0 1 0 0 0 0 0 0 0 1 0 1 0 3 0,23 0,00152
Knautia dispacifolia-h1 0 0 0 0 0 0 0 0 0 0 0 1 1 2 0,15 0,01332
Luzula sylvatica-h1 0 0 0 0 0 0 0 0 0 0 0 1 1 2 0,15 0,01359
Sorbus aucuparia-h1 0 0 0 0 1 0 0 0 0 0 0 0 1 2 0,15 0,01366
Loeskeobryum brevirostre 0 0 0 0 0 0 0 1 1 0 0 0 0 2 0,15 0,01383
Sphagnum squarrosum 0 0 0 0 0 0 0 0 1 0 0 1 0 2 0,15 0,01404
Table 11. Species of the Alder woodlands with Sphagnum, with a relative frequency statistically higher than in
the whole of relevés. The species names are followed by their membership to a layer. = frequency, Fr =
relative frequency, Pr = probability calculated by the test.
Based on the frequency test, this syntaxon is characterized by the juxtaposition of (table 11):
- woody species: Salix aurita quite common in the Alder woodlands, Lonicera periclymenym much less frequent
on the whole in the shrub layer,
- very frequent herbaceous species (Molinia caerulea and Lonicera periclymenum here only in the herbaceous
layer, both with the lowest probabilities <0.0001 and Rubus fruticosus),
- three Sphagnum species, S. palustre quite common as well as S. flexuosum and S. squarrosum, infrequent and
exclusive of this association but also of Thuidium tamariscinum quite common in the whole.
26
It should be noted that BAILLY (2012) does not put woody species in the characteristic set of the
association. It contains, with significant frequencies, Sphagnum palustre, S. flexuosum, S. squarrosum, Molinia
caerulea, Osmunda regalis, Carex echinata but not Scutellaria minor.
The sub-association polytrichastretosum formosi is characterized by the juxtaposition of several woody
species, other species already characteristic of the association, with additionally Polytrichastrum formosum as
expected.
In the typicum sub-association, in addition to the characteristic set of BAILLY (2012), there is a mixture of
differential species of the Alder woodlands with ferns and differentials of the sub-association.
27
Hygrophilous Alder woodlands with Lady-fern, Club-rush and Carex brizoides: Athyrio filicis-feminae – Alnetum glutinosae caricetosum
brizoidis
Espèces/relevés
AtA
1
AtA
2
AtA
3
AtA
4
AtA
5
AtA
6
AtA
7
AtA
8
AtA
9
AtA
10
AtA
11
AtA
12
AtA
13
AtA
14
AtA
15
AtA
16
AtA
17
AtA
18
AtA
19
AtA
20
AtA
21
AtA
22
AtA
23
AtA
24
AtA
25
AtA
26
AtA
27
Fr Pr
Athyrium filix femina-h1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 26 0,96 0,0006
Lysimachia vulgaris-h1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 26 0,96 0,0114
Galium palustre-h1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 24 0,89 0,0001
Rubus fruticosus-h1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 24 0,89 0,0343
Dryopteris carthusiana-h1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 0 23 0,85 0,0319
Juncus effusus-h1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 0 1 1 1 23 0,85 0,0013
Scirpus sylvaticus-h1 1 1 1 1 1 0 0 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 22 0,81 0,0000
Lonicera periclymenum-h1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 0 1 0 0 0 0 1 19 0,70 0,0220
Plagiomnium undulatum 0 0 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 1 1 19 0,70 0,0000
Thuidium tamariscinum 1 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 0 0 0 0 1 19 0,70 0,0035
Corylus avellana-b1 0 1 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 0 0 0 1 1 0 1 1 1 1 17 0,63 0,0170
Lonicera periclymenum-b1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 1 0 0 0 1 0 17 0,63 0,0024
Carex elongata-h1 0 0 0 1 0 1 1 1 1 0 0 0 1 1 0 0 0 1 0 0 1 1 1 1 0 1 1 14 0,52 0,0248
Calliergonella cuspidata 1 0 1 0 1 1 0 1 0 1 0 0 1 1 1 1 0 1 0 1 1 1 0 0 0 0 0 14 0,52 0,0181
Oxalis acetosella-h1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 0 0 0 1 1 0 0 0 0 1 11 0,41 0,0002
Plagiomnium affine 1 1 0 0 1 0 1 0 0 0 1 1 0 1 1 0 1 1 0 0 0 1 0 0 0 0 0 11 0,41 0,0299
Cardamine pratensis-h1 0 0 1 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 10 0,37 0,0065
Lythrum salicaria-h1 0 0 0 0 0 0 1 1 0 1 1 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 1 9 0,33 0,0379
Rubus idaeus-h1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 1 7 0,26 0,0436
Athyrium filix-femina-ep1 0 0 0 0 1 0 0 1 0 0 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 6 0,22 0,0075
Anemone nemorosa-h1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 6 0,22 0,0449
Lamium galeobdolon-h1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 6 0,22 0,0262
Cirriphyllum piliferum 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 6 0,22 0,0149
Lophocolea bidentata 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 5 0,19 0,0220
Lonicera periclymenum-ep 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 4 0,15 0,0135
Stachys officinalis-h1 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0,11 0,0478
Table 12. Species of the Alder woodlands with Lady-fern, Club-rush and Carex brizoides, with a relative frequency statistically higher than in the whole of relevés. The
species names are followed by their membership to a layer. = frequency, Fr = relative frequency, Pr = probability calculated by the test.
28
Several species are distinguished with very low probabilities related to their frequencies (table 12):
Plagiomnium undulatum, Scirpus sylvaticus, Galium palustre, Oxalis acetosella and Athyrium filix-femina. Other
common species include two woody species (Corylus avellana and Lonicera periclymenun, the latter also in the
herbaceous layer), Dryopteris carthusiana, Juncus effusus, Lysimachia vulgaris, Rubus fruticosus (herbaceous
layer) and Thuidium tamariscinum. There is a mixture of species from the differential set of the Alder woodlands
with ferns, hyphrophilic differentials of the Athyrio-Alnetum and the subgroup caricetosum brizoidis. This shows
that the syntaxon is clearly defined, but curiously enough, the two most common species Plagiomnium
undulatum and Thuidium tamariscinum are not considered as character-species by BAILLY (2012). The
permutation test also indicates several other bryophytes as possible character-species.
The mesoacidiphilic variant with Molinia caerulea and Sphagnum palustre is poorly defined in relation to
the subgroup and the three species cited as differentials of the variant, i.e. Molinia caerulea, Sphagnum palustre
and Scutellaria minor, do not appear as character-species with the test by permutation.
In the acidiclinous to neutroacidiclinous variant with Caltha palustris and Filipendula ulmaria, among the
two differentials of the variant cited by BAILLY (2012), only Caltha palustris presents a statistically significant
frequency. Filipendula ulmaria is not. On the other hand, Carex brizoides and Cardamine pratensis have
significant and highly significant frequencies. Mention may also be made of Carex vesicaria, Scirpus sylvaticus,
Calliergonella cuspidata, Plagiomnium undulatum and Thuidium tamariscinum.
The transition variant to Peucedano - Alnetum, with Filipendula ulmaria and Iris pseudacorus is more
clearly defined since it is found, with significant frequencies, Filipendula ulmaria, Impatiens noli-tangere, cited
as differentials of the variant but additionally Galium aparine subsp . aparine.
29
Swamp acidiclinous Alder woodlands with Elongated Sedge : Peucedano palustris –
Alnetum glutinosae
Species/relevés
PA
1
PA
2
P
A3
P
A4
P
A5
P
A6
P
A7
P
A8
P
A9
PA
10
PA
11
PA
12
PA
13
PA
14
PA
15
PA
16
PA
17 Fr Pr
Galium palustre-h1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 15
0,88
0,0025
Carex elongata-h1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0
1
4
0,8
2
0,00
00
Iris pseudacorus-h1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 14
0,82
0,0000
Lycopus europaeus-h1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1
1
3
0,7
6
0,00
00
Carex vesicaria-h1 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 12
0,71
0,0001
Scutellaria galericulata-
h1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 0 1 1 8
0,4
7
0,00
01
Agrostis canina-h1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 6 0,3
5 0,00
35
Phalaris arundinacea-h1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 6
0,3
5
0,00
93
Carpinus betulus-b1 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 5 0,2
9 0,03
14
Phragmites australis-h1 0 1 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 5
0,2
9
0,00
87
Ranunculus flammula-h1 0 0 0 0 0 0 1 1 0 0 0 1 1 0 1 0 0 5 0,2
9 0,00
01
Equisetum fluviatile-h1 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 4
0,2
4
0,01
05
Frangula dodonei subsp. dodonei-h1 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 4
0,24
0,0330
Thysselinum palustre-h1 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 4
0,2
4
0,04
94
Valeriana dioica-h1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 4
0,2
4
0,04
93
Populus tremula-b1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 3
0,1
8
0,02
68
Persicaria hydropiper-h1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 3
0,1
8
0,04
94
Ranunculus repens-h1 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 3
0,1
8
0,04
86
Rumex sanguineus-h1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 2
0,1
2
0,02
42
Table 13. Species of the Alder woodlands with Carex elongata, with a relative frequency statistically higher than
in the whole of relevés. The species names are followed by their membership to a layer. = frequency, Fr =
relative frequency, Pr = probability calculated by the test.
With the lowest probabilities associated with frequencies (table 13), Carex elongata (characteristic of the
association), Carex vesicaria, and species of the Phragmito australis-Magnocaricetea elatae, namely Iris
pseudacorus, Lycopus europaeus, Galium palustre and Scutellaria vesiculata. Among the species of the
characteristic set, only Carex elongata and Thysselinum palustre have significant frequencies; On the other hand,
a species with only one presence can not be tested.
Carex acutiformis and Phalaris arundinacea are among the differential species of the variant with Carex
acutiformis and Phalaris arundinacea, but their significant frequencies include Phragmites australis and
Thysselinum palustre.
30
In the variant with Carex vesicaria, the test defines a differential set consisting of three Carex: C. elongata,
C. remota and C. vesicaria, Iris pseudacorus, Lycopus europaeus and Valeriana dioica.
This sub-association agrostietosum caninae is well diversified and is found among the statistically most
frequent species in the sub-association, namely Salix aurita-b1, Agrostis canina-h1, Quercus robur-a1, Frangula
dodonei subsp. dodonei-b1, Carex vesicaria-h1, Carpinus betulus-h1, Iris pseudacorus-h1, Juncus effusus-h1,
Scutellaria galericulata-h1, Polytrichastrum formosum and Sphagnum auriculatum, many of the species
presented as differentials of the sub-association by BAILLY (2012 ).
Hygrophilous neutroacidiclinous Alder woodlands with Enchanter’s nightshade and Lesser
Pond-sedge : Carici acutiformis – Alnetum glutinosae
Espèces/Relevés CA1
CA2
CA3
CA4
CA5
CA6
CA7
CA8
CA9
CA10
CA11
CA12
CA13
CA14
CA15
CA16 S Fr Pr
Fraxinus excelsior-b1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1
6 1 0
Carex acutiformis-h1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 16 1 0
Circaea lutetiana-h1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1
1
3
0,8
1 0
Filipendula ulmaria-h1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 12
0,75
0,0004
Caltha palustris-h1 1 0 0 1 0 1 0 1 0 1 1 1 1 1 1 1
1
1
0,6
9
0,01
16
Crataegus monogyna-b1 1 1 0 0 1 0 1 0 0 0 1 1 0 0 1 1 8 0,5
0 0,00
04
Solanum dulcamara-h1 0 0 0 0 1 0 1 1 0 1 1 0 0 0 1 1 7
0,4
4
0,04
20
Galeopsis tetrahit-h1 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 0 6 0,3
8 0,00
01
Poa trivialis-h1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 5
0,3
1
0,01
66
Humulus lupulus-b1 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 4 0,2
5 0,04
03
Prunus padus subsp.
padus-b1 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 4
0,2
5
0,00
43
Galium aparine subsp. aparine-h1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 4
0,25
0,0087
Geranium robertianum-
h1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 4
0,2
5
0,00
18
Geum urbanum-h1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 4 0,2
5 0,00
43
Glechoma hederacea-h1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 1 0 4
0,2
5
0,00
42
Phragmites australis-h1 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 4
0,2
5
0,03
95
Rubus caesius-h1 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 4
0,2
5
0,01
69
Dryopteris filix-mas-h1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 3 0,1
9 0,02
27
Impatiens glandulifera-
h1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 3
0,1
9
0,02
22
Ribes nigrum-b1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 2 0,1
3 0,02
13
Crataegus monogyna-h1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 2
0,1
3
0,02
09
Epilobium hirsutum-h1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 2 0,1
3 0,02
16
Ligustrum vulgare-h1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2
0,1
3
0,02
07
Ribes nigrum-h1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 2
0,1
3
0,02
06
31
Table 14. Species of the neutroacidiclinous Alder woodlands with Circaea lutetiana and Carex acutiformis, with
a relative frequency statistically higher than in the whole of relevés. The species names are followed by their
membership to a layer. = frequency, Fr = relative frequency, Pr = probability calculated by the test.
The statistical analysis (table 14) reproduces three of the character-species according to BAILLY (2012),
namely Carex acutiformis, Circaea lutetiana and Filipendula ulmaria but excludes Dryopteris carthusiana and
Athyrium filix-femina. On the other hand, the analysis adds Fraxinus excelsior to the shrub layer, Caltha
palustris and Circaea lutetiana.
In the typical variant, there are naturally many species of the association but here without Caltha palustris.
The variant with Poa trivialis is distinguished mainly by the discovery of its nitrophilous species: Galium
aparine subsp. Aparine, Geranium robertianum, Geum urbanum, Glechoma hederacea, Poa trivialis, Stachys
sylvatica and Urtica dioica, which fully agrees with BAILLY's analysis (2012).
32
Mountaineer Alder woodlands with Monk’s wood : Aconito napelli – Alnetum glutinosae
Species/relevés AcA1 AcA2 AcA3 AcA4 AcA5 AcA6 AcA7 Fr Pr
Caltha palustris-h1 1 1 1 1 1 1 1 7 1 0,0012
Filipendula ulmaria-h1 1 1 1 1 1 1 1 7 1 0,0004
Calliergonella cuspidata 1 1 1 1 1 1 1 7 1 0,0003
Fraxinus excelsior-b1 1 1 1 1 1 1 0 6 0,86 0,0369
Angelica sylvestris-h1 1 1 1 0 1 1 1 6 0,86 0,0026
Carex acutiformis-h1 1 1 1 1 0 1 1 6 0,86 0,0085
Euonymus europaeus-b1 1 0 1 1 1 1 0 5 0,71 0,0002
Galium mollugo subsp. mollugo-h1 1 1 1 1 0 1 0 5 0,71 0,0000
Ranunculus aconitifolius-h1 1 1 0 1 1 0 1 5 0,71 0,0000
Aconitum napellus-h1 1 1 0 1 0 0 1 4 0,57 0,0000
Cirsium oleraceum-h1 0 0 1 1 1 0 1 4 0,57 0,0001
Eupatorium cannabinum-h1 0 0 1 1 1 1 0 4 0,57 0,0023
Solanum dulcamara-h1 0 0 1 1 1 1 0 4 0,57 0,0486
Valeriana officinalis-h1 1 1 0 1 1 0 0 4 0,57 0,0008
Plagiomnium elatum 0 0 1 1 1 1 0 4 0,57 0,0000
Carex appropinquata-h1 0 0 0 0 1 1 1 3 0,43 0,0002
Carex elata-h1 0 1 0 0 1 0 1 3 0,43 0,0002
Poa trivialis-h1 0 1 0 0 1 1 0 3 0,43 0,0301
Scutellaria galericulata-h1 1 1 0 1 0 0 0 3 0,43 0,0377
Thalictrum aquilegiifolium-h1 1 0 1 1 0 0 0 3 0,43 0,0002
Valeriana dioica-h1 0 0 1 0 0 1 1 3 0,43 0,0171
Ligustrum vulgare-b1 0 0 1 1 0 0 0 2 0,29 0,0332
Ribes rubrum-b1 1 0 0 0 0 1 0 2 0,29 0,0329
Sambucus nigra-b1 0 0 1 0 0 1 0 2 0,29 0,0107
Acer campestre ep1 0 0 0 0 1 1 0 2 0,29 0,0035
Brachypodium sylvaticum-h1 1 0 1 0 0 0 0 2 0,29 0,0109
Lysimachia nummularia-h1 1 1 0 0 0 0 0 2 0,29 0,0204
Mentha aquatica-h1 0 0 0 0 1 1 0 2 0,29 0,0476
Ranunculus auricomus-h1 1 1 0 0 0 0 0 2 0,29 0,0345
Cratoneuron filicinum 0 0 1 1 0 0 0 2 0,29 0,0040
Table 15. Species of the mountainer Alder woodlands with Aconitum napellus,, with a relative frequency
statistically higher than in the whole of relevés. The species names are followed by their membership to a layer.
= frequency, Fr = relative frequency, Pr = probability calculated by the test.
The statistical analysis (table 15) is quite similar to that of BAILLY (2012), as regards both the shrub layer
and the herbaceous and muscular layer. Nine of the ten species of the characteristic set of mountaineer Alder
woodlands with Aconitum napellus are among the species with a significant frequency, namely Caltha palustris,
Filipendula ulmaria, Carex acutiformis, Angelica sylvestris, Ranunculus aconitifolius, Galium mollugo subsp.
33
mollugo, Aconitum napellus, Cirsium oleraceum and Thalictrum aquilegiifolium. The same applies to the
subunits.
The subunits are not detailed due to too few relevés, which does not warrant statistical analysis.
Amphibious Alder woodlands with Water Violet : Hottonio palustris – Alnetum glutinosae
Espèces/relevés HA1 HA2 HA3 HA4 HA5 S Fr Pr
Acer pseudoplatanus-b1 1 1 1 0 1 4 0,8 0,0012
Glyceria fluitans-h1 1 0 1 1 1 4 0,8 0,0001
Quercus petraea-a1 1 1 0 0 1 3 0,6 0,0005
Lemna minor-h1 1 1 1 0 0 3 0,6 0,0001
Carex elongata-ep1 0 0 0 1 1 2 0,4 0,0096
Carex riparia-h1 1 1 0 0 0 2 0,4 0,0016
Alnus glutinosa-ep1 0 0 0 1 0 1 0,2 0,0458
Calliergonella cuspidata-ep1 0 0 0 0 1 1 0,2 0,0460
Frangula dodonei subsp. dodonei-ep1 0 0 0 1 0 1 0,2 0,0467
Lysimachia vulgaris-ep1 0 0 0 1 0 1 0,2 0,0453
Polytrichastrum formosum-ep1 0 0 0 0 1 1 0,2 0,0464
Thuidium tamariscinum-ep1 0 0 0 0 1 1 0,2 0,0474
Thysselinum palustre-ep1 0 0 0 0 1 1 0,2 0,0466
Alisma plantago-aquatica-h1 0 0 1 0 0 1 0,2 0,0457
Carex pseudocyperus-h1 1 0 0 0 0 1 0,2 0,0450
Glyceria maxima-h1 1 0 0 0 0 1 0,2 0,0465
Hottonia palustris-h1 1 0 0 0 0 1 0,2 0,0465
Rorippa amphibia-h1 1 0 0 0 0 1 0,2 0,0461
Table 16. Species of the amphibious Alder woodlands with Hottonia palustris with a relative frequency
statistically higher than in the whole of relevés. The species names are followed by their membership to a layer.
= frequency, Fr = relative frequency, Pr = probability calculated by the test.
The two species with the lowest probabilities are Glyceria fluitans and Lemna minor, which are part of the
differential hydrophytes of the association. There are also two woody species in the shrub layer, i.e. Quercus
petraea and Acer pseudoplatanus, many epiphytes and other rarer species. As BAILLY points out, this syntaxon
is well polymorphic and the subunit with Glyceria fluitans and Lemna minor is the most frequent in Franche-
Comté (table 16). The small number of relevés makes statistical analysis difficult.
This Alder woodland is clearly distinguished from other associations.
34
Data analysis of the complete file
The file, consisting finally of 108 columns and 330 lines, is too important to be presented here, it is
appended. As before, we include all species, even those present only once. There are 91.51% empty cells in the
presence table, which does not facilitate analysis.
The tree layers (species names followed by a1) includes 20 species, the shrub layer 42 (species names
followed by b1), the epiphytes 31 (species names followed by ep1), the herbaceous layer 184, including the
hydrophyte Lemna minor (name followed by m1), and the moss layer 53. Some species are present in several
layers. With such data, multiple factor analyses always end up being imposed.
The analysis of the data is conducted in the same spirit as for the ROYER’s file. First, the presence table is
carried out with correspondence analysis, with all the species. We have already seen that this technique is
inadequate to relevé tables, a fortiori with data of abundance because it is then necessary to digitize all the
coefficients and the coefficients of type +, r, m for example are converted into scores1 or lower scores 1,
arbitrarily fixed. One can of course transform the presence files by removing the rare species, present once, twice
or more, but this choice remains arbitrary and not very acceptable; in addition, it sometimes makes disappear
some rare species with a located high biomass, which is then a real amputation. The presence tables are then
subjected to a non-symmetric correspondence analysis, better adapted to these data (see Chapter 5) and which
favors frequent species. Then come the multiple factor analyses since the table presents several layers; in this file
and in order to best respect BAILLY’s work, the species present in several layers are treated separately in each
layer. Finally, in order to exploit at best all the nuances of the relevé table, a simple disjunctive table is created,
that is to say without the lines corresponding to the absence of the species; for each species in each layer, there
are as many lines as there are different coefficients of abundance-dominance in each row of the original table.
This simple disjunctive table is then submitted to non-symmetric correspondence. The "simplified" disjunctive
table is also tested, with one line for presence, one for abundances 1 and 2 and one for abundances 3, 4 and 5.
Another type of simplification is tested again, with three possible lines for each species: one for presence, one
for abundances> 1 and one for abundance> 3. Classifications of the relevés then follow, on the basis of the
transformed variables coming from the non-symmetric correspondence analyses; the number of transformed
variables is fixed by the permutation technique on the basis of 1000 permutations. Classification and ranking
techniques (see also chapters 12 and 13) are used as before.
Covariance matrix and the choice of a technique
The covariance matrices of six analyses are compared (figure 12). A single correspondence is shown and
the results are sufficiently clear; we find once more that this technique is inadequate to the relevé tables and it is
useless to detail the results; the analysis presented by BAILLY (2012, in figure 2) shows well the defaults of the
technique. The non-symmetric correspondence analysis of the complete disjunctive table is no longer presented
either because it favors absences which are much more numerous than the presences.
35
Figure 12. Distribution of covariances in six multivariate analyses of the BAILLY’s file.
There is a clear difference between correspondence analysis and non-symmetric analyses. On the other
hand, the four non-symmetric analyses are very similar. We favor multiple factor analyses that exploit to the best
all the nuances expressed by the phytosociologist, either with the presence data or with the disjunctive tables
constructed from the coefficients of abundance-dominance, because they place the layers on the same level,
without the variability of one crushing that of the others.
36
Multiple factor analysis based on non-symmetric correspondence analysis of the presence
table
First of all, the permutation test (10,000) on eigenvalues, developed from multiple factor analysis based on
non-symmetric correspondence analysis, indicates that the first nine eigenvalues (figure 14) are significant at
level = 0.05.
Figure 14. The first 12 eigenvalues of the non-symmetric correspondence analysis of the presence file.
The coordinates of the relevés are presented axis by axis for the first three (figure 16); the relevés are
placed in the same order in which they are in the association tables in order to compare these results directly with
those of the phytosociologist.
0
2
4
6
8
10
12
1 2 3 4 5 6 7 8 9 10 11 12
37
Figure 15. Multiple factor analysis based on non symmetric correspondence analysis of the presence table.
Representation of relevés on axes 1 to 3. Dryopterido carthusianae – Alnetum glutinosae, subass. typicum (DA1
à 17) and the subass. circaetosum (DA18 à 23). Sphagno flexuosi – Alnetum glutinosae, subass.
polytrichastretosum formosi (SA1 à 6), subass. typicum (SA7 à 13). Athyrio filicis-feminae – Alnetum glutinosae
caricetosum brizoidis, mesoacidiphilous variant with Molinia caerulea and Sphagnum palustre (AtA1 à 12),
acidiclinous to neutroacidiclinous variant acidicline with Caltha palustris and Filipendula ulmaria (AtA 13 à 22)
and transition variant to the Peucedano – Alnetum, with Filipendula ulmaria and Iris pseudacorus (AtA23 à 27).
Peucedano palustris – Alnetum glutinosae, typical variant with Dryopteris cristata (PA1), variant with Carex
acutiformis and Phalaris arundinacea (PA2 à 6), variant with Carex vesicaria (PA7 à 11) and subass.
agrostietosum caninae (PA12 à 17). Carici acutiformis – Alnetum glutinosae, typical variant (CA1 à 12) and
variant with Poa trivialis (CA13 à 16). Aconito napelli – Alnetum glutinosae, alluvial sub-unit (AcA1 et 2),
fontinal sub-unit (AcA3 et 4), and peri-lacustrin sub-unit with Carex appropinquata (AcA5 à 7). Hottonio
palustris – Alnetum glutinosae, sub-unit with Hottonia palustris (HA1), sub-unit with Glyceria fluitans and
Lemna minor (HA2 à 5).
On the first axis, there is an opposition between the three associations of the Alder woodland with ferns
(left) and the four associations of the Alder woodlands with Sedges (right). There is therefore a certain
-3
-2
-1
0
1
2
3
DA
1
DA
4
DA
7
DA
10
DA
13
DA
16
DA
19
DA
22
SA
2
SA
5
SA
8
SA
11
AtA
1
AtA
4
AtA
7
AtA
10
AtA
13
AtA
16
AtA
19
AtA
22
AtA
25
PA
1
PA
4
PA
7
PA
10
PA
13
PA
16
CA
2
CA
5
CA
8
CA
11
CA
14
AcA
1
AcA
4
AcA
7
HA
3
aulnaies01-mfansca-axe 1
Dryopterido
carthusianae-
Alnetum glutinosae
Sphagno
flexuosi –
Alnetum
glutinosae
Athyrio filicis-feminae
– Alnetum glutinosae
caricetosum brizoidis
Peucedano
palustris –
Alnetum
glutinosae
Carici
acutiformis
– Alnetum
glutinosae Aco
nit
o n
ap
elli
–
Aln
etu
m
glu
tin
osa
e Ho
tto
nio
pa
lust
ris –
Aln
etu
m g
luti
no
sae
-4
-3
-2
-1
0
1
2
3
DA
1
DA
4
DA
7
DA
10
DA
13
DA
16
DA
19
DA
22
SA
2
SA
5
SA
8
SA
11
AtA
1
AtA
4
AtA
7
AtA
10
AtA
13
AtA
16
AtA
19
AtA
22
AtA
25
PA
1
PA
4
PA
7
PA
10
PA
13
PA
16
CA
2
CA
5
CA
8
CA
11
CA
14
AcA
1
AcA
4
AcA
7
HA
3
axe 2
-3
-2
-1
0
1
2
3
4
DA
1
DA
4
DA
7
DA
10
DA
13
DA
16
DA
19
DA
22
SA
2
SA
5
SA
8
SA
11
AtA
1
AtA
4
AtA
7
AtA
10
AtA
13
AtA
16
AtA
19
AtA
22
AtA
25
PA
1
PA
4
PA
7
PA
10
PA
13
PA
16
CA
2
CA
5
CA
8
CA
11
CA
14
AcA
1
AcA
4
AcA
7
HA
3
axe 3
38
agreement between these results and the associations, but they are only partial and in the following axes, we
depart more and more from the initial model. The coordinates of the relevés on the following axes are poorly
structured and do not give any easy interpretation.
Figure 16. Multiple factor analysis based on non-symmetric correspondence analysis of the presence data.
Representation of species in the plane of axes 1 and 2. The specific names are followed by their membership to
one of the strata.
If we divide figure 16 into four parts, based on the coordinates of the species, we see:
- in the upper left part, the ferns Athyrium filix-femina (common) and Dryopteris dilatata (less common), the
woody species Corylus avellana, Betula pendula and Lonicera periclymenum in the tree layer, the same species
in the shrub and herbaceous layers, the herbaceous species Molinia caerulea and Carex brizoides, the liana
Rubus fruticosus in the herbaceous layer and the mosses Eurhynchium striatum, Kindbergia praelonga,
Plagiomnium affine, P. undulatum and Thuidium tamariscinum;
- in the lower left part, the fern Dryopteris carthusiana, the tree Quercus robur, the shrub Salix aurita, the
herbaceous species Juncus effusus and the mosses Polytrichastrum formosum and Sphagnum palustre;
- in the upper right part, Fraxinus excelsior present in the tree, shrub and herbaceous strata, and the herbaceous
species Angelica sylvestris, Caltha palustris, Carex acutiformis and Circaea lutetiana;
- on the lower right, the herbaceous species Carex elongata, C. vesicaria, Galium palustre, Iris pseudacorus and
Solanum dulcamara.
-0,45
-0,35
-0,25
-0,15
-0,05
0,05
0,15
0,25
-0,3 -0,2 -0,1 0 0,1 0,2
aulnaies01-mfanasca
axe 1
axe
Caltha palustris
Filipendula ulmaria
Carex acutiformis
Iris pseudacorus
Fraxinus excelsior-b1Angelica sylvestris
Solanum dulcamara
Lonicera periclymenum
Thuidium tamariscinum
Athyrium filix-femina
Rubus fruticosus-h1
Eurynchium striatum
Salix aurita-b1
Dryopteris carthusianaSphagnum palustre
Mc
Bp = Betula pendula, Lp =
Lonicera periclymenum, Mc =
Molinia caerulea, Ph =
Polytrichastrum formosum, Qr =
Quercus robur
Corylus avellana-b1
PhQr-a1
Carex brizoides
Lp
Juncus effusus
Plagiomnium affine
Dryopteris dilatata
Bp-
Kindbergia praelonga
Carex elongata
Carex vesicaria
Galium palustreScirpus sylvaticus
Plagiomnium undulatum
Circaea lutetiana
Fraxinus excelsior-h1
39
Axis three opposes
- on one side Alnus glutinosa in the shrub layer, the ferns Athyrium filix-femina and Dryopteris carthusiana and
the herbaceous plants Carex brizoides, Impatiens noli-tangere, Rubus fruticosus (in its herb layer) and Scirpus
sylvaticus;
- on the other side, the mosses Calliergonella cuspidata and Sphagnum palustre as well as the herbaceous plants
Moninia caerulea and Angelica sylvestris.
Multiple factor analysis based on the disjunctive table brings rather poor results, putting only few floristic
variables and is not detailed here. The simplified table analysis is now presented.
The analysis is carried out with two sub-tables: a first for woody plants and epiphytes, a second for
herbaceous plants and bryophytes. The permutation test, still based on simple analysis, indicates that the first
nine eigenvalues are significant. The densities of the two sub-tables are very similar and multiple analysis
provides nothing more than a simple analysis. The results are very close to those of the previous analysis and are
not detailed.
Classification and ranking of the relevés set
Several classifications and renkings have been made, with the two programs usually used in our work. All
these analyses yield results which are sometimes very different, depending on the options chosen. Multiplying
the techniques would only bring more confusion.
First, let us consider the first steps of the hierarchical divisive classification. The first division separates a
single HA4 (Hottonio-Alnetum) relevé from the107 others. The next step creates a group of 103 relevés, the HA4
relevé and a group consisting of the other four Hottonio-Alnetum relevés. The fourth step maintains the two
groups of the Hottonio-Alnetum and divides the whole of the 103 other relevés into a group of 59 relevés and
another of 44. Finally, the division is stopped with 10 clusters because the sequence mainly produces unit
groups.
If we classify all the relevés into two groups with the mobile center program, the two groups obtained
are practically identical to the two major groups produced by the hierarchical descending classification, with the
exception of the five Hottonio-Alnetum relevés. By subjecting these two groups to tests on the frequencies of the
floristic variables (simplified disjunctive table) by means of 100,000 permutations, the characteristic variables of
each group are easily defined, based on the risk = 0.05.
The main floristic variables of each group are :
- In the first group (62 relevés),
40
In the tree layer, Alnus glutinosa >3 (48 presences out of 74 in the whole of the relevés) and Fraxinus excelsior
(22 présences out of 30 in the whole of the relevés),
in the shrub layer, mainlyFraxinus excelsior (40 presences out of 50 in the whole of the relevés),
in the herbaceous layer, mainly Angelica sylvestris (28 presences out of 32 in the whole of the relevés), Caltha
palustris (37 presences out of 43 in the whole of the relevés), Filipendula ulmaria (32 presences out of 37 in the
whole of the relevés), Iris pseudacorus (27 presences out of 28 in the whole of the relevés), Carex acutiformis
(28 presences and 26 avec une abondance >1, out of 39 in the whole of the relevés), Carex elongata (28
presences out of 37 in the whole of the relevés), Circaea lutetiana (23 presences out of 27 in the whole of the
relevés), Solanum dulcamara (23 presences out of 25 in the whole of the relevés), Carex vesicaria (22 presences
out of 30 in the whole of the relevés). Also note Carex remota (13 presences out of 15 in the whole of the
relevés).
A single moss is statistically more frequent than the whole: Brachythecium rivulare (14 out of 17).
The Alder woodland with Sedges is therefore clearly defined in relation to Alder woodland with ferns, with
several almost exclusive differentials.
- In the second group (46 relevés),
In the shrub layer, mainly Salix aurita (36 presences out of 59 in the whole of the relevés), Corylus avellana (33
presences out of 47 in the whole of the relevés), Lonicera periclymenum (29 presences out of 41 in the whole of
the relevés), Rubus fruticosus (20 presences out of 25),
In the herbaceous layer, mainly Athyrium filix-femina (45 presences with 29 abondances > 1 out of 79 in the
whole of the relevés), Lonicera periclymenum (42 presences with 28 abondances > 1 out of 56 in the whole of
the relevés), Dryopteris carthusiana (41 presences with 21 abondances > 1 out of 75 in the whole of the relevés),
Juncus effusus (34 presences out of 64 in the whole of the relevés), Carex brizoides (24 presences with 14
abondances > 1 out of 42 in the whole of the relevés) and Molinia caerulea (24 presences out of 32 in the whole
of the relevés),
In the moss layer, Thuidium tamariscinum (36 presences with 18 abondances >1 out of 50 in the whole of the
relevés), Eurhynchium striatum (28 presences out of 40 in the whole of the relevés), Sphagnum palustre (22
presences out of 27 in the whole of the relevés) et Plagiomnium affine (19 presences out of 27 in the whole of
the relevés). On a statistical point of view, this grouping is less clearly defined than the preceding one.
We thus find several species of the differential set of the Alger woodlands with ferns according to BAILLY
namely: Athyrium filix-femina, Rubus fruticosus, Dryopteris carthusiana, Dryopteris dilatata, Juncus effusus,
Lonicera periclymenum, Oxalis acetosella, but not Lysimachia vulgaris, very common with its 87 presences in
the whole of 108 relevés.
The first group corresponds very well to the Alder woodlands with Sedges and the second to the Alder
woodlands with ferns. The sequel is less easy.
For the final ranking, we selected 8 clusters, in order to compare them with the ascending hierarchical
BAILLY’s classification (2012). The classifications and the ranking obtained are presented in table 35.
41
Table 17. Comparison of the BAILLY’s numerical classification, the agglomerative hierarchical classification
and a ranking in eight groups.
These three results in table 17 are quite different and none can be preferred at this step of the analysis. In
each of the analyses, the extracted groups usually include relevés from two or more associations. There are two
main pieces of information:
- The two main types of Alder woodlands are easily found in both analyses, namely the Alder woodlands with
ferns and the Alder woodlands with Sedges,
- The five relevés of the Hottonio - Alnetum are fairly easily removed from the set.
How to continue?
The easy solution is to split the table of 108 relevés into three:
- the five Hottonio - Alnetum relevés that do not require further analysis due to the small number of relevés,
- the set of 63 relevés of Alder woodlands with ferns,
- and the set of 40 relevés of Alder woodlands with sedges.
These last two sets are again subjected to multivariate analyses. As these are smaller files, it is useful to
take into account the abundance of species and it is the simplified disjunctive files that are selected.
Multiple factor analyses based on non-symmetric correspondence analysis are best suited to this kind of
file.
42
Data analysis of the fern Alder file
Multiple factor analysis of the simplified disjunctive table
As before, the quality of the multiple factor analysis is evaluated with the covariance distribution (figure
28).
Figure 17. Covariance distribution of the multiple factor analysis of the fern Alders.
Figure 18. The first 12 eigenvalues of the multiple factor analysis based non-symmetric correspondence analysis
of the simplified disjunctive table.
The permutation test indicates that only the first four eigenvalues are significant (figure 18). There is a net
fall after the fourth eigenvalue.
The results are first presented with the coordinates of the relevés on the first four axes, placed in the order
of the plant associations.
0
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8 9 10 11 12
43
Figure 19. Multiple factor analysis based on non-symmetric analysis of the simplified disjunctive table of the
Alder woodlands with ferns. Representation of relevés on axes 1 to 4. Dryopterido carthusianae – Alnetum
glutinosae (DA1 to 23). Sphagno flexuosi – Alnetum glutinosae (SA1 to 13). Athyrio filicis-feminae – Alnetum
glutinosae caricetosum brizoidis, mesoacidiphilous variant with Molinia caerulea et Sphagnum palustre (AtA1
to 27).
-3
-2
-1
0
1
2
3aulnaies à fougères113 - mfansca- Axe 1
Dryopterido carthusianae
– Alnetum glutinosae
Sphagno flexuosi
– Alnetum
glutinosae
Athyrio filicis-feminae – Alnetum
glutinosae caricetosum brizoidis
-4
-3
-2
-1
0
1
2
DA
1
DA
3
DA
5
DA
7
DA
9
DA
11
DA
13
DA
15
DA
17
DA
19
DA
21
DA
23
SA2
SA4
SA6
SA8
SA1
0
SA1
2
AtA
1
AtA
3
AtA
5
AtA
7
AtA
9
AtA
11
AtA
13
AtA
15
AtA
17
AtA
19
AtA
21
AtA
23
AtA
25
AtA
27
Axe 2
-3
-2
-1
0
1
2
Axe 3
-3
-2
-1
0
1
2
3
Axe 4
44
At this step, it is not possible to find a good coincidence between factor analysis and the three
associations and their divisions. First, let's analyze the species ranked in descending order of relative
contribution on the first four axes.
Espèces coord 1 CR 1 P 1
Scirpus sylvaticus-h1 0.2205736 4.86527148 18.77
Dryopteris carthusiana-h1 >1 -0.21866923 4.78162306 9.84
Galium palustre-h1 0.21592822 4.66249963 19.57
Sphagnum palustre -0.1910561 3.65024341 17.01
Quercus robur-a1 -0.19094621 3.64604549 1.17
Caltha palustris-h1 0.18802559 3.53536215 3.67
Lonicera periclymenum-h1 >1 -0.1867205 3.48645436 26.86
Polytrichastrum formosum -0.18397008 3.38449897 5.34
Molinia caerulea-h1 -0.17346687 3.00907556 29.13
Eurhynchium striatum -0.16994186 2.88802355 33.36
Filipendula ulmaria-h1 0.16225767 2.63275519 11.55
Lonicera periclymenum-h1 -0.15896932 2.52712461 11.12
Rubus fruticosus-h1 >1 -0.15555463 2.41972432 29.86
Betula pendula-a1 -0.14891668 2.21761764 4.54
Scirpus sylvaticus-h1 >1 0.1444689 2.08712625 19.67
Carex elongata-h1 0.13934935 1.94182404 19.29
Cardamine pratensis-h1 0.13725027 1.88376361 8.66
Plagiomnium undulatum 0.13707333 1.87890968 42.83
Thuidium tamariscinum -0.12923712 1.67022323 31.98
Frangula dodonei subsp. dodonei-b1 -0.12000139 1.44003336 26.6
Table 18. Species ranked in decreasing order of relative contribution on the first axis. Coord: coordinates on the
axis, CR: relative contribution, P: probability associated with the relative contribution. A1: tree layer, b1: shrub
layer, h1: herbaceous layer. > 1: abundance greater than 1.
Among the twenty floristic variables with the highest relative contributions on axis 1, the following two
groups are distinguished:
- a first group (negative coordinates) composed of species of the woody stratum with Quercus robur and Betula
pendula, of species of the shrubby stratum with Frangula dodonei subsp. dodonei, species of herbaceous layer
with Dryopteris carthusianana (abundance> 1), Lonicera periclymenum, Molinia caerulea, Lonicera
periclymenum, Rubus fruticosus (with abundance> 1) and moss species with Eurhynchium striatum,
Polytrichastrum formosum, Sphagnum palustre and Thuidium tamariscinum;
- a second group (positive coordinates) with a set of herbaceous species, namely Caltha palustris, Galium
palustre, Carex elongata, Cardamine pratensis, Filipendula ulmaria, Scirpus sylvaticus (present and abundant),
the moss Plagiomnium undulatum.
Axis 2 is especially marked,
- in its negative values, by Alnus glutinosa, both in the tree layer (abundance> 3) and the shrub layer, in the
herbaceous layer by Athyrium filix-femina (abundance> 1), Carex brizoides (present and abundance> 1 and> 3),
Molinia caerulea (abundance> 1) and Stellaria holostea and in the muscle layer by Plagiomnium affine;
45
- in its positive values, by elements of the shrub stratum like Salix aurita, of the herbaceous stratum, with
Circaea lutetiana, Lysimachia vulgaris, Scirpus sylvaticus (abundance> 3) and Viburnum opulus and of the
muscular stratum like Atrichum undulatum, Brachythecium rivulare and Sphagnum palustre.
On axes three and four, we note many species already highlighted on the first two axes.
In order to synthesize this information, the 63 relevés are classified on the basis of the first four
coordinates, since only the first four eigenvalues of the non-symmetric correspondence analysis (simplified
disjunctive table) are significant.
Classification and ranking of the fern Alders
The divisive hierarchical classification with reallocations is tested via the evolution of the total occupied
space (see chapter 12).
Figure 20. Evolution of the total occupied space following the steps of the hierarchical division.
This evolution shows that with the descending classification (CENVI), we manage to split the whole into
four clusters.
CENVI MC4 CENVI3 MC3
DA8 DA2 DA7 DA1 DA7 DA1 DA3 DA2 DA8 DA1 DA7 DA14 DA1 DA7
DA10 DA3 DA18 DA5 DA10 DA5 DA8 DA4 DA10 DA2 DA18 DA16 DA2 DA8
DA13 DA4 DA19 SA12 DA18 SA7 DA9 DA6 DA13 DA3 DA19 SA7 DA3 DA9
DA14 DA6 DA21 SA13 DA19 SA11 DA12 DA11 DA14 DA4 DA21 SA8 DA4 DA10
DA15 DA9 DA22 AtA17 DA20 SA12 DA13 SA2 DA15 DA5 DA22 SA9 DA5 DA11
DA16 DA11 DA23 AtA23 DA21 SA13 DA14 SA4 DA16 DA6 DA23 SA11 DA6 DA17
DA17 DA12 AtA19 AtA24 DA22 AtA4 DA15 SA5 DA17 DA9 AtA19 AtA1 DA12 DA18
DA20 SA1 AtA25 DA23 AtA10 DA16 SA8 DA20 DA11 AtA4 DA13 DA19
SA7 SA2 AtA3 AtA12 DA17 SA9 SA7 DA12 AtA5 DA15 DA20
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Total occupied space
46
SA8 SA3 AtA13 AtA16 SA1 SA10 SA8 SA1 AtA6 SA1 DA21
SA9 SA4 AtA14 AtA17 SA3 AtA1 SA9 SA2 AtA7 SA2 DA22
SA11 SA5 AtA15 AtA20 SA6 AtA2 SA11 SA3 AtA8 SA3 DA23
AtA3 SA6 AtA19 AtA21 AtA7 AtA5 SA13 SA4 AtA9 SA5 SA4
AtA4 SA10 AtA23 AtA8 AtA6 AtA3 SA5 AtA10 SA6 AtA3
AtA5 AtA1 AtA24 AtA9 AtA18 AtA4 SA6 AtA11 SA10 AtA15
AtA7 AtA2 AtA25 AtA11 AtA5 SA10 AtA12 SA12 AtA19
AtA8 AtA6 AtA26 AtA22 AtA7 SA12 AtA13 SA13
AtA9 AtA27 AtA8 AtA1 AtA14 AtA2
AtA10 AtA9 AtA2 AtA16 AtA25
AtA11 AtA10 AtA6 AtA17
AtA12 AtA11 AtA18
AtA13 AtA12 AtA20
AtA14 AtA13 AtA21
AtA15 AtA14 AtA22
AtA16 AtA15 AtA23
AtA18 AtA16 AtA24
AtA20 AtA17 AtA26
AtA21 AtA18 AtA27
AtA22 AtA20
AtA26 AtA21
AtA27 AtA22
AtA23
AtA24
AtA25
AtA26
AtA27 Table 19. Comparison between the descending hierarchical classification and a classification into three or four
group groups from the transformed file of alder ferns.
If, however, we stick to three clusters, the classification by mobile centers most closely resembles the
classification of the phytosociologist. It is easy to see that the group of AtA surveys remains the most cohesive
and that it is associated with a small number of DA and SA relevés. The relevés of the DA and SA associations
fall into the three groups.
Let us test this choice with the characteristic species defined by means of the permutation test. The three
defined groupings are considered as elementary syntaxons.
47
Fern Alder with Galium palutre and Lysimachia vulgaris
The main results are shown in table 20.
sum
fr
DA
14
DA
16
SA
7
SA
8
SA
9
SA
11
AtA
1
AtA
4
AtA
5
AtA
6
AtA
7
AtA
8
AtA
9
AtA
10
AtA
11
AtA
12
AtA
13
AtA
14
AtA
16
AtA
17
AtA
18
AtA
20
AtA
21
AtA
22
AtA
23
AtA
24
AtA
26
AtA
27
sum
.1
fr.1
pr
Carex elongata-h1 16 0.253968 0 0 0 0 0 1 0 1 0 1 1 1 1 0 0 0 1 1 0 0 1 0 1 1 1 1 1 1 15 0.53571 0
Galium palustre-h1 33 0.52381 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 23 0.8214 0
Oxalis acetosella-h1 15 0.238095 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 0 0 1 0 0 1 1 0 0 0 1 13 0.46429 0
Plagiomnium undulatum 27 0.428571 1 1 1 1 1 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 22 0.78571 0
Scirpus sylvaticus-h1 33 0.52381 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 22 0.78571 0.001
Plagiomnium undulatum
>1 11 0.174603 0 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 0 0 0 0 1 0 10 0.35714 0.001
Lythrum salicaria-h1 14 0.222222 0 0 0 0 1 1 0 0 0 0 1 1 0 1 1 1 1 0 0 0 1 0 0 1 0 0 0 1 11 0.39286 0.002
Caltha palustris-h1 20 0.31746 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 0 15 0.53571 0.003
Lysimachia vulgaris-h1 50 0.79365 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 27 0.9643 0.004
Rubus idaeus-h1 9 0.142857 1 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 1 0 0 0 1 8 0.28571 0.004
Caltha palustris-h1 >1 9 0.142857 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 0 8 0.28571 0.005
Calliergonella cuspidata 21 0.333333 0 0 0 1 1 1 1 0 1 1 0 1 0 1 0 0 1 1 1 0 1 1 1 1 0 0 0 0 15 0.53571 0.005
Carex echinata-h1 6 0.095238 1 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0.21429 0.008
Lysimachia vulgaris-h1
>1 19 0.301587 0 0 1 1 1 1 1 1 1 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 0 1 13 0.46429 0.012
Lophocolea bidentata 7 0.111111 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 6 0.21429 0.016
Athyrium filix-femina-ep1 7 0.111111 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 6 0.21429 0.017
Thuidium delicatulum 5 0.079365 0 0 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 5 0.17857 0.019
Humulus lupulus-b1 5 0.079365 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 0 1 5 0.17857 0.02
Filipendula ulmaria-h1
>1 5 0.079365 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 5 0.17857 0.026
Lycopus europaeus-h1 9 0.142857 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0 0 7 0.25 0.027
48
sum
fr
DA
1
DA
2
DA
3
DA
4
DA
5
DA
6
DA
12
DA
13
DA
15
SA
1
SA
2
SA
3
SA
5
SA
6
SA
10
SA
12
SA
13
AtA
2
AtA
25
sum
.2
fr.2
pr.
1
Molinia caerulea-h1 27 0.428571 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1 1 1 1 0 15 0.78947368 0
Sphagnum palustre 22 0.349206 0 1 1 1 0 0 1 0 0 1 1 1 1 1 1 1 1 1 0 13 0.68421053 0
Molinia caerulea-h1 >1 10 0.15873016 1 1 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 9 0.473684211 0
Molinia caerulea-h1 >3 5 0.07936508 1 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 5 0.263157895 0
Polytrichastrum formosum 15 0.23809524 0 1 1 1 0 1 1 1 0 1 1 0 1 1 0 0 0 0 0 10 0.526315789 0.001
Sphagnum palustre >1 10 0.15873016 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 8 0.421052632 0.001
Betula pubescens-a1 >1 5 0.07936508 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 1 0 0 0 5 0.263157895 0.001
Salix aurita-b1 >1 21 0.33333333 0 1 1 0 1 0 0 1 1 0 1 1 0 1 1 1 1 1 0 12 0.631578947 0.002
Betula pubescens-a1 8 0.12698413 0 0 0 0 1 1 1 0 1 1 0 0 0 0 0 1 0 0 0 6 0.315789474 0.004
Quercus robur-a1 16 0.25396825 1 1 1 0 0 1 1 1 0 1 1 0 0 1 0 0 0 0 0 9 0.473684211 0.009
Sphagnum flexuosum 3 0.04761905 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 3 0.157894737 0.017
Rubus fruticosus-h1 >3 5 0.07936508 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 4 0.210526316 0.021
Sorbus aucuparia-b1 5 0.07936508 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 4 0.210526316 0.022
Frangula dodonei subsp. dodonei-b1 24 0.38095238 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 1 11 0.578947368 0.03
Betula pendula-a1 15 0.23809524 1 1 1 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 1 8 0.421052632 0.036
Table 20. Species of the elementary syntaxon 2 of fern Alder with a statistically higher relative frequency than in all the relevés. The specific names are followed by their
membership to one of the strata. sum and fr: sum of the presences and relative frequency in the Alder. sum.2 and fr.2: sum of the presences and relative frequency in the
grouping; pr = probability calculated by the test.
Among the species with a probability less than 0.05, four have a zero probability: Carex elongata. Galium palustre. Oxalis acetosella and Plagiomnium undulatum. Two
species have both a high relative frequency and a very low probability: Lysimachia vulgaris and Galium palustre. Note also that several species of sedge (Carex echinata. C.
elongata. C. remota and C. vesicaria) also have probabilities of less than 0.5%.
This grouping includes two relevés of Dryopterido carthusianae - Alnetum glutinosae. three relevés from Sphagno flexuosi - Alnetum glutinosae and 22 from Athyrio
filicis-feminae - Alnetum glutinosae caricetosum brizoidis, mesoacidiphilic variant with Molinia caerulea and Sphagnum palustre. The fern Athyrium filix-femina is present in
all the relevés and Dryopteris carthusiana in 22 of the 27 relevés.
49
It seems logical to name this grouping: fern Alder with Lysimachia vulgaris and Galium palustre.
Fern Alder with Molinia caerulea and Sphagnum palustre
sum
fr
DA
1
DA
2
DA
3
DA
4
DA
5
DA
6
DA
12
DA
13
DA
15
SA
1
SA
2
SA
3
SA
5
SA
6
SA
10
SA
12
SA
13
AtA
2
AtA
25
sum
.2
fr.2
pr.
1
Molinia caerulea-h1 27 0.428571 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1 1 1 1 0 15 0.78947368 0
Sphagnum palustre 22 0.349206 0 1 1 1 0 0 1 0 0 1 1 1 1 1 1 1 1 1 0 13 0.68421053 0
Molinia caerulea-h1 >1 10 0.15873016 1 1 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 9 0.473684211 0
Molinia caerulea-h1 >3 5 0.07936508 1 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 5 0.263157895 0
Polytrichastrum formosum 15 0.23809524 0 1 1 1 0 1 1 1 0 1 1 0 1 1 0 0 0 0 0 10 0.526315789 0.001
Sphagnum palustre >1 10 0.15873016 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 8 0.421052632 0.001
Betula pubescens-a1 >1 5 0.07936508 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 1 0 0 0 5 0.263157895 0.001
Salix aurita-b1 >1 21 0.33333333 0 1 1 0 1 0 0 1 1 0 1 1 0 1 1 1 1 1 0 12 0.631578947 0.002
Betula pubescens-a1 8 0.12698413 0 0 0 0 1 1 1 0 1 1 0 0 0 0 0 1 0 0 0 6 0.315789474 0.004
Quercus robur-a1 16 0.25396825 1 1 1 0 0 1 1 1 0 1 1 0 0 1 0 0 0 0 0 9 0.473684211 0.009
Sphagnum flexuosum 3 0.04761905 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 3 0.157894737 0.017
Rubus fruticosus-h1 >3 5 0.07936508 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 4 0.210526316 0.021
Sorbus aucuparia-b1 5 0.07936508 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 4 0.210526316 0.022
Frangula dodonei subsp. dodonei-b1 24 0.38095238 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 1 11 0.578947368 0.03
Betula pendula-a1 15 0.23809524 1 1 1 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 1 8 0.421052632 0.036
Table 21. Species of the elementary syntaxon 2 of fern Alder with a statistically higher relative frequency than in all the relevés. The specific names are followed by their
.membership to one of the strata. sum and fr: sum of the presences and relative frequency in the fer Alder. sum.2 and fr.2: sum of the presences and relative frequency in the
grouping; pr = probability calculated by the test.
Among the species with a probability lower than 0.05, two have a zero probability: Sphagnum palustre and Molinia caerulea (represented by the presence and two
degrees of abundance).
50
This grouping includes nine relevéss of the Dryopterido carthusianae - Alnetum glutinosae, nine relevéss of the Sphagno flexuosi - Alnetum glutinosae and only one of
the Athyrio filicis-feminae - Alnetum glutinosae caricetosum brizoidis, mesoacidiphilic variant with Molinia caerulea and Sphagnum palustre.
The combination of Sphagnum palustre, S. flexuosum, Molinia caerulea, Frangula dodonei subsp. dodonei and Betula pendula form a characteristic whole.
The fern Athyrium filix-femina is present in all the relevés and Dryopteris carthusiana in 18 of the 19 surveys.
51
Fern Alder with Carex brizoides
Espèces/relevés
sum
fr
DA
7
DA
8
DA
9
DA
10
DA
11
DA
17
DA
18
DA
19
DA
20
DA
21
DA
22
DA
23
SA
4
AtA
3
AtA
15
AtA
19
sum
.3
fr.3
pr.
2
Carex brizoides-h1 34 0,5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 16 1 0
Carex brizoides-h1 >1 21 0,3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 16 1 0
Carex brizoides-h1 >3 16 0,3 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 14 0,875 0
Stellaria holostea-h1 3 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 3 0,187
5 0,01
9
Athyrium filix femina-
h1 >1 41 0,7 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 14 0,875
0,02
6
Table 24. Species of the elementary syntaxon 2 of the fern Alders woodlands with a relative frequency
statistically higher than in the whole of relevés. The species names are followed by their membership to a layer.
sum and fr: sum of the presences and relative frequency in the fern Alder. sum.3 and fr.3: sum of the presences
and relative frequency in the grouping; pr = probability calculated by the permutation test.
This grouping gathers 12 relevés of the Dryopterido carthusianae-Alnetum glutinosae, one of the Sphagno
flexuosi - Alnetum glutinosae and three of the l’Athyrio filicis-feminae – Alnetum glutinosae caricetosum
brizoidis, variante mésoacidiphile à Molinia caerulea et Sphagnum palustre..Note that Carex brizoides is
considered by BAILLY as a differential of the Athyrio filicis feminae-Alnetum glutinosae caricetosum brizoidis.
The character-species of the grouping is Carex brizoides, mainly by its abundance. This shows how useful it is to
take abundance into account when analyzing data. Stellaria holostea is only present in this grouping and the fern
Athyrium filix-femina is abundant there.
It seems logical to name that grouping : fern Alder with Carex brizoides.
Data analysis of the sedge Alder file
Multiple factor analysis of the simplified disjunctive table
As previous, the quality of multiple factor analysis is evaluated with the covariance distribution (figure 17).
52
Figure 17. Covariance distribution of multiple factor analysis of the sedge alder file.
The curve has a fairly pronounced asymmetry with two well-marked peaks.
Figure 18. The first 12 eigenvalues of the multiple factor analysis based on non-symmetric correspondence
analysis of the simplified disjunctive table.
In figure 18, one observes a clear slowing down after the fourth eigenvalue. The permutation test indicates
that the first four axes are significant. The interpretation continues with the coordinates and relative contributions
of the first four axes.
0
2
4
6
8
10
12
14
1 2 3 4 5 6 7 8 9 10 11 12
53
Figure 19. Multiple factor analysis based on non-symmetric analysis of the correspondences of the simplified
disjunctive file of the alder groves. Representation of the relevés on axes 1 to 4. Peudedano palustris - Alnetum
glutinosae, typical variant with Dryopteris cristata (PA1 to 17). Carici acutiformis - Alnetum glutinosae, typical
variant (CA1 to 16). Aconito napelli - Alnetum glutinosae, alluvial subunit (AcA1 and 7).
In view of these results, it is just possible to separate the whole into two entities from axis 1. On one side,
the Peudedano palustris - Alnetum glutinosae, a typical variant of Dryopteris cristata; on the other, Carici
acutiformis - Alnetum glutinosae, typical variant and Aconito napelli - Alnetum glutinosae.
-3
-2
-1
0
1
2
PA
1
PA
2
PA
3
PA
4
PA
5
PA
6
PA
7
PA
8
PA
9
PA
10
PA
11
PA
12
PA
13
PA
14
PA
15
PA
16
PA
17
CA
1
CA
2
CA
3
CA
4
CA
5
CA
6
CA
7
CA
8
CA
9
CA
10
CA
11
CA
12
CA
13
CA
14
CA
15
CA
16
AcA
1
AcA
2
AcA
3
AcA
4
AcA
5
AcA
6
AcA
7
Aulnaies à laîches113 - mfansca- Axe 1
-4
-3
-2
-1
0
1
2
PA
1
PA
2
PA
3
PA
4
PA
5
PA
6
PA
7
PA
8
PA
9
PA
10
PA
11
PA
12
PA
13
PA
14
PA
15
PA
16
PA
17
CA
1
CA
2
CA
3
CA
4
CA
5
CA
6
CA
7
CA
8
CA
9
CA
10
CA
11
CA
12
CA
13
CA
14
CA
15
CA
16
AcA
1
AcA
2
AcA
3
AcA
4
AcA
5
AcA
6
AcA
7
Axe 2
-3
-2
-1
0
1
2
3
PA
1
PA
2
PA
3
PA
4
PA
5
PA
6
PA
7
PA
8
PA
9
PA
10
PA
11
PA
12
PA
13
PA
14
PA
15
PA
16
PA
17
CA
1
CA
2
CA
3
CA
4
CA
5
CA
6
CA
7
CA
8
CA
9
CA
10
CA
11
CA
12
CA
13
CA
14
CA
15
CA
16
AcA
1
AcA
2
AcA
3
AcA
4
AcA
5
AcA
6
AcA
7
Axe 3
-4
-3
-2
-1
0
1
2
3
PA
1
PA
2
PA
3
PA
4
PA
5
PA
6
PA
7
PA
8
PA
9
PA
10
PA
11
PA
12
PA
13
PA
14
PA
15
PA
16
PA
17
CA
1
CA
2
CA
3
CA
4
CA
5
CA
6
CA
7
CA
8
CA
9
CA
10
CA
11
CA
12
CA
13
CA
14
CA
15
CA
16
AcA
1
AcA
2
AcA
3
AcA
4
AcA
5
AcA
6
AcA
7
Axe 4
54
At this step, we find only a partial coincidence between factorial analysis and the three associations. First,
let's analyze the species ranked in decreasing order of relative contribution on the first four significant axes.
Espèces coord 1 CR 1 P 1
Carex acutiformis-h1 >1 0.236860547 5.610291889 3.4
Carex acutiformis-h1 0.232975348 5.427751287 3.75
Carex vesicaria-h1 -0.222772345 4.962751779 3.89
Juncus effusus-h1 -0.21690429 4.704747082 4.51
Salix aurita-b1 -0.209624276 4.394233699 7.54
Filipendula ulmaria-h1 0.204499372 4.181999326 12.8
Carex elongata-h1 -0.196493357 3.860963948 12.8
Fraxinus excelsior-b1 0.187948761 3.532473688 17.36
Lycopus europaeus-h1 -0.1798207 3.233548409 14.43
Salix aurita-b1 >1 -0.165599395 2.742315971 4.12
Carex acutiformis-h1 >3 0.161659561 2.613381356 12.29
Carex elongata-h1 >1 -0.160362975 2.571628372 9.36
Filipendula ulmaria-h1 >1 0.155642221 2.422450095 18.86
Caltha palustris-h1 0.154655791 2.391841381 27.14
Circaea lutetiana-h1 0.154378565 2.383274134 19.38
Galium palustre-h1 -0.132635513 1.75921792 33
Lonicera periclymenum-h1 -0.123190886 1.517599428 4.47
Agrostis canina-h1 -0.120495273 1.45191108 5.07
Agrostis canina-h1>1 -0.120495273 1.45191108 5.09
Frangula dodonei subsp. dodonei-b1 -0.116615826 1.359925088 30.95
Table 23. Species ranked in decreasing order of relative contribution on the first axis. Coord: coordinates on the
axis, CR: relative contribution, P: probability associated with the relative contribution. A1: tree layer, b1: shrub
layer, h1: herbaceous layer. > 1: abundance greater than 1.
On this first axis, Carex acutiformis (present and abundant> 1) is easily separated from Carex vesicaria,
Juncus effusus, Salix aurita (abundant> 1) and Lonicera periclymenum.
coord 2 CR 2 P 2
Alnus glutinosa-a1 >3 -0.24088628 5.80262007 1.06
Carex elongata-h1 -0.22528134 5.07516825 6.46
Scirpus sylvaticus-h1 -0.21329103 4.54930629 3.7
Dryopteris carthusiana-h1 -0.20534096 4.21649088 10.16
Iris pseudacorus-h1 -0.20445262 4.18008721 10.21
Phragmites australis-h1 -0.20040051 4.01603661 2.16
Calliergonella cuspidata 0.18486703 3.41758198 11.33
Solanum dulcamara-h1 -0.17760939 3.15450941 16.26
Carex acutiformis-h1 -0.16142122 2.60568108 17.16
Alnus glutinosa-b1 -0.14979655 2.24390075 32.59
Carex acutiformis-h1 >1 -0.14085751 1.98408385 25.74
55
Lycopus europaeus-h1 -0.13937998 1.94267781 27.51
Angelica sylvestris-h1 0.13842587 1.91617204 31.06
Phalaris arundinacea-h1 -0.13414336 1.79944407 5.95
Scirpus sylvaticus-h1 >1 -0.12620908 1.59287327 4.4
Iris pseudacorus-h1 >1 -0.12399212 1.53740466 5.47
Frangula dodonei subsp. dodonei-b1 0.11825426 1.39840702 29.25
Rubus fruticosus-h1 -0.11449342 1.31087433 40.86
Carex vesicaria-h1 >1 -0.11066728 1.22472465 4.77
Agrostis canina-h1 0.10802953 1.16703787 9.41
Table 24. Species ranked in decreasing order of relative contribution on the first axis. Coord: coordinates on the
axis, CR: relative contribution, P: probability associated with the relative contribution. A1: tree layer, b1: shrub
layer, h1: herbaceous layer. > 1: abundance greater than 1.
There is a group of variables, all negative, with significant relative contributions, including several with an
abundance greater than 1 or 3: Alnus glutinosa (> 3), Scirpus sylvaticus (present and> 1), Phragmites australis
and Carex vesicaria (abundance> 1). They are therefore dense alder with a high biomass of Alnus glutinosa.
Axis 3 opposes species like Rubus fruticosus, Dryopteris carthusiana, Circaea lutetiana, Carex acutiformis
(> 3) to Alnus glutinosa (in the shrub layer), Salix cinerea (shrub layer, present and> 1), Solanum dulcamara,….
Axis 4 opposes Athyrium filix-femina and Salix cinerea (shrub layer, present and> 1) to Carex remota,
Fraxinus excelsior (tree and shrub strata), Iris pseudacorus, Viburnum opulus (grass layer),…
As before, we submit the transformed table, with the coordinates of the statements on the first four axes, to
classification.
Classification and ranking of the Alders with Sedge
The classification and the ranking are realised as above.
Figure 20. evolution of the total occupied space according to the steps of the hiérachical descending
classification.
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Total occupied space
56
The evolution of the total occupied space shows that 6 clusters must be retained (Table 25). However, one
of the surveys is isolated and the virtual center program is applied for 5 clusters.
CENVI MC
CA1 PA1 CA8 CA11 PA7 PA12 PA7 CA1 PA2 PA1 CA11
CA2 PA2 CA12 PA8 PA13 PA8 CA2 PA3 PA14 CA12
CA3 PA3 CA16 PA9 PA14 PA9 CA3 PA4 PA15 CA16
CA4 PA4 AcA1 PA10 PA15 PA10 CA4 PA5 PA16 AcA1
CA5 PA5 AcA2 PA11 PA16 PA11 CA5 PA6 PA17 AcA2
CA6 PA6 AcA3 PA17 PA12 CA6 CA8 AcA7 AcA3
CA7 AcA4 PA13 CA7 AcA4
CA9 AcA5 CA9 AcA5
CA10 AcA6 CA10 AcA6
CA13 AcA7 CA13
CA14 CA14
CA15 CA15
Table 25. Comparison of the hierarchical descending classification and a ranking into three clusters, from a
transformed sedge Alder file.
We choose the CENVI classificationwith the relevé CA8 that joins the cluster of the PA1 to 6.
Sedge Alder with Carex acutiformis and Circaea lutetiana
sum
fr
CA
1
CA
2
CA
3
CA
4
CA
5
CA
6
CA
7
CA
9
CA
10
CA
13
CA
14
CA
15
sum
fr
pr
Carex acutiformis-h1 >3 12 0.3 1 1 0 1 1 1 1 1 1 0 1 0 9 0.75 0
Circaea lutetiana-h1 14 0.35 1 1 1 1 1 1 1 1 1 0 1 1 11 0.9167 0
Carex acutiformis-h1 >1 26 0.65 1 1 1 1 1 1 1 1 1 1 1 1 12 1 0.0014
Circaea lutetiana-h1 >1 5 0.125 0 0 0 0 1 1 0 1 1 0 1 0 5 0.4167 0.0014
Carex acutiformis-h1 27 0.675 1 1 1 1 1 1 1 1 1 1 1 1 12 1 0.0033
Fraxinus excelsior-b1 27 0.675 1 1 1 1 1 1 1 1 1 1 1 1 12 1 0.0035
Dryopteris carthusiana-ep1 10 0.25 0 1 0 0 1 1 0 1 1 1 1 0 7 0.5833 0.0041
Galium aparine subsp. aparine-h1 4 0.1 0 0 0 0 0 0 0 1 0 1 1 1 4 0.3333 0.006
Filipendula ulmaria-h1 >1 14 0.35 1 1 1 1 0 0 0 0 1 1 1 1 8 0.6667 0.0079
Dryopteris carthusiana-h1 21 0.525 1 1 1 0 1 1 1 0 1 1 1 1 10 0.8333 0.0114
Filipendula ulmaria-h1 >3 3 0.075 0 1 0 0 0 0 0 0 0 1 1 0 3 0.25 0.0193
Dryopteris dilatata-h1 3 0.075 0 0 1 0 0 0 1 0 0 0 0 1 3 0.25 0.0203
Alnus glutinosa-a1 >3 31 0.775 1 1 1 1 1 1 1 1 1 1 1 1 12 1 0.0212
Rubus fruticosus-ep1 3 0.075 0 0 0 0 0 0 1 1 0 0 1 0 3 0.25 0.0214
Glechoma hederacea-h1 5 0.125 0 1 0 1 0 0 0 0 0 0 1 1 4 0.3333 0.0218
Plagiomnium affine 3 0.075 0 1 0 0 0 0 0 0 0 1 1 0 3 0.25 0.0227
Humulus lupulus-b1 5 0.125 0 0 1 1 1 0 0 0 1 0 0 0 4 0.3333 0.0229
Impatiens glandulifera-h1 >1 3 0.075 0 0 1 1 1 0 0 0 0 0 0 0 3 0.25 0.0233
Rubus fruticosus-h1 22 0.55 1 1 1 0 1 1 1 1 1 0 1 1 10 0.8333 0.024
57
Kindbergia praelonga 8 0.2 0 1 0 0 1 0 1 0 1 0 1 0 5 0.4167 0.037
Galeopsis tetrahit-h1 8 0.2 0 0 0 0 0 1 1 0 0 1 1 1 5 0.4167 0.0376
Cardamine pratensis-h1 8 0.2 1 0 0 1 0 1 0 0 0 1 1 0 5 0.4167 0.0415
Table 26. Species of elementary syntaxon 1 of sedge Alders with a statistically higher relative frequency than in
all the relevés. The specific names are followed by their memebership to one of the strata. = frequency, Fr =
relative frequency, Pr = probability calculated by the permutation test.
This grouping includes 12 of the 16 relevés of the hygrophilous neutroacidicline sedge Alder with Carex
acutiformis and Circaea lutetiana. The essential difference with the BAILLY’s association is the taking into
account of the abundance of Carex acutiformis and Circaea lutetiana.
Sedge Alder with Carex elongata and Phalaris arundinacea
sum
fr
PA
1
PA
2
PA
3
PA
4
PA
5
PA
6
CA
8
sum
fr
pr
Phalaris arundinacea-h1 7 0.175 0 1 1 1 1 1 0 5 0.7143 2.00E-04
Phalaris arundinacea-h1 >1 4 0.1 0 0 1 1 1 1 0 4 0.5714 3.00E-04
Salix cinerea-b1 >1 7 0.175 1 1 1 1 1 0 0 5 0.7143 7.00E-04
Thysselinum palustre-h1 5 0.125 0 1 1 1 0 1 0 4 0.5714 0.002
Phragmites australis-h1 10 0.25 0 1 1 0 1 1 1 5 0.7143 0.0059
Carex elongata-h1 18 0.45 1 1 1 1 0 1 1 6 0.8571 0.0245
Salix cinerea-b1 13 0.325 1 1 1 1 1 0 0 5 0.7143 0.0264
Table 27. Species of elementary syntaxon 2 of sedge Alders with a statistically higher relative frequency than in
all the relevés. The specific names are followed by their memebership to one of the strata. = frequency, Fr =
relative frequency, Pr = probability calculated by the permutation test.
There are six of the Carex elongata acidicline paludal alder relevés (Peucedano palustris - Alnetum
glutinosae) with two of the three variants, namely the typical Dryopteris cristata variant (1 relevé named PA1)
and the Carex acutiformis and Phalaris arundinacea variant. It is the combination of Carex elongata, Phalaris
arundinacea, Phragmites australis, Salix cinerea and Thysselinum palustre which constitutes the characteristic
set.
Sedge Alder with Caltha palustris and Filipendula ulmaria
sum
fr
CA
11
CA
12
CA
16
AcA
1
AcA
2
AcA
3
AcA
4
AcA
5
AcA
6
AcA
7
sum
fr
pr
Cirsium oleraceum-h1 6 0.2 1 0 1 0 0 1 1 1 0 1 6 0.6 0
Galium mollugo subsp. mollugo-h1 5 0.1 0 0 0 1 1 1 1 0 1 0 5 0.5 2.00E-04
Filipendula ulmaria-h1 21 0.5 1 1 1 1 1 1 1 1 1 1 10 1 4.00E-04
Ranunculus aconitifolius-h1 5 0.1 0 0 0 1 1 0 1 1 0 1 5 0.5 4.00E-04
Caltha palustris-h1 23 0.6 1 1 1 1 1 1 1 1 1 1 10 1 0.001
Aconitum napellus-h1 4 0.1 0 0 0 1 1 0 1 0 0 1 4 0.4 0.0017
Plagiomnium elatum 4 0.1 0 0 0 0 0 1 1 1 1 0 4 0.4 0.0023
Calliergonella cuspidata 15 0.4 0 1 0 1 1 1 1 1 1 1 8 0.8 0.0029
58
Eupatorium cannabinum-h1 9 0.2 1 0 1 0 0 1 1 1 1 0 6 0.6 0.0032
Table 28. Species of elementary syntaxon 3 of sedge Alders with a statistically higher relative frequency than in
all the relevés. The specific names are followed by their memebership to one of the strata. = frequency, Fr =
relative frequency, Pr = probability calculated by the permutation test.
We mix three relevés of the acidicline paludal alder with Carex elongata: Peucedano palustris -
Alnetum glutinosae Noirfalise & Sougnez 1961, with a relevé of the variant with Carex vesicaria and two
relevés of the subassassociation agrostietosum caninae, as well as seven relevés of mountain alder with
Aconitum napellus.
Sedge Alde with Carex remota and Carec vesicaria
sum
fr
PA
7
PA
8
PA
9
PA
10
PA
11
sum
fr
pr
Carex remota-h1 8 0.2 1 0 1 1 1 4 0.8 0.0032
Carex vesicaria-h1 14 0.35 1 1 1 1 1 5 1 0.0033
Lycopus europaeus-h1 16 0.4 1 1 1 1 1 5 1 0.0064
Carex vesicaria-h1 >1 5 0.125 0 0 1 1 1 3 0.6 0.01
Rumex sanguineus-h1 2 0.05 1 0 1 0 0 2 0.4 0.0127
Carex elongata-h1 18 0.45 1 1 1 1 1 5 1 0.0152
Lonicera periclymenum-h1 6 0.15 1 1 0 0 1 3 0.6 0.0162
Scirpus sylvaticus-h1 >1 6 0.15 1 0 0 1 1 3 0.6 0.0167
Scirpus sylvaticus-h1 13 0.325 1 0 1 1 1 4 0.8 0.03
Salix aurita-b1 13 0.325 0 1 1 1 1 4 0.8 0.0346
Myosotis scorpioides-h1 3 0.075 1 0 1 0 0 2 0.4 0.0356
Juncus effusus-h1 14 0.35 1 1 1 1 0 4 0.8 0.0411
Rubus fruticosus-h1 22 0.55 1 1 1 1 1 5 1 0.043
Salix aurita-b1 >1 8 0.2 0 0 1 1 1 3 0.6 0.0459
Iris pseudacorus-h1 23 0.575 1 1 1 1 1 5 1 0.0466
Table 29. Species of elementary syntaxon 4 of sedge Alders with a statistically higher relative frequency than in
all the relevés. The specific names are followed by their memebership to one of the strata. = frequency, Fr =
relative frequency, Pr = probability calculated by the permutation test.
These seven relevés correspond perfectly to the acidicline paludal Alder with Carex elongata: Peucedano
palustris - Alnetum glutinosae, variant with Carex vesicaria.
Sedge Alder with Agrostis canina
sum
fr
PA
12
PA
13
PA
14
PA
15
PA
16
PA
17
sum
fr
pr
Agrostis canina-h1 6 0.15 1 1 1 1 1 1 6 1 0
Agrostis canina-h1 >1 6 0.15 1 1 1 1 1 1 6 1 0
Carpinus betulus-h1 4 0.1 1 1 0 1 1 0 4 0.666666667 1.00E-04
Polytrichastrum formosum 4 0.1 1 1 0 0 1 1 4 0.666666667 1.00E-04
Sphagnum auriculatum 4 0.1 1 0 1 0 1 1 4 0.666666667 1.00E-04
59
Molinia caerulea-h1 5 0.125 0 0 1 1 1 1 4 0.666666667 6.00E-04
Salix aurita-b1 13 0.325 1 1 1 1 1 1 6 1 7.00E-04
Carex vesicaria-h1 14 0.35 1 1 1 1 1 1 6 1 7.00E-04
Juncus effusus-h1 14 0.35 1 1 1 1 1 1 6 1 0.001
Populus tremula-a1 3 0.075 1 0 0 0 1 1 3 0.5 0.0013
Sphagnum palustre 3 0.075 0 0 1 1 0 1 3 0.5 0.0017
Populus tremula-b1 3 0.075 0 1 0 0 1 1 3 0.5 0.002
Quercus robur-a1 6 0.15 1 1 1 0 1 0 4 0.666666667 0.0023
Sphagnum inundatum 3 0.075 1 1 0 1 0 0 3 0.5 0.0029
Frangula dodonei subsp. dodonei-b1 11 0.275 0 1 1 1 1 1 5 0.833333333 0.0042
Frangula dodonei subsp. dodonei-h1 4 0.1 1 1 0 1 0 0 3 0.5 0.0076
Alnus glutinosa-h1 4 0.1 0 0 1 1 1 0 3 0.5 0.0078
Thuidium tamariscinum 4 0.1 0 0 0 1 1 1 3 0.5 0.008
Salix aurita-b1 >1 8 0.2 1 1 1 0 0 1 4 0.666666667 0.011
Populus tremula-h1 2 0.05 1 0 0 0 1 0 2 0.333333333 0.0167
Sphagnum auriculatum >1 2 0.05 1 0 0 0 0 1 2 0.333333333 0.0168
Agrostis canina-h1 >3 2 0.05 0 0 0 1 1 0 2 0.333333333 0.017
Populus tremula-h1>1 2 0.05 1 0 0 0 1 0 2 0.333333333 0.0183
Ranunculus flammula-h1 5 0.125 1 1 0 1 0 0 3 0.5 0.0191
Pellia epiphylla 2 0.05 0 0 0 0 1 1 2 0.333333333 0.0191
Carpinus betulus-b1 5 0.125 0 1 0 1 1 0 3 0.5 0.0192
Carex viridula subsp. oedocarpa-h1 2 0.05 1 0 0 0 0 1 2 0.333333333 0.0192
Sphagnum inundatum >1 2 0.05 1 1 0 0 0 0 2 0.333333333 0.0192
Fagus sylvatica-h1 2 0.05 0 0 1 0 1 0 2 0.333333333 0.0194
Juncus effusus-h1 >1 2 0.05 0 0 0 1 1 0 2 0.333333333 0.0202
Pseudoscleropodium purum 2 0.05 0 0 0 1 1 0 2 0.333333333 0.0206
Carex echinata-h1 2 0.05 0 0 0 1 0 1 2 0.333333333 0.0213
Lonicera periclymenum-h1 6 0.15 0 0 1 1 1 0 3 0.5 0.0292
Lonicera periclymenum-b1 6 0.15 0 0 1 1 1 0 3 0.5 0.033
Carex elongata-h1 >1 11 0.275 0 1 1 1 1 0 4 0.666666667 0.0353
Scutellaria galericulata-h1 11 0.275 1 1 0 0 1 1 4 0.666666667 0.039
Viola palustris-h1 3 0.075 0 0 0 1 0 1 2 0.333333333 0.0468
Viola palustris-h1 >1 3 0.075 0 0 0 1 0 1 2 0.333333333 0.0495
Table 30. Species of elementary syntaxon 5 of sedge Alders with a statistically higher relative frequency than in
all the relevés. The specific names are followed by their memebership to one of the strata. = frequency, Fr =
relative frequency, Pr = probability calculated by the permutation test.
This alder is particularly well-typed, very diverse, with a characteristic set which is particularly well
represented. It corresponds perfectly to the acidicline paludal alder with Carex elongata: Peucedano palustris -
Alnetum glutinosae, subass. agrostietosum caninae.
60
Conclusions on the analysis of the BAILLY’s table
The comparison between the classification of the Alder woodlands proposed by BAILLY (2012) and that
resulting from the numerical classification resulting from our own analyses. leads us to propose the diagram of
figure 21.
Figure 21. Proposal for a classification of the Alder woodlands
Although it is easy to separate the Fern Alders and the Sdge Alders, this is not the case in the following.
and statistical analysis only partially correlates with the classification of the phytosociologist. Several well-typed
associations are also well recognized, or in large part, by the phytosociologist or the biometrician; for many
others, the difference is important. Despite the differences observed. we are convinced that the statistical analysis
is likely to help the phytosociologist in his search for a classification integrated into a hierarchical system.
The work would have been facilitated if accurate environmental data and soil characteristics were available.
Swampy Alder of
Franche-Comté
Fern Alder Sedge Alder
Amphibious
Alder with
Hottonia
palustris
Fern Alder with
Galium palustre
and Lysimachie
vulgaris
FernAlder
with
Molinia
caerulea
and
Sphagnum
palustre
Fern Alder
with Carex
brizoides
Sedge Alder
with Carex
acutiformis
and Circaea
lutetiana
Sedge Alder
with Carex
elongata
and
Phalaris
arundinacea
Sedge Alder
with Caltha
palustris
and
Filipendula
ulmaria
Sedge Alder
with Carex
remota and C.
vesicaria
Sedge Alder with
Agrostis canina
61
General conclusions
The statistical analysis of a small file is relatively easy especially when the data are well structured, as is
the case in the ROYER’s file. In this example. it corresponds. to a large extent. to the analysis of the
phytosociologist. provided that it is based solely on presence data. The non-symmetric correspondence analysis
is best suited to this type of data. This leads to a good agreement between the analysis of the phytosociologist
and the statistical analysis. However. the statistical analysis is not adapted to the few data and it is difficult to
discriminate plant groups represented by a very small number of relevés.
Another way to process a phytosociological table, without losing any nuance provided by the field
observer, is to create a disjunctive table, complete or simplified. In the two files covered in this chapter. the
analysis of a complete disjunctive table, with a line for absences for each species and a line for each category of
abundance, yielded only results that were difficult to interpret. Even after removing the zeros, the data remained
inadequate for multivariate analyses. The disjunctive tables which we call simplified, that is to say without the
lines of zeros and by grouping several categories of abundance into a single line, have proved compatible with a
good multivariate analysis. The way of grouping several categories of abundance remains relatively empirical
but it must adapt to the kinds of data tables, depending on the number of relevés and the structure of the data.
The examination of the distributions of covariances in the multivariate analyses seems to be an important step in
the choice of the multivariate analysis best suited to the table to be analysed; a fairly symmetric and relatively
flattened bell covariance distribution is a promise of success for multivariate analysis. In the case of a clearly
asymmetric distribution, multivariate analysis can do nothing.
Finally, with pluristratal vegetation. multiple factor analysis is a very powerful tool, which I strongly
advise.
However, when you have a fairly large file, such as the Alder woodland file, you can not use all the
variability of the data with single-scale analyses. In this file. it has proved essential to analyse the data on two
successive scales: that of the 108 relevés and then that of the two Alder woodlands. These two scales have their
own sensitivity and a single-scale analysis of the large picture can not, in our opinion, lead to a good
understanding of the structure of the data. This methodology increases the time given to the analysis and
interpretation of the relevé tables, but this complementary time is only a small fraction of the time and energy
spent collecting the field data.
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