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ECOGRAPHY 24: 659–670. Copenhagen 2001

Methods for comparison of biotic regionalizations: the case of

pteridophytes in the Iberian Peninsula

Ana L. Marquez, Raimundo Real and J. Mario Vargas

Marquez, A. L., Real, R. and Vargas, J. M. 2001. Methods for comparison of bioticregionalizations: the case of pteridophytes in the Iberian Peninsula. – Ecography 24:659–670.

We made several regionalizations of the Iberian Peninsula based on the distributionsof the pteridophyte flora to see whether the regionalization depended on the type andscale of lattice or the similarity index considered. We used five types of lattice inwhich the scale also varied: river basins, mountains and plains, natural regions,physiographic and geological regions, and administrative provinces; and two similar-ity indices: those of Jaccard and of Baroni-Urbani and Buser. The regionalizationsvaried according to the type of lattice, the grain size, and the similarity index used.To assess the different regionalizations we used four methods: 1) the coefficient of variation of the size of sites in each lattice, 2) the bestblock method, which considersas the best lattice that which maximizes the number of matches between presencesover all pairwise site comparisons, 3) the Mantel test, to assess the statisticalsignificance of the regionalizations obtained, and 4) mapability, which considers themost contiguous regionalization to be the best. The best regionalization according toour four criteria was that based on administrative provinces and Jaccard’s index. Thisyielded a small central region and three large regions: northern, western, and eastern.

A. L. Marquez ( [email protected] ) , R. Real and J . M . Vargas, Dept de BiologıaAnimal , Fac. de Ciencias, Uni 6. de Malaga, E -29071 Malaga, Spain.

A major objective of descriptive biogeography is to

simplify the complex patterns of contemporary species’

distributions by classifying areas based on their biotic

composition. That areas of the world can be character-

ized on the basis of the presence of certain taxa and the

absence of others has long been recognised by biogeo-graphers (Buffon 1761), and is a deeply entrenched

component of much contemporary biogeographical

thinking. In addition, classifying geographical areas

into groups with different species composition is valu-

able for nature conservation planning (Brown et al.

1993), so as to ensure that all groups are represented in

the selection of natural reserves (Margules 1986), and

to evaluate the biological resources of an area in a

regional and global context (Carey et al. 1995). How-

ever, currently administrators are often confused by the

number of different classifications of their country pro-

posed by ecologists and phytogeographers. In addition,

as Thaler and Plowright (1973) pointed out, phytogeo-

graphers have disagreed about whether floristic areas

represent real entities in nature or whether they are

simply convenient, subjective constructs that lack any

objective and unambiguous basis.

Operationally, it is possible to identify bioticboundaries when a group of areas with similar biota

shares fewer species than expected at random with

other group of areas with similar biota. Then the

Operational Geographic Units (OGUs; Crovello 1981)

of this territory can be grouped into biotic regions

(Real et al. 1992a, Myklestad and Birks 1993,

McLaughlin 1994). Clustering methods represent one

approach to this problem (Birks 1987, Legendre 1990),

but only when a probabilistic procedure allows the

researcher to distinguish between statistically significant

clusters and those indistinguishable from random ex-

pectation (Marquez et al. 1997). Area clusters may be

Accepted 6 March 2001

Copyright © ECOGRAPHY 2001ISSN 0906-7590Printed in Ireland – all rights reserved

ECOGRAPHY 24:6 (2001) 659



considered as biotic regions when a group of OGUs is

statistically significant. Legendre (1987) advocated con-

straining the clustering to respect spatial contiguities.

However, in some cases, biotic regions may reflect a

climatic or ecological pattern that may be not strictly

contiguous in space, and then they may be better

detected with clusters only defined by the similarity of

their species composition. Then, area clusters can be

related to environmental variables by techniques such

as regression or canonical variates analysis (Carey et al.

1995, Olivero et al. 1998) to investigate possible causes

of the regionalization pattern.

However, to analyse biogeographic patterns, any ter-

ritory must be subdivided initially into different types

of OGUs (Crovello 1981, Kenkel et al. 1989, Mandrak

1995). This establishes a lattice that influences the bio-

geographic regions subsequently obtained, because any

biotic boundary necessarily has to follow along the

edges of the sites used to partition the study area.

Cressie (1993) defined a lattice as a countable collection

of spatial sites that are spatially regular or irregular,

represent points or regions, and are indices for continu-

ous or discrete variables. In biogeographic regionaliza-

tion the concept of lattice corresponds to any kind of

area subdivision, irrespective of its size and the criteria

used to define it, and the sites correspond to the OGUs.

The lattices can be natural (e.g., watersheds, Vargas etal. 1998), arbitrary (e.g., latitude-longitude cells, Schall

and Pianka 1977, or equal-area quadrats, Marquez et

al. 1997). The sites can have the same size when the

lattice is regular, such as those based on grid-squares,

or different sizes when the lattice is irregular, such as

those made according to, for example, physical, geolo-

gical, or political viewpoints. Variation in size and

shape may affect the species richness of each site and

hence the results of the subsequent regionalization.

Square equal-area quadrats are considered not to be

subject to these problems as quadrat size and shape are

uniform (Mandrak 1995), although coastal quadrats

may vary in area when terrestrial organisms are stud-

ied, and mountainous areas have more surface areathan flat areas in a ‘‘equal-area quadrat’’.

There are also problems in defining the scale of the

grain used (Jardine 1972, Birks 1987, Carey et al. 1995).

Scale is dependent on both the extent of the study area

and the size of organism studied (Wiens 1989). If too

coarse a lattice is used, biotic regions will be corre-

spondingly coarse. Conversely, the use of too fine a

lattice may fail to reveal major biotic regions and

generate many spurious small regions where recordings

may have been uneven. Results obtained using small

sites may be different from those obtained using larger

sites, although these different patterns might be interre-

lated (Blondel 1985, Vargas 1993). However, this does

not mean that there are no criteria for comparing theresults obtained using different types of sites or differ-

ent scales (Levin 1992). These criteria, however, need

proper definition and testing.

Ferns could provide a valuable source of biogeo-

graphical information that is distinct from, or at least

complementary to, that provided by other types of

plant (Marquez et al. 1997). Pteridophytes are a group

of species with a great dispersal capacity due to the

lightness of their spores (Jermy 1984). However, most

fern species are restricted in distribution and only a

limited number have wide ranges (Kato and Iwatsuki

1983), because their distribution is highly related to

climate and substratum (Barrington 1993, Given 1993,

Kornas 1993). The 113 Iberian pteridophyte species are

well recorded and well understood taxonomically in theIberian Peninsula (Salvo et al. 1984, Castroviejo et al.

1986), and are an important number of species in a

European context.

In this paper we have used several criteria to select

the best biotic regionalization among several partitions

obtained using a quantitative method of classification.

With this aim, we have used fern distributions in the

Iberian Peninsula a) to establish whether the Iberian

Peninsula may be divided into pteridogeographic re-

gions or whether the pteridophyte species distributions

follow a mainly gradual pattern; b) to verify whether

the resulting regionalization patterns are different ac-

cording to the type of lattice, the number of sites

considered, and the similarity index used; and c) toapply several criteria to select the best regionalization

pattern.

Material and methods

Study area

The Iberian Peninsula is situated on the south-western

end of Europe, and presents a stronger peninsular

condition than other large Mediterranean peninsulas

because its isthmus is relatively narrow. In addition, the

presence of the Pyrenees in the isthmus hinders the

spread of propagules between the Iberian Peninsula andthe rest of the European continent. The interchange of

biota with Africa is also hindered by the Straits of

Gibraltar. Climatically, the Iberian Peninsula is placed

in the southern band of the temperate zone.

Species distribution and Operational Geographic

Units (OGUs)

The distribution of the 113 species of pteridophytes

were obtained from Salvo et al. (1984), supplemented

with new records published later.

We considered five types of OGUs in the Iberian

Peninsula: river basins, mountains and plains, naturalregions, physiographic and geological regions, and ad-

ministrative provinces (Anon. 1980) (Fig. 1). The

province lattice is political-administrative, although is

660 ECOGRAPHY 24:6 (2001)



partially based on natural partitions, whereas the other

four lattices have natural borders. Natural regions and

physiographic and geological regions are partially

based on vegetation, and so some circular reasoning

may be involved in their use as phytogeographic re-

gions (Birks 1987, Real and Ramırez 1992, Vargas

1993).

Classification analysis

Initially we constructed a presence-absence matrix forthe 113 species in each lattice considered in the area.

We thus had five presence-absence matrices, in which

OGU size and number varied: river basins (11×113),

mountains and plains (12×113), natural regions (17×

113), physiographical regions (22×113), and adminis-

trative provinces (56×113).

We applied two similarity indices to each pair of

OGUs: Jaccard’s (1908) index and Baroni-Urbani and

Buser’s (1976). The Jaccard index considers only double

presences, whereas the Baroni-Urbani and Buser index

incorporates double absences. Jaccard values may be

considered as absolute measures of biotic similarity,

because they are not affected by other species absent

from the two OGUs compared, while the Baroni-Ur-

bani and Buser coef ficient measures similarity in thecontext of the Iberian Peninsula, because species absent

from the two OGUs but present in other Iberian OGUs

increase the similarity between the two OGUs analysed

Fig. 1. The five differentlattices considered in the study(Anon. 1980).

ECOGRAPHY 24:6 (2001) 661



(Real et al. 1992b). However, the possibility that two

OGUs are considered similar exclusively because of

double absences is avoided in the Baroni-Urbani and

Buser index by multiplying double absences by double

presences.

We used UPGMA (Unweighted Pair-Group

Method using Arithmetic Averages) as our clustering

method (Sneath and Sokal 1973). Agglomerative tech-

niques are preferred to divisive techniques because the

former maximizes the similarity within a group, which

defines biotic regions. We represented the results as

dendrograms.To test the groups obtained in any association

analysis several authors use a null model based on a

Monte Carlo randomization procedure (Connor and

Simberloff 1979, Oden et al. 1993). However, this

model uses the observed data matrix to generate a

null distribution, and so observed and null distribu-

tions lack statistical independence (Grant and Abbot

1980). Notwithstanding, it is feasible to determine all

the possible distributions of N species in any of the

OGUs compared for each value of N, and so an

exact randomization test (Sokal and Rohlf 1981, p.

788) can be performed to determine whether an ob-

served value of the Jaccard index or the Baroni-Ur-

bani and Buser index is significantly different fromthose expected at random. We obtained the statistical

significance of the observed similarity values, accord-

ing to the exact randomization tests in Real and Var-

gas (1996) for the Jaccard index, and in

Baroni-Urbani and Buser (1976) for the Baroni-Ur-

bani and Buser index. In this way, the similarity ma-

trices were transformed into matrices of statistical

significance (Marquez et al. 1997) that consisted of

pluses, for similarity values significantly higher than

those expected at random, minuses, for similarity val-

ues significantly lower than those expected at random,

and zeros, for similarity values compatible with ran-

dom expectation.

Our null hypothesis is that biotic boundaries donot exist, so that we started searching for boundaries

at the level of the dendrogram with the lowest simi-

larity value, and then moved to the higher similarity

nodes, finishing when no more significant boundaries

appeared. This divisive procedure does not contradict

the use of an agglomerative classification, because sig-

nificant boundaries divide the space into biotic re-

gions that require not only the existence of a biotic

boundary, but also a biotic af finity between OGUs in

the region, which is favoured by the agglomerative

method.

We tested at every node of the dendrogram for the

existence of significant biotic boundaries between the

OGUs separated by the node using the method of McCoy et al. (1986), as modified by Real et al.

(1992b) for application to dendrograms, as indicated

in Appendix 1.

To determine which lattice and similarity index best

define the biotic regions we used four methods: 1)

Coef ficient of variation of the OGU’s size in each

lattice (Sokal and Rohlf 1981). Differences in the size

of the OGUs within a lattice produce area-related

distortions, such as differences in the number of spe-

cies in different parts of the study area. So, the lattice

with the lowest coef ficient of variation of the OGUs’

size is considered the best one. This method selects

the best lattice regardless of the distribution data. 2)

Bestblock (Phipps 1975), which considers the best lat-

tice to be that which maximizes the number of matches between presences over all pairwise OGU

comparisons. This method selects the best lattice after

taking into account the distribution data regardless of

the regionalization obtained. 3) We used the Mantel

test of matrix comparison (Mantel 1967) to compare

each original similarity matrix with each matrix of

hypothetical similarities according to the resulting re-

gionalizations. The matrices of hypothetical similari-

ties were obtained by considering all the similarities

within a biotic region to be 1, all the similarities be-

tween OGUs separated by weak boundaries to be the

random expectation (0.33 for Jaccard’s index and 0.5

for Baroni-Urbani and Buser’s index), and all thesimilarities between OGUs separated by strong

boundaries to be 0. Only significant regionalizations

were considered. The most significant regionalization

is that which is most consistent with the original simi-

larities and is thus considered the best. 4) Mapability

(Harper 1978). Contiguity is preferred to discontiguity

of the biotic regions obtained using each similarity

index in each lattice. We measured the mapability in

terms of the minimum number of quadrats UTM

50×50 km necessary to join together the parts of all

fragmented regions. The lower this number of

quadrats is, the more mapable the regionalization is.

We applied the two former criteria to the five lat-

tices and the two latter criteria to the ten regionaliza-tions resulting from using each similarity index in

each lattice.

Results

We found significant biotic boundaries for all types

of OGU using both similarity indices. All the region-

alization patterns obtained using the Jaccard index

(Table 1) and most of the regionalizations obtained

using Baroni-Urbani and Buser’s index (Table 2) were

statistically significant according to the Mantel test of

matrix comparison (Table 3). Only the regionalizationobtained using mountains and plains and the Baroni-

Urbani and Buser index was found to be non-signifi-

cant (p\0.01) using the Mantel test.

662 ECOGRAPHY 24:6 (2001)



Table 1. Statistically significant boundaries between groups of OGUs formed by UPGMA using the Jaccard similarity index.DW\0 and significant GW indicate weak boundary between the groups; DS\0 and significant GS indicate a strong boundarybetween the groups. N.S.: p\0.05; *: pB0.05; **: pB0.01; ***: pB0.005.

Biotic boundaryGroups set up byUPGMA

StrongWeak

Group Group DW DW DW GW p DS GS pA B (A×A) (B×B)

River basins 3 –5 9 –8 0.206 0.168 N.S0.187 9.074 *** −0.501 0Mountains and plains 2 –9 4 0.562 0.627 0.595 20.249 *** −0.079 0 N.S.

2 –5 10 –9 0.153 0.153 N.S.0.153 8.573 *** −0.555 0Natural regions 2 –13 4 –9 0.219 N.S.0.209 0.214 24.756 *** −0.457 0

Physiographical regions 7 –2 13 –14 0.372 0.571 0.472 28.758 *** −0.099 0.781 N.S.7 –17 4 –2 0.239 0.280 N.S.0.259 28.422 *** −0.349 0.606

N.S.7 –16 20 –17 0.201 0.222 0.211 16.107 *** −0.486 0Administrative 16 –54 27 0.189 0.707 0.448 27.311 *** 0.183 19.153 ***provinces 16 –40 14 –54 0.439 0.356 ***0.397 208.640 *** 0.011 80.326

14 –24 49 –54 0.387 ***0.348 0.367 176.987 *** −0.049 18.98649 –43 37 –54 0.522 0.592 0.557 45.891 *** −0.033 0 N.S.14 –12 23 –24 0.254 0.191 N.S.0.222 38.099 *** −0.351 1.365

N.S.14 –9 12 0.320 0.392 0.356 8.727 *** −0.316 023 –33 21 –10 0.407 0.389 0.398 13.508 *** −0.300 0 N.S.14 –15 20 –9 0.202 0.162 N.S.0.182 6.812 ** −0.505 0

N.S.37 –36 42 –54 0.126 0.126 0.126 6.328 * 0.581 020 –29 2 –9 0.080 0.080 0.080 5.555 N.S.* −0.627 0

Table 2. Statistical significant boundaries between groups of OGUs formed by UPGMA using the Baroni-Urbani and Buser

similarity index. DW\0 and significant GW indicate weak boundary between the groups; DS\0 and significant GS indicatea strong boundary between the groups. N.S.: p\0.05; *: pB0.05; **: pB0.01; ***: pB0.005.

Groups set up by Biotic boundaryUPGMA

StrongWeak

Group Group DW DW DW GW p DS GS pA B (A×A) (B×B)

River basins 3 –5 9 –8 0.116 0.116 0.116 6.98 ** −0.591 0 N.SMou ntains and p lain s 2 –4 1 –5 0.307 0.307 0.307 24.015 *** −0.400 0 N.SNatural regions 6 –14 5 –11 0.114 0.114 N.S.0.114 22.100 *** −0.593 0Physiographical regions 7 –14 4 –2 0.140 0.147 N.S.0.144 43.864 *** −0.551 0.007Administrative 16 –12 27 0.513 – 0.575 94.044 *** 0.089 28.972 N.S.

16 –40 49 –12 0.193provinces 0.008 ***0.10 1 16 1.90 9 ** * −0.456 23.21449 –54 20 –12 0.096 0.091 0.093 89.621 *** −0.611 0 N.S.20 –24 12 0.099 0.099 N.S.0.099 9.930 *** −0.608 0

16 –56 N.S.18 –40 0.062 0.072 0.067 9.620 *** −0.635 0

Table 3. Results of the application of the four criteria used to determine which is the best regionalization. CV: Coef ficient of variation of the OGUs’ size; TM: Total matches between presences in all pair-wise comparisons; SQ: Number of squares 50×50km necessary to join together each fragmented region.

Mantel testOGU Systems Coef ficient Best Mapabilityblockof variation

JaccardJaccard Baroni-Urbani Baroni-Urbaniand Buser and Buser

SQCV TM z p(z obsBz exp) z p(z obsBz exp ) S Q

River basins 0.481 20 983 10.17 0.002 5.33 0.002 0 0Mountains and plains 0.445 21 754 13.72 00.001 3.91 0.014 0

Natural regions 0.360 26 885 24.92 0.001 12.36 0.001 00Physiographical regions 0.447 28 977 60.75 00.001 20.06 0.001 1Administrative 0 30.359 47 881 544.9 0.001 212.9 0.001

provinces

ECOGRAPHY 24:6 (2001) 663



Area classification using the Jaccard similarityindex

Figure 2 shows the biotic boundaries found using each

lattice and the Jaccard similarity index. The lattices of

river basins and natural regions present only a weak

biotic boundary that divides the Iberian Peninsula into

a northern and a southern region, whereas two or more

boundaries are obtained using the other lattices (Fig. 2,

Table 1).

In the administrative provinces lattice, three strong

boundaries divide the Iberian Peninsula into four

supraregions: northern supraregion, western suprare-gion, eastern supraregion, and a small central suprare-

gion. The western and eastern supraregions are divided

by weak biotic boundaries into four and three regions,

respectively (Fig. 2).

Area classification using the Baroni-Urbani andBuser similarity index

Figure 3 shows the biotic boundaries found using

each lattice and the Baroni-Urbani and Buser index.

In four lattices (river basins, mountains and plains,

natural regions, and physiographical regions) there are

only weak biotic boundaries (Table 2) that divide theIberian Peninsula into northern and southern regions,

although using mountains and plains the regionaliza-

tion was not statistically significant (Table 3). However,

using the provinces there are three big regions

(northern, western, and eastern) and three small regions

(Fig. 3).

Which lattice defines best the biotic regions?

The administrative provinces have the lowest coef ficient

of variation for the size of the sites (Table 3). That

means that using the provinces the Iberian territory is

more evenly distributed than using the other lattices.

According to the bestblock method, the administrative

provinces lattice maximizes the number of positive

matches over all pairwise species comparisons (Table

3). The significance values associated with the Mantel

text are lower for river basins and nonsignificant for

mountains and plains when using the Baroni-Urbani

and Buser’s index, whereas the other regionalizationsall have the same high probability value (Table 3). The

regions obtained from physiographical regions using

the Jaccard index and from administrative provinces

using the Baroni-Urbani and Buser index are frag-

mented (Table 3, Figs 2 and 3), whereas the other

lattices yield continuous regions.

Therefore, the only regionalization that obtains the

best scores according to the four criteria is the one

obtained using administrative provinces and the Jac-

card index (Fig. 2).

DiscussionAlthough there is no absolute regionalization of the

Iberian Peninsula according to the distribution of pteri-

dophytes, the concept of the biotic region is not an

useless artefact. Regionalizations vary according to the

type of OGU, the grain size, and the similarity index

used. In this way, any regionalization must indicate

Fig. 2.

664 ECOGRAPHY 24:6 (2001)



Fig. 2. Dendrograms andbiotic regions forpteridophytes in the IberianPeninsula using the Jaccardsimilarity index on eachlattice considered. Numbers of the units as in Fig. 1. W:weak boundary; S: strongboundary; *: pB0.05;**: pB0.01; ***: pB0.005.

those characteristics, which are inseparable from the

pattern obtained. This is especially true given the ex-

ploratory nature of current approaches to biotic re-

gionalization (Carey et al. 1995). However, the

biogeographic regions and boundaries are useful for

understanding the mechanisms underlying the distribu-tion of organisms, provided that each regionalization

reflects a distribution pattern that is statistically signifi-

cant and may be related to environmental conditions,

although detected through the filters of the OGUs, the

scale of grain, and the similarity index.

The indices of similarity

Oden et al. (1993) modified the method of Womble

(1951) to detect intervals of marked change in categori-

cal variables between contiguous sites. When the vari-

ECOGRAPHY 24:6 (2001) 665



able analysed is the presence or absence of species this

method could be used to obtain biotic boundaries and

regions. However, the basic statistic that results from

the method of Oden et al. (1993) is the complement of

the simple matching coef ficient, which is not recom-

mended for biogeographical regionalizations, since re-

gions may be defined only on the basis of shared

absences, even with no single species in common (Ba-

roni-Urbani and Buser 1976).

We opted for using the Jaccard and Baroni-Urbani

and Buser similarity indices to estimate the associations

between the OGUs and, later, to test the statisticalsignificance of such associations, because they are com-

monly used and are somewhat complementary. The

Jaccard index only takes into account the double pres-

ences of species in the two OGUs compared, and the

similarity between two OGUs is not affected by other

species present in other OGUs in the study area. The

Baroni-Urbani and Buser index takes into account dou-

ble absences, which offers potentially useful informa-

tion because if a species is absent from two OGUs, it

may be due to ecological or historical factors impacting

in a similar way on the species in the context of the area

studied. If the pattern obtained considering the similar-

ities between each pair of OGUs only (using the Jac-

card index) is maintained when the similarities take intoaccount all the study area (using the Baroni-Urbani and

Buser index), then the lattice used may be considered

suitable for revealing a consistent distribution pattern

of the species.

The regionalizations obtained using the two indices

are identical when based on river basins and on natural

regions, partially similar using physiographical regions

and provinces, and very different using mountains and

plains. The differences seem to be more related to the

type of OGU than to the scale of grain. It may be that

when using river basins and natural regions the distri-

bution of pteridophytes is very well defined, because the

double absences do not modify the overall relationship

pattern obtained using only the presences, whereas

mountains and plains are very unsuitable units for

recording the distribution of pteridophytes, so that

double absences greatly alter the relationship pattern

between the OGUs, with physiographical regions and

provinces in an intermediate position.The number of boundaries obtained using the Ba-

roni-Urbani and Buser coef ficient tends to be lower

than that obtained using the Jaccard index, probably

because the double absences considered in the Baroni-

Urbani and Buser index tend to homogenize the re-

gions. This may be seen especially in the south, that has

a lower number of species than in the north. Perhaps

this tendency should be taken into account when a

researcher decides which index to use to reveal a re-

gionalization pattern, according to the underlying

knowledge and assumptions.

The criteria to select the best regionalization

Even when using an numerical method of classification

and a probabilistic procedure to assess the groups of

OGUs obtained, several regionalizations may result

from the use of different types of OGUs or different

similarity indices, so that several criteria are needed to

compare the suitability of the regionalizations obtained.

Fig. 3.

666 ECOGRAPHY 24:6 (2001)



Fig. 3. Dendrograms and bioticregions for pteridophytes in theIberian Peninsula using theBaroni-Urbani and Busersimilarity index on each latticeconsidered. Numbers of theunits as in Fig. 1. W: weakboundary; S: strong boundary;*: pB0.05; **: pB0.01;***: pB0.005.

We used two criteria prior to the classification proce-

dure, and two criteria after the classification. The co-

ef ficient of variation (Sokal and Rohlf 1981) indicated

that the size of each OGU in the provinces is more

similar than in the other lattices and is thus to be

preferred independently of the distribution data. The

‘‘bestblock’’ method (Phipps 1975) showed that admin-

istrative provinces provide the best lattice for establish-ing the biotic boundaries of the Iberian Peninsula

according to its pteridoflora (Table 3), because the finer

scale of the partition produced more units, and because

the presences are more equitably distributed through

the OGUs, thus producing more matches of presences

in pairwise comparisons. The regionalization obtained

using provinces and the Jaccard index was one of five

regionalizations that were suitable according to both

the Mantel test and the mapability criterion, because it

had the highest statistical significance and was totally

mapable. Mantel and mapability tests were appliedto the final regionalization patterns, and showed

whether the patterns were in accordance with the origi-

nal similarities between OGUs and with the within-

ECOGRAPHY 24:6 (2001) 667



region continuity recommendable for a biotic region,

respectively.

The higher number of units in the provinces lattice is

not the only cause of this partitioning being selected.

These four criteria are not biased towards partitionings

with a large number of units nor more isodiametrically-

shaped units. The coef ficient of variation selects a parti-

tioning of more equal-sized units, but not more circular

in shape, and irrespective of the number of units. The

Phipps algorithm not always chooses the partitioning

with the greatest number of units (see Phipps 1975).

Although the provinces lattice has more units it is notmore likely to produce statistically significant results

after using Mantel’s test, and, in fact, the partitioning

obtained using provinces has the same high significance

level than other partitionings. As regards the criterion

of mapability, a partitioning based on more units is

more likely to produce fragmented regions, although

this is not the case for provinces when using Jaccard’s

index.

Administrative provinces as operational geographicunits

In the Iberian Peninsula, provinces provide the latticethat yields the most appropriate regionalization accord-

ing to our four statistical criteria when using Jaccard’s

index, and is thus the regionalization to be preferred in

attempting to identify the biogeographical processes

affecting the distribution of pteridophytes. One reason

for this may be that provinces are administrative units

of ancient origin and are not completely arbitrary. This

is likely to be true elsewhere, at least in Europe, where

administrative units are partially based on natural par-

titions perceived by local people, as is the case, for

example, with vice-counties in the British Isles (Baroni-

Urbani and Collingwood 1976).

Different types of arbitrary areas within a study

region can be used, such as countries, counties,provinces, river basins, latitude/longitude blocks, or

equal size U.T.M. squares (Birks 1987). In the last

decade regular geographical units, like networks of

regular squares, have been commonly used (e.g. Mart ın

and Gurrea 1990, Lausini and Nimis 1991, Myklestad

and Birks 1993, Carey et al. 1995, Moreno-Saiz et al.

1998). However, regular squares have artificial borders

and, therefore, may include several fragments of differ-

ent geographic or environmental units, so hindering the

search for biogeographical processes that may only act

on natural units (Palomo and Antunez 1992). The

division in provinces is also arbitrary, but the adminis-

trative borders between provinces follow, in part, natu-

ral boundaries such as geographical ranges, so that theymay be more appropriate to assess the environmental

explanations for species distributions. In addition,

provinces may be a suitable type of OGU for analysing

human influence on natural distributions, because in

most countries human activities follow political-admin-

istrative borders.

Acknowledgements – We thank H. J. B. Birks, S. P. McLaugl-hin and P. L. Nimis for revisions of the manuscript and theirvaluable suggestions. We are also grateful to M. A. Rendon, J.C. Guerrero and J. Olivero for their help with the statisticalprocedures.

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Appendix 1. Calculation of parameters used to test theexistence of significant biotic boundaries.

For each dendrogram node we established a submatrix of significant similarities that only included the two groups of

OGUs separated by that node, which we named group A andgroup B, respectively. This submatrix was divided into threezones: zone A×A and zone B×B, which corresponded to thesignificant similarities between OGUs of group A and betweenOGUs of group B, respectively; and zone A×B, correspond-ing to the significant similarities between the two groups of OGUs.

We call Pp(A×A) the number of pluses within zone A×Adivided by the total number of pairwise OGU comparisons inzone A×A. So, Pp(A×A) is the proportion of pluses in zoneA×A. We call Psp(A×A) the number of OGUs in group Athat have at least one plus divided by the total number of OGUs in group A. We can then compute d1(A×A) asfollows: if the number of pluses in A×A is zero, then d1(A×A)=0; otherwise,

d1(A×A)=Pp(A×A)×Psp(A×A)

(Pp(A×A))2

+(Psp(A×A))2

The values of d1(A×A) range from 0 to 0.707, estimating towhat extent similarities higher than expected at random (+)predominate within zone A×A.

We define Pm(A×A) and Psm(A×A) as the proportion of minuses in zone A×A and the proportion of OGUs in groupA with at least one minus, respectively, and these are com-puted in the same way as Pp(A×A) and Psp(A×A), buttaking into account the minuses. We then define d2(A×A) inthe following way: if the number of minuses in zone A×A iszero, then d2(A×A)=0; otherwise,

d2(A×A)=Pm(A×A)×Psm(A×A)

(Pm(A×A))2+(Psm(A×A))2

The values of d2(A×A) range from 0 to 0.707, estimating to

what extent similarities lower than expected at random (−)predominate within zone A×A. We d efine Pp(A×B) andPsp(A×B) in a similar way to Pp(A×A) and Psp(A×A),but with reference to zone A×B. So, d3 is zero when thenumber of pluses in A×B is zero; otherwise,

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d3=Pp(A×B)×Psp(A×B)

(Pp(A×B))2+(Psp(A×B))2

The values of d3 range from 0 to 0.707, estimating to whatextent similarities higher than expected at random (+) pre-dominate within zone A×B.

The parameter DW(A×A) measures to what extent thesimilarities that are higher than expected (+) tend to be inzones A×A but not in A×B (see McCoy et al. 1986), whereDW(A×A)=d1(A×A)−d2(A×A)−d3.

Similarly, DW(B×B)=d1(B×B)−d2(B×B)−d3, whered1(B×B) and d2(B×B) are calculated as d1(A×A) andd2(A×A), but computing the pluses and minuses in zoneB×B. The average of DW(A×A) and DW(B×B), named

DW, measures to what extent similarities that are higher thanexpected (+) tend to be in either zones A×A o r B×B butnot in A×B.

We define d4 in the same way as d3, but compute theminuses in A×B. We then compute the parameter DS=d4−d3−d2(A×A)−d2(B×B), which gives a measure o f whether the similarities that are lower than expected (−) tendto be located in A×B, but not in A×A or B×B.

The statistical significance of a node was assessed using aG-test of independence (Sokal and Rohlf 1981, McCoy et al.1986) of the distribution of the signs ‘‘+’’, ‘‘−’’ and ‘‘0’’ inthe three zones of the submatrix, and so we obtained theparameters GW, for weak boundaries, and GS, for strongboundaries. If similarities higher than expected (+) tendsignificantly to be in zones A×A or B×B, but not in A×B,that is, if DW\0 and GW is statistically significant, thenthere is at least a weak biotic boundary between both groupsof OGUs. In this case, if DW(A×A)\0 then the group of OGUs A constitutes a biotic region, and the same applies forDW(B×B) and the group of OGUs B, because then a groupof OGUs with similar biota shares a number of species com-patible with random expectation with another group of OGUsthat also has a similar biota. If similarities significantly lower

than expected (−) tend to be located in A×B, but not inA×A or B×B, that is, if DS\0 and GS is significant, thena strong biotic boundary exists between the groups of OGUs.In this case a group of OGUs shares fewer species thanexpected at random with another group of OGUs. The areasdelimited by strong boundaries are biotic supraregions. Asupraregion can consist of several biotic regions separated byweak boundaries.

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biotics regionalizations methods

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