a probabilistic test of the neutral model c. m. mutshinda 1, r.b. o’hara 1, i.p. woiwod 2 1...
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A Probabilistic Test of the Neutral Model
C. M. Mutshinda1, R.B. O’Hara1, I.P. Woiwod2
1University of Helsinki, and 2Rothamsted Research, UK.
Plan of the talk
IntroductionModelResultsConclusionSuggestions
INTRODUCTION•There is a long-standing interest in identifying the mechanisms underlying the dynamics of ecological communities
•The list of presumed mechanisms is still growing
•Existing theories can be subdivised in two categories: neutral and non-neutral models
•The debate between the two sides is still very much alive
•Neutral models assume Ecological Equivalence of species, i.e. same demographic properties (birth death immigration speciation rates) for all individuals irrespective of species.
Consequence: Species richness and relative species abundance distributions (SAD) are assumed to be generated entirely by drift between species
An ecological community is a group of trophically similar species that actually or potentially compete in a local area for the same or similar resources.
•Non-neutral models consider that species may differ in their demographic properties, their competitive abilities or their responses to environmental fluctuations
The most documented version of neutral models is the Unified Neutral Theory of Biodiversity and Biogeography (UNTBB) developed by Hubbell in 2001.
From now on, neutral theory refers to Hubbell's model
• The UNTBB considers communities on two scales of communities:
Local Community
Governed by birth, death, immigration (from a
metacommunity)
Dynamics taking place an ecological time scale.
Metacommunity Include an additional mechanism of speciation taking
place on an evolutionary time scale.
•Main Assumptions of the UNTBB:
Ecological Equivalence
Zero-Sum (ZS) assumption : constant
community size (saturated communities)
Consequences of the assumptions
A typical SAD, the zero – sum multinomial
(ZSM).
Relative Species Abundance entirely
genarated by random Drift
•Criticisms of the UNTBB: have concerned both assumptions
Ecological Equivalence (e.g. Mauer &Mc Gill
2004; Poulin 2004; Chase2005) Zero-Sum assumption (e.g. Alder 2003; McGill 2003; Williamson & Gaston 2005 )
The critics of the ZSM have generally assumed equilibrium and have proceeded by comparing the fit of the ZSM to a theoretical distribution mainly the Lognormal
how realistic the parameter estimates are
if the changes in the abundance of the species can be explained by the model with a realistic community size
A sensible way of examining the neutral model would would consist of fitting the model to the data and assessing:
However, over the last 30 years, ecologists have been moving away from equilibrium ideas (e.g. Wallington et al. 2005), but Hubbell leaps straight back in.
A dynamical model such as the UNTBB can be examined without assuming equilibrium.
We Develop and fit a discrete-time neutral model identical to Hubbell's in all other aspects except that
We relax the assumption of constant community size
3 macro-moth (Lepidoptera) time series from the
Rothamsted Insect Survey light-traps network in
the UK: Geescroft I & II (from the Rothamsted farm
in Hertfordshire) and Tregaron (from a Nature
reserve in mid-Wales)
Data
Geescroft I (352, 40); Geescroft II (319, 26); Tregaron
(371, 28).
Number of species and years:
THE MODEL
Immigration rate at time tRelative abundance of sp. i at t-1
•Process Model
, 1 , 1 ,1 * *i t t t i t t i tJ m C m P
)(~1, ii PoisN
)(~ ,, titi PoisN
:community size at time t,t i tiJ N
Nber of ind. of species i at time t
,i t iP P
, , 1 ,1 * *i t t i t t i tm N m JP
, 1 *i t t iJP J P
(time-scale separation)
•Sampling Model
, ,~ *i t i t ty Pois N q
Sampling rate (observed proportion) at time t
The same analyses were carried out on the geometrid
(Geometridae) species alone which are known to
respond in a similar way to light (Taylor and French
1974).
Nber of geometrid species in the 3 datasets: 135, 127
& 135 respectively.
Model Fitting
Bayesian approach
Noninformative priors
: (1,1)tm Beta , : (5,100)i tJP U : 0.1, 0.2tq
We used MCMC via OpenBUGS to fit the model
~ 0.01,0.01i
RESULTS1
97
0
19
80
19
90
20
00
2.0
2.5
3.0
3.5
4.0
Greescroft I A
Lo
g1
0(C
om
mu
nit
y s
ize
)
19
70
19
80
19
90
20
00
2.0
2.5
3.0
3.5
4.0Observed
Expected
19
75
19
80
19
85
19
90
19
95
2.0
2.5
3.0
3.5
4.0
Greescroft II B
19
75
19
80
19
85
19
90
19
95
2.0
2.5
3.0
3.5
4.0
19
75
19
80
19
85
19
90
19
95
20
00
2.0
2.5
3.0
3.5
4.0
TregaronC
19
75
19
80
19
85
19
90
19
95
20
00
2.0
2.5
3.0
3.5
4.0
Fig. 1: Unrealistic Community sizes
1970 1980 1990 2000
05
10
15
20
Sa
mp
lin
g R
ate
Greescroft I
1975 1985 1995
05
10
15
20
Greescroft II
1980 1990 2000
05
10
15
20
Tregaron
Fig. 2: Unrealistic Sampling Rates
The horizontal dashed line is drawn at height 1!
CONCLUSION
The neutral model does not fit the data well as it
would need parameter values that are impossible
Thus, random drift alone cannot explain the
variation in species abundances
environmental stochasticityDensity-dependenceSpecies heterogeneity
Effects of species interactions
Possible reasons for the excess of temporal variation:
A number of important mechanisms are simply ignored. These include:
SUGGESTIONS
The model can be extended to include the missing components, this will result in a complex model
Ecological hypotheses such as neutral community structure can be examined from the results
Complex models can be developed and fitted under the hierarchical Bayesian framework
We examined if parameters of such a model may be identifiable, we developed a dynamical model including environmental stochasticity and interaction coefficients
The model was fitted to a dataset comprising 10 among the most abundant species at Geescroft I
All the parameters turned out to be identifiable
Nber Scientific name Common name
1 Selenia dentaria Early Thorn
2 Selenia tetralunaria Purple Thorn
3 Apeira syringaria Lilac beauty
4 Odontopera bidentata Scalloped Hazel
5 Colotois pennaria Feathered Thorn
6 Crocallis elinguaria Scalloped oak
7 Opistograptis luteolata Brimstone moth
8 Ourapteryx sambucaria Swallow-tail
9 Opocheima pilosaria Pale brinbley beauty
10 Lycia hispidaria Brindley beauty
Scientific and common names of the 10 species
Process model
, ,1, 1 , , ,exp 1
S
i j j tji t i t i t i t
i
NE N N r
K
: density-independent per capita growth rate of species i at time t,
:per capita effect of species j on the growth of species i,
:carrying capacity for species i,
: number of species in the community
,i tr
,i j
iK
S
1, ~ ,i t i ir N
, , ,~ *i t i t i ty Pois N q
1, ~ 0,i j N
Sampling model
Parameter model
, 1 ~i iN Pois
, , 1~ , 2i t i tN Pois t
~ (0,0.1)i N ~ (0.001, 0.001)i
, ~ (1,1)i tq Beta ~ (0.0001)iK Exp
~ 0.01,0.01i
Priors
Model fitting by MCMC via OpenBUGS
,
Results
•The posterior estimates of the interaction coefficients
reveal a significant negative effect of the Opistograptis
luteolata (species #7) on the reminder as illustrated in
the following table
• Significant differences in species-specific
environmental variances
The results suggest a non-neutral community structure
Species 1 2 3 4 5 6 7 8 9 10
1 -0.32 0.12 -0.02 0.13 0.13 0.08 0.69 0.05 0.08 0.00
2 0.31 -1.07 -0.05 0.01 0.00 -0.11 0.58 -0.02 -0.11 0.07
3 0.27 0.05 0.00 0.09 0.11 0.13 0.52 0.05 0.05 0.01
4 0.13 0.01 0.00 -0.10 0.03 0.08 0.32 0.04 0.13 0.01
5 0.15 -0.02 0.00 0.08 0.19 0.03 0.53 0.03 0.13 -0.01
6 0.01 -0.09 0.01 0.00 -0.04 0.21 0.51 0.10 0.14 -0.03
7 0.3 0.26 -0.02 0.21 0.02 -0.13 0.94 -0.01 0.12 -0.05
8 0.29 0.05 0.02 0.07 0.10 0.10 0.65 0.03 0.10 0.01
9 0.20 0.04 0.02 0.06 0.07 0.07 0.06 0.04 0.04 0.00
10 0.2 0.06 0.02 0.08 0.09 0.08 0.58 0.05 0.06 -0.02
posterior means of the interaction coefficients
posterior means of the interaction coefficients
Remarks
•Real communities are typically much larger than 10
species. Hence, The dimensionality of the model
may be too large
•Some interaction coefficients are almost zero or
insignificant, it might be worth not estimating them
•Sensible ways of pulling the model's dimensionality
down to a tractable level are needed, and this is where
variable selection comes into play.
We are now working on Bayesian variable selection
methods such as Gibbs Variable Selection, Stochastic
Search Variable Selection or Reversible Jump MCMC
to extend the applicability of the model to large
community datasets.
Work in Progress
Alder, P. B. (2003) Neutral models fail to reproduce observed species-area and species-time relationships in Kansas grasslands Ecology 85(5), 1265-1272. Chase, J. M. (2005) Towards a really unified theory for metacommunities, Functional Ecology 19, 182-186.Gelman, A., Carlin, J.B, Hal, Stern, H.S. & Rubin, D.B. 2003. Bayesian Data Analysis. Second Edition, Chapman& Hall.Hubbell, S.P. 2001. The unified Neutral Theory of Biodiversity and Biogeography, Princeton University Press.Mauer, B.A. & McGill, B.J. 2004. Neutral and non-neutral macroecology. Basic & Applied Ecology 5, 413 – 422McGill, B.J. 2003. A test of the unified neutral theory. Nature 422, 881-885.Poulin, R. 2004. Parasites and the neutral theory of biodiversity. Ecography 27,1: 119-123.Wallington, T. J., Hobbs, R. & Moore, S.A. (2005) Implications of Current Ecological Thinking for Biodiversity Conservation: a Review of Salient Issues. Ecology and Society 10(1), 15.Williamson, M & Gaston, K.J. 2005. The lognormal is not an appropriate null hypothesis for the species- abundance distribution. Journal of Animal Ecology.Woiwod, I. P. & Harrington, R. 1994. Flying in the face of change: The Rothamsted Insect Survey. In Long- term Experiments in Agricultural and Ecological Sciences (ed. R. A. Leigh & A. E. Johnston), pp. 321-342. Wallingford: CAB International