A Probabilistic Test of the Neutral Model

1. A Probabilistic Test of the Neutral Model C. M. Mutshinda1, R.B. O’Hara1, I.P. Woiwod2 1University of Helsinki, and 2Rothamsted Research, UK.

2. Plan of the talk • Introduction • Model • Results • Conclusion • Suggestions

3. 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: neutraland non-neutralmodels • The debate between the two sides is still very much alive

4. An ecological community is a group of trophically similar species that actually or potentially compete in a local areafor the same or similar resources. • Neutral models assume Ecological Equivalence of species, i.e. same demographic properties (birth death immigration speciation rates) for all individualsirrespective of species. • Consequence: Species richness and relative species abundance distributions (SAD) are assumed to be generated entirely by drift between species

5. Non-neutral models consider that species may differ in their demographic properties, their competitive abilities or their responses to environmental fluctuations

6. 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

7. 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.

8. Main Assumptions of the UNTBB: • Ecological Equivalence • Zero-Sum (ZS) assumption : constant community size (saturated communities)

9. Consequences of the assumptions • Relative Species Abundance entirely genarated by random Drift • A typical SAD, the zero – summultinomial (ZSM).

10. 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

11. 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. A sensible way of examining the neutral model would would consist of fitting the model to the data and assessing: • 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

12. 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

13. Data • 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)

14. Number of species and years: Geescroft I (352, 40); Geescroft II (319, 26); Tregaron (371, 28).

15. THE MODEL • Process Model Nber of ind. of species i at time t Relative abundance of sp. i at t-1 Immigration rate at time t :community size at time t

16. (time-scale separation)

17. Sampling Model Sampling rate (observed proportion) at time t

18. 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.

19. Model Fitting • Bayesian approach • Noninformative priors • We used MCMC via OpenBUGS to fit the model

20. RESULTS Fig. 1: Unrealistic Community sizes

21. Fig. 2: Unrealistic Sampling Rates The horizontal dashed line is drawn at height 1!

22. 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

23. Possible reasons for theexcess of temporal variation: A number of important mechanisms are simply ignored. These include: • environmental stochasticity • Density-dependence • Species heterogeneity • Effectsof species interactions

24. SUGGESTIONS The model can be extended to include the missing components, this will result in a complex model Complex models can be developed and fitted under the hierarchical Bayesian framework Ecological hypotheses such as neutral community structure can be examined from the results

25. 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

26. Scientific and commonnames of the 10 species

27. Process model : 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

28. Sampling model Parameter model

29. Priors Model fitting by MCMC via OpenBUGS

30. Results • Significant differences in species-specific environmental variances • 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 , The results suggest a non-neutral community structure

31. posterior means of the interaction coefficients posterior means of the interaction coefficients

32. 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, andthis is where variable selection comes into play.

33. Work in Progress 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.

34. THANK YOU

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