Elsevier

Ecological Informatics

Volume 3, Issue 3, 1 July 2008, Pages 259-271
Ecological Informatics

A coalescence approach to spatial neutral ecology

https://doi.org/10.1016/j.ecoinf.2008.05.001Get rights and content

Abstract

Neutral models in ecology have attracted much attention in recent literature. They can provide considerable insight into the roles of non-species-specific factors (e.g. stochasticity, dispersal, speciation) on community dynamics but often require intensive simulations, particularly in spatial settings. Here, we clearly explain existing techniques for modelling spatially explicit neutral processes in ecology using coalescence. Furthermore, we present several novel extensions to these methods including procedures for dealing with system boundaries which enable improved investigation of the effects of dispersal. We also present a semi-analytical algorithm that calculates the expected species richness in a sample, for any speciation rate. By eliminating the effect of stochasticity in the speciation process, we reduce the variance in estimates of species richness. Our benchmarks show that the combination of existing coalescence theory and our extensions produces higher quality results in vastly shorter time scales than previously possible: years of simulation time are reduced to minutes. As an example application, we find parameters for a spatially explicit neutral model to approximate the species richness of a tropical forest dataset.

Introduction

Advances in the analysis of neutral evolutionary processes have taken advantage of fast algorithms based on coalescence techniques (Felsenstein, 2004, Kingman, 1982, Wakeley, 2006, Notohara, 1990). These are primarily used to model the evolution of DNA sequences but can be applied more generally to asexually reproducing individuals, words and other patterns resulting from a process of lineage branching (Blythe and McKane, 2007). Hubbell's “Unified Neutral Theory” (2001) was formulated as an ecological analogue to these evolutionary processes, and stimulated much debate (Alonso et al., 2006, Gewin, 2006, Leigh, 2007, Holyoak and Loreau, 2006, Hubbell, 2005) by making the assumption that every individual behaves in the same way regardless of its species. Recent studies of neutral ecological processes have exploited coalescence techniques, both analytically (Etienne, 2007, Etienne and Olff, 2004, Etienne, 2005) and computationally (Chave and Leigh, 2002, Chave et al., 2002), but no detailed explanation has yet been provided of the implementation and benefits for ecological simulations. We aim to both enable, promote and further develop the use of these methods in ecology.

In this paper, we explain the precise details of the coalescence method of simulation in ecology and provide several novel and powerful extensions. We use quantitative benchmarks to show that unmanageably large simulations for traditional methods are rendered straightforward with our approach. The exact methods we describe have already led to advances in the understanding of species–area curves from neutral models (Rosindell and Cornell, 2007). We illustrate our algorithms by finding the manifold in parameter space that gives rise to an empirically observed species richness, an analysis which would be impossible using traditional methods.

Section snippets

Neutral models in ecology

Neutral models in ecology make the controversial assumption of ecological equivalence among individuals regardless of their species identity. Despite the evident falsity of this assumption, they have done remarkably well at reproducing empirical data. Neutral models can, therefore, provide insight into the roles of non-species-specific (or trait-neutral) factors such as stochasticity, dispersal or speciation on community dynamics. It is clear that non-neutral processes exist in ecosystems, but

Basic concepts of coalescence with worked example

For simplicity we illustrate the process with a miniature yet spatially explicit example in one dimension. Imagine a population consisting of eight individuals on a line (a landscape area of eight), we wish to simulate the equilibrium species abundance distribution of three adjacent individuals (a survey area of three).

Fig. 1a shows one possible outcome of a forward simulation of this starting at generation t  10. The eight individuals in the population are each present in cells labelled A–H,

Simulation efficiency

The coalescence method displays greatly improved efficiency over the forward algorithm. In a forward simulation, every time step is associated with a birth–death event, represented in Fig. 1a by a pair of symbols, a bar and a circle. In any reasonable implementation, the majority of the computational burden is associated with these events. Using the coalescence approach means that many of these birth–death events need not be considered for a number of reasons.

Firstly, the coalescence method

Infinite landscape areas

Finite landscape areas — either with periodic, reflective, or absorbing boundaries — can be simulated using either standard coalescence methods or forwards methods. For many ecological applications, however, it is preferable to eschew boundary conditions altogether by extending the landscape area to infinity (Hubbell, 2001, Rosindell and Cornell, 2007). Infinite landscape areas can only be simulated using the novel method that we now describe and this yields qualitatively different results from

Speciation spectra

The speciation rate (ν) is an important parameter in neutral models (Hubbell, 2001). The coalescence approach opens the door to a novel, elegant method for investigating different values of ν in a semi-analytical manner. This makes it possible to simulate an entire “spectrum” of speciation rates with negligible extra effort over that required for a single value of ν. We treat speciation in a similar way to that in which mutation is treated in genetic coalescence (Wakeley, 2006). We produce a

Benchmarks

Two independent implementations were written, one using our coalescence methods and the other using traditional forward methods. We aim to quantify the benefits of our methods by making comparisons for Hubbell's patch model (2001). The forward method used the same parameters as Hubbell (2001): a grid of 402 × 402 cells grouped into 201 × 201 patches each of size 2 × 2 simulated for 5000 turnovers (generations) of the community, with dispersal parameter of 0.5. We also included smaller simulations of

Example application

As an illustration of the power and efficiency of our method, we wish to obtain the manifold of model parameter values that give rise to the empirically observed species richness for the Barro Colorado Island (BCI) forest census plot data (Condit, 1998, Condit et al., Hubbell et al., 1999). Our spatially explicit neutral model features normally distributed dispersal kernels (of different widths) and a rectangular survey area of the same shape and average density as the true BCI data, set in an

Discussion

We have presented a set of novel algorithms, adapted from population genetics techniques, that provide considerable benefits for simulating ecological neutral models. Considering the power of this coalescence method, there have been surprisingly few applications of these techniques in the ecology literature to date, but where they have been used, considerable insight has been gained (Chave and Leigh, 2002, Chave et al., 2002, Etienne and Olff, 2004, Etienne, 2005). As a computing method, few of

Acknowledgements

We thank Stephen Cornell and Jerome Chave for their feedback and Luis Borda de Agua for his advice. James Rosindell was funded by a University of Leeds Research Scholarship under supervision of Stephen Cornell and Bill Kunin. Rampal S. Etienne thanks the support of the Netherlands Organisation of Scientific Research (NWO). The Forest Dynamics Plot of Barro Colorado Island has been made possible through the generous support of the U.S. National Science Foundation, The John D. and Catherine T.

References (31)

  • AlonsoD. et al.

    The merits of neutral theory

    Trends Ecol. Evol.

    (2006)
  • EtienneR.S. et al.

    The zero-sum assumption in neutral biodiversity theory

    J. Theor. Biol.

    (2007)
  • UlrichW. et al.

    Are ground beetles neutral?

    Basic Appl. Ecol.

    (2007)
  • AlonsoD. et al.

    The implicit assumption of symmetry and the species abundance distribution

    Ecol. Lett.

    (2008)
  • R.A. Blythe et al.

    Stochastic models of evolution in genetics, ecology and linguistics

    J. Stat. Mech.-Theory Exp.

    (2007)
  • ChaveJ.

    Neutral theory and community ecology

    Ecol. Lett.

    (2004)
  • ChaveJ. et al.

    A spatially explicit neutral model of beta-diversity in tropical forests

    Theor. Popul. Biol.

    (2002)
  • ChaveJ. et al.

    Comparing classical community models: Theoretical consequences for patterns of diversity

    Am. Nat.

    (2002)
  • Condit, R., 1998. Tropical Forest Census Plots. Springer–Verlag and R. G. Landes company, Berlin,...
  • Condit, R., Hubbell, S.P., Foster, R.B., 2005. Barro colorado forest census plot data....
  • EtienneR.S.

    A new sampling formula for neutral biodiversity

    Ecol. Lett.

    (2005)
  • EtienneR.S.

    A neutral sampling formula for multiple samples and an ’exact’ test of neutrality

    Ecol. Lett.

    (2007)
  • R.S. Etienne et al.

    Neutral community theory: how stochasticity and dispersal-limitation can explain species coexistence

    J. Stat. Phys.

    (2007)
  • EtienneR.S. et al.

    A novel genealogical approach to neutral biodiversity theory

    Ecol. Lett.

    (2004)
  • EtienneR.S. et al.

    Modes of speciation and the neutral theory of biodiversity

    Oikos

    (2007)
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