In This Article Stochastic Processes

  • Introduction
  • General Overview
  • Key to Understanding Stochastic Processes
  • Historical Contingency and Stochastic Processes
  • Stochastic Processes in Evolutionary Ecology
  • Stochastic Processes in Eco-evolutionary Dynamics

Ecology Stochastic Processes
by
Kohmei Kadowaki
  • LAST MODIFIED: 28 August 2019
  • DOI: 10.1093/obo/9780199830060-0224

Introduction

Chance events (such as lightning strikes or floods) occur commonly in nature. In ecology, unpredictable events that can affect population and community dynamics are called stochastic processes. Although ecologists recognize that stochastic processes occur, their importance in shaping populations and communities has been controversial. Determining when and how stochastic processes are important ecologically is critical for predicting extinction events or responses to climate change and explaining tropical biodiversity. Many population dynamics appears to be stochastic, particularly when the environment fluctuates or the population is small. For example, environmental variation that can reduce population size can increase the likelihood of stochastic extinction, because a small population is prone to go extinct due to random fluctuation in population size. Community dynamics can also be influenced by stochastic processes such as chance colonization, random order of immigration/emigration, and random fluctuations of population size. For example, community succession depends on which species arrive first, when early-arriving species outcompete later-arriving species. Modern ecologists generally agree that dynamics of most populations and communities have both deterministic (predictable) and stochastic (unpredictable) components that operate simultaneously. I thank Stacey Halpern for comments.

General Overview

Early studies such as Gleason 1917 and Clements 1916 differed in terms of which processes were thought to operate: Clements suggested deterministic processes (such as competition) and structured succession, whereas Gleason argued that stochastic processes (chance dispersal events, followed by individualistic life history traits of the species) drove plant community assembly. The importance of stochastic processes was put forward by Palmgren 1926, in which Palmgren found that the floristic composition of vegetation in various similar places present differences due to chance, and even if natural conditions are equally suitable, the particular species are found very unevenly dispersed over various places of the same area. Diamond 1975 emphasized, in an extensive survey of avifauna, that what Diamond called “checkerboard distribution” (i.e., mutually exclusive distributions of bird species pairs) is considered a result of stochastic colonization of islands. This study ignited intense debates about how to test the role of deterministic competitive exclusion versus stochastic processes in driving community patterns in the 1970s and 1980s (Connor and Simberloff 1979, Lewin 1983). Connor and Simberloff 1979 argued that to know if competition is important, ecologists have to compare distribution patterns to what would have happened if competition was not important. An outcome of the debate is that the importance of stochastic processes came to be gradually accepted among ecologists, with more sophisticated modeling framework to test for stochastic processes. In parallel, the importance of stochastic processes gained increased recognition with the development and sophistication of the influential idea of metapopulation ecology (and metacommunity ecology as its extension) (Levins 1969, Hanski 1998). Metapopulation ecology emphasizes that small local populations stochastically go extinct and (re)establish. Organismal dispersal among local populations can counteract stochastic extinctions, and there are many such examples (Hanski 1998). A number of stochastic modeling, metapopulation, and metacommunity studies are summarized in edited collections, such as Lande, et al. 2003. The schisms between deterministic and stochastic processes has continued to fuel even recent debates. For example, a rather extreme view of the importance of stochastic processes was formulated by the neutral theory presented in Hubbell 2001, which argued that tropical plant communities are not shaped by competition but by stochastic, random events related to dispersal, establishment, mortality, and speciation. In Hubbell’s model, although competition acts very strongly, species are identical with respect to competitive ability, and hence stochastic processes dominate community patterns. Although the neutral theory itself has been rejected repeatedly, the stochastic modeling approach used by Hubbell has gradually become a common tool with which to explain community patterns. A modern understanding of deterministic versus stochastic processes—that is, both processes jointly shape population and community dynamics, and the relative roles of the two can vary depending on environmental context—appears in Segre, et al. 2014 and Gilbert and Levine 2017.

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    DOI: 10.5962/bhl.title.56234E-mail Citation »

    This author argued that the formation of vegetation is shaped by deterministic processes, and that vegetation behaves like an organism—it grows, matures, and dies as a unit. His view of an ecological community has exerted a strong influence on later debates.

  • Connor, E. F, and D. Simberloff. 1979. The assembly of species communities: Chance or competition? Ecology 60:1132–1140.

    DOI: 10.2307/1936961E-mail Citation »

    In response to Diamond 1975, this paper sparked a controversy about the role of deterministic and stochastic community assembly, and also called for critical analysis of community assembly.

  • Diamond, J. M. 1975. Assembly of species communities. In Ecology and evolution of communities. Edited by M. L. Cody, and J. M. Diamond, 342–444. Cambridge, MA: Belknap Press of Harvard Univ. Press.

    E-mail Citation »

    Diamond developed the concept of assembly rules to discuss causes of mutually exclusive distribution patterns of birds on islands. This study ignited one of the most controversial debates in ecology, now known as the null model controversy.

  • Gilbert, B., and J. M. Levine. 2017. Ecological drift and the distribution of species diversity. Proceedings of the Royal Society B: Biological Sciences 284:2017.0507.

    DOI: 10.1098/rspb.2017.0507E-mail Citation »

    This experimental study shows that the importance of ecological drift (i.e., each species shows random fluctuations in population size) appears greater than previously recognized in communities where deterministic processes may play some role. The authors argue that ecological drift varies with community size and the type and strength of density dependence.

  • Gleason, H. A. 1917. The structure and development of the plant association. Bulletin of the Torrey Botanical Club 44:463–481.

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    This classic paper addressed the forces structuring plant communities, focusing on stochastic processes such as chance dispersal, as well as species’ life history traits. It initiated discussions about the role that stochastic processes play in structuring the diversity and composition of species in ecological communities.

  • Hanski, I. 1998. Metapopulation dynamics. Nature 396:41–49.

    DOI: 10.1038/23876E-mail Citation »

    Hanski reviews principles in metapopulation ecology and uses stochastic processes as a modeling tool to predict the movement patterns of individuals, the dynamics of species, and the distributional patterns in multispecies communities in real fragmented landscapes.

  • Hubbell, S. 2001. The unified neutral theory of biodiversity and biogeography. Princeton, NJ: Princeton Univ. Press.

    E-mail Citation »

    This book develops stochastic dynamics of ecological community assembly, and argues that much of large-scale biodiversity patterns in nature may be driven by stochastic forces such as ecological drift (where each species fluctuates randomly) and species equivalence (all species in an ecological community have equal fitness).

  • Lande, R., S. Engen, and B. E. Saether. 2003. Stochastic population dynamics in ecology and conservation. Oxford: Oxford Univ. Press.

    DOI: 10.1093/acprof:oso/9780198525257.001.0001E-mail Citation »

    This book is an edited collection of theoretical and empirical studies on stochastic population dynamics, and it provides a useful overview of the key topics presented in this article.

  • Levins, R. 1969. Some demographic and genetic consequences of environmental heterogeneity for biological control. Bulletin of the Entomological Society of America 15:237–240.

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    This study developed a simple model of metapopulation distributed over many patches of suitable habitat connected by dispersal for the purpose of illustrating the impacts of habitat heterogeneity on effectiveness of pest control through demographic and genetic mechanisms.

  • Lewin, R. 1983. Santa Rosalia was a goat. Science 221:636–639.

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    The article reported on a long-standing debate between Jared Diamond and Daniel Simberloff regarding the relative importance of stochastic and deterministic community assembly.

  • Palmgren, A. 1926. Chance as an element in plant geography. In Proceedings of the International Congress of Plant Sciences, Ithaca, New York. Vol. 1. Edited by B. M. Duggar, 591–602. Menasha, WI: George Banta.

    E-mail Citation »

    This paper presents a carefully organized, narrative discussion of the concept of chance in plant geography. Citing a comprehensive survey of the flora in the Ålands, Finland, the author emphasized the influence of chance on the development of plant communities.

  • Segre, H., R. Levine, N. De Malach, Z. Henkin, M. Henkin, and R. Kadmon. 2014. Competitive exclusion, beta diversity, and deterministic vs. stochastic drivers of community assembly. Ecology Letters 17:1400–1408.

    DOI: 10.1111/ele.12343E-mail Citation »

    This article illustrates an updated view of the relative role of stochastic and deterministic community assembly. The authors argue that interspecific competition may influence the number of species and spatial turnover in species composition (beta diversity) in the same direction or in opposite directions, depending on whether competitive exclusions are deterministic or stochastic.

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