Local Frequency Dependence and Global Coexistence

Molofsky, Jane; Durrett, Richard; Dushoff, Jonathan; Griffeath, David; Levin, Simon A.

doi:10.1006/tpbi.1998.1404

Cited by 79 publications

(83 citation statements)

References 24 publications

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“…Indeed, the interactions between egoistic and altruistic individuals are similar to the frequencydependent interactions between two discrete species, which lead to similar spatial patterns (Molofsky et al 1999). More generally, the patterns found here and in earlier studies (Molofsky et al 1999), which describe interactions that are governed by random processes, re£ect the spatial patterns that can be found in deterministic systems of interacting populations (Hassell et al 1994;Molofsky 1994;Okubo 1980). Overall, the model presented here, together with previous models of the spread of cooperation in spatially structured populations (Killingback et al 1999;Nowak & May 1992;Van Baalen & Rand 1998), provides a basis for the understanding of cooperative and altruistic behaviour.…”

Section: Discussionsupporting

confidence: 75%

The spatial spread of altruism versus the evolutionary response of egoists

Koella

2000

Proc. R. Soc. Lond. B

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Several recent models have shown that altruism can spread in viscous populations, i.e. in spatially structured populations within which individuals interact only with their immediate neighbours and disperse only over short distances. I ¢rst con¢rm this result with an individual-based model of a viscous population, where an individual can vary its level of investment into a behaviour that is bene¢cial to its neighbours but costly to itself. Two distinct classes of individuals emerge: egoists with no or very little investment into altruism, and altruists with a high level of investment; intermediate levels of altruism are not maintained. I then extend the model to investigate the consequences of letting interaction and dispersal distances evolve along with altruism. Altruists maintain short distances, while the egoists respond to the spread of altruism by increasing their interaction and dispersal distances. This allows the egoistic individuals to be maintained in the population at a high frequency. Furthermore, the coevolution of investment into altruism and interaction distance can lead to a stable spatial pattern, where stripes of altruists (with local interactions) alternate with stripes of egoists (with far-reaching interactions). Perhaps most importantly, this approach shows that the ease with which altruism spreads in viscous populations is maintained despite countermeasures evolved by egoists.

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Section: Discussionsupporting

confidence: 75%

The spatial spread of altruism versus the evolutionary response of egoists

Koella

2000

Proc. R. Soc. Lond. B

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“…It is established that, in well mixed systems, negative density-dependence significantly favors species coexistence [89]. Versions of the voter model implementing a negative densitydependence have been studied in the literature [90,91]. In these models, the reproduction probability of an individual depends on the number of conspecific individuals in a given local neighborhood.…”

Section: F Models With Density Dependencementioning

confidence: 99%

Stochastic Spatial Models in Ecology: A Statistical Physics Approach

et al. 2017

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Ecosystems display a complex spatial organization. Ecologists have long tried to characterize them by looking at how different measures of biodiversity change across spatial scales. Ecological neutral theory has provided simple predictions accounting for general empirical patterns in communities of competing species. However, while neutral theory in well-mixed ecosystems is mathematically well understood, spatial models still present several open problems, limiting the quantitative understanding of spatial biodiversity. In this review, we discuss the state of the art in spatial neutral theory. We emphasize the connection between spatial ecological models and the physics of non-equilibrium phase transitions and how concepts developed in statistical physics translate in population dynamics, and vice versa. We focus on non-trivial scaling laws arising at the critical dimension D = 2 of spatial neutral models, and their relevance for biological populations inhabiting two-dimensional environments. We conclude by discussing models incorporating non-neutral effects in the form of spatial and temporal disorder, and analyze how their predictions deviate from those of purely neutral theories.

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“…This influence was demonstrated mathematically by Armstrong (1989) for a nonspatial model with global dispersal. Molofsky et al (1999) explored the effects of both negative (as here) and positive density dependence on the coexistence of two species in a spatially-explicit, individual-based model with nearestneighbor dispersal.…”

Section: Specific Modelsmentioning

confidence: 99%

“…Whether these patterns are generic and potentially shared by other models or whether communities are actually neutral and nonequilibrium has been much debated (Connor and Simberloff 1979;Terborgh et al 1996;Hubbell 1997;Ashton 1998). Yet, little theoretical work has been done to establish whether the presence, much less the strength, of equilibrium mechanisms such as niche differences or Janzen-Connell effects will change these patterns qualitatively (however, see Molofsky et al 1999). Here, we provide the first broad comparison incorporating niche differences and other equilibrium, diversity-maintaining mechanisms using a framework of community models of sessile organisms competing for space.…”

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confidence: 99%

Comparing Classical Community Models: Theoretical Consequences for Patterns of Diversity

Chave

Muller‐Landau

Levin

2002

The American Naturalist

501

344

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Mechanisms proposed to explain the maintenance of species diversity within ecological communities of sessile organisms include niche differentiation mediated by competitive trade-offs, frequency dependence resulting from species-specific pests, recruitment limitation due to local dispersal, and a speciationextinction dynamic equilibrium mediated by stochasticity (drift). While each of these processes, and more, have been shown to act in particular communities, much remains to be learned about their relative importance in shaping community-level patterns. We used a spatially-explicit, individual-based model to assess the effects of each of these processes on species richness, relative abundance, and spatial patterns such as the species-area curve. Our model communities had an order-of-magnitude more individuals than any previous such study, and we also developed a finite-size scaling analysis to infer the large-scale properties of these systems in order to establish the generality of our conclusions across system sizes. As expected, each mechanism can promote diversity. We found some qualitative differences in community patterns across communities in which different combinations of these mechanisms operate. Species-area curves follow a power law with short-range dispersal and a logarithmic law with global dispersal. Relativeabundance distributions are more even for systems with competitive differences and trade-offs than for those in which all species are competitively equivalent, and they are most even when frequency dependence (even if weak) is present. Overall, however, communities in which different processes operated showed surprisingly similar patterns, which suggests that the form of community-level patterns cannot in general be used to distinguish among mechanisms maintaining diversity there. Nevertheless, parameterization of models such as these from field data on the * Corresponding author. Present address: Laboratoire d'Ecologie Terrestre, Centre National de la Recherche Scientifique, UMR 5552, 13 avenue du Colonel Roche, F-31029 Toulouse cedex 4, France; e-mail: chave@cict.fr. † E-mail: helene@eno.princeton.edu. ‡ E-mail: slevin@eno.princeton.edu. strengths of the different mechanisms could yield insight into their relative roles in diversity maintenance in any given community.

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Local Frequency Dependence and Global Coexistence

Cited by 79 publications

References 24 publications

The spatial spread of altruism versus the evolutionary response of egoists

The spatial spread of altruism versus the evolutionary response of egoists

Stochastic Spatial Models in Ecology: A Statistical Physics Approach

Comparing Classical Community Models: Theoretical Consequences for Patterns of Diversity

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