Oligomorphic dynamics for analyzing the quantitative genetics of adaptive speciation

Sasaki, Akira; Dieckmann, Ulf

doi:10.1007/s00285-010-0380-6

Cited by 57 publications

(170 citation statements)

References 124 publications

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“…The result of our model should be easily extended to resource-competition models, which have been intensively studied in adaptive dynamics ( e.g. , Dieckmann and Doebeli 1999; Sasaki and Dieckmann 2011; Mirrahimi et al 2012). …”

Section: Discussionmentioning

confidence: 99%

Evolutionary Branching in a Finite Population: Deterministic Branching vs. Stochastic Branching

Wakano

Iwasa

2013

Genetics

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Adaptive dynamics formalism demonstrates that, in a constant environment, a continuous trait may first converge to a singular point followed by spontaneous transition from a unimodal trait distribution into a bimodal one, which is called “evolutionary branching.” Most previous analyses of evolutionary branching have been conducted in an infinitely large population. Here, we study the effect of stochasticity caused by the finiteness of the population size on evolutionary branching. By analyzing the dynamics of trait variance, we obtain the condition for evolutionary branching as the one under which trait variance explodes. Genetic drift reduces the trait variance and causes stochastic fluctuation. In a very small population, evolutionary branching does not occur. In larger populations, evolutionary branching may occur, but it occurs in two different manners: in deterministic branching, branching occurs quickly when the population reaches the singular point, while in stochastic branching, the population stays at singularity for a period before branching out. The conditions for these cases and the mean branching-out times are calculated in terms of population size, mutational effects, and selection intensity and are confirmed by direct computer simulations of the individual-based model.

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Section: Discussionmentioning

confidence: 99%

Evolutionary Branching in a Finite Population: Deterministic Branching vs. Stochastic Branching

Wakano

Iwasa

2013

Genetics

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“…Such selforganized platykurtosis could thus contribute to the clustering tendency of competition kernels (Sasaki and Dieckmann, 2011). Other causes of withinpopulation trait variation will also influence the nature of the population's total competitive effect in a similar way.…”

Section: Within-population Trait Distributionsmentioning

confidence: 99%

Limiting similarity, species packing, and the shape of competition kernels

Leimar

Sasaki

Doebeli

et al. 2013

Journal of Theoretical Biology

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A traditional question in community ecology is whether species' traits are distributed as more-or-less regularly spaced clusters. Interspecific competition has been suggested to play a role in such structuring of communities. The seminal theoretical work on limiting similarity and species packing, presented four decades ago by Robert MacArthur, Richard Levins and Robert May, has recently been extended. There is now a deeper understanding of how competitive interactions influence community structure, for instance, how the shape of competition kernels can determine the clustering of species' traits. Competition is typically weaker for greater phenotypic difference, and the shape of the dependence defines a competition kernel. The clustering tendencies of kernels interact with other effects, such as variation in resource availability along a niche axis, but the kernel shape can have a decisive influence on community structure. Here we review and further extend the recent developments and evaluate their importance.

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“…There is, however, another approach to study the branching condition. Instead of considering a mutant-resident system, we can study the dynamics of a continuous trait distribution and identify evolutionary branching as the increase of the variance of the distribution (Sasaki and Dieckmann, 2011;Wakano and Iwasa, 2012). In a case of a well-mixed population, the branching condition derived by calculating invasion fitness and that by calculating variance dynamics have been shown to be identical when the trait distribution is approximated by the Gaussian distribution.…”

Section: Introductionmentioning

confidence: 99%

The effect of fecundity derivatives on the condition of evolutionary branching in spatial models

Parvinen

Ohtsuki

Wakano

2017

Journal of Theoretical Biology

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By investigating metapopulation fitness, we present analytical expressions for the selection gradient and conditions for convergence stability and evolutionary stability in Wright's island model in terms of fecundity function. Coefficients of each derivative of fecundity function appearing in these conditions have fixed signs. This illustrates which kind of interaction promotes or inhibits evolutionary branching in spatial models. We observe that Taylor's cancellation result holds for any fecundity function: Not only singular strategies but also their convergence stability is identical to that in the corresponding well-mixed model. We show that evolutionary branching never occurs 1 when the dispersal rate is close to zero. Furthermore, for a wide class of fecundity functions (including those determined by any pairwise game), evolutionary branching is impossible for any dispersal rate if branching does not occur in the corresponding well-mixed model. Spatial structure thus often inhibits evolutionary branching, although we can construct a fecundity function for which evolutionary branching only occurs for intermediate dispersal rates.

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Oligomorphic dynamics for analyzing the quantitative genetics of adaptive speciation

Cited by 57 publications

References 124 publications

Evolutionary Branching in a Finite Population: Deterministic Branching vs. Stochastic Branching

Evolutionary Branching in a Finite Population: Deterministic Branching vs. Stochastic Branching

Limiting similarity, species packing, and the shape of competition kernels

The effect of fecundity derivatives on the condition of evolutionary branching in spatial models

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