Ecological stability, evolutionary stability and the ESS maximum principle

Vincent, Thomas L.; Văn, Mai Viết; Goh, B. S.

doi:10.1007/bf01237708

Cited by 48 publications

(59 citation statements)

References 19 publications

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“…This definition is a modification of the definition of Vincent et al [59] for a point process ecological equilibrium. As for the point-process case, a spatial ecological equilibriumz (x) may or may not be locally stable.…”

Section: Ecologically Stable Equilibriummentioning

confidence: 99%

“…In this section, we extend the point process G-function formalism by extending the point process work of Vincent and co-workers [59,56] to the case of a spatially homogeneous equilibrium. We define an ecological equilibrium and an evolutionary equilibrium within a reaction-diffusion model, derive a maximum principle, and derive sufficient conditions for a spatially homogeneous ESS to exist.…”

Section: Ess For a Spatially Homogeneous Equilibriummentioning

confidence: 99%

“…A mutant strategy is a rare alternative strategy different from that of the ESS. This definition guarantees the long-term survival of the evolutionarily stable strategies, even if those do not result in maximal fitness [59,56]. We note that here we follow the modern ESS terminology, but a surviving strategy that is uninvadible by rare mutant strategies was discussed as early as the '30s of the previous century [28,20].…”

Section: Introductionmentioning

confidence: 99%

“…This is achieved by proving a generalization of the maximum principle of Vincent et al [59,56]. In Section 3, we develop a spatial generalization to strategy dynamics and pursue the CS properties of spatially homogeneous steady state solutions, based on the spatial G−function generalization developed in Section 2.…”

Section: Introductionmentioning

confidence: 99%

“…[59], and references therein) developed a mathematical formalism for predicting the number and values of the pure strategies that comprise the ESS. This formalism is based on a fitness generating function (G−function) that can be used to analyze population and strategy dynamics.…”

Section: Introductionmentioning

confidence: 99%

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Evolutionary Games in Space

Kronik

Cohen

2009

Math. Model. Nat. Phenom.

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Abstract. The G-function formalism has been widely used in the context of evolutionary games for identifying evolutionarily stable strategies (ESS). This formalism was developed for and applied to point processes. Here, we examine the G-function formalism in the settings of spatial evolutionary games and strategy dynamics, based on reaction-diffusion models. We start by extending the point process maximum principle to reaction-diffusion models with homogeneous, locally stable surfaces. We then develop the strategy dynamics for such surfaces. When the surfaces are locally stable, but not homogenous, the standard definitions of ESS and the maximum principle fall apart. Yet, we show by examples that strategy dynamics leads to convergent stable inhomogeneous strategies that are possibly ESS, in the sense that for many scenarios which we simulated, invaders could not coexist with the exisiting strategies.

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Section: Ecologically Stable Equilibriummentioning

confidence: 99%

Section: Ess For a Spatially Homogeneous Equilibriummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Evolutionary Games in Space

Kronik

Cohen

2009

Math. Model. Nat. Phenom.

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Population and Evolutionary Dynamics of Consumer‐Resource Systems

Getz

1999

Advanced Ecological Theory

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IntroductionConsumer-resource systems can be regarded as any system in which a population of organisms exploits either an energy flux, a detritus or nutrient pool, or another population. This definition then includes plants growing in sunlight, parasites growing in or on hosts, predators exploiting prey, herbivores grazing or browsing on plants, and even humans harvesting trees, fish or game. For such a vast array of systems, no single best paradigm exists for modelling the dynamics of the populations under consideration.Here I will focus on two paradigms: a discrete-time paradigm that is suitable for modelling populations with nonoverlapping generations and a continuous-time paradigm that is suitable for modelling the flow of biomass from the resource to the consumer, and its conversion from resource mass (biomass, nutrients, or energy) into consumer mass. I will also consider the extension of the discrete-time paradigm to include overlapping generations (age structure) and the application of the models to resource management problems.The discrete-time models fall within the class of iterative maps (7.1)where, for the systems considered here, the elements of the vector x t = (x 1t , x 2t , . . ., x nt )¢ (¢denotes the transpose of a vector) typically represent the densities of individuals in n biological populations at time t = 0, 1, 2, 3, . . . or the densities of individuals in n classes (e.g., age or size) of one population at time t, or even some combination of several populations each with several classes of individuals. The continuous-time models fall within the class of vector differential equation systemswhere, for the systems considered here, the elements of the vector x(t) = (x 1 (t), x 2 (t), . . ., x n (t))¢ typically represent the biomass densities of n interacting biological populations at time d d x x t = ( ) y , x x t t t + = ( ) = 1 0 1 2 y , , , . . .

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Phenological evolution in annual plants under light competition, changes in the growth season and mass loss

Silva,

Hansson,

Johansson

2024

Ecology and Evolution

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Flowering time is an important phenological trait in plants and a critical determinant of the success of pollination and fruit or seed development, with immense significance for agriculture as it directly affects crop yield and overall food production. Shifts in the growth season, changes in the growth season duration and changes in the production rate are environmental processes (potentially linked to climate change) that can lead to changes in flowering time in the long‐term due to selection. In contrast, biomass loss (due to, for example, herbivory or diseases) can have profound consequences for plant mass production and food security. We model the effects of these environmental processes on the flowering time evolutionarily stable strategy (ESS) of annual plants and the potential consequences for reproductive output. Our model recapitulates previous theoretical results linked to climate change and light competition and makes novel predictions about the effects of biomass loss on the evolution of flowering time. Our analysis elucidates how both the magnitude and direction of the evolutionary response can depend on whether biomass loss occurs during the earlier vegetative phase or during the later reproductive phase and on whether or not plants are adapted to grow in dense, competitive environments. Specifically, light competition generates an asymetric effect of mass loss on flowering time even when loss is indiscriminate (equal rates), with vegetative mass loss having a stronger effect on flowering time (resulting in greater ESS change) and final reproductive output.

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Ecological stability, evolutionary stability and the ESS maximum principle

Cited by 48 publications

References 19 publications

Evolutionary Games in Space

Evolutionary Games in Space

Population and Evolutionary Dynamics of Consumer‐Resource Systems

Phenological evolution in annual plants under light competition, changes in the growth season and mass loss

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