Function-valued adaptive dynamics and optimal control theory

Parvinen, Kalle; Heino, Mikko; Dieckmann, Ulf

doi:10.1007/s00285-012-0549-2

Cited by 23 publications

(51 citation statements)

References 34 publications

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“…We would ideally not put any restrictions at all on the shape, and for some deterministic models that can be done using optimal control theory or the calculus of variations (Parvinen, Dieckmann & Heino ; Parvinen, Heino & Dieckmann ). For stochastic IPMs with density or frequency dependence, and many other models, we do not know of any analytical solution method, so we take a computational approach using methods from functional data analysis (Ramsay & Silverman ; Ramsay, Hooker & Graves ).…”

Section: Function‐valued Traitsmentioning

confidence: 99%

Evolving integral projection models: evolutionary demography meets eco‐evolutionary dynamics

Rees

Ellner

2016

Methods Ecol Evol

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1. Patterns of survival and reproduction determine fitness, and there is a rich body of theory linking demography with evolution. For example, selection analysis can be used to predict changes in trait values, and by approximating selection, equations describing trait dynamics derived and evolutionary endpoints predicted. Here, we provide an overview of how these methods can be used to understand evolutionary dynamics and selection in a structured population modelled by an integral projection model (IPM). 2. General expressions for selection are given, and we show how these can be approximated using eigenvalue sensitivities. Approximations for the dynamics of both the trait mean and variance are presented and compared to simulation results (IPMs and individual-based models) for monocarpic perennials. 3. We describe how selection can be decomposed into components related to survival and reproduction and into components resulting from changes in demography versus changes in population structure. We show that, in an empirically based IPM, effects of changes in population structure can be a major component of the overall selection pressure. Most studies of selection in natural populations have focused entirely on selection due to changes in demography, so our results may help explain why directional selection is often predicted but no evolutionary response is observed. 4. The endpoints of evolution, what we expect to see in nature, are explored using ideas from adaptive dynamics theory. The key methods are based on evolutionarily stable strategies (ESS) and convergence stability. Efficient methods for finding an ESS are described. We then extend these ideas to function-valued traits, where it is assumed that an entire function can evolve, rather than a few parameters defining it. 5. By combining theory for IPMs with ideas from several different fields, we show how the dynamics of ecologically complex, evolving systems can be understood.

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Section: Function‐valued Traitsmentioning

confidence: 99%

Evolving integral projection models: evolutionary demography meets eco‐evolutionary dynamics

Rees

Ellner

2016

Methods Ecol Evol

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“…The fitness return, which can be determined for any u , is in many ways similar to the fitness gradient in adaptive‐dynamics theory for the evolution of function‐valued traits (Dieckmann, Heino, & Parvinen, ; see also Metz et al., ). This connection provides an inroad to study allocation problems under the influence of environmental feedback (see also Parvinen, Dieckmann, & Heino, ). This is an interesting possibility for extensions of our present model, as optimization approaches inherently are directly applicable to a relatively narrow range of competitive scenarios, such as nursery competition (Metz, Mylius, & Diekmann, ).…”

Section: Discussionmentioning

confidence: 99%

Twelve fundamental life histories evolving through allocation‐dependent fecundity and survival

Johansson

Brännström

Metz

et al. 2018

Ecology and Evolution

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An organism's life history is closely interlinked with its allocation of energy between growth and reproduction at different life stages. Theoretical models have established that diminishing returns from reproductive investment promote strategies with simultaneous investment into growth and reproduction (indeterminate growth) over strategies with distinct phases of growth and reproduction (determinate growth). We extend this traditional, binary classification by showing that allocation‐dependent fecundity and mortality rates allow for a large diversity of optimal allocation schedules. By analyzing a model of organisms that allocate energy between growth and reproduction, we find twelve types of optimal allocation schedules, differing qualitatively in how reproductive allocation increases with body mass. These twelve optimal allocation schedules include types with different combinations of continuous and discontinuous increase in reproduction allocation, in which phases of continuous increase can be decelerating or accelerating. We furthermore investigate how this variation influences growth curves and the expected maximum life span and body size. Our study thus reveals new links between eco‐physiological constraints and life‐history evolution and underscores how allocation‐dependent fitness components may underlie biological diversity.

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“…In terms of the adaptive landscape (a plot of G versus v) [45], the ESS appear as peaks when the population is at its ESS ( figure 1a -c). This is the ESS maximum principle [22,46]. Strategies that satisfy G ¼ 0 (ecological equilibrium) and dG/dv ¼ 0 (evolutionary equilibrium) when v ¼ u i can be minima or maxima of the adaptive landscape.…”

Section: (A) Evolutionarily Stable Strategiesmentioning

confidence: 99%

Why Darwin would have loved evolutionary game theory

Brown¹

2016

Proc. R. Soc. B.

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Humans have marvelled at the fit of form and function, the way organisms' traits seem remarkably suited to their lifestyles and ecologies. While natural selection provides the scientific basis for the fit of form and function, Darwin found certain adaptations vexing or particularly intriguing: sex ratios, sexual selection and altruism. The logic behind these adaptations resides in frequency-dependent selection where the value of a given heritable phenotype (i.e. strategy) to an individual depends upon the strategies of others. Game theory is a branch of mathematics that is uniquely suited to solving such puzzles. While game theoretic thinking enters into Darwin's arguments and those of evolutionists through much of the twentieth century, the tools of evolutionary game theory were not available to Darwin or most evolutionists until the 1970s, and its full scope has only unfolded in the last three decades. As a consequence, game theory is applied and appreciated rather spottily. Game theory not only applies to matrix games and social games, it also applies to speciation, macroevolution and perhaps even to cancer. I assert that life and natural selection are a game, and that game theory is the appropriate logic for framing and understanding adaptations. Its scope can include behaviours within species, state-dependent strategies (such as male, female and so much more), speciation and coevolution, and expands beyond microevolution to macroevolution. Game theory clarifies aspects of ecological and evolutionary stability in ways useful to understanding eco-evolutionary dynamics, niche construction and ecosystem engineering. In short, I would like to think that Darwin would have found game theory uniquely useful for his theory of natural selection. Let us see why this is so.

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Function-valued adaptive dynamics and optimal control theory

Cited by 23 publications

References 34 publications

Evolving integral projection models: evolutionary demography meets eco‐evolutionary dynamics

Evolving integral projection models: evolutionary demography meets eco‐evolutionary dynamics

Twelve fundamental life histories evolving through allocation‐dependent fecundity and survival

Why Darwin would have loved evolutionary game theory

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