The adaptive dynamics of function-valued traits

Dieckmann, Ulf; Heino, Mikko; Parvinen, Kalle

doi:10.1016/j.jtbi.2005.12.002

Cited by 66 publications

(106 citation statements)

References 67 publications

(68 reference statements)

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“…Considering the other components of the selection gradient derived by Dieckmann et al (2006), the mutation probability µ(s) and the equilibrium population sizen(s) require no special treatment compared with the case without the s ′ dependence. It is also reasonable to assume that the derivative s ′ has no effect on the variance-covariance function σ 2 of the mutation distribution.…”

Section: Direct-effect Models and The Calculus Of Variationsmentioning

confidence: 99%

“…Adaptive dynamics (Metz et al, 1992(Metz et al, , 1996Dieckmann and Law, 1996;Geritz et al, 1997Geritz et al, , 1998 was originally formulated for scalar strategies s ∈ R. Dieckmann et al (2006) and Parvinen et al (2006) presented theory for the adaptive dynamics of function-valued traits, i.e., strategies of the form s(a) ∈ R for a ∈ R. In addition to developing this theory, Dieckmann et al (2006) studied the evolution of metabolic investment strategies and the evolution of seasonal flowering schedules. Parvinen et al (2006) further investigated models of metabolic investment strategies.…”

Section: Introductionmentioning

confidence: 99%

“…This illustrates the wide applicability of function-valued traits to questions in evolutionary ecology. Dieckmann et al (2006) introduced the canonical equation of functionvalued adaptive dynamics, which describes the expected rate of evolutionary change in a function-valued strategy. This canonical equation can be used to study the transient dynamics and convergence towards evolutionarily singular strategies (see, e.g., Heino et al, 2008).…”

Section: Introductionmentioning

confidence: 99%

“…To facilitate future applications, we present two worked-out examples by extending the seasonal flowering model of Dieckmann et al (2006). In the first process-mediated extension (section 5), plants have a limited amount of resources that they can allocate to flower production at different times of the season.…”

Section: Introductionmentioning

confidence: 99%

“…Let S denote the set of possible strategies, often called the strategy space. According to Dieckmann et al (2006), the following equation, referred to as the canonical equation of function-valued adaptive dynamics, describes the rate d dt s of expected evolutionary change in a function-valued strategy s ∈ S,…”

Section: Introductionmentioning

confidence: 99%

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Function-valued adaptive dynamics and optimal control theory

2012

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In this article we further develop the theory of adaptive dynamics of function-valued traits. Previous work has concentrated on models for which invasion fitness can be written as an integral in which the integrand for each argument value is a function of the strategy value at that argument value only. For this type of models of direct effect, singular strategies can be found using the calculus of variations, with singular strategies needing to satisfy Euler's equation with environmental feedback. In a broader, more mechanistically oriented class of models, the function-valued strategy affects a process described by differential equations, and fitness can be expressed as an integral in which the integrand for each argument value depends both on the strategy and on process variables at that argument value. In general, the calculus of variations cannot help analyzing this much broader class of models. Here we explain how to find singular strategies in this class of process-mediated models using optimal control theory. In particular, we show that singular strategies need to satisfy Pontryagin's maximum principle with environmental feedback. We demonstrate the utility of this approach by studying the evolution of strategies determining seasonal flowering schedules.

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Section: Direct-effect Models and The Calculus Of Variationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Function-valued adaptive dynamics and optimal control theory

2012

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Frequency‐dependent two‐sex models: a new approach to sex ratio evolution with multiple maternal conditions

Shyu

Caswell

2016

Ecology and Evolution

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Mothers that experience different individual or environmental conditions may produce different proportions of male to female offspring. The Trivers‐Willard hypothesis, for instance, suggests that mothers with different qualities (size, health, etc.) will use different sex ratios if maternal quality differentially affects sex‐specific reproductive success. Condition‐dependent, or facultative, sex ratio strategies like these allow multiple sex ratios to coexist within a population. They also create complex population structure due to the presence of multiple maternal conditions. As a result, modeling facultative sex ratio evolution requires not only sex ratio strategies with multiple components, but also two‐sex population models with explicit stage structure. To this end, we combine nonlinear, frequency‐dependent matrix models and multidimensional adaptive dynamics to create a new framework for studying sex ratio evolution. We illustrate the applications of this framework with two case studies where the sex ratios depend one of two possible maternal conditions (age or quality). In these cases, we identify evolutionarily singular sex ratio strategies, find instances where one maternal condition produces exclusively male or female offspring, and show that sex ratio biases depend on the relative reproductive value ratios for each sex.

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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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The adaptive dynamics of function-valued traits

Cited by 66 publications

References 67 publications

Function-valued adaptive dynamics and optimal control theory

Function-valued adaptive dynamics and optimal control theory

Frequency‐dependent two‐sex models: a new approach to sex ratio evolution with multiple maternal conditions

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

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