When Do Optimisation Arguments Make Evolutionary Sense?

Gyllenberg, Mats; Metz, J.A.J.

doi:10.1007/978-3-0348-0122-5_12

Cited by 19 publications

(15 citation statements)

References 39 publications

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“…The results in (Gyllenberg and Service 2011 ; Gyllenberg et al. 2011 ) reviewed above then show that after introducing the conditions of sign anti-symmetry and sign transitivity there is no need for further conditions, since these conditions together imply that one can linearly order the phenotypes (or rather equivalence classes of mutually neutral phenotypes) according to their “evolutionary quality”, which is also the main qualitative property of the frequency independent fitnesses of the population geneticists.…”

Section: Frequency Dependence 30: Towards An Improved Definitionmentioning

confidence: 99%

“…2008 ; Gyllenberg and Service 2011 ; Gyllenberg et al. 2011 ) dealing with the question under which conditions the ESSes of an eco-evolutionary model satisfy an optimisation principle. Below we give a quick summary of the relevant ideas from those papers.…”

Section: On 1-dimensional Environments and Optimisation Principlesmentioning

confidence: 99%

“…2008 , Gyllenberg et al. 2011 ). Another matter is how to find for a given weakly frequency dependent fitness function an associated approximate optimisation principle .…”

Section: Closing Remarksmentioning

confidence: 99%

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Frequency dependence 3.0: an attempt at codifying the evolutionary ecology perspective

Metz

Geritz

2016

J. Math. Biol.

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The fitness concept and perforce the definition of frequency independent fitnesses from population genetics is closely tied to discrete time population models with non-overlapping generations. Evolutionary ecologists generally focus on trait evolution through repeated mutant substitutions in populations with complicated life histories. This goes with using the per capita invasion speed of mutants as their fitness. In this paper we develop a concept of frequency independence that attempts to capture the practical use of the term by ecologists, which although inspired by population genetics rarely fits its strict definition. We propose to call the invasion fitnesses of an eco-evolutionary model frequency independent when the phenotypes can be ranked by competitive strength, measured by who can invade whom. This is equivalent to the absence of weak priority effects, protected dimorphisms and rock–scissor–paper configurations. Our concept differs from that of Heino et al. (TREE 13:367–370, 1998) in that it is based only on the signs of the invasion fitnesses, whereas Heino et al. based their definitions on the structure of the feedback environment, summarising the effect of all direct and indirect interactions between individuals on fitness. As it turns out, according to our new definition an eco-evolutionary model has frequency independent fitnesses if and only if the effect of the feedback environment on the fitness signs can be summarised by a single scalar with monotonic effect. This may be compared with Heino et al.’s concept of trivial frequency dependence defined by the environmental feedback influencing fitness, and not just its sign, in a scalar manner, without any monotonicity restriction. As it turns out, absence of the latter restriction leaves room for rock–scissor–paper configurations. Since in ‘realistic’ (as opposed to toy) models frequency independence is exceedingly rare, we also define a concept of weak frequency dependence, which can be interpreted intuitively as almost frequency independence, and analyse in which sense and to what extent the restrictions on the potential model outcomes of the frequency independent case stay intact for models with weak frequency dependence.

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Section: Frequency Dependence 30: Towards An Improved Definitionmentioning

confidence: 99%

Section: On 1-dimensional Environments and Optimisation Principlesmentioning

confidence: 99%

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Frequency dependence 3.0: an attempt at codifying the evolutionary ecology perspective

Metz

Geritz

2016

J. Math. Biol.

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“…Moreover, in the case of fixed strategies the basic reproduction numbers of the types are decreasing functions of I. Diekmann and Mylius (1995) (see also Metz et al 2008, Gyllenberg et al 2011 showed that it follows from this that if population dynamics leads to a steady state with constant I, then a type x is evolutionarily stable if and only if the function which assigns to a type the environmental value at which the population will be steady has a maximum at x. The results above show that for our model of fixed strategies the same is true even if stabilization of population dynamics does not occur.…”

Section: Fixed Reproductive Strategiesmentioning

confidence: 98%

Conditional Reproductive Strategies Under Variable Environmental Conditions

Gyllenberg

Hanski

Lindström

2017

Annales Zoologici Fennici

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Gyllenberg, M., Hanski, I. & Lindström, T. 2017: Conditional reproductive strategies under variable environmental conditions. Within the framework of adaptive dynamics we consider the evolution by natural selection of reproductive strategies in which individuals may adjust their reproductive behaviour in response to changing environmental conditions. As a specific example we considered a discrete-time model in which possible fluctuations in the environmental conditions are caused by predator-prey interaction. Our main findings include:(1) Coexistence between two fixed strategies (i.e., strategies that do not adjust to changing environmental conditions) is impossible; there exists a best fixed strategy, which invades and ousts all other fixed strategies. (2) A necessary condition for conditional (adjustable) strategies to evolve is that there are fluctuations in the environmental conditions. Predator-prey interactions may cause such fluctuations and under natural assumptions there exists an optimal conditional strategy which is uninvadable and invades and ousts all other strategies. # An earlier version of this article was completed while Ilkka Hanski was still alive. The co-authors dedicate the paper to the memory of Ilkka -a friend and collaborator for almost 30 years.

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“…Using adaptive dynamics, it was shown that under some rather strict assumptions about environmental feedback, the evolutionary outcome can be found by no more than maximisation of invasion fitness (Gyllenberg and Service 2011; Gyllenberg et al. 2011). Another class of generic modelling techniques known as genetic algorithms is designed to imitate long-time evolutionary dynamics including the processes of mutation, crossover, selection and replacement (Hamblin 2013; Sumida et al.…”

Section: Introductionmentioning

confidence: 99%

Revealing Evolutionarily Optimal Strategies in Self-Reproducing Systems via a New Computational Approach

2019

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Modelling the evolution of complex life history traits and behavioural patterns observed in the natural world is a challenging task. Here, we develop a novel computational method to obtain evolutionarily optimal life history traits/behavioural patterns in population models with a strong inheritance. The new method is based on the reconstruction of evolutionary fitness using underlying equations for population dynamics and it can be applied to self-reproducing systems (including complicated age-structured models), where fitness does not depend on initial conditions, however, it can be extended to some frequency-dependent cases. The technique provides us with a tool to efficiently explore both scalar-valued and function-valued traits with any required accuracy. Moreover, the method can be implemented even in the case where we ignore the underlying model equations and only have population dynamics time series. As a meaningful ecological case study, we explore optimal strategies of diel vertical migration (DVM) of herbivorous zooplankton in the vertical water column which is a widespread phenomenon in both oceans and lakes, generally considered to be the largest synchronised movement of biomass on Earth. We reveal optimal trajectories of daily vertical motion of zooplankton grazers in the water column depending on the presence of food and predators. Unlike previous studies, we explore both scenarios of DVM with static and dynamic predators. We find that the optimal pattern of DVM drastically changes in the presence of dynamic predation. Namely, with an increase in the amount of food available for zooplankton grazers, the amplitude of DVM progressively increases, whereas for static predators DVM would abruptly cease. Electronic supplementary materialThe online version of this article (10.1007/s11538-019-00663-4) contains supplementary material, which is available to authorized users.

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When Do Optimisation Arguments Make Evolutionary Sense?

Cited by 19 publications

References 39 publications

Frequency dependence 3.0: an attempt at codifying the evolutionary ecology perspective

Frequency dependence 3.0: an attempt at codifying the evolutionary ecology perspective

Conditional Reproductive Strategies Under Variable Environmental Conditions

Revealing Evolutionarily Optimal Strategies in Self-Reproducing Systems via a New Computational Approach

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