Long-term evolution of multilocus traits

Matessi, Carlo; Pasquale, Cristina Di

doi:10.1007/s002850050023

Cited by 28 publications

(37 citation statements)

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“…For µ ≈ 0.305 this boundary at the singular dispersal rate becomes evolutionarily repelling, and an internal singular strategy appears (See also Figure 4). From the shape of the zero-isoclines and directions of the arrows near the singular strategy it is clear that strategies will converge to this singular strategy (see Matessi and Di Pasquale, 1996). This singular strategy is first a fitness minimum with respect to the cooperation component (Figure 2bcd), but becomes evolutionarily stable for larger values of µ, around µ ≈ 0.62 ( Figure 2e).…”

Section: Resultsmentioning

confidence: 93%

“…A singular strategy s * is an evolutionary attractor (Eshel, 1983) if the repeated invasion of nearby mutant strategies into resident strategies will lead to the convergence of resident strategies towards s * . For scalar strategies, the condition for such convergence is D ′ (s * ) < 0, whereas the situation with vector-valued strategies is more complicated (Christiansen, 1991;Marrow et al, 1996;Matessi and Di Pasquale, 1996;Geritz et al, 1998;Leimar, 2001;Meszéna et al, 2001). Because cooperation and dispersal are physiologically rather different traits, we find it realistic to assume that these traits evolve independently.…”

Section: Adaptive Dynamicsmentioning

confidence: 99%

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Joint evolution of altruistic cooperation and dispersal in a metapopulation of small local populations

Parvinen

2013

Theoretical Population Biology

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We investigate the joint evolution of public goods cooperation and dispersal in a metapopulation model with small local populations. Altruistic cooperation can evolve due to assortment and kin selection, and dispersal can evolve because of demographic stochasticity, catastrophes and kin selection. Metapopulation structures resulting in assortment have been shown to make selection for cooperation possible. But how does dispersal affect cooperation and vice versa, when both are allowed to evolve as continuous traits? We found four qualitatively different evolutionary outcomes. (1) Monomorphic evolution to full defection with positive dispersal. (2) Monomorphic evolution to an evolutionarily stable state with positive cooperation and dispersal. In this case, parameter changes selecting for increased cooperation typically also select for increased dispersal. (3) Evolutionary branching can result in the evolutionarily stable coexistence of defectors and cooperators. Although defectors could be expected to disperse more than cooperators, here we show that also the opposite case is possible: Defectors tend to disperse less than cooperators when the total amount of cooperation in the dimorphic population is low enough. (4) 1 Selection for too low cooperation can cause the extinction of the evolving population. For moderate catastrophe rates dispersal needs to be initially very frequent for evolutionary suicide to occur. Although selection for less dispersal in principle could prevent such evolutionary suicide, in most cases this rescuing effect is not sufficient, because selection in the cooperation trait is typically much stronger. If the catastrophe rate is large enough, a part of the boundary of viability can be evolutionarily attracting with respect to both strategy components, in which case evolutionary suicide is expected from all initial conditions.

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Section: Resultsmentioning

confidence: 93%

Section: Adaptive Dynamicsmentioning

confidence: 99%

Joint evolution of altruistic cooperation and dispersal in a metapopulation of small local populations

Parvinen

2013

Theoretical Population Biology

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“…This canonical equation can be used to study the transient dynamics and convergence towards evolutionarily singular strategies (see, e.g., Heino et al, 2008). Already for vector-valued strategies, conditions for such convergence are more complicated than for scalar strategies (Christiansen, 1991;Marrow et al, 1996;Matessi and Di Pasquale, 1996;Geritz et al, 1998;Leimar, 2001;Meszéna et al, 2001), usually requiring dynamical analysis of the kind the canonical equation allows. In some simple cases, the equilibria of the canonical equation can be solved analytically, and singular strategies thus can be obtained.…”

Section: Introductionmentioning

confidence: 99%

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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“…Lande, 1981;Friedman, 1991;Pomiankowski et al, 1991;Abrams et al, 1993;Motro, 1994;Eshel et al, 1997), including the idea that mutation can have a qualitative influence on the outcome of evolution (Matessi and Di Pasquale, 1996). Compared to earlier work, my emphasis will be on considering all changes that are consistent with natural selection, corresponding to the concept of a Darwinian demon, rather than on the question of which changes are expected given some mutational process.…”

Section: Introductionmentioning

confidence: 99%

Evolutionary Change and Darwinian Demons

Leimar¹

2002

Selection

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Models of adaptive evolution often have the property that change is guided by, but not fully determined by fitness. In a given situation many different mutant phenotypes may have a fitness advantage over the residents, and are thus potential invaders, implying that the mutational process plays an important role in deciding which particular invasion will take place. By introducing an imaginary 'Darwinian demon' in charge of mutations, one can examine the maximal role that mutation could play in determining evolutionary change. Taking into account pleiotropic mutations and shifting fitness landscapes, it seems likely that a Darwinian demon could exert considerable influence and most likely would be able to produce any viable form of organism. This kind of perspective can be helpful in clarifying concepts of evolutionary stability.

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Long-term evolution of multilocus traits

Cited by 28 publications

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Joint evolution of altruistic cooperation and dispersal in a metapopulation of small local populations

Joint evolution of altruistic cooperation and dispersal in a metapopulation of small local populations

Function-valued adaptive dynamics and optimal control theory

Evolutionary Change and Darwinian Demons

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