Kalle Parvinen

Evolution of dispersal in metapopulations with local density dependence and demographic stochasticity.

In this paper, we predict the outcome of dispersal evolution in metapopulations based on the following assumptions: (i) population dynamics within patches are density‐regulated by realistic growth functions; (ii) demographic stochasticity resulting from finite population sizes within patches is accounted for; and (iii) the transition of individuals between patches is explicitly modelled by a disperser pool. We show, first, that evolutionarily stable dispersal rates do not necessarily increase with rates for the local extinction of populations due to external disturbances in habitable patches. Second, we describe how demographic stochasticity affects the evolution of dispersal rates: evolutionarily stable dispersal rates remain high even when disturbance‐related rates of local extinction are low, and a variety of qualitatively different responses of adapted dispersal rates to varied levels of disturbance become possible. This paper shows, for the first time, that evolution of dispersal rates may give rise to monotonically increasing or decreasing responses, as well as to intermediate maxima or minima.

Joint evolution of specialization and dispersal in structured metapopulations.

We study the joint evolution of dispersal and specialization concerning resource usage in a mechanistically underpinned structured discrete-time metapopulation model. We show that dispersal significantly affects the evolution of specialization and that specialization is a key factor that determines the possibility of evolutionary branching in dispersal propensity. Allowing both dispersal propensity and specialization to evolve as a consequence of natural selection is necessary in order to understand the evolutionary dynamics. The joint evolution of dispersal and specialization forms a natural evolutionary path leading to the coexistence of generalists and specialists. We show that in this process, the number of different patch types and the resource distribution are essential.

A novel fitness proxy in structured locally finite metapopulations with diploid genetics, with an application to dispersal evolution

Many studies of evolutionarily stable strategies (ESS) for technical reasons make the simplification that reproduction is clonal. A post-hoc justification is that in the simplest eco-evolutionary models more realistic genetic assumptions, such as haploid sexual or diploid sexual cases, yield results compatible with the clonal ones. For metapopulations the technical reasons were even more poignant thanks to the lack of accessible fitness proxies for the diploid case. However, metapopulations are also precisely the sort of ecological backdrop for which one expect discrepancies between the evolutionary outcomes derived from clonal reproduction and diploid genetics, because substantially many mutant homozygotes appear locally even though the mutant is rare globally. In this paper we devise a fitness proxy applicable to the haploid sexual and diploid sexual case, in the style of Metz and Gyllenberg [Metz, J.A.J., Gyllenberg, M., 2001. How should we define fitness in structured metapopulation models? Including an application to the calculation of ES dispersal strategies. Proc. R. Soc. Lond. B 268, 499-508], that can cope with local population fluctuations due to environmental and demographic stochasticity. With the use of this fitness proxy we find that in dispersal evolution the studied clonal model is equivalent with the haploid sexual model, and that there are indeed many differences between clonal and diploid ESS dispersal rates. In a homogenous landscape the discrepancy is but minor (less than 2%), but the situation is different in a heterogeneous landscape: Not only is the quantitative discrepancy between the two types of ESSs appreciable (around 10%-20%), but more importantly, at the same parameter values, evolutionarily stability properties may differ. It is possible, that the singular strategy is evolutionarily stable in the clonal case but not in the diploid case, and vice versa.

On the evolution of specialization with a mechanistic underpinning in structured metapopulations

We analyze the evolution of specialization in resource utilization in a discrete-time metapopulation model using the adaptive dynamics approach. The local dynamics in the metapopulation are based on the Beverton-Holt model with mechanistic underpinnings. The consumer faces a trade-off in the abilities to consume two resources that are spatially heterogeneously distributed to patches that are prone to local catastrophes. We explore the factors favoring the spread of generalist or specialist strategies. Increasing fecundity or decreasing catastrophe probability favors the spread of the generalist strategy and increasing environmental heterogeneity enlarges the parameter domain where the evolutionary branching is possible. When there are no catastrophes, increasing emigration diminishes the parameter domain where the evolutionary branching may occur. Otherwise, the effect of emigration on evolutionary dynamics is non-monotonous: both small and large values of emigration probability favor the spread of the specialist strategies whereas the parameter domain where evolutionary branching may occur is largest when the emigration probability has intermediate values. We compare how different forms of spatial heterogeneity and different models of local growth affect the evolutionary dynamics. We show that even small changes in the resource dynamics may have outstanding evolutionary effects to the consumers.

Adaptive dynamics of cooperation may prevent the coexistence of defectors and cooperators and even cause extinction

It has recently been demonstrated that ecological feedback mechanisms can facilitate the emergence and maintenance of cooperation in public goods interactions: the replicator dynamics of defectors and cooperators can result, for example, in the ecological coexistence of cooperators and defectors. Here we show that these results change dramatically if cooperation strategy is not fixed but instead is a continuously varying trait under natural selection. For low values of the factor with which the value of resources is multiplied before they are shared among all participants, evolution will always favour lower cooperation strategies until the population falls below an Allee threshold and goes extinct, thus evolutionary suicide occurs. For higher values of the factor, there exists a unique evolutionarily singular strategy, which is convergence stable. Because the fitness function is linear with respect to the strategy of the mutant, this singular strategy is neutral against mutant invasions. This neutrality disappears if a nonlinear functional response in receiving benefits is assumed. For strictly concave functional responses, singular strategies become uninvadable. Evolutionary branching, which could result in the evolutionary emergence of cooperators and defectors, can occur only with locally convex functional responses, but we illustrate that it can also result in coevolutionary extinction.

The Allee Effect in Mechanistic Models Based on Inter-individual Interaction Processes

Recently, Eskola and Geritz (Bull. Math. Biol. 69:329–346, 2007) showed that several discrete-time population models can be derived mechanistically within a single ecological framework by varying the within-season patterns of reproduction and inter-individual aggression. However, these models do not have the Allee effect. In this paper, we modify the original modelling framework by adding different mate finding processes, and thus derive mechanistically several population models with the Allee effect.

Evolution of Complex Density-Dependent Dispersal Strategies

The question of how dispersal behavior is adaptive and how it responds to changes in selection pressure is more relevant than ever, as anthropogenic habitat alteration and climate change accelerate around the world. In metapopulation models where local populations are large, and thus local population size is measured in densities, density-dependent dispersal is expected to evolve to a single-threshold strategy, in which individuals stay in patches with local population density smaller than a threshold value and move immediately away from patches with local population density larger than the threshold. Fragmentation tends to convert continuous populations into metapopulations and also to decrease local population sizes. Therefore we analyze a metapopulation model, where each patch can support only a relatively small local population and thus experience demographic stochasticity. We investigated the evolution of density-dependent dispersal, emigration and immigration, in two scenarios: adult and natal dispersal. We show that density-dependent emigration can also evolve to a nonmonotone, “triple-threshold” strategy. This interesting phenomenon results from an interplay between the direct and indirect benefits of dispersal and the costs of dispersal. We also found that, compared to juveniles, dispersing adults may benefit more from density-dependent vs. density-independent dispersal strategies.

Adaptive dynamics of altruistic cooperation in a metapopulation: evolutionary emergence of cooperators and defectors or evolutionary suicide?

We investigate the evolution of public goods cooperation in a metapopulation model with small local populations, where altruistic cooperation can evolve due to assortment and kin selection, and the evolutionary emergence of cooperators and defectors via evolutionary branching is possible. Although evolutionary branching of cooperation has recently been demonstrated in the continuous snowdrift game and in another model of public goods cooperation, the required conditions on the cost and benefit functions are rather restrictive, e.g., altruistic cooperation cannot evolve in a defector population. We also observe selection for too low cooperation, such that the whole metapopulation goes extinct and evolutionary suicide occurs. We observed intuitive effects of various parameters on the numerical value of the monomorphic singular strategy. Their effect on the final coexisting cooperator–defector pair is more complex: changes expected to increase cooperation decrease the strategy value of the cooperator. However, at the same time the population size of the cooperator increases enough such that the average strategy does increase. We also extend the theory of structured metapopulation models by presenting a method to calculate the fitness gradient in a general class of metapopulation models, and try to make a connection with the kin selection approach.

Self-extinction through optimizing selection.

Evolutionary suicide is a process in which selection drives a viable population to extinction. So far, such selection-driven self-extinction has been demonstrated in models with frequency-dependent selection. This is not surprising, since frequency-dependent selection can disconnect individual-level and population-level interests through environmental feedback. Hence it can lead to situations akin to the tragedy of the commons, with adaptations that serve the selfish interests of individuals ultimately ruining a population. For frequency-dependent selection to play such a role, it must not be optimizing. Together, all published studies of evolutionary suicide have created the impression that evolutionary suicide is not possible with optimizing selection. Here we disprove this misconception by presenting and analyzing an example in which optimizing selection causes self-extinction. We then take this line of argument one step further by showing, in a further example, that selection-driven self-extinction can occur even under frequency-independent selection.

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

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 the opposite case is also possible: Defectors tend to disperse less than cooperators when the total amount of cooperation in the dimorphic population is low enough. (4) 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.