Evolutionary suicide and evolution of dispersal in structured metapopulations

 We study the evolution of dispersal in a structured metapopulation model. The metapopulation consists of a large (infinite) number of local populations living in patches of habitable environment. Dispersal between patches is modelled by a disperser pool and individuals in transit between patches are exposed to a risk of mortality. Occasionally, local catastrophes eradicate a local population: all individuals in the affected patch die, yet the patch remains habitable. We prove that, in the absence of catastrophes, the strategy not to migrate is evolutionarily stable. Under a given set of environmental conditions, a metapopulation may be viable and yet selection may favor dispersal rates that drive the metapopulation to extinction. This phenomenon is known as evolutionary suicide. We show that in our model evolutionary suicide can occur for catastrophe rates that increase with decreasing local population size. Evolutionary suicide can also happen for constant catastrophe rates, if local growth within patches shows an Allee effect. We study the evolutionary bifurcation towards evolutionary suicide and show that a discontinuous transition to extinction is a necessary condition for evolutionary suicide to occur. In other words, if population size smoothly approaches zero at a boundary of viability in parameter space, this boundary is evolutionarily repelling and no suicide can occur. Received: 10 November 2000 / Revised version: 13 February 2002 / Published online: 17 July 2002     

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.     

On fitness in structured metapopulations

In this paper we derive a general expression measuring fitness in general structured metapopulation models. We apply the theory to a model structured by local population size and in which local dynamics is explicitly modelled. In particular, we calculate the evolutionarily stable dispersal strategy for individuals that can assess the local population density in the case where only dispersal is subject to evolutionary control but all other model ingredients are assumed fixed. We show that there exists a threshold size such that at ESS everyone should stay as long as the population size is below the threshold and everyone should disperse immediately as the population size reaches the threshold. Received: 13 August 1999 / Revised version: 2 May 2001 / Published online: 12 October 2001     

复合种群中扩散的研究进展

复合种群理论是近年来景观生态学和保护生物学研究的热点之一,但有关复合种群的野外试验研究大多集中在面积和隔离度等方面,对影响复合种群动态因子的具体报道较少。事实上,复合种群的影响因子还有很多,如连通性、扩散和生境质量等。本文就复合种群中扩散进行了综述,主要包括以下的几个方面:(1)扩散的影响因子。生境质量、斑块连通性和种群自身密度等;(2)扩散方向与测定。扩散的方向是有选择的,在其方向的测定中微卫星标记(microsatellitemarker)得到了较广泛的应用;(3)扩散距离与测定。扩散的距离除受到物种自身特性的影响外,还受到踏脚石等生境因素的影响;(4)扩散对复合种群的影响。扩散受到复合种群空间结构以及生境质量等自身条件的影响,同时又反作用于复合种群的动态变化,在以后物种保护工作中必须加以重视。     

Selection on dispersal in isolated butterfly metapopulations

In most metapopulation models dispersal is assumed to be a fixed species-specific trait, but in reality dispersal abilities are highly sensitive to various selective pressures. Strict isolation of a metapopulation, which precludes any influx of immigrants (and their genes) from outside and makes it impossible for emigrants to reach other localities with suitable habitat, thus reducing fitness benefits of long-distance dispersal to zero, may be expected to impose strong selection against dispersal. We tested the above prediction by comparing dispersal parameters derived with the Virtual Migration model for isolated and non-isolated metapopulations of two species of large blue Maculinea (= Phengaris) butterflies, surveyed with intensive mark-recapture. Mortality during dispersal was found to be twice (in M. teleius) to five times higher (in M. arion) in isolated metapopulations. Isolation also resulted in significantly reduced dispersal distances in isolated metapopulations, with the effect being particularly strong in M. arion females. Apart from its evolutionary and ecological consequences, dispersal depression in isolated butterfly metapopulations implied by our results has serious conservation implications. It provides a clear argument against using parameter values obtained in a different environmental setting in modelling applications, e.g., Population Viability Analyses or environmental impact assessment. Furthermore, it underlines the importance of establishing well-connected networks of suitable habitats prior to species release in areas where reintroductions are planned.     

Evolutionary stability of ideal free dispersal strategies in patchy environments

A central question in the study of the evolution of dispersal is what kind of dispersal strategies are evolutionarily stable. Hastings (Theor Pop Biol 24:244-251, 1983) showed that among unconditional dispersal strategies in a spatially heterogeneous but temporally constant environment, the dispersal strategy with no movement is convergent stable. McPeek and Holt's (Am Nat 140:1010-1027, 1992) work suggested that among conditional dispersal strategies in a spatially heterogeneous but temporally constant environment, an ideal free dispersal strategy, which results in the ideal free distribution for a single species at equilibrium, is evolutionarily stable. We use continuous-time and discrete-space models to determine when the dispersal strategy with no movement is evolutionarily stable and when an ideal free dispersal strategy is evolutionarily stable, both in a spatially heterogeneous but temporally constant environment.     

Vertically transmitted symbionts in structured host metapopulations

We develop a structured metapopulation model for vertically transmitted symbionts in natural host populations. We focus primarily on two questions: Are mutualism and high transmission probability prerequisites for the survival of symbionts in structured host metapopulations? What are the ecological conditions under which coexistence of infected and uninfected hosts is possible? We start with studying in depth the case of qualitatively identical patches and derive conditions for invasion and coexistence of uninfected and infected hosts. Our model predicts that, in a qualitatively uniform environment, coexistence is possible only if the symbionts increase the fitness of their host, so the mutualism is indeed needed for coexistence. We also prove that evolution selects for 100% infection frequency in the metapopulation. Then we generalize the model for different patch qualities and get conditions for invasion in a virgin environment.     

Climate-dependent dispersal rates in metapopulations of burnet moths

Predicted climate change implies warmer weather and a higher frequency of extreme weather situations. The consequences of the warm July in 2003 was investigated in contrast to the cold July in 2004 in southern Sweden with focus on the dispersal rate of two species of burnet moths (Zygaenidae). During an extensive mark-release-recapture program in metapopulations of burnet moths substantial differences in inter habitat patch dispersal rates were observed. For two species of Zygaena it was 2.14 and 2.18 times higher during the warm year. Measured patch dispersal rate significantly declined towards the edges of the large study-area, suggesting that individuals disperse outside the study-area. No significant differences in dispersal rates were found between the two species studied. The dispersal rates were similar for both females and males, and no density dependent effects on dispersal or effects of amount of nectar rich flowers were found. Dispersal events appeared as distinct movements, often reaching several kilometres. We conclude that dispersal depend on climatic conditions. Exceptionally warm years may be especially important for survival of certain species in metapopulation systems and this may be crucial for the survival of populations during scenarios of climate change.     

Controlling spatial chaos in metapopulations with long-range dispersal

We propose two methods to control spatial chaos in an ecological metapopulation model with long-range dispersal. The metapopulation model consists of local populations living in a patchily distributed habitat. The habitat patches are arranged in a one-dimensional array. In each generation, density-dependent reproduction occurs first in each patch. Then individuals disperse according to a Gaussian distribution. The model corresponds to a chain of coupled oscillators with long-range interactions. It exhibits chaos for a broad range of parameters. The proposed control methods are based on the method described by Güémez and Matías for single difference equations. The methods work by adjusting the local population sizes in a selected subset of all patches. In the first method (pulse control), the adjustments are made periodically at regular time intervals, and consist of always removing (or adding) a fixed proportion of the local populations. In the second method (wave control), the adjustments are made in every generation, but the proportion of the local population that is affected by the control changes sinusoidally. As long as dispersal distances are not too low, these perturbations can drive chaotic metapopulations to cyclic orbits whose period is a multiple of the control period. we discuss the influence of the magnitude of the pulses and wave amplitudes, and of the number and the distribution of controlled patches on the effectiveness of control. When the controls start to break down, interesting dynamic phenomena such as intermittent chaos can be observed.     

The intermediate dispersal principle in spatially explicit metapopulations

Aim of this paper is to assess the fate of metapopulations described by spatially explicit models. To this end, we first present an interacting particle system (IPS) where individuals of a single species compete logistically at the local scale and can move among patches according to various dispersal kernels. As the IPS is a complex stochastic system, it is impossible to determine the persistence-extinction boundaries in any relevant parameter space with analytical methods or numerical continuation techniques. We thus resort to a heuristic method that lets us determine the boundaries as space-time percolation thresholds with a relatively modest computational effort. Such boundaries are qualitatively consistent with those we obtained with spatial implicit modelling. In particular, we find that the intermediate dispersal principle, namely that globally persistent metapopulations correspond to dispersal rates that are neither too low nor too high, turns out to be very robust even in this explicit context. However, the quantification of the boundaries strongly depends upon the number of patches, the dispersal kernels and the border conditions. Finally, we show that there exists a scaling law that relates the number of species lost in a fragmented landscape to the number of patches. Thus, the law allows a rough estimation of the cost of destroying a patch.     

Evolution of specialization in resource utilization in structured metapopulations

We study the evolution of resource utilization in a structured discrete-time metapopulation model with an infinite number of patches, prone to local catastrophes. The consumer faces a trade-off in the abilities to consume two resources available in different amounts in each patch. We analyse how the evolution of specialization in the utilization of the resources is affected by different ecological factors: migration, local growth, local catastrophes, forms of the trade-off and distribution of the resources in the patches. Our modelling approach offers a natural way to include more than two patch types into the models. This has not been usually possible in the previous spatially heterogeneous models focusing on the evolution of specialization.     

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.     

Evolution of specialization in resource utilization in structured metapopulations

We study the evolution of resource utilization in a structured discrete-time metapopulation model with an infinite number of patches, prone to local catastrophes. The consumer faces a trade-off in the abilities to consume two resources available in different amounts in each patch. We analyse how the evolution of specialization in the utilization of the resources is affected by different ecological factors: migration, local growth, local catastrophes, forms of the trade-off and distribution of the resources in the patches. Our modelling approach offers a natural way to include more than two patch types into the models. This has not been usually possible in the previous spatially heterogeneous models focusing on the evolution of specialization.     

Evolution of body condition‐dependent dispersal in metapopulations

Body condition‐dependent dispersal strategies are common in nature. Although it is obvious that environmental constraints may induce a positive relationship between body condition and dispersal, it is not clear whether positive body conditional dispersal strategies may evolve as a strategy in metapopulations. We have developed an individual‐based simulation model to investigate how body condition–dispersal reaction norms evolve in metapopulations that are characterized by different levels of environmental stochasticity and dispersal mortality. In the model, body condition is related to fecundity and determined either by environmental conditions during juvenile development (adult dispersal) or by those experienced by the mother (natal dispersal). Evolutionarily stable reaction norms strongly depend on metapopulation conditions: positive body condition dependency of dispersal evolved in metapopulation conditions with low levels of dispersal mortality and high levels of environmental stochasticity. Negative body condition‐dependent dispersal evolved in metapopulations with high dispersal mortality and low environmental stochasticity. The latter strategy is responsible for higher dispersal rates under kin competition when dispersal decisions are based on body condition reached at the adult life stage. The evolution of both positive and negative body condition‐dependent dispersal strategies is consequently likely in metapopulations and depends on the prevalent environmental conditions.     

The effects of density-dependence and local dispersal in individual-based stochastic metapopulations

We describe simulation models for metapopulations of individual‐based random walk populations with local dispersal on a coupled map lattice. The models were used to assess the factors determining persistence time, in particular the incidence of density‐dependence required for long‐term persistence of a temporally and spatially stochastic metapopulation, the extent of persistence possible in the absence of density‐dependence, and the factors that affect this.
Metapopulation persistence depended on the overall rate of increase of the metapopulation mean. This was maximised by (in order of importance) high mean and variance in the local rate of increase, high dispersal rates (20% or more of individuals dispersing each generation), large lattice size, and large dispersal range (to at least 24 neighbouring subpopulations).
With density‐dependence, the emergent dynamics of the metapopulation mean following global perturbation (reduction in density) resembled those of the logistic growth model. However, the overall metapopulation rate of increase and equilibrium level bore no resemblance to those of the subpopulations: rate of increase was higher (negative mean local rates of increase may give positive overall growth), and equilibrium mean metapopulation density was well below the local carrying capacity. This highlights the need to sample populations at an appropriate scale when seeking to understand regulatory mechanisms.
Metapopulations with the strongest tendency to grow gave the highest equilibrium mean density, the highest incidence of density‐dependence, and the longest persistence time. However, long‐term persistence with low average density and very low incidence of density‐dependence was possible on a sufficiently large lattice. For example, with 40×40 subpopulations, mean metapopulation persistence time was around 10⁴ generations, with mean subpopulation size of 2% of the carrying capacity, and local density‐dependence acting just once every 2500 generations on average. Metapopulation processes may explain our inability to detect density‐dependence in many real populations, and may also play an important part in the persistence of rare species.     

Stabilization through spatial pattern formation in metapopulations with long-range dispersal

Many studies of metapopulation models assume that spatially extended populations occupy a network of identical habitat patches, each coupled to its nearest neighbouring patches by density-independent dispersal. Much previous work has focused on the temporal stability of spatially homogeneous equilibrium states of the metapopulation, and one of the main predictions of such models is that the stability of equilibrium states in the local patches in the absence of migration determines the stability of spatially homogeneous equilibrium states of the whole metapopulation when migration is added. Here, we present classes of examples in which deviations from the usual assumptions lead to different predictions. In particular, heterogeneity in local habitat quality in combination with long-range dispersal can induce a stable equilibrium for the metapopulation dynamics, even when within-patch processes would produce very complex behaviour in each patch in the absence of migration. Thus, when spatially homogeneous equilibria become unstable, the system can often shift to a different, spatially inhomogeneous steady state. This new global equilibrium is characterized by a standing spatial wave of population abundances. Such standing spatial waves can also be observed in metapopulations consisting of identical habitat patches, i.e. without heterogeneity in patch quality, provided that dispersal is density dependent. Spatial pattern formation after destabilization of spatially homogeneous equilibrium states is well known in reaction–diffusion systems and has been observed in various ecological models. However, these models typically require the presence of at least two species, e.g. a predator and a prey. Our results imply that stabilization through spatial pattern formation can also occur in single-species models. However, the opposite effect of destabilization can also occur: if dispersal is short range, and if there is heterogeneity in patch quality, then the metapopulation dynamics can be chaotic despite the patches having stable equilibrium dynamics when isolated. We conclude that more general metapopulation models than those commonly studied are necessary to fully understand how spatial structure can affect spatial and temporal variation in population abundance.     

Fitness-dependent dispersal in metapopulations and its consequences for persistence and synchrony

1. We present a novel metapopulation model where dispersal is fitness dependent: the strength of migration from a site is dependent on the expected reproductive fitness of individuals there. Furthermore, individuals continue to migrate until they reach a suitable habitat where their expected fitness is above a threshold value.
2. Fitness-dependent dispersal has a very strong stabilizing effect on population dynamics, even when the intrinsic dynamics of populations in the absence of dispersal exhibit complex high-amplitude oscillations. This stabilizing effect is much stronger than that of the density-independent dispersal normally considered in metapopulation models.
3. Even when fitness-dependent dispersal does not stabilize the dynamics in a formal sense, it generally leads to simplification, with complex or even chaotic fluctuations being reduced to simple cycles.
4. This form of dispersal also has a strong tendency to synchronize local population dynamics across the spatial extent of the metapopulation.
5. These conclusions are robust to the addition of strong stochasticity in the migration threshold.     

Evolutionary dynamics in structured populations

Evolutionary dynamics shape the living world around us. At the centre of every evolutionary process is a population of reproducing individuals. The structure of that population affects evolutionary dynamics. The individuals can be molecules, cells, viruses, multicellular organisms or humans. Whenever the fitness of individuals depends on the relative abundance of phenotypes in the population, we are in the realm of evolutionary game theory. Evolutionary game theory is a general approach that can describe the competition of species in an ecosystem, the interaction between hosts and parasites, between viruses and cells, and also the spread of ideas and behaviours in the human population. In this perspective, we review the recent advances in evolutionary game dynamics with a particular emphasis on stochastic approaches in finite sized and structured populations. We give simple, fundamental laws that determine how natural selection chooses between competing strategies. We study the well-mixed population, evolutionary graph theory, games in phenotype space and evolutionary set theory. We apply these results to the evolution of cooperation. The mechanism that leads to the evolution of cooperation in these settings could be called ‘spatial selection’: cooperators prevail against defectors by clustering in physical or other spaces.     

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.