Optimal harvesting for a predator-prey metapopulation

In this paper we present a deterministic, discrete-time model for a two-patch predator-prey metapopulation. We study optimal harvesting for the metapopulation using dynamic programming. Some rules are established as generalizations of rules for a single-species metapopulation harvesting theory. We also establish rules to harvest relatively more (or less) vulnerable prey subpopulations and more (or less) efficient predator subpopulations.     

Metapopulation dynamics: Does it help to have more of the same?

With the interest in conservation biology shifting towards processes from patterns, and to populations from communities, the theory of metapopulation dynamics is replacing the equilibrium theory of island biogeography as the population ecology paradigm in conservation biology. The simplest models of metapopulation dynamics make predictions about the effects of habitat fragmentation - size and isolation of habitat patches - on metapopulation persistence. The simple models may be enriched by considerations of the effects of demographic and environmental stochasticity on the size and extinction probability of local populations. Environmental stochasticity affects populations at two levels: it makes local extinctions more probable, and it also decreases metapopulation persistence time by increasing the correlation of extinction events across populations. Some controversy has arisen over the significance of correlated extinctions, and how they may affect the optimal subdivision of metapopulations to maximize their persistence time.     

局域种群的Allee效应和集合种群的同步性

从包含Allee效应的局域种群出发,建立了耦合映像格子模型,即集合种群模型.通过分析和计算机模拟表明:(1)当局域种群受到Allee效应强度较大时,集合种群同步灭绝;(2)而当Allee效应强度相对较弱时,通过稳定局域种群动态(减少混沌)使得集合种群发生同步波动,而这种同步波动能够增加集合种群的灭绝风险;(3)斑块间的连接程度对集合种群同步波动的发生有很大的影响,适当的破碎化有利于集合种群的续存.全局迁移和Allee效应结合起来增加了集合种群同步波动的可能,从而增加集合种群的灭绝风险.这些结果对理解同步性的机理、利用同步机理来制定物种保护策略和害虫防治都有重要的意义.     

The applicability of metapopulation theory to large mammals

Metapopulation theory has become a common framework in conservation biology and it is sometimes suggested that a metapopulation approach should be used for management of large mammals. However, it has also been suggested that metapopulation theory would not be applicable to species with long generations compared to those with short ones. In this paper, we review how and on what empirical ground metapopulation terminology has been applied to insects, small mammals and large mammals. The review showed that the metapopulation term sometimes was used for population networks which only fulfilled the broadest possible definition of a metapopulation, i.e. they were subpopulations connected by migrating individuals. We argue that the metapopulation concept should be reserved for networks that also show some kind of metapopulation dynamics. Otherwise it applies to almost all populations and loses its substance. We found much empirical support for metapopulation dynamics in both insects and small mammals, but not in large mammals. A possible reason is the methods used to confirm the existence of metapopulation dynamics. For insects and small mammals, the common approach is to study population turnover through patch occupancy data. Such data is difficult to obtain for large mammals, since longer temporal scales need to be covered to record extinctions and colonizations. Still, many populations of large mammals are exposed to habitat fragmentation and the resulting subpopulations sometimes have high risks of extinction. If there is migration between the subpopulations, the metapopulation framework could provide valuable information on their population dynamics. We suggest that a metapopulation approach can be interesting for populations of large mammals, when there are discrete breeding subpopulations and when these subpopulations have different growth rates and demographic fates. Thus, a comparison of the subpopulations’ demographic fates, rather than subpopulation turnover, can be a feasible alternative for studies of metapopulation dynamics in large mammals.     

On valuing patches: estimating contributions to metapopulation growth with reverse-time capture-recapture modelling

Metapopulation ecology has historically been rich in theory, yet analytical approaches for inferring demographic relationships among local populations have been few. We show how reverse-time multi-state capture-recapture models can be used to estimate the importance of local recruitment and interpopulation dispersal to metapopulation growth. We use 'contribution metrics' to infer demographic connectedness among eight local populations of banner-tailed kangaroo rats, to assess their demographic closure, and to investigate sources of variation in these contributions. Using a 7 year dataset, we show that: (i) local populations are relatively independent demographically, and contributions to local population growth via dispersal within the system decline with distance; (ii) growth contributions via local survival and recruitment are greater for adults than juveniles, while contributions involving dispersal are greater for juveniles; (iii) central populations rely more on local recruitment and survival than peripheral populations; (iv) contributions involving dispersal are not clearly related to overall metapopulation density; and (v) estimated contributions from outside the system are unexpectedly large. Our analytical framework can classify metapopulations on a continuum between demographic independence and panmixia, detect hidden population growth contributions, and make inference about other population linkage forms, including rescue effects and source-sink structures. Finally, we discuss differences between demographic and genetic population linkage patterns for our system.     

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.     

Support for a metapopulation structure among mammals

• 1 The metapopulation metaphor is increasingly used to explain the spatial dynamics of animal populations. However, metapopulation structure is difficult to identify in long‐lived species that are widely distributed in stochastic environments, where they can resist extinctions. The literature on mammals may not provide supporting evidence for classic metapopulation dynamics, which call for the availability of discrete habitat patches, asynchrony in local population dynamics, evidence for extinction and colonization processes, and dispersal between local populations.
• 2 Empirical evidence for metapopulation structure among mammals may exist when applying more lenient criteria. To meet these criteria, mammals should live in landscapes as discrete local breeding populations, and their demography should be asynchronous.
• 3 We examined the literature for empirical evidence in support of the classical criteria set by Hanski (1999 ), and for the more lenient subset of criteria proposed by Elmhagen & Angerbjörn (2001 ). We suggest circumstances where metapopulation theory could be important in understanding population processes in mammals of different body sizes.
• 4 The patchy distribution of large (>100 kg) mammals and dispersal often motivate inferences in support of a metapopulation structure. Published studies seldom address the full suite of classical criteria. However, studies on small mammals are more likely to record classic metapopulation criteria than those on large mammals. The slow turnover rate that is typical for medium‐sized and large mammals apparently makes it difficult to identify a metapopulation structure during studies of short duration.
• 5 To identify a metapopulation structure, studies should combine the criteria set by Hanski (1999 ) and Elmhagen & Angerbjörn (2001 ). Mammals frequently live in fragmented landscapes, and processes involved in the maintenance of a metapopulation structure should be considered in conservation planning and management.

     

The maintenance of nucleocytoplasmic polymorphism in a metapopulation: the case of gynodioecy

In gynodioecious species, gender is generally determined by epistatic interactions between cytoplasmic and nuclear loci. However, theoretical studies suggest that, for a joint polymorphism at both cytoplasmic and nuclear loci to be maintained in a panmictic population, selection must act differently on the various genotypes that determine the same gender. Here we show that, in a metapopulation with local extinction and restricted gene flow, nucleocytoplasmic polymorphism can be maintained without these differences. We use deterministic simulations. We assume that gene flow occurred only at recolonization. Founder effects create genetic variance between populations in the metapopulation, and local population growth is faster when the local frequency of females is high. Group selection phenomena are involved in the maintenance of the joint polymorphism in the metapopulation. The frequency of females in the metapopulation at equilibrium is higher than in a panmictic population with the same genetic system. However, these conclusions hold only if nuclear alleles restoring male fertility are dominant.     

Harvesting in seasonal environments

Most harvest theory is based on an assumption of a constant or stochastic environment, yet most populations experience some form of environmental seasonality. Assuming that a population follows logistic growth we investigate harvesting in seasonal environments, focusing on maximum annual yield (M.A.Y.) and population persistence under five commonly used harvest strategies. We show that the optimal strategy depends dramatically on the intrinsic growth rate of population and the magnitude of seasonality. The ordered effectiveness of these alternative harvest strategies is given for different combinations of intrinsic growth rate and seasonality. Also, for piecewise continuous-time harvest strategies (i.e., open / closed harvest, and pulse harvest) harvest timing is of crucial importance to annual yield. Optimal timing for harvests coincides with maximal rate of decline in the seasonally fluctuating carrying capacity. For large intrinsic growth rate and small environmental variability several strategies (i.e., constant exploitation rate, linear exploitation rate, and time-dependent harvest) are so effective that M.A.Y. is very close to maximum sustainable yield (M.S.Y.). M.A.Y. of pulse harvest can be even larger than M.S.Y. because in seasonal environments population size varies substantially during the course of the year and how it varies relative to the carrying capacity is what determines the value relative to optimal harvest rate. However, for populations with small intrinsic growth rate but subject to large seasonality none of these strategies is particularly effective with M.A.Y. much lower than M.S.Y. Finding an optimal harvest strategy for this case and to explore harvesting in populations that follow other growth models (e.g., involving predation or age structure) will be an interesting but challenging problem.     

The genetic effective size of a metapopulation

The structure of a population over time, space and categories of social and sexual role governs its ability to retain genetic variation in the face of drift. A metapopulation is an extreme form of spatial structure in which loosely coupled local populations 'turnover', that is, suffer extinction followed by recolonization from elsewhere within the metapopulation. These local populations turn over with a characteristic half-life. Based on a simulation model that incorporates both realistic features of population ecology and population genetics, the ability of such a metapopulation to retain genetic variation, which may be defined as proportional to its so-called effective population size, denoted N_e(^meta), can be one to two orders of magnitude lower than the maximum total number of individuals in the system. N_e(meta) depends on the persistence time associated with longevity of local populations (the turnover half-life), the average number of local populations extant in the metapopulation and the gene flow between local populations. Habitat fragmentation, which can create a metapopulation from a formerly continuously distributed species, may have unappreciated large genetic consequences for species impacted by human development.     

Predation of experimental nests is linked to local population dynamics in a fragmented bird population

Artificial nest experiments (ANEs) are widely used to obtain proxies of natural nest predation for testing a variety of hypotheses, from those dealing with variation in life-history strategies to those assessing the effects of habitat fragmentation on the persistence of bird populations. However, their applicability to real-world scenarios has been criticized owing to the many potential biases in comparing predation rates of artificial and natural nests. Here, we aimed to test the validity of estimates of ANEs using a novel approach. We related predation rates on artificial nests to population viability analyses in a songbird metapopulation as a way of predicting the real impact of predation events on the local populations studied. Predation intensity on artificial nests was negatively related to the species' annual population growth rate in small local populations, whereas the viability of large local populations did not seem to be influenced, even by high nest predation rates. The potential of extrapolation from ANEs to real-world scenarios is discussed, as these results suggest that artificial nest predation estimates may predict demographic processes in small structured populations.     

Allee-like effects in metapopulation dynamics

The existences of the Allee effect at the local population level and of the Allee-like effect at the metapopulation level are important for both ecology and conservation. Although there have been a great many papers on the Allee effect, they have mainly referred to only local populations and have not dealt with the relationship between the two. In this paper, we begin with local population dynamics and then construct a model including both local population and metapopulation dynamics. Then we simulate with computer at these two levels. The results indicate that the Allee-like effect in a metapopulation may emerge from the imposed Allee effect at the local population level. This threshold fraction of occupied patches below which the metapopulation goes extinct is seriously affected by the per capita migration rate, the survival rate during migration and the initial population size on the occupied patches. We also find that severe demographic stochasticity may compound the metapopulation extinction risk posed by the Allee effect. These conclusions are helpful for nature conservation, especially for the preservation of rare species.     

Do invasive species undergo metapopulation dynamics? A case study of the invasive Caspian gull,Larus cachinnans,in Poland

Aim The mechanisms of initial dispersal and habitat occupancy by invasive alien species are fundamental ecological problems. Most tests of metapopulation theory are performed on local population systems that are stable or in decline. In the current study we were interested in the usefulness of metapopulation theory to study patch occupancy, local colonization, extinction and the abundance of the invasive Caspian gull (Larus cachinnans) in its initial invasion stages. Location Waterbodies in Poland. Methods Characteristics of the habitat patches (waterbodies, 35 in total) occupied by breeding pairs of Caspian gulls and an equal sample of randomly selected unoccupied patches were compared with t‐tests. Based on presence–absence data from 1989 to 2006 we analysed factors affecting the probability of local colonization, extinction and the size of local populations using generalized linear models. Results Occupied habitat patches were significantly larger and less isolated (from other habitat patches and other local populations) and were located closer to rivers than empty patches. The proximity of local food resources (fish ponds, refuse dumps) positively affected the occurrence of breeding pairs. The probability of colonization was positively affected by patch area, and negatively by distances to fish ponds, nearest habitat patch, nearest breeding colony and to a river, and by higher forest cover around the patch boundaries. The probability of extinction was lower in patches with a higher number of breeding pairs and with a greater area of islets. The extinction probability increased with distances to other local populations, other habitat patches, fish ponds and to refuse dumps and with a higher cover of forest around the patch boundaries. The size of the local population decreased with distances to the nearest habitat patch, local population, river, fish pond and refuse dump. Local abundance was also positively affected by the area of islets in the patch. Main conclusions During the initial stages of the invasion of Caspian gulls in Poland the species underwent metapopulation‐like dynamics with frequent extinctions from colonized habitat patches. The results prove that metapopulation theory may be a useful conceptual framework for predicting which habitats are more vulnerable to invasion.     

Metapopulation dynamics for spatially extended predator–prey interactions

Traditional metapopulation theory classifies a metapopulation as a spatially homogeneous population that persists on neighboring habitat patches. The fate of each population on a habitat patch is a function of a balance between births and deaths via establishment of new populations through migration to neighboring patches. In this study, we expand upon traditional metapopulation models by incorporating spatial heterogeneity into a previously studied two-patch nonlinear ordinary differential equation metapopulation model, in which the growth of a general prey species is logistic and growth of a general predator species displays a Holling type II functional response. The model described in this work assumes that migration by generalist predator and prey populations between habitat patches occurs via a migratory corridor. Thus, persistence of species is a function of local population dynamics and migration between spatially heterogeneous habitat patches. Numerical results generated by our model demonstrate that population densities exhibit periodic plane-wave phenomena, which appear to be functions of differences in migration rates between generalist predator and prey populations. We compare results generated from our model to results generated by similar, but less ecologically realistic work, and to observed population dynamics in natural metapopulations.     

Linking extinction-colonization dynamics to genetic structure in a salamander metapopulation

Theory predicts that founder effects have a primary role in determining metapopulation genetic structure. However, ecological factors that affect extinction-colonization dynamics may also create spatial variation in the strength of genetic drift and migration. We tested the hypothesis that ecological factors underlying extinction-colonization dynamics influenced the genetic structure of a tiger salamander (Ambystoma tigrinum) metapopulation. We used empirical data on metapopulation dynamics to make a priori predictions about the effects of population age and ecological factors on genetic diversity and divergence among 41 populations. Metapopulation dynamics of A. tigrinum depended on wetland area, connectivity and presence of predatory fish. We found that newly colonized populations were more genetically differentiated than established populations, suggesting that founder effects influenced genetic structure. However, ecological drivers of metapopulation dynamics were more important than age in predicting genetic structure. Consistent with demographic predictions from metapopulation theory, genetic diversity and divergence depended on wetland area and connectivity. Divergence was greatest in small, isolated wetlands where genetic diversity was low. Our results show that ecological factors underlying metapopulation dynamics can be key determinants of spatial genetic structure, and that habitat area and isolation may mediate the contributions of drift and migration to divergence and evolution in local populations.     

Population differentiation and gene flow within a metapopulation of a threatened tree, Magnolia stellata (Magnoliaceae)

We examined genetic differentiation among eight local populations of a metapopulation of Magnolia stellata using 10 nuclear and three chloroplast microsatellite (nSSR and cpSSR) markers and evaluated the influence of historical gene flow on population differentiation. The coefficient of genetic differentiation among populations for nSSR (F(ST) = 0.053) was less than half that for cpSSR (0.137). An isolation-by-distance pattern was detected for nSSRs, but not cpSSRs. These results suggest that pollen flow, as well as seed dispersal, has significantly reduced genetic differentiation among populations. We also examined patterns of contemporary pollen flow by paternity analysis of seeds from nine seed parents in one of the populations using the nSSR markers and found it to be greatly restricted by the distance between parents. Although most pollen flow occurred within the population, pollen flow from outside the population accounted for 2.5% of the total. When historical and contemporary pollen flows among populations were compared, the levels of pollen flow seem to have declined recently. We conclude that to conserve M. stellata, it is important to preserve the whole population by maintaining its metapopulation structure and the gene flow among its populations.     

Capercaillie in the Alps: genetic evidence of metapopulation structure and population decline

In the Alps, the capercaillie is distributed in a metapopulation pattern with local populations on mountain ranges separated by farmland valleys. Habitat deterioration, primarily related to human land use, resulted in population declines and range contractions became obvious. At the edge of a species' range, lower connectivity and less gene flow may render populations more susceptible to decline and extinction than in the core of the range. If this were true for the capercaillie in the Alps, edge populations should be subject to limited gene flow and should show genetic signs of a more severe population decline than core populations. To test this hypothesis, we used microsatellite DNA typing techniques. We assessed genetic variation within and among 18 local capercaillie populations across the Alps in relation to geographical distribution within the metapopulation system. All populations showed high levels of genetic variation in terms of average number of alleles, allelic richness and heterozygosity. Excess heterozygosity suggested a recent population decline, that was more pronounced in edge than core populations. We found high gene flow, but also significant differentiation among populations. Differentiation among edge populations was related to geographical distance, and appeared to be a recent process, most probably caused by reduced gene flow after population decline. In the core group, the high mountains of the central Alps seem to limit dispersal, and genetic drift was the most likely explanation for the observed differentiation among populations. We conclude that maintaining connectivity within the metapopulation system is vital for capercaillie conservation in the Alps.     

Adaptive dispersal strategies and the dynamics of a range expansion

In species undergoing range expansion, newly established populations are often more dispersive than older populations. Because dispersal phenotypes are complex and often costly, it is unclear how highly dispersive phenotypes are maintained in a species to enable their rapid expression during periods of range expansion. Here I test the idea that metapopulation dynamics of local extinction and recolonization maintain distinct dispersal strategies outside the context of range expansion. Western bluebirds display distinct dispersal phenotypes where aggressive males are more dispersive than nonaggressive males, resulting in highly aggressive populations at the edge of their expanding range. I experimentally created new habitat interior to the range edge to show that, as on the range front, it was colonized solely by aggressive males. Moreover, fitness consequences of aggression depended on population age: aggressive males had high fitness when colonizing new populations, while nonaggressive males performed best in an older population. These results suggest that distinct dispersal strategies were maintained before range expansion as an adaptation for the continual recolonization of new habitat. These results emphasize similarities between range expansion and metapopulation dynamics and suggest that preexisting adaptive dispersal strategies may explain rapid changes in dispersal phenotypes during range expansion.     

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