Single-species metapopulation dynamics: concepts, models and observations

This paper outlines a conceptual and theoretical framework for single-species metapopulation dynamics based on the Levins model and its variants. The significance of the following factors to metapopulation dynamics are explored: evolutionary changes in colonization ability; habitat patch size and isolation; compensatory effects between colonization and extinction rates; the effect of immigration on local dynamics (the rescue effect); and heterogeneity among habitat patches. The rescue effect may lead to alternative stable equilibria in metapopulation dynamics. Heterogeneity among habitat patches may give rise to a bimodal equilibrium distribution of the fraction of patches occupied in an assemblage of species (the core-satellite distribution). A new model of incidence functions is described, which allows one to estimate species' colonization and extinction rates on islands colonized from mainland. Four distinct kinds of stochasticity affecting metapopulation dynamics are discussed with examples. The concluding section describes four possible scenarios of metapopulation extinction.     

Asynchronization of local population dynamics and persistence of a metapopulation: a lesson from an endangered composite plant, Aster kantoensis

Fragmentation of a large habitat makes local populations less linked to others, and a whole population structure changes to a metapopulation. The smaller a local population is, the more strengthened extinction factors become. Then, frequent extinctions of local populations threaten persistence of the metapopulation unless recolonizations occur rapidly enough after local extinctions. Spatially structured models have been more widely used for predicting future population dynamics and for assessing the extinction risk of a metapopulation. In this article, we first review such spatially structured models that have been applied to conservation biology, focusing on effects of asynchronization among local population dynamics on persistence of the whole metapopulation. Second, we introduce our ongoing project on extinction risk assessment of an endangered composite biennial plant, Aster kantoensis, in the riverside habitat, based on a lattice model for describing its spatiotemporal population dynamics. The model predicted that the extinction risk of A. kantoensis depends on both the frequency of flood occurrence and the time to coverage of a local habitat by other competitively stronger perennials. Finally, we present a measure (Hassell and Pacala's CV ²) for quantifying the effect of asynchronization among local population dynamics on the persistence of a whole metapopulation in conservation ecology. Received: January 12, 2000 / Accepted: February 8, 2000     

Habitat shape, metapopulation processes and the dynamics of multispecies predator-prey interactions

1. The effects of habitat shape, connectivity and the metapopulation processes of persistence and extinction are explored in a multispecies resource-consumer interaction. 2. The spatial dynamics of the indirect interaction between two prey species (Callosobruchus chinensis, Callosobruchus maculatus) and a predator (Anisopteromalus calandrae) are investigated and we show how the persistence time of this interaction is altered in different habitat configurations by the presence of an apparent competitor. 3. Habitat structure has differential effects on the dynamics of the resource-consumer interaction. Across all habitat types, the pairwise interaction between C. chinensis and A. calandrae is highly prone to extinction, while the interaction between C. maculatus and A. calandrae shows sustained long-term fluctuations. Contrary to expectations from theory, habitat shape has no significant effect on persistence time of the full, three-species resource-consumer assemblage. 4. A stochastic metapopulation model for a range of habitat configurations, incorporating different forms of regulatory processes, highlights that it is the spatially explicit population dynamics rather than the shape of the metapopulation that is the principal determinant of interaction persistence time.     

生境破坏的模式对集合种群动态和续存的影响

构建了空间关联的集合种群模型,该模型不但包含了种群的空间结构信息,而且引入了破坏生境的全局密度和局部密度两个指标,它们描述了破坏生境的模式.模型揭示了破坏生境的空间分布格局复杂地影响了集合种群的动态和续存,破坏和未破坏生境斑块的均匀混合不利于集合种群的增长和续存,而生境类型聚集分布可以促进集合种群的快速增长和长期续存;对于两种斑块类型相对均匀混合的生境来说,均匀场假设可能会高估集合种群的续存,对于相对斑块类型高度聚集的生境,均匀场假设可能会低估集合种群的续存;物种的迁移范围也会影响集合种群的续存,迁移范围越大的物种越容易抵御生境的破坏而免遭灭绝.这意味着在生物保护中不能仅仅考虑生境的恢复和斑块质量的改善,生境结构的构建也是很重要的,加强生境斑块之间的连通性也有利于物种的长期续存.     

Dances with fire: Tracking metapopulation dynamics of<Emphasis Type="Italic">polygonella basiramia</Emphasis> in Florida scrub (USA)

The regional persistence of species subject to local population colonization and extinction necessarily depends on how landscape features and disturbance affect metapopulation dynamics. Here, we characterize the metapopulation structure and short-term dynamics ofPolygonella basiramia. This rare, short-lived perennial herb is endemic to Florida scrublands and lacks a seed bank. Fires create the open sand gaps within a shrub matrix that support this species but also kill established plants. Thus, persistence depends on frequent colonization of unoccupied gaps. We are monitoring population dynamics within and among 1204 gaps distributed among 19 shrub patches. Considerable subpopulation turnover is evident at the gap level with rates of gap extinction exceeding rates of colonization in the first year. Whether declines in overall abundance continue is likely to depend on patterns of disturbance and regional stochasticity in this dynamic landscape.Polygonella is more likely to occupy larger and less isolated gaps, demonstrating that landscape features and disturbance strongly affect metapopulation dynamics. BecausePolygonella basiramia displays characteristics, occupancy patterns, and turnover dynamics consistent with metapopulation theory, it represents a model system for studying plant metapopulations.     

Rules of thumb for conservation of metapopulations based on a stochastic winking-patch model

From a theoretical viewpoint, nature management basically has two options to prolong metapopulation persistence: decreasing local extinction probabilities and increasing colonization probabilities. This article focuses on those options with a stochastic, single-species metapopulation model. We found that for most combinations of local extinction probabilities and colonization probabilities, decreasing the former increases metapopulation extinction time more than does increasing the latter by the same amount. Only for relatively low colonization probabilities is an effort to increase these probabilities more beneficial, but even then, decreasing extinction probabilities does not seem much less effective. Furthermore, we found the following rules of thumb. First, if one focuses on extinction, one should preferably decrease the lowest local extinction probability. Only if the extinction probabilities are (almost) equal should one prioritize decreases in the local extinction probability of the patch with the best direct connections to and from other patches. Second, if one focuses on colonization, one should preferably increase the colonization probability between the patches with the lowest local extinction probability. Only if the local extinction probabilities are (almost) equal should one instead prioritize increases in the highest colonization probability (unless extinction probabilities and colonization probabilities are very low). The rules of thumb have an important common denominator: the local extinction process has a greater bearing on metapopulation extinction time than colonization.     

Environment,but not migration rate,influences extinction risk in experimental metapopulations

Ecological theory suggests that several demographic factors influence metapopulation extinction risk, including synchrony in population size between subpopulations, metapopulation size and the magnitude of fluctuations in population size. Theoretically, each of these is influenced by the rate of migration between subpopulations. Here we report on an experiment where we manipulated migration rate within metapopulations of the freshwater zooplankton Daphnia magna to examine how migration influenced each of these demographic variables, and subsequent effects on metapopulation extinction. In addition, our experimental procedures introduced unplanned but controlled differences between metapopulations in light intensity, enabling us to examine the relative influences of environmental and demographic factors. We found that increasing migration rate increased subpopulation synchrony. We failed to detect effects of migration on population size and fluctuations in population size at the metapopulation or subpopulation level, however. In contrast, light intensity did not influence synchrony, but was positively correlated with population size and negatively correlated with population fluctuation. Finally, synchrony did not influence time to extinction, while population size and the magnitude of fluctuations did. We conclude that environmental factors had a greater influence on extinction risk than demographic factors, and that metapopulation size and fluctuation were more important to extinction risk than metapopulation synchrony.     

Generalizing Levins metapopulation model in explicit space: models of intermediate complexity

A recent study [Harding and McNamara, 2002. A unifying framework for metapopulation dynamics. Am. Nat. 160, 173-185] presented a unifying framework for the classic Levins metapopulation model by incorporating several realistic biological processes, such as the Allee effect, the Rescue effect and the Anti-rescue effect, via appropriate modifications of the two basic functions of colonization and extinction rates. Here we embed these model extensions on a spatially explicit framework. We consider population dynamics on a regular grid, each site of which represents a patch that is either occupied or empty, and with spatial coupling by neighborhood dispersal. While broad qualitative similarities exist between the spatially explicit models and their spatially implicit (mean-field) counterparts, there are also important differences that result from the details of local processes. Because of localized dispersal, spatial correlation develops among the dynamics of neighboring populations that decays with distance between patches. The extent of this correlation at equilibrium differs among the metapopulation types, depending on which processes prevail in the colonization and extinction dynamics. These differences among dynamical processes become manifest in the spatial pattern and distribution of “clusters” of occupied patches. Moreover, metapopulation dynamics along a smooth gradient of habitat availability show significant differences in the spatial pattern at the range limit. The relevance of these results to the dynamics of disease spread in metapopulations is discussed.     

Allee效应对具有生境恢复的集合种群的影响

Allee效应与种群的灭绝密切相关,其研究对生态保护和管理至关重要。Allee效应对物种续存是潜在的干扰因素,濒危物种更容易受其影响,可能会增加生存于生境破碎化斑块的濒危物种的死亡风险,因此研究Allee效应对种群的动态和续存的影响是必要的。从包含由生物有机体对环境的修复产生的Allee效应的集合种群模型出发,引入由其他机制形成的Allee效应,建立了常微分动力系统模型和基于网格模型的元胞自动机模型。通过理论分析和计算机模拟表明:(1)强Allee效应不利于具有生境恢复的集合种群的续存;(2)生境恢复有利于种群续存;(3)局部扩散影响了集合种群的空间结构、动态行为和稳定性,生境斑块之间的局部作用将会减缓或消除集合种群的Allee效应,有利于集合种群的续存。     

Approximate Bayesian estimation of extinction rate in the Finnish Daphnia magna metapopulation

Approximate Bayesian computation (ABC) is useful for parameterizing complex models in population genetics. In this study, ABC was applied to simultaneously estimate parameter values for a model of metapopulation coalescence and test two alternatives to a strict metapopulation model in the well‐studied network of Daphnia magna populations in Finland. The models shared four free parameters: the subpopulation genetic diversity (θ_S), the rate of gene flow among patches (4Nm), the founding population size (N₀) and the metapopulation extinction rate (e) but differed in the distribution of extinction rates across habitat patches in the system. The three models had either a constant extinction rate in all populations (strict metapopulation), one population that was protected from local extinction (i.e. a persistent source), or habitat‐specific extinction rates drawn from a distribution with specified mean and variance. Our model selection analysis favoured the model including a persistent source population over the two alternative models. Of the closest 750 000 data sets in Euclidean space, 78% were simulated under the persistent source model (estimated posterior probability = 0.769). This fraction increased to more than 85% when only the closest 150 000 data sets were considered (estimated posterior probability = 0.774). Approximate Bayesian computation was then used to estimate parameter values that might produce the observed set of summary statistics. Our analysis provided posterior distributions for e that included the point estimate obtained from previous data from the Finnish D. magna metapopulation. Our results support the use of ABC and population genetic data for testing the strict metapopulation model and parameterizing complex models of demography.     

THE MAINTENANCE OF GYNODIOECY AND ANDRODIOECY IN A METAPOPULATION

Males and females are at a selective disadvantage relative to hermaphrodites (cosexuals) in species with a colonizing habit, as only cosexuals are able to establish new colonies on their own. The implications of this disadvantage are assessed by means of a computer model of metapopulation dynamics, in which individual colonies are established through different rates of immigration and suffer different rates of local extinction. Results are given for simulations of an island model, a stepping-stone model, and for a partial analysis of the island model with simplifying assumptions. It is shown that: (1) unisexual frequencies in a metapopulation can be reasonably approximated by a linear function of the logarithm of the ratio of the immigration rate to the colony extinction rate; (2) metapopulation dynamics favor the maintenance of females (gynodioecy) over males (androdioecy) with cosexuals when they would otherwise be equally likely in a panmictic situation; (3) the way in which extinction and immigration rates affect unisexual frequencies at metapopulation equilibrium interacts with whether sterility is determined by a dominant or a recessive allele; and (4) unisexual frequencies are affected in a qualitatively similar way by the dynamics of a metapopulation when cosexuals are self-incompatible to when they are self-compatible, although only in the former case are high frequencies of unisexuals maintained when extinction and colonization rates approach the threshold at which the metapopulation goes extinct. These results are discussed with reference to existing data from species with nuclear male or female sterility.     

The role of landscape-dependent disturbance and dispersal in metapopulation persistence

The fundamental processes that influence metapopulation dynamics (extinction and recolonization) will often depend on landscape structure. Disturbances that increase patch extinction rates will frequently be landscape dependent such that they are spatially aggregated and have an increased likelihood of occurring in some areas. Similarly, landscape structure can influence organism movement, producing asymmetric dispersal between patches. Using a stochastic, spatially explicit model, we examine how landscape-dependent correlations between dispersal and disturbance rates influence metapopulation dynamics. Habitat patches that are situated in areas where the likelihood of disturbance is low will experience lower extinction rates and will function as partial refuges. We discovered that the presence of partial refuges increases metapopulation viability and that the value of partial refuges was contingent on whether dispersal was also landscape dependent. Somewhat counterintuitively, metapopulation viability was reduced when individuals had a preponderance to disperse away from refuges and was highest when there was biased dispersal toward refuges. Our work demonstrates that landscape structure needs to be incorporated into metapopulation models when there is either empirical data or ecological rationale for extinction and/or dispersal rates being landscape dependent.     

Metapopulation models for historical inference

The genealogical process for a sample from a metapopulation, in which local populations are connected by migration and can undergo extinction and subsequent recolonization, is shown to have a relatively simple structure in the limit as the number of populations in the metapopulation approaches infinity. The result, which is an approximation to the ancestral behaviour of samples from a metapopulation with a large number of populations, is the same as that previously described for other metapopulation models, namely that the genealogical process is closely related to Kingman's unstructured coalescent. The present work considers a more general class of models that includes two kinds of extinction and recolonization, and the possibility that gamete production precedes extinction. In addition, following other recent work, this result for a metapopulation divided into many populations is shown to hold both for finite population sizes and in the usual diffusion limit, which assumes that population sizes are large. Examples illustrate when the usual diffusion limit is appropriate and when it is not. Some shortcomings and extensions of the model are considered, and the relevance of such models to understanding human history is discussed.     

Colonization and extinction dynamics of an annual plant metapopulation in an urban environment

The metapopulation framework considers that the spatiotemporal distribution of organisms results from a balance between the colonization and extinction of populations in a suitable and discrete habitat network. Recent spatially realistic metapopulation models have allowed patch dynamics to be investigated in natural populations but such models have rarely been applied to plants. Using a simple urban fragmented population system in which favourable habitat can be easily mapped, we studied patch dynamics in the annual plant Crepis sancta (Asteraceae). Using stochastic patch occupancy models (SPOMs) and multi‐year occupancy data we dissected extinction and colonization patterns in our system. Overall, our data were consistent with two distinct metapopulation scenarios. A metapopulation (sensu stricto) dynamic in which colonization occurs over a short distance and extinction is lowered by nearby occupied patches (rescue effect) was found in a set of patches close to the city centre, while a propagule rain model in which colonization occurs from a large external population was most consistent with data from other networks. Overall, the study highlights the importance of external seed sources in urban patch dynamics. Our analysis emphasizes the fact that plant distributions are governed not only by habitat properties but also by the intrinsic properties of colonization and dispersal of species. The metapopulation approach provides a valuable tool for understanding how colonization and extinction shape occupancy patterns in highly fragmented plant populations. Finally, this study points to the potential utility of more complex plant metapopulation models than traditionally used for analysing ecological and evolutionary processes in natural metapopulations.     

生境丧失对具有似Allee效应集合种群的影响及对策——以江苏盐城为例

似Allee效应对物种续存是潜在的扰动因素,稀有物种更易受其影响,可能增加生存于破碎化栖息地中的珍稀物种的死亡风险;但似Allee效应对多物种集合种群续存的影响及其在珍稀物种保护中的应用未能引起足够重视。将似Allee效应引入集合种群动力模式,建立了生境丧失下具有似Allee效应的n-珍稀物种的集合种群模式,并以江苏盐城滩涂湿地中的29种珍稀物种为研究实例。研究结果表明:(1)似Allee效应导致n-物种集合种群多度作长期变周期振荡,原本竞争共存物种可能无法继续共存,甚至灭绝。(2)似Allee效应增强对次强种及劣势种的生存极为不利,导致次强物种由强至弱灭绝,劣势物种由弱至强依次灭绝。(3)盐城天然湿地丧失29%后,11种劣势物种的集合种群由弱到强将最终依次灭绝,灭绝迟豫时间为304～890a,这些物种即Hanski所指的"活死者"。(4)适度增加栖息地面积是保护珍稀物种多样性的有效方法之一,在盐城现存3200km2的天然湿地基础上适度增加1801～2064km2左右栖息地面积,可以有效保护29种濒危物种的多样性,同时应注意结合针对具体物种的保护措施来提高濒危物种多度。研究结果对物种多样性保护及自然保护区建设具有重要的理论指导意义。     

Evolution of complex life cycles of amphibians: bridging the gap between metapopulation dynamics and life history evolution

Current evolutionary models for amphibian life cycles reflect tradeoffs in size-specific growth and mortality rates between the aquatic and terrestrial stages. A limitation of these models is that they do not incorporate evolutionary phenomena that are associated with metapopulation structure. In this work I address components of the evolution of complex life cycles (CLCs) that are tied to the metapopulation dynamics of amphibians that use seasonal wetlands that vary in hydroperiod. In particular, I describe how selection for the minimum length of the larval period affects metapopulation viability and the selection/migration equilibrium. Selection to increase the minimum length of the larval period functionally reduces the number of viable breeding sites on the landscape, increases the average distance between neighboring sites, and increases the risk of metapopulation extinction. Within a metapopulation, asymmetric gene flow between populations that are adapted to different hydroperiods tends to swamp local selection for long larval periods at sites with long hydroperiods. The evolutionary stability of CLCs of many species with metapopulation structure may reflect the fact that extremely small metamorphs cannot survive on land, while lineages with long larval periods incur a high risk of metapopulation extinction. I encourage theorists to more carefully consider how life history traits and metapopulation viability are related for these and other taxa.     

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.     

Simple discrete-time metapopulation models of patch occupancy

Simple models in theoretical ecology have a long-standing history of being used to understand how specific processes influence population dynamics as well as providing a foundation for future endeavors. The Levins model is the seminal example of this for continuous-time metapopulation dynamics. However, many natural populations have a distinct separation between processes and data is not collected continuously leading to the need for using a discrete-time model. Our goal is to develop a simple discrete-time metapopulation model of patch occupancy using difference equations. In our formulation, we consider the two fundamental processes of colonization and extinction that will be treated as sequential events and will only consider patch occupancy. To achieve this, we use a composition of two functions where one will reflect the extinction process and the other for the colonization process. Under some mild assumptions, we are able determine the dynamic behavior of the metapopulation. In addition, we provide numerous examples for the functions used to emulate the colonization and extinction processes. Our results illustrate that the dynamics of the model are tied to properties such as convexity and monotonicity of the colonization and extinction functions. In particular, if the model is non-monotone, then complex dynamics can arise such as cyclic and even chaotic behavior. Overall, our approach shows how certain properties of the colonization and extinction functions can influence metapopulation dynamics.     

Metapopulation models for seasonally migratory animals

Metapopulation models are widely used to study species that occupy patchily distributed habitat, but are rarely applied to migratory species, because of the difficulty of identifying demographically independent subpopulations. Here, we extend metapopulation theory to describe the directed seasonal movement of migratory populations between two sets of habitat patches, breeding and non-breeding, with potentially different colonization and extinction rates between patch types. By extending the classic metapopulation model, we show that migratory metapopulations will persist if the product of the two colonization rates exceeds the product of extinction rates. Further, we develop a spatially realistic migratory metapopulation model and derive a landscape metric-the migratory metapopulation capacity-that determines persistence. This new extension to metapopulation theory introduces an important tool for the management and conservation of migratory species and may also be applicable to model the dynamics of two host-parasite systems.