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.     

Finite metapopulation models with density-dependent migration and stochastic local dynamics

The effects of small density-dependent migration on the dynamics of a metapopulation are studied in a model with stochastic local dynamics. We use a diffusion approximation to study how changes in the migration rate and habitat occupancy affect the rates of local colonization and extinction. If the emigration rate increases or if the immigration rate decreases with local population size, a positive expected rate of change in habitat occupancy is found for a greater range of habitat occupancies than when the migration is density-independent. In contrast, the reverse patterns of density dependence in respective emigration and immigration reduce the range of habitat occupancies where the metapopulation will be viable. This occurs because density-dependent migration strongly influences both the establishment and rescue effects in the local dynamics of metapopulations.     

Testing metapopulation dynamics using genetic, demographic and ecological data

The metapopulation concept is a cornerstone in the recent history of ecology and evolution. However, determining whether a natural system fits a metapopulation model is a complex issue. Extinction-colonization dynamics are indeed often difficult to quantify because species detectability is not always 100%, resulting in an imperfect record of extinctions. Here, we explore whether combining population genetics with demographic and ecological surveys can yield more realistic estimates of metapopulation dynamics. We apply this approach to the freshwater snail Drepanotrema depressissimum in a fragmented landscape of tropical ponds. In addition to studying correlations between genetic diversity and demographical or ecological characteristics, we undertake, for the first time, a detailed search for genetic signatures of extinction-recolonization events using temporal changes in allele frequencies within sites. Surprisingly, genetic data indicate that extinction is much rarer than suggested by demographic surveys. Consequently, this system is better described as a set of populations with different sizes and immigration rates than as a true metapopulation. We identify several cases of apparent extinction owing to nondetection of low-density populations, and of aestivating individuals in desiccated ponds. More generally, we observed a frequent mismatch between genetic and demographical/ecological information at small spatial and temporal scales. We discuss the causes of these discrepancies and show how these two types of data provide complementary information on population dynamics and history, especially when temporal genetic samples are available.     

THE CONSEQUENCES OF DIOECY FOR SEED DISPERSAL: MODELING THE SEED-SHADOW HANDICAP

Abstract.— Recent evidence has suggested that clades of dioecious angiosperms have fewer extant species on average than those of cosexual (hermaphroditic and monoecious) relatives. Reasons for the decrease in speciation rates and/or increase in extinction rates are only beginning to be investigated. One possibility is that dioecious species suffer a competitive disadvantage with cosexuals because only half of the individuals in a dioecious population are seed bearing. When only females produce seed, offspring will be more spatially clumped and will experience more local resource competition than when every individual produces seed. We examine two spatially explicit models to determine the effect of a reduction in seed dispersers on the invasibility and persistence of dioecious populations. Even though dioecious females were allowed to produce twice as many seeds as cosexuals, our results show that a reduction in the number of seed dispersers causes a decrease in the ability of dioecious progeny to find uninhabited sites, thus reducing persistence times. These results suggest that the maintenance of dioecy in the presence of hermaphroditic competitors requires a substantial increase in relative fitness and/or a large dispersal advantage of dioecious seeds.     

Estimating rates of local extinction and colonization in colonial species and an extension to the metapopulation and community levels

Coloniality has mainly been studied from an evolutionary perspective, but relatively few studies have developed methods for modelling colony dynamics. Changes in number of colonies over time provide a useful tool for predicting and evaluating the responses of colonial species to management and to environmental disturbance. Probabilistic Markov process models have been recently used to estimate colony site dynamics using presence–absence data when all colonies are detected in sampling efforts. Here, we define and develop two general approaches for the modelling and analysis of colony dynamics for sampling situations in which all colonies are, and are not, detected. For both approaches, we develop a general probabilistic model for the data and then constrain model parameters based on various hypotheses about colony dynamics. We use Akaike's Information Criterion (AIC) to assess the adequacy of the constrained models. The models are parameterised with conditional probabilities of local colony site extinction and colonization. Presence–absence data arising from Pollock's robust capture–recapture design provide the basis for obtaining unbiased estimates of extinction, colonization, and detection probabilities when not all colonies are detected. This second approach should be particularly useful in situations where detection probabilities are heterogeneous among colony sites. The general methodology is illustrated using presence–absence data on two species of herons. Estimates of the extinction and colonization rates showed interspecific differences and strong temporal and spatial variations. We were also able to test specific predictions about colony dynamics based on ideas about habitat change and metapopulation dynamics. We recommend estimators based on probabilistic modelling for future work on colony dynamics. We also believe that this methodological framework has wide application to problems in animal ecology concerning metapopulation and community dynamics.     

Interspecific competition in metapopulations

The assumptions and predictions of metapopulation models for competing species are discussed in relation to empirical studies of colonization and extinction in metapopulations. In three species of Daphnia in rockpools, interspecific competition increased local extinction rates, while no effects on colonization rates were detected. Distributional patterns were consistent with several predictions of the competition model; for example, the number of species on an island increased with the number of pools and the proportion of pools occupied by each species decreased with increasing species number. It is concluded that interspecific competition is important for the distributional dynamics of Daphnia species in rockpools, but the question whether the coexistence of these species depends on metapopulation dynamics is still unresolved. Other studies on the effects of interspecific competition on colonization and extinction rates are discussed.     

Climate, social factors and research disturbance influence population dynamics in a declining sociable weaver metapopulation

Population trends are determined by gains through reproduction and immigration, and losses through mortality and emigration. These demographic quantities and resulting population dynamics are affected by different external and internal drivers. We examined how these demographic quantities were affected by weather, research-induced disturbance, local density, colony site and year in a metapopulation of 17 sociable weaver (Philetairus socius) colonies over 17 years of study (4 years for reproduction). Most colonies declined, but at different rates. The four demographic quantities were related to different drivers. Survival strongly varied among years and colonies and was positively related to rainfall and negatively related to extreme temperature (together explaining 30 % of variation) and disturbance (measured as number of captures conducted at a colony; 7 %). There was a trend for a positive relationship between reproduction and rainfall (50 %). Movement was mainly related to local density: individuals were more likely to emigrate from small to large colonies and from colonies that were either well below or above their long-term mean. They were more likely to immigrate into colonies that were nearby, and below their mean size. We then quantified the effects of these relationships on metapopulation dynamics using a multi-site matrix projection model. Rainfall was potentially a strong driver of metapopulation dynamics. In addition, field-work disturbance might have contributed to the decline of this metapopulation but could not explain its full magnitude. Hence, through a combination of analytical methods we were able to obtain information on the main drivers affecting dynamics in a declining metapopulation.     

The Effective Size of a Subdivided Population

This paper derives the long-term effective size, N(e), for a general model of population subdivision, allowing for differential deme fitness, variable emigration and immigration rates, extinction, colonization, and correlations across generations in these processes. We show that various long-term measures of N(e) are equivalent. The effective size of a metapopulation can be expressed in a variety of ways. At a demographic equilibrium, N(e) can be derived from the demography by combining information about the ultimate contribution of each deme to the future genetic make-up of the population and Wright's F(ST)'s. The effective size is given by N(e) = 1/(1 + var ( &))<(1 - f(STi))/N(i)n>, where n is the number of demes, &(i) is the eventual contribution of individuals in deme i to the whole population (scaled such that σ(i) &(i) = n), and < > denotes an average weighted by &(i)(2). This formula is applied to a catastrophic extinction model (where sites are either empty or at carrying capacity) and to a metapopulation model with explicit dynamics, where extinction is caused by demographic stochasticity and by chaos. Contrary to the expectation from the standard island model, the usual effect of population subdivision is to decrease the effective size relative to a panmictic population living on the same resource.     

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.     

Influential factors for natal dispersal in an avian island metapopulation

Dispersal is a key parameter in evolutionary, demographic and conservation theory, but the factors influencing dispersal between populations are rarely known, and the contribution of immigrants to population stability remains uncertain. Using dispersal data from nine island populations of song sparrows, we show that female and male immigrants responded differently to population structure: in females, immigration varied with adult sex ratio; whereas immigration by males was more influenced by population density. These patterns are consistent with the hypothesis that intra-sexual competition for breeding resources influenced recruitment patterns. Immigrants often constituted a substantial fraction of local population size, and in six cases immigration by females prevented the extirpation of that sex from the island. Breeding vacancies and extirpations may have been more likely in females because their apparent survival was lower than in males. Local recruitment and immigration varied markedly among islands, perhaps as consequence of island size and isolation. Overall, our results suggest that immigration varied with local demography in a sex-specific way, stabilized population numbers and reduced extinction rates in the smallest populations.     

物种保护的理论基础——从岛屿生物地理学理论到集合种群理论

全球面临着生境破碎化的危机,物种保护已成为人类面临的重大课题,并不是所有的人对岛屿生物地理学理论的产生及其关注的海洋岛屿都很熟悉,但是越来越多生物赖以生存的自然栖息地的丧失和破碎化都是有目共睹的,岛屿生物地理学和集合种群理论是目前物种保护的两个基本理论,物种迁入率和绝灭率的动态变化决策岛屿上的物种丰富度是岛屿生物地理学理论的核心内容,而集合种群理论关注的是局部种群之间个体迁移的动态以及物种的续存条件,在概述两个理论形成、发展及其核心内容的基础上,着重比较它们的异同点以及在生态学理论和实践中的应用,并论述物种保护理论范式从岛屿生物地理学向集合种群理论转变的基本背景和原因。     

Patch quality and context, but not patch number, drive multi-scale colonization dynamics in experimental aquatic landscapes

Colonization and extinction are primary drivers of local population dynamics, community structure, and spatial patterns of biological diversity. Existing paradigms of island biogeography, metapopulation biology, and metacommunity ecology, as well as habitat management and conservation biology based on those paradigms, emphasize patch size, number, and isolation as primary characteristics influencing colonization and extinction. Habitat selection theory suggests that patch quality could rival size, number, and isolation in determining rates of colonization and resulting community structure. We used naturally colonized experimental landscapes to address four issues: (a) how do colonizing aquatic beetles respond to variation in patch number, (b) how do they respond to variation in patch quality, (c) does patch context affect colonization dynamics, and (d) at what spatial scales do beetles respond to habitat variation? Increasing patch number had no effect on per patch colonization rates, while patch quality and context were critical in determining colonization rates and resulting patterns of abundance and species richness at multiple spatial scales. We graphically illustrate how variation in immigration rates driven by perceived predation risk (habitat quality) can further modify dynamics of the equilibrium theory of island biogeography beyond predator-driven effects on extinction rates. Our data support the importance of patch quality and context as primary determinants of colonization rate, occupancy, abundance, and resulting patterns of species richness, and reinforce the idea that management of metapopulations for species preservation, and metacommunities for local and regional diversity, should incorporate habitat quality into the predictive equation.     

Lost and found: Short-term dynamics of the flora on 100 small islands in the White Sea

The aim was to uncover factors that influence short-term (decade) flora dynamics and species richness of northern marine islets characterized by poor flora and weak anthropogenic pressure. The study used presence–absence data of vascular plant species on 100 small uprising islets of the Kandalaksha Gulf of White Sea (Northern Karelia, Russia). We investigated the influence of islands' attributes on species richness and rates of flora dynamics. Two island types were analyzed separately: younger, stone-like and older, islet-like (which generally are larger and have higher diversity of habitats). Sampled islands were studied via classical biogeographical per island approach and metapopulation per species approach. Stone-like islands had noticeably poorer flora with higher rates of immigration and extinction when compared to those of islet-like islands. The species number for islet-like islands correlated positively with number of habitats, abundance of different habitat types and island area. Species richness of stone-like islands correlated positively only with number of habitat types. Plant species associated with birds, crowberry thickets and coastal rocks were the most stable, and the species of disturbed habitats were significantly less stable. Floristic changes that have occurred have been caused by the massive establishment of new species rather than the extinction of pre-existing taxa. Thus, most of these islands are still in the colonization (assortative) stage. While we found no relationship between island area and species number for stone-like islands, this relationship was seen on islet-like islands.     

Extinction dynamics in mainland-island metapopulations: an N-patch stochastic model

A generalization of the well-known Levins’ model of metapopulations is studied. The generalization consists of (i) the introduction of immigration from a mainland, and (ii) assuming the dynamics is stochastic, rather than deterministic. A master equation, for the probability that n of the patches are occupied, is derived and the stationary probability P _s (n), together with the mean and higher moments in the stationary state, determined. The time-dependence of the probability distribution is also studied: through a Gaussian approximation for general n when the boundary at n = 0 has little effect, and by calculating P(0, t), the probability that no patches are occupied at time t, by using a linearization procedure. These analytic calculations are supplemented by carrying out numerical solutions of the master equation and simulations of the stochastic process. The various approaches are in very good agreement with each other. This allows us to use the forms for P _s 0) and P(0, t) in the linearization approximation as a basis for calculating the mean time for a metapopulation to become extinct. We give an analytical expression for the mean time to extinction derived within a mean field approach. We devise a simple method to apply our mean field approach even to complex patch networks in realistic model metapopulations. After studying two spatially extended versions of this nonspatial metapopulation model—a lattice metapopulation model and a spatially realistic model—we conclude that our analytical formula for the mean extinction time is generally applicable to those metapopulations which are really endangered, where extinction dynamics dominates over local colonization processes. The time evolution and, in particular, the scope of our analytical results, are studied by comparing these different models with the analytical approach for various values of the parameters: the rates of immigration from the mainland, the rates of colonization and extinction, and the number of patches making up the metapopulation.     

Relative importance of landscape and species characteristics on extinction debt,immigration credit and relaxation time after habitat turnover

Habitat turnover concomitantly causes destruction and creation of habitat patches. Following such a perturbation, metapopulations harbor either an extinction debt or an immigration credit, that is the future decrease or increase in population numbers due to this disturbance. Extinction debt and immigration credit are rarely considered simultaneously and disentangled from the relaxation time (time to new equilibrium). In this contribution, we test the relative importance of two potential drivers of time-delayed metapopulation dynamics: the spatial configuration of the habitat turnover and species dispersal ability. We provide a simulation-based investigation projecting metapopulation dynamics following habitat turnover in virtual landscapes. We consider two virtual species (a short-distance and a long-distance disperser) and five scenarios of habitat turnover depending on net habitat loss or gain and habitat aggregation. Our analyses reveal that (a) the main determinant of the magnitude of the extinction debt or immigration credit is the net change in total habitat area, followed by species dispersal distance and finally by the post-turnover habitat aggregation; (b) relaxation time weakly depends on the magnitude of the immigration credit or of the extinction debt; (c) the main determinant of relaxation time is dispersal distance followed by the net change in total habitat area and finally by the post-turnover habitat aggregation. These results shed light on the relative importance of dispersal ability and habitat turnover spatial structure on the components of time-delayed metapopulation dynamics.     

The form of the curves: a direct evaluation of MacArthur & Wilson's classic theory

1. We calculate the yearly numbers of bird species immigrating to – and becoming extinct on – 13 small islands of the British Isles, using a long and relatively complete data record.
2. We estimate the size of the colonist pool for each island using four methods.
3. We assume that immigrations and extinctions are distributed binomially, and use a maximum likelihood method to fit concave immigration and extinction functions to the data, utilizing all four species pool estimates.
4. Extinction rates increase significantly and consistently with increasing numbers of breeding species on each island. For nine of the 13 islands the extinction functions are significantly concave.
5. Immigration rates decrease consistently with increasing numbers of breeding species on each island. Seven islands have significantly concave immigration functions.
6. Immigration rates and extinction rates decline consistently, but not significantly, with island distance and island size, respectively. The number of breeding species does not always reflect the number of species likely to have reached an island. Moreover, some species may choose not to breed when their chance of extinction is high. These factors, plus the modest range of island areas and distances in our database, reduce our chances of finding the theoretically predicted effects of area and distance on extinction and immigration rates.     

Eco-evolutionary dynamics of dispersal in spatially heterogeneous environments

Ecology Letters (2011) 14: 1025-1034 ABSTRACT: Evolutionary changes in natural populations are often so fast that the evolutionary dynamics may influence ecological population dynamics and vice versa. Here we construct an eco-evolutionary model for dispersal by combining a stochastic patch occupancy metapopulation model with a model for changes in the frequency of fast-dispersing individuals in local populations. We test the model using data on allelic variation in the gene phosphoglucose isomerase (Pgi), which is strongly associated with dispersal rate in the Glanville fritillary butterfly. Population-specific measures of immigration and extinction rates and the frequency of fast-dispersing individuals among the immigrants explained 40% of spatial variation in Pgi allele frequency among 97 local populations. The model clarifies the roles of founder events and gene flow in dispersal evolution and resolves a controversy in the literature about the consequences of habitat loss and fragmentation on the evolution of dispersal.     

How patch configuration affects the impact of disturbances on metapopulation persistence

Disturbances affect metapopulations directly through reductions in population size and indirectly through habitat modification. We consider how metapopulation persistence is affected by different disturbance regimes and the way in which disturbances spread, when metapopulations are compact or elongated, using a stochastic spatially explicit model which includes metapopulation and habitat dynamics. We discover that the risk of population extinction is larger for spatially aggregated disturbances than for spatially random disturbances. By changing the spatial configuration of the patches in the system--leading to different proportions of edge and interior patches--we demonstrate that the probability of metapopulation extinction is smaller when the metapopulation is more compact. Both of these results become more pronounced when colonization connectivity decreases. Our results have important management implication as edge patches, which are invariably considered to be less important, may play an important role as disturbance refugia.     

Metapopulation dynamics of a flightless alpine insect Hemideina maori in a naturally fragmented habitat

Abstract 1. Despite widespread acceptance of metapopulation theory, the effects that inter-patch dispersal and variability in patch size have on metapopulation dynamics in insects are two issues that require further study. In addition, previous studies of metapopulations have tended to focus on organisms with high dispersal capabilities such as some species of butterfly and bird.
2. Mountain stone weta Hemideina maori are a long-lived, flightless orthopteran that live on island rock outcrops or tors in the alpine region of southern New Zealand. A total of 480 adults and 789 juveniles was marked over three seasons on four large and 14 small tors to assess the effects of habitat fragmentation on the population dynamics of H. maori .
3. Only 12 adults (2.5% of marked adults and 4.0% of recaptured adults) and two juveniles (0.3% of marked juveniles and 0.7% of recaptured juveniles) dispersed between tors. The mean dispersal distance was 361 m (range = 36–672 m). Larger tors supported larger populations and had a higher number of emigrants and immigrants while smaller tors had proportionally higher emigration and immigration rates. Although adults on large and small tors had similar mean lifespans, five extinction events and three recolonisation events occurred during the study period, all on small tors.
4. Hemideina maori conform to many of the predictions of metapopulation theory even though they are flightless, show relatively low dispersal rates, and occur at low densities. Extinction and colonisation events are more common on small tors but may be relatively unimportant for the long-term survival of the metapopulation because they occur on the smallest habitat patches, which support the smallest proportion of the overall population.     

A spatially structured metapopulation model with patch dynamics

Metapopulation models that incorporate both spatial and temporal structure are studied in this paper. The existence and stability of equilibria are provided, and an extinction threshold condition is derived which depends on patch dynamics (patch destruction and creation) and metapopulation dynamics (patch colonization and extinction). These results refine threshold conditions given by previous metapopulation models. By comparing landscapes with different spatial heterogeneities with respect to weighted long-term patch occupancies, we conclude that the pattern of a landscape is of overwhelming importance in determining metapopulation persistence and patch occupancy. We show that the same conclusion holds when a rescue effect is considered. We also derive a stochastic differential equations (SDE) model of the It? type based on our deterministic model. Our simulations reveal good agreement between the deterministic model and the SDE model.