Niche models tell half the story: spatial context and life‐history traits influence species responses to global change

Aim While niche models are typically used to assess the vulnerability of species to climate change, they have been criticized for their limited assessment of threats other than climate change. We attempt to evaluate this limitation by combining niche models with life‐history models to investigate the relative influence of climate change and a range of fire regimes on the viability of a long‐lived plant population. Specifically, we investigate whether range shift due to climate change is a greater threat to an obligate seeding fire‐prone shrub than altered fire frequency and how these two threatening processes might interact. Location Australian sclerophyll woodland and heathland. Methods The study species is Leucopogon setiger, an obligate seeding fire‐prone shrub. A spatially explicit stochastic matrix model was constructed for this species and linked with a dynamic niche model and fire risk functions representing a suite of average fire return intervals. We compared scenarios with a variety of hypothetical patches, a patch framework based upon current habitat suitability and one with dynamic habitat suitability based on climate change scenarios A1FI and A2. Results Leucopogon setiger was found to be sensitive to fire frequency, with shorter intervals reducing expected minimum abundances (EMAs). Spatial decoupling of fires across the landscape reduced the vulnerability of the species to shortened fire frequencies. Shifting habitat, while reducing EMAs, was less of a threat to the species than frequent fire. Main conclusions Altered fire regime, in particular more frequent fires relative to the historical regime, was predicted to be a strong threat to this species, which may reflect a vulnerability of obligate seeders in general. Range shifts induced by climate change were a secondary threat when habitat reductions were predicted. Incorporating life‐history traits into habitat suitability models by linking species distribution models with population models allowed for the population‐level evaluation of multiple stressors that affect population dynamics and habitat, ultimately providing a greater understanding of the impacts of global change than would be gained by niche models alone. Further investigations of this type could elucidate how particular bioecological factors can affect certain types of species under global change.     

Viability analyses with habitat-based metapopulation models

Population viability analysis (PVA) models incorporate spatial dynamics in different ways. At one extreme are the occupancy models that are based on the number of occupied populations. The simplest occupancy models ignore the location of populations. At the other extreme are individual-based models, which describe the spatial structure with the location of each individual in the population, or the location of territories or home ranges. In between these are spatially structured metapopulation models that describe the dynamics of each population with structured demographic models and incorporate spatial dynamics by modeling dispersal and temporal correlation among populations. Both dispersal and correlation between each pair of populations depend on the location of the populations, making these models spatially structured. In this article, I describe a method that expands spatially structured metapopulation models by incorporating information about habitat relationships of the species and the characteristics of the landscape in which the metapopulation exists. This method uses a habitat suitability map to determine the spatial structure of the metapopulation, including the number, size, and location of habitat patches in which subpopulations of the metapopulation live. The habitat suitability map can be calculated in a number of different ways, including statistical analyses (such as logistic regression) that find the relationship between the occurrence (or, density) of the species and independent variables which describe its habitat requirements. The habitat suitability map is then used to calculate the spatial structure of the metapopulation, based on species-specific characteristics such as the home range size, dispersal distance, and minimum habitat suitability for reproduction. Received: April 1, 1999 / Accepted: October 29, 1999     

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.     

Dispersal-induced desynchronization: from metapopulations to metacommunities

The conceptualization of fragmented populations in terms of metapopulation theory has become standard over the last three decades. It is well known that increases in between‐patch migration rates cause more synchronous population fluctuations and that this coherence increases the risk of global metapopulation extinction. Because species’ migration rates and the probability of individuals surviving migration events depend on the effective distance between patches, the benefit of improving conservation corridors or the matrix between habitat patches has been questioned. As populations occur in the context of larger communities, moving from a metapopulation to a metacommunity model framework is a natural extension to address the generality of these conclusions. We show how considering a metacommunity can modify the conclusion that decreasing the effective distance between habitat patches (via improving matrix quality or other measures) necessarily increases the degree of metapopulation synchrony. We show that decreases in effective between‐patch distance may deter population synchrony because of the simultaneous effect this change has on the migration patterns of other species. These results indicate that species interactions need to be considered when the effect of conservation measures on population synchrony, and ultimately persistence, is addressed.     

Metapopulation dynamics of a beetle species confined to burned forest sites in a managed forest region

Despite increasing awareness of the theoretical importance of habitat dynamics on metapopulations, only a few empirical studies have been conducted. We aimed to increase our understanding of how patch size, dynamics and connectivity affect colonization–extinction dynamics and the occurrence patterns of a beetle (Stephanopachys linearis), which breeds only in burned trees, existing as dynamic habitat patches that have become rare in managed forest landscapes. We assessed species’ presence/absence twice in all known habitat patches (i.e. > 1 ha sites where forest fires had occurred during the previous 2–15 yr) in a 200 × 150 km region of central Sweden, dominated by managed boreal forest. Evaluated over six years, the colonization rate was 47% and the local extinction risk was 65%. Probability of colonization increased with patch size (number of suitable trees in a site) and connectivity to occupied patches within 30 km, and decreased with increasing time since fire. Local extinction risk decreased with habitat patch size but increased, unexpectedly, with connectivity. Occurrence increased with patch size and decreased with increasing time since fire. At a regional scale, S. linearis tracks the fire dynamics by colonising sites with burned trees and by becoming extinct at rates which make the species rare at sites where burnt trees are more than eight years old. In managed boreal forest landscapes, a large proportion of sites may be created by prescribed burning (in our study area: 82%), and consequently human decisions strongly affect the future amount of habitat for fire‐dependent species and its spatial distribution. Stephanopachys linearis uses burned sites more often if more trees are retained and, to some extent, if sites are concentrated in those parts of a region that already support high population densities of the species.     

荒漠破碎化生境中长爪沙鼠集合种群野外验证研究

近年来,人类活动和自然干扰,导致内蒙古阿拉善荒漠区生境的破碎化,出现了长爪沙鼠在不同斑块间的不连续分布,每一斑块内可能存在一个局域种群,而集合种群建立的前提条件,是局域种群斑块状分布在离散的栖息地环境中。2002~2012年每年的4~10月,在阿拉善荒漠区禁牧、轮牧、过牧和开垦4种人为不同利用方式形成的生境斑块中,采用标志重捕法对长爪沙鼠（Meriones unguiculatus）种群进行定点监测。通过分析长爪沙鼠种群动态,计算各局域种群的灭绝风险,利用Spearman秩相关系数检验种群动态的空间同步性,同时以种群周转率对长爪沙鼠扩散能力进行评估,以检验阿拉善荒漠区长爪沙鼠种群空间结构是否具有经典集合种群的功能。结果表明：（1） 不同生境斑块可被长爪沙鼠局域种群占据,11年间捕获长爪沙鼠2~7次不等;（2） 长爪沙鼠所有局域种群均具有灭绝风险,在轮牧区和禁牧区灭绝率高达1.000 0,开垦区灭绝率最低,也达到0.333 4,而本研究期间最大局域种群（2008年过牧区,26只/hm²）,在2010年发生了局域灭绝;（3） 不同生境斑块间没有明显的空间隔离而阻碍局域种群的重新建立,长爪沙鼠扩散能力较强,绝大部分月份的种群周转率在50.0%以上,特别是周转率达到100.0%的月份较多;（4） 不同生境斑块间仅轮牧区和禁牧区中长爪沙鼠种群密度显著正相关（P<0.05）,而其他生境斑块间相关性均不显著（P >0.05）,长爪沙鼠局域种群整体显示出明显的非同步空间动态。阿拉善荒漠区长爪沙鼠种群满足作为经典集合种群物种区域续存的4个条件,具有作为研究小哺乳动物集合种群的潜在价值。     

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.     

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.     

A Stochastic Metapopulation Model with Variability in Patch Size and Position

Analytically tractable metapopulation models usually assume that every patch is identical, which limits their application to real metapopulations. We describe a new single species model of metapopulation dynamics that allows variation in patch size and position. The state of the metapopulation is defined by the presence or absence of the species in each patch. For a system of n patches, this gives 2ⁿ possible states. We show how to construct and analyse a matrix describing transitions between all possible states by first constructing separate extinction and colonisation matrices. We illustrate the model′s application to metapopulations by considering an example of malleefowl, Leipoa ocellata, in southern Australia, and calculate extinction probabilities and quasi-stationary distributions. We investigate the relative importance of modelling the particular arrangement of patches and the variation in patch sizes for this metapopulation and we use the model to examine the effects of further habitat loss on extinction probabilities.     

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.     

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.     

Modelling epiphyte metapopulation dynamics in a dynamic forest landscape

We combine simulations with spatial statistics to estimate the parameters of a metapopulation model for the epiphytic lichen Lobaria pulmonaria specializing on aspen ( Populus tremula ) and goat willow ( Salix caprea ) in Fennoscandian boreal old-growth forests. We estimated the parameters of a forest landscape model (FIN-LANDIS) by repeatedly running simulations and selecting the set of parameters for tree ecology and fire regime that reproduced empirical host tree density and spatial patterns. Second, we tested which variables were important in epiphyte colonization and estimated the dispersal kernel. Third, we run a metapopulation model for the lichen across the estimated landscape scenarios and selected values for the remaining parameters that reproduced the empirical patterns of epiphyte occurrence. There was little variation in predicted dynamics, occupancy and spatial patterns between replicate metapopulation simulations. However, more data would be required for accurately estimating the parameters of FIN-LANDIS primarily because of the inherent stochasticity in large scale forest fires. Following the beginning of fire suppression in the study area 150 years ago, the model predicts that lichen occupancy first increases but subsequently declines. The lower occupancy in the past than at present is explained by high rate of tree destruction by fires, which increases local extinction rate in patch-tracking metapopulations. In the absence of fires, the occupancy increases because of lower extinction rate, but without forest fires or alternative means of host tree regeneration, the lichen is predicted to go ultimately extinct because of severely reduced density of aspen and goat willow.     

Correlated extinctions, colonizations and population fluctuations in a highly connected ringlet butterfly metapopulation

 The persistence of metapopulations is likely to be highly dependent on whether population dynamics are correlated among habitat patches as a result of migration between patches and spatially-correlated environmental stochasticity (weather effects). We examined whether population dynamics of the ringlet butterfly, Aphantopus hyperantus, were synchronous in an area of approximately 0.5 km², with respect to extinction, colonization and population fluctuations. Monks Wood Butterfly Monitoring Scheme transect count data from 1973 to 1995, revealed (A) a major environmental perturbation, the drought of 1976, which caused synchronized extinctions of A. hyperantus in subsequent years, (B) synchronized recolonization in years following the large number of apparent extinctions, and (C) population changes by A. hyperantus were highly correlated in many of the 14 sections of the transect, presumably reflecting similar responses to environmental stochasticity, and the exchange of individuals among sections. However, extinction and population synchrony depended on habitat type. Following the 1976 drought, A. hyperantus apparently became extinct from the most open and most shady habitats it occupied, with some persistence in habitats of intermediate shading, thus showing retraction to core populations in central parts of an environmental gradient, albeit with an average shift to relatively open habitat. Populations at extreme ends of the environmental gradient occupied by A. hyperantus fluctuated least synchronously, suggesting a potential buffering effect of habitat heterogeneity, but this was not crucial to survival after the 1976 drought. Thus, not all habitats are equally important to persistence. Correlated temporal dynamics, variation in habitat quality and the interaction between habitat quality and temporal environmental stochasticity are important determinants of metapopulation persistence and should be incorporated in metapopulation models. Received: 26 April 1996 / Accepted: 17 July 1996     

Metapopulation Dynamics of the Mistletoe and Its Host in Savanna Areas with Different Fire Occurrence

Mistletoes are aerial hemiparasitic plants which occupy patches of favorable habitat (host trees) surrounded by unfavorable habitat and may be possibly modeled as a metapopulation. A metapopulation is defined as a subdivided population that persists due to the balance between colonization and extinction in discrete habitat patches. Our aim was to evaluate the dynamics of the mistletoe Psittacanthus robustus and its host Vochysia thyrsoidea in three Brazilian savanna areas using a metapopulation approach. We also evaluated how the differences in terms of fire occurrence affected the dynamic of those populations (two areas burned during the study and one was fire protected). We monitored the populations at six-month intervals. P. robustus population structure and dynamics met the expected criteria for a metapopulation: i) the suitable habitats for the mistletoe occur in discrete patches; (ii) local populations went extinct during the study and (iii) colonization of previously non-occupied patches occurred. The ratio of occupied patches decreased in all areas with time. Local mistletoe populations went extinct due to two different causes: patch extinction in area with no fire and fire killing in the burned areas. In a burned area, the largest decrease of occupied patch ratios occurred due to a fire event that killed the parasites without, however, killing the host trees. The greatest mortality of V. thyrsoidea occurred in the area without fire. In this area, all the dead trees supported mistletoe individuals and no mortality was observed for parasite-free trees. Because P. robustus is a fire sensitive species and V. thyrsoidea is fire tolerant, P. robustus seems to increase host mortality, but its effect is lessened by periodic burning that reduces the parasite loads.     

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.     

Spatially structured metapopulation models: global and local assessment of metapopulation capacity

We model metapopulation dynamics in finite networks of discrete habitat patches with given areas and spatial locations. We define and analyze two simple and ecologically intuitive measures of the capacity of the habitat patch network to support a viable metapopulation. Metapopulation persistence capacity lambda(M) defines the threshold condition for long-term metapopulation persistence as lambda(M)>delta, where delta is defined by the extinction and colonization rate parameters of the focal species. Metapopulation invasion capacity lambda(I) sets the condition for successful invasion of an empty network from one small local population as lambda(I)>delta. The metapopulation capacities lambda(M) and lambda(I) are defined as the leading eigenvalue or a comparable quantity of an appropriate "landscape" matrix. Based on these definitions, we present a classification of a very general class of deterministic, continuous-time and discrete-time metapopulation models. Two specific models are analyzed in greater detail: a spatially realistic version of the continuous-time Levins model and the discrete-time incidence function model with propagule size-dependent colonization rate and a rescue effect. In both models we assume that the extinction rate increases with decreasing patch area and that the colonization rate increases with patch connectivity. In the spatially realistic Levins model, the two types of metapopulation capacities coincide, whereas the incidence function model possesses a strong Allee effect characterized by lambda(I)=0. For these two models, we show that the metapopulation capacities can be considered as simple sums of contributions from individual habitat patches, given by the elements of the leading eigenvector or comparable quantities. We may therefore assess the significance of particular habitat patches, including new patches that might be added to the network, for the metapopulation capacities of the network as a whole. We derive useful approximations for both the threshold conditions and the equilibrium states in the two models. The metapopulation capacities and the measures of the dynamic significance of particular patches can be calculated for real patch networks for applications in metapopulation ecology, landscape ecology, and conservation biology.     

Plant extinction risk under climate change: are forecast range shifts alone a good indicator of species vulnerability to global warming?

Models that couple habitat suitability with demographic processes offer a potentially improved approach for estimating spatial distributional shifts and extinction risk under climate change. Applying such an approach to five species of Australian plants with contrasting demographic traits, we show that: (i) predicted climate‐driven changes in range area are sensitive to the underlying habitat model, regardless of whether demographic traits and their interaction with habitat patch configuration are modeled explicitly; and (ii) caution should be exercised when using predicted changes in total habitat suitability or geographic extent to infer extinction risk, because the relationship between these metrics is often weak. Measures of extinction risk, which quantify threats to population persistence, are particularly sensitive to life‐history traits, such as recruitment response to fire, which explained approximately 60% of the deviance in expected minimum abundance. Dispersal dynamics and habitat patch structure have the strongest influence on the amount of movement of the trailing and leading edge of the range margin, explaining roughly 40% of modeled structural deviance. These results underscore the need to consider direct measures of extinction risk (population declines and other measures of stochastic viability), as well as measures of change in habitat area, when assessing climate change impacts on biodiversity. Furthermore, direct estimation of extinction risk incorporates important demographic and ecosystem processes, which potentially influence species’ vulnerability to extinction due to climate change.     

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.     

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     

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.