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.     

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.     

物种灭绝对不同时间尺度栖息地毁坏响应的空间模拟

人类活动所引起的栖息地毁坏已成为当前物种多样性丧失的最主要的原因之一。空间显含模型相对于空间隐含模型来说,更加接近于现实,因此,通过元胞自动机,模拟了物种多样性对万年、千年、百年时间尺度人类活动所引起的栖息地毁坏的响应。研究结果表明：万年时间尺度上,物种是由强到弱的灭绝;而在千年时间尺度上,物种灭绝的序受集合种群结构的影响较大;在百年时间尺度上。物种由于栖息地毁坏过于剧烈和迅速,来不及作出响应。在栖息地完全毁坏时集体灭绝。因此,物种灭绝序不只是受竞争-侵占均衡机制的影响,还受不同时间尺度（不同速率）栖息地毁坏的影响。以及集合种群结构的影响。     

Non-equilibria in small metapopulations: comparing the deterministic Levins model with its stochastic counterpart

In this paper, we examine, for small metapopulations, the stochastic analog of the classical Levins metapopulation model. We study its basic model output, the expected time to metapopulation extinction, for systems which are brought out of equilibrium by imposing sudden changes in patch number and the colonization and extinction parameters. We find that the expected metapopulation extinction time shows different behavior from the relaxation time of the original, deterministic, Levins model. This relaxation time is therefore limited in value for predicting the behavior of the stochastic model. However, predictions about the extinction time for deterministically unviable cases remain qualitatively the same. Our results further suggest that, if we want to counteract the effects of habitat loss or increased dispersal resistance, the optimal conservation strategy is not to restore the original situation, that is, to create habitat or decrease resistance against dispersal. As long as the costs for different management options are not too dissimilar, it is better to improve the quality of the remaining habitat in order to decrease the local extinction rate.     

Species richness patterns and metapopulation processes – evidence from epiphyte communities in boreo-nemoral forests

For several epiphyte species, dispersal limitation and metapopulation dynamics have been suggested. We studied the relative importance of local environmental conditions and spatial aggregation of species richness of facultative and obligate epiphytic bryophytes and lichens within two old‐growth forests in eastern Sweden. The effect of the local environment was analyzed using generalized linear models (GLM). We tested whether species richness was spatially structured by fitting variogram models to the residuals of the GLM. In addition, we analyzed the species‐area relationship (area=tree diameter). Different environmental variables explained the richness of different species groups (bryophytes vs lichens, specialists vs generalists, sexual vs asexual dispersal). In most groups, the total variation explained by environmental variables was higher than the variation explained by the spatial model. Spatial aggregation was more pronounced in asexually than in sexually dispersed species. Bryophyte species richness was only poorly predicted by area, and lichen species richness was not explained by area at all. Spatial aggregation may indicate effects of dispersal limitation and metapopulation dynamics on community species richness. Our results suggest that species groups differ in habitat requirements and dispersal abilities; there were indications that presence of species with different dispersal strategies is linked to the age of the host tree. Separate analyses of the species richness of species groups that differ in the degree of habitat specialization and dispersal ability give insights into the processes determining community species richness. The poor species‐area relationship, especially in lichens, may indicate species turnover rather than accumulation during the lifetime of the host tree. Epiphyte species extinctions may be mainly caused by deterministic processes, e.g. changes in habitat conditions as the host tree grows, ages and dies, rather than by stochastic population processes.     

Is the population turnover of patchy‐distributed annuals determined by dormancy dynamics or dispersal processes?

In species with fragmented distribution, regional turnover dynamics is given by the processes of local population extinction and patch (re)colonization by migrants spreading from neighboring occupied patches. In plants with dormant stages (e.g. seeds) and limited dispersal capacity, regional dynamics based on dispersal processes can be overridden by pseudo-turnover determined by signals inducing or breaking dormancy (e.g. due to changes in habitat quality) resulting in a low importance of habitat configuration and size.
In this study, I investigated the turnover dynamics of 5 annual plant species growing on ant mounds of Lasius flavus over three years. I analyzed whether the grassland-scale dynamics of these annuals is influenced by dispersal processes, or alternatively, by pseudo-turnover of soil seed populations. For that purpose I 1) searched for populations formed from soil seeds only, 2) compared the relative contribution of the soil seed bank and seed rain for population restoration after disappearance from the vegetation and 3) investigated whether colonization and extinction events are affected by patch isolation. I assumed if population turnover was rather a result of the soil seed bank dynamics then spatial effects would be hard to detect.
In spite of the presence of populations formed from soil seed and the relatively more important soil seed bank for potential population reestablishment, turnover dynamics followed the predictions of metapopulation theory. Population appearance was more probable in larger and less isolated patches. Probability of disappearance increased with decrease of population size that was negatively influenced by the patch size and its isolation. These findings indicate dispersal processes to be important in the turnover dynamics and only limited contribution of soil seed populations. Their small effectiveness is probably related to the low chance of recurrent disturbance on the mound surface.     

Effect of habitat fragmentation on dispersal in the butterfly Proclossiana eunomia

Comparison of dispersal rates of the bog fritillary butterfly between continuous and fragmented landscapes indicates that between patch dispersal is significantly lower in the fragmented landscape, while population densities are of the same order of magnitude. Analyses of the dynamics of the suitable habitat for the butterfly in the fragmented landscape reveal a severe, non linear increase in spatial isolation of patches over a time period of 30 years (i.e. 30 butterfly generations), but simulations of the butterfly metapopulation dynamics using a structured population model show that the lower dispersal rates in the fragmented landscape are far above the critical threshold leading to metapopulation extinction. These results indicate that changes in individual behaviour leading to the decrease of dispersal rates in the fragmented landscape were rapidly selected for when patch spatial isolation increased. The evidence of such an adaptive answer to habitat fragmentation suggests that dispersal mortality is a key factor for metapopulation persistence in fragmented landscapes. We emphasise that landscape spatial configuration and patch isolation have to be taken into account in the debate about large-scale conservation strategies.     

Spatial variation in branch size promotes metapopulation persistence in dendritic river networks

1. Despite years of attention, the dynamics of species constrained to disperse within riverine networks are not well captured by existing metapopulation models, which often ignore local dynamics within branches.
2. We develop a modelling framework, based on traditional metapopulation theory, for patch occupancy dynamics subject to local colonisation–extinction dynamics within branches and regional dispersal between branches in size-structured, bifurcating riverine networks. Using this framework, we investigate whether and how spatial variation in branch size affects species persistence for dendritic systems with directional dispersal, including one-way (up- or downstream only) and two-way (both up- and downstream) dispersal.
3. Variation in branch size generally promotes species persistence more obviously at higher relative extinction rate, suggesting that previous studies ignoring differences in branch size in real riverine systems might overestimate species extinction risk.
4. Two-way dispersal is not always superior to one-way dispersal as a strategy for metapopulation persistence especially at high relative extinction rate. The type of dispersal that maximises species persistence is determined by the hierarchical level of the largest, and hence most influential, branch within the network. When considering the interactive effects of up- and downstream dispersal, we find that moderate upstream-biased dispersal maximises metapopulation viability, mediated by spatial branch arrangement.
5. Overall, these results suggest that both branch-size variation and species traits interact to determine species persistence, theoretically demonstrating the ecological significance of their interplay.

     

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.     

Long-term persistence of species and the SLOSS problem

The single large or several small (SLOSS) problem has been addressed in a large number of empirical and theoretical studies, but no coherent conclusion has yet been reached. Here I study the SLOSS problem in the context of metapopulation dynamics. I assume that there is a fixed total amount A(0) of habitat available, and I derive formulas for the optimal number n and area A of habitat patches, where n=A(0)/A. I consider optimality in two ways. First, I attempt to maximize the time to metapopulation extinction, which is a relevant measure for metapopulation viability for rare and threatened species. Second, I attempt to maximize the metapopulation capacity of the habitat patch network, which corresponds both with maximizing the distance to the deterministic extinction threshold and with maximizing the fraction of occupied patches. I show that in the typical case, a small number of large patches maximizes the metapopulation capacity, while an intermediate number of habitat patches maximizes the time to extinction. The main conclusion stemming from the analysis is that the optimal number of patches is largely affected by the relationship between habitat patch area and rates of immigration, emigration and local extinction. Here this relationship is summarized by a single factor zeta, termed the patch area scaling factor.     

Long‐term metapopulation study of the Glanville fritillary butterfly (Melitaea cinxia): survey methods,data management,and long‐term population trends

Long‐term observational studies conducted at large (regional) spatial scales contribute to better understanding of landscape effects on population and evolutionary dynamics, including the conditions that affect long‐term viability of species, but large‐scale studies are expensive and logistically challenging to keep running for a long time. Here, we describe the long‐term metapopulation study of the Glanville fritillary butterfly (Melitaea cinxia) that has been conducted since 1991 in a large network of 4000 habitat patches (dry meadows) within a study area of 50 by 70 km in the Åland Islands in Finland. We explain how the landscape structure has been described, including definition, delimitation, and mapping of the habitat patches; methods of field survey, including the logistics, cost, and reliability of the survey; and data management using the EarthCape biodiversity platform. We describe the long‐term metapopulation dynamics of the Glanville fritillary based on the survey. There has been no long‐term change in the overall size of the metapopulation, but the level of spatial synchrony and hence the amplitude of fluctuations in year‐to‐year metapopulation dynamics have increased over the years, possibly due to increasing frequency of exceptional weather conditions. We discuss the added value of large‐scale and long‐term population studies, but also emphasize the need to integrate more targeted experimental studies in the context of long‐term observational studies. For instance, in the case of the Glanville fritillary project, the long‐term study has produced an opportunity to sample individuals for experiments from local populations with a known demographic history. These studies have demonstrated striking differences in dispersal rate and other life‐history traits of individuals from newly established local populations (the offspring of colonizers) versus individuals from old, established local populations. The long‐term observational study has stimulated the development of metapopulation models and provided an opportunity to test model predictions. This combination of empirical studies and modeling has facilitated the study of key phenomena in spatial dynamics, such as extinction threshold and extinction debt.     

Extinction–immigration dynamics lag behind environmental filtering in shaping the composition of tropical dry forests within a changing landscape

The impact of rapid habitat loss and fragmentation on biodiversity is a major issue. However, we still lack an integrative understanding of how these changes influence biodiversity dynamics over time. In this study, we investigate the effects of these changes in terms of both niche-based and neutral dynamics. We hypothesize that habitat loss has delayed effects on neutral immigration–extinction dynamics, while edge effects and environmental heterogeneity in habitat patches have rapid effects on niche-based dynamics. We analyzed taxonomic and functional composition of 100 tree communities in a tropical dry forest landscape of New-Caledonia subject to habitat loss and fragmentation. We designed an original, process-based simulation framework, and performed Approximate Bayesian Computation to infer the influence of niche-based and neutral processes. Then, we performed partial regressions to evaluate the relationships between inferred parameter values of communities and landscape metrics (distance to edge, patch area, and habitat amount around communities), derived from either recent or past (65 yr ago) aerial photographs, while controlling for the effect of soil and topography. We found that landscape structure influences both environmental filtering and immigration. Immigration rate was positively related to past habitat amount surrounding communities. In contrast, environmental filtering was mostly affected by present landscape structure and mainly influenced by edge vicinity and topography. Our results highlight that landscape changes have contrasting spatio-temporal influences on niche-based and neutral assembly dynamics. First, landscape-level habitat loss and community isolation reduce immigration and increase demographic stochasticity, resulting in slow decline of local species diversity and extinction debt. Second, recent edge creation affects environmental filtering, incurring rapid changes in community composition by favoring species with edge-adapted strategies. Our study brings new insights about temporal impacts of landscape changes on biodiversity dynamics. We stress that landscape history critically influences these dynamics and should be taken into account in conservation policies.     

Understanding extinction debts: spatio–temporal scales,mechanisms and a roadmap for future research

Extinction debt refers to delayed species extinctions expected as a consequence of ecosystem perturbation. Quantifying such extinctions and investigating long‐term consequences of perturbations has proven challenging, because perturbations are not isolated and occur across various spatial and temporal scales, from local habitat losses to global warming. Additionally, the relative importance of eco‐evolutionary processes varies across scales, because levels of ecological organization, i.e. individuals, (meta)populations and (meta)communities, respond hierarchically to perturbations. To summarize our current knowledge of the scales and mechanisms influencing extinction debts, we reviewed recent empirical, theoretical and methodological studies addressing either the spatio–temporal scales of extinction debts or the eco‐evolutionary mechanisms delaying extinctions. Extinction debts were detected across a range of ecosystems and taxonomic groups, with estimates ranging from 9 to 90% of current species richness. The duration over which debts have been sustained varies from 5 to 570 yr, and projections of the total period required to settle a debt can extend to 1000 yr. Reported causes of delayed extinctions are 1) life‐history traits that prolong individual survival, and 2) population and metapopulation dynamics that maintain populations under deteriorated conditions. Other potential factors that may extend survival time such as microevolutionary dynamics, or delayed extinctions of interaction partners, have rarely been analyzed. Therefore, we propose a roadmap for future research with three key avenues: 1) the microevolutionary dynamics of extinction processes, 2) the disjunctive loss of interacting species and 3) the impact of multiple regimes of perturbation on the payment of debts. For their ability to integrate processes occurring at different levels of ecological organization, we highlight mechanistic simulation models as tools to address these knowledge gaps and to deepen our understanding of extinction dynamics.     

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。     

Metapopulation theory for fragmented landscapes

We review recent developments in spatially realistic metapopulation theory, which leads to quantitative models of the dynamics of species inhabiting highly fragmented landscapes. Our emphasis is in stochastic patch occupancy models, which describe the presence or absence of the focal species in habitat patches. We discuss a number of ecologically important quantities that can be derived from the full stochastic models and their deterministic approximations, with a particular aim of characterizing the respective roles of the structure of the landscape and the properties of the species. These quantities include the threshold condition for persistence, the contributions that individual habitat patches make to metapopulation dynamics and persistence, the time to metapopulation extinction, and the effective size of a metapopulation living in a heterogeneous patch network.     

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.     

Transient dynamics in metapopulation response to perturbation

Transient time in population dynamics refers to the time it takes for a population to return to population-dynamic equilibrium (or close to it) following a perturbation in the environment or in population size. Depending on the direction of the perturbation, transient time may either denote the time until extinction (or until the population has decreased to a lower equilibrium level), or the recovery time needed to reach a higher equilibrium level. In the metapopulation context, the length of the transient time is set by the interplay between population dynamics and landscape structure. Assuming a spatially realistic metapopulation model, we show that transient time is a product of four factors: the strength of the perturbation, the ratio between the metapopulation capacity of the landscape and a threshold value determined by the properties of the species, and the characteristic turnover rate of the species, adjusted by a factor depending on the structure of the habitat patch network. Transient time is longest following a large perturbation, for a species which is close to the threshold for persistence, for a species with slow turnover, and in a habitat patch network consisting of only a few dynamically important patches. We demonstrate that the essential behaviour of the n-dimensional spatially realistic Levins model is captured by the one-dimensional Levins model with appropriate parameter transformations.     

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.     

Metapopulation models for extinction threshold in spatially correlated landscapes

Simple analytical models assuming homogeneous space have been used to examine the effects of habitat loss and fragmentation on metapopulation size. The models predict an extinction threshold, a critical amount of suitable habitat below which the metapopulation goes deterministically extinct. The consequences of non-random loss of habitat for species with localized dispersal have been studied mainly numerically. In this paper, we present two analytical approaches to the study of habitat loss and its metapopulation dynamic consequences incorporating spatial correlation in both metapopulation dynamics as well as in the pattern of habitat destruction. One approach is based on a measure called metapopulation capacity, given by the dominant eigenvalue of a "landscape" matrix, which encapsulates the effects of landscape structure on population extinctions and colonizations. The other approach is based on pair approximation. These models allow us to examine analytically the effects of spatial structure in habitat loss on the equilibrium metapopulation size and the threshold condition for persistence. In contrast to the pair approximation based approaches, the metapopulation capacity based approach allows us to consider species with long as well as short dispersal range and landscapes with spatial correlation at different scales. The two methods make dissimilar assumptions, but the broad conclusions concerning the consequences of spatial correlation in the landscape structure are the same. Our results show that increasing correlation in the spatial arrangement of the remaining habitat increases patch occupancy, that this increase is more evident for species with short-range than long-range dispersal, and that to be most beneficial for metapopulation size, the range of spatial correlation in landscape structure should be at least a few times greater than the dispersal range of the species.     

Life history traits and abundance can predict local colonisation and extinction rates of freshwater mussels

1. A critical need in conservation biology is to determine which species are most vulnerable to extinction. Freshwater mussels (Bivalvia: Unionacea) are one of the most imperilled faunal groups globally. Freshwater mussel larvae are ectoparasites on fish and depend on the movement of their hosts to maintain connectivity among local populations in a metapopulation. 2. I calculated local colonisation and extinction rates for 16 mussel species from 14 local populations in the Red River drainage of Oklahoma and Texas, U.S. I used general linear models and AIC comparisons to determine which mussel life history traits best predicted local colonisation and extinction rates. 3. Traits related to larval dispersal ability (host infection mode, whether a mussel species was a host generalist or specialist) were the best predictors of local colonisation. 4. Traits related to local population size (regional abundance, time spent brooding) were the best predictors of local extinction. The group of fish species used as hosts by mussels also predicted local extinction and was probably related to habitat fragmentation and host dispersal abilities. 5. Overall, local extinction rates exceeded local colonisation rates, indicating that local populations are becoming increasingly isolated and suffering an ‘extinction debt’. This study demonstrates that analysis of species traits can be used to predict local colonisation and extinction patterns and provide insight into the long‐term persistence of populations.