Synchronous dynamics and rates of extinction in spatially structured populations

We explore extinction rates using a spatially arranged set of subpopulations obeying Ricker dynamics. The population system is subjected to dispersal of individuals among the subpopulations as well as to local and global disturbances. We observe a tight positive correlation between global extinction rate and the level of synchrony in dynamics among thesubpopulations. Global disturbances and to a lesser extent, migration, are capable of synchronizing the temporal dynamics of the subpopulations over a rather wide span of the population growth rate r. Local noise decreases synchrony, as does increasing distance among the subpopulations. Synchrony also levels off with increasing r: in the chaotic region, subpopulations almost invariably behave asynchronously. We conclude that it is asynchrony that reduces the probability of global extinctions, not chaos as such: chaos is a special case only. The relationship between global extinction rate, synchronous dynamics and population growth rate is robust to changes in dispersal rates and ranges.     

Local extinction and the evolution of dispersal rates: causes and correlations

We present the results of individual-based simulation experiments on the evolution of dispersal rates of organisms living in metapopulations. We find conflicting results regarding the relationship between local extinction rate and evolutionarily stable (ES) dispersal rate depending on which principal mechanism causes extinction: if extinction is caused by environmental catastrophes eradicating local populations, we observe a positive correlation between extinction and ES dispersal rate; if extinction is a consequence of stochastic local dynamics and environmental fluctuations, the correlation becomes ambiguous; and in cases where extinction is caused by dispersal mortality, a negative correlation between local extinction rate and ES dispersal rate emerges. We conclude that extinction rate, which both affects and is affected by dispersal rates, is not an ideal predictor for optimal dispersal rates.     

Effects of habitat destruction and resource supplementation in a predator-prey metapopulation model

We developed a mean field, metapopulation model to study the consequences of habitat destruction on a predator-prey interaction. The model complements and extends earlier work published by Bascompte and Solé (1998, J. theor. Biol.195, 383-393) in that it also permits use of alternative prey (i.e., resource supplementation) by predators. The current model is stable whenever coexistence occurs, whereas the earlier model is not stable over the entire domain of coexistence. More importantly, the current model permits an assessment of the effect of a generalist predator on the trophic interaction. Habitat destruction negatively affects the equilibrium fraction of patches occupied by predators, but the effect is most pronounced for specialists. The effect of habitat destruction on prey coexisting with predators is dependent on the ratio of extinction risk due to predation and prey colonization rate. When this ratio is less than unity, equilibrial prey occupancy of patches declines as habitat destruction increases. When the ratio exceeds one, equilibrial prey occupancy increases even as habitat destruction increases; i.e., prey "escape" from predation is facilitated by habitat loss. Resource supplementation reduces the threshold colonization rate of predators necessary for their regional persistence, and the benefit derived from resource supplementation increases in a nonlinear fashion as habitat destruction increases. We also compared the analytical results to those from a stochastic, spatially explicit simulation model. The simulation model was a discrete time analog of our analytical model, with one exception. Colonization was restricted locally in the simulation, whereas colonization was a global process in the analytical model. After correcting for differences between nominal and effective colonization rates, most of the main conclusions of the two types of models were similar. Some important differences did emerge, however, and we discuss these in relation to the need to develop fully spatially explicit analytical models. Finally, we comment on the implications of our results for community structure and for the conservation of prey species interacting with generalist predators.     

Demographic and genetic consequences of population subdivision in Formosa land-locked salmon <Emphasis Type="Italic">Oncorhynchus masou formosanus</Emphasis>, the southernmost subspecies of the salmonids

A few studies have evaluated demographic and genetic consequences of population subdivision by damming on the population as a whole. Formosa landlocked salmon Oncorhynchus masou formosanus have persisted as a relatively large population that has recently been subdivided into seven subpopulations by erosion-control dams and a natural waterfall. The present study simulated the demographic and genetic dynamics of this subdivided salmon population using VORTEX, an individual-based stochastic model. Although the population as a whole did not experience extinction over 200 simulation years, the loss of genetic variation was often detrimental (>10% loss). Isolated headwater subpopulations frequently reached extinction. Even when the subpopulations did persist through the 200 years, they experienced dramatic loss of genetic variation, suggesting short-term genetic threats. Due to the unidirectional dispersal of the fish, the damming puts headwater subpopulations at higher risk of extinction and loss of genetic variation, which affects persistence of the population as a whole, particularly from a genetic perspective.     

Adaptation of timing of life history traits and population dynamic responses to climate change in spatially structured populations

Changes in the seasonal timing of life history events are documented effects of climate change. We used a general model to study how dispersal and competitive interactions affect eco-evolutionary responses to changes in the temporal distribution of resources over the season. Specifically, we modeled adaptation of the timing of reproduction and population dynamic responses in two competing populations that disperse between two habitats characterized by an early and late resource peak. We investigated three scenarios of environmental change: (1) food peaks advance in both habitats, (2) in the late habitat only and (3) in the early habitat only. At low dispersal rates the evolutionarily stable timing of reproduction closely matched the local resource peak and the environmental change typically caused population decline. Larger dispersal rates rendered less intuitive eco-evolutionary population responses. First, dispersal caused mismatch between evolutionarily stable timing of reproduction and local resource peaks and as a result, reproductive output for subpopulations could increase as well as decrease when resource availability underwent temporal shifts. Second, population responses were contingent on competition between populations. This could accelerate population declines and cause extinctions or even reverse population trends from negative to positive compared to the low dispersal case. When dispersal rate was large and the early resource peak was advanced available niche space was reduced. Hence, even when a population survived the environmental change and obtained positive equilibrium population density, subsequent adaptation of competing populations could drive it to extinction due to convergent evolution and competitive exclusion. These results shed new light on the role of competition and dispersal for the evolution of timing of life history events and provide guidelines for understanding short and long-term population response to climate change.     

Rapid assessment of metapopulation viability under climate and land-use change

In order to predict species response to climate and land-use change, numerically fast and easily applicable assessment tools for species survival are required. We present a set of formulae to calculate the mean lifetime of a metapopulation in a spatially heterogeneous and dynamic landscape subject to habitat patch diminution, loss and/or spatial shift of the habitat network. The formulae require as inputs (i) information about the number, location and size of the habitat patches for several time steps to quantify landscape dynamics in terms of patch destruction, diminution or shifting rates and (ii) data on species traits such as their vulnerability to environmental variation and their dispersal ability to quantify local colonisation and extinction rates. We validate the formulae with a spatially explicit simulation. The analysis is complemented by a protocol for the easy use of the approach and practical application examples. A software implementation is available on request from the authors.     

Habitat destruction and the extinction debt revisited: The Allee effect

Habitat destruction, often caused by anthropogenic disturbance, can lead to the extinction of species at an unprecedented rate. It is important, therefore, to consider habitat destruction when assessing population viability. Another factor often ignored in population viability analysis, is the Allee effect that adds to the risk of populations already on the verge of extinction. Understanding the Allee effect on species dynamics and response to habitat destruction has intrinsic value in conservation prioritization. Here, the Allee effect was considered in a multi-species hierarchical competition model. Results showed that species persistence declines dramatically due to the Allee effect, and certain species become more susceptible to habitat destruction than others. Two extinction orders emerged under habitat destruction: either the best competitor becomes extinct first or the best colonizer first. The extinction debt and order, as well as the time lag between habitat destruction and species extinction, were found to be determined by species abundance and the intensity of the Allee effect.     

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.     

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。     

Patchy population structure in a short-distance migrant: evidence from genetic and demographic data

Species often occur in subdivided populations as a consequence of spatial heterogeneity of the habitat. To describe the spatial organization of subpopulations, existing theory proposes three main population models: patchy population, metapopulation and isolated populations. These models differ in their predicted levels of connectivity among subpopulations, and in the risk that a subpopulation will go extinct. However, spatially discrete subpopulations are commonly considered to be organized as metapopulations, even though explicit tests of metapopulation assumptions are rare. Here, we test predictions of the three models on the basis of demographic and genetic data, a combined approach so far surprisingly little used in mobile organisms. From 2002 to 2005, we studied nine subpopulations of the wetland-restricted reed bunting ( Emberiza schoeniclus ) in the southeastern part of the Canton Zurich (Switzerland), from which local declines of this species have been reported. Here, wetlands are as small as 2.7 ha and separated through intensively used agricultural landscapes. Demographic data consisted of dispersal of colour-banded individuals among subpopulations, immigration rates and extinction-/recolonization dynamics. Genetic data were based on the distribution of genetic variability and gene flow among subpopulations derived from the analysis of nine microsatellite loci. Both demographic and genetic data revealed that the patchy population model best described the spatial organization of reed bunting subpopulations. High levels of dispersal among subpopulations, high immigration into the patchy population, and genetic admixture suggested little risk of extinction of both subpopulations and the entire patchy population. This study exemplifies the idea that spatially discrete subpopulations may be organized in ways other than a metapopulation, and hence has implications for the conservation of subpopulations and species.     

Modelling effects of habitat fragmentation on the ability of trees to respond to climatic warming

The ability of trees to migrate in response to climatic warming was simulated under various conditions of habitat availability. The model uses Holocene tree migration rates to approximate maximum migration rates in a forested landscape. Habitat availability and local population size was varied systematically under two dispersal and colonization models. These dispersal models varied in the likelihood of long-distance dispersal events. The first model used a negative exponential function that severely limited the probability of long-distance dispersal. The results of this model indicate that migration rate could decline an order of magnitude where the habitat availability is reduced from 80 to 20% of the matrix. The second model, using an inverse power function, carried a higher probability of long-distance dispersal events. The results from this model predict relatively small declines in migration rates when habitat availability is reduced to 50% of the simulation matrix. Below 50% habitat availability, mean migration rate was similar to the negative exponential model. These results predict a failure of many trees to respond to future climatic change through range expansion.     

Metacommunity,mainland‐island system or island communities? Assessing the regional dynamics of plant communities in a fragmented landscape

Understanding the regional dynamics of plant communities is crucial for predicting the response of plant diversity to habitat fragmentation. However, for fragmented landscapes the importance of regional processes, such as seed dispersal among isolated habitat patches, has been controversially debated. Due to the stochasticity and rarity of among‐patch dispersal and colonization events, we still lack a quantitative understanding of the consequences of these processes at the landscape‐scale. In this study, we used extensive field data from a fragmented, semi‐arid landscape in Israel to parameterize a multi‐species incidence‐function model. This model simulates species occupancy pattern based on patch areas and habitat configuration and explicitly considers the locations and the shapes of habitat patches for the derivation of patch connectivity. We implemented an approximate Bayesian computation approach for parameter inference and uncertainty assessment. We tested which of the three types of regional dynamics – the metacommunity, the mainland‐island, or the island communities type – best represents the community dynamics in the study area and applied the simulation model to estimate the extinction debt in the investigated landscape. We found that the regional dynamics in the patch‐matrix study landscape is best represented as a system of highly isolated ‘island’ communities with low rates of propagule exchange among habitat patches and consequently low colonization rates in local communities. Accordingly, the extinction rates in the local communities are the main drivers of community dynamics. Our findings indicate that the landscape carries a significant extinction debt and in model projections 33–60% of all species went extinct within 1000 yr. Our study demonstrates that the combination of dynamic simulation models with field data provides a promising approach for understanding regional community dynamics and for projecting community responses to habitat fragmentation. The approach bears the potential for efficient tests of conservation activities aimed at mitigating future losses of biodiversity.     

HOW DOES POLLEN VERSUS SEED DISPERSAL AFFECT NICHE EVOLUTION?

In heterogeneous landscapes, the genetic and demographic consequences of dispersal influence the evolution of niche width. Unless pollen is limiting, pollen dispersal does not contribute directly to population growth. However, by disrupting local adaptation, it indirectly affects population dynamics. We compare the effect of pollen versus seed dispersal on the evolution of niche width in heterogeneous habitats, explicitly considering the feedback between maladaptation and demography. We consider two scenarios: the secondary contact of two subpopulations, in distinct, formerly isolated habitats, and the colonization of an empty habitat with dispersal between the new and ancestral habitat. With an analytical model, we identify critical levels of genetic variance leading to niche contraction (secondary contact scenario), or expansion (new habitat scenario). We confront these predictions with simulations where the genetic variance freely evolves. Niche contraction occurs when habitats are very different. It is faster as total gene flow increases or as pollen predominates in overall gene flow. Niche expansion occurs when habitat heterogeneity is not too high. Seed dispersal accelerates it, whereas pollen dispersal tends to retard it. In both scenarios very high seed dispersal leads to extinction. Overall, our results predict a wider niche for species dispersing seeds more than pollen.     

Integrating the effects of area, isolation, and habitat heterogeneity on species diversity: a unification of island biogeography and niche theory

We present an analytical model that unifies two of the most influential theories in community ecology, namely, island biogeography and niche theory. Our model captures the main elements of both theories by incorporating the combined effects of area, isolation, stochastic colonization and extinction processes, habitat heterogeneity, and niche partitioning in a unified, demographically based framework. While classical niche theory predicts a positive relationship between species richness and habitat heterogeneity, our unified model demonstrates that area limitation and dispersal limitation (the main elements of island biogeography) may create unimodal and even negative relationships between species richness and habitat heterogeneity. We attribute this finding to the fact that increasing heterogeneity increases the potential number of species that may exist in a given area (as predicted by niche theory) but simultaneously reduces the amount of suitable area available for each species and, thus, increases the likelihood of stochastic extinction. Area limitation, dispersal limitation, and low reproduction rates intensify the latter effect by increasing the likelihood of stochastic extinction. These analytical results demonstrate that the integration of island biogeography and niche theory provides new insights about the mechanisms that regulate the diversity of ecological communities and generates unexpected predictions that could not be attained from any single theory.     

Demographic consequences of population subdivision on the long-furred woolly mouse opossum (Micoureus paraguayanus) from the Atlantic Forest

Habitat destruction and fragmentation severely affected the Atlantic Forest. Formerly contiguous populations may become subdivided into a larger number of smaller populations, threatening their long-term persistence. The computer package VORTEX was used to simulate the consequences of habitat fragmentation and population subdivision on Micoureus paraguayanus, an endemic arboreal marsupial of the Atlantic Forest. Scenarios simulated hypothetical populations of 100 and 2000 animals being partitioned into 1–10 populations, linked by varying rates of inter-patch dispersal, and also evaluated male-biased dispersal. Results demonstrated that a single population was more stable than an ensemble of populations of equal size, irrespective of dispersal rate. Small populations (10–20 individuals) exhibited high instability due to demographic stochasticity, and were characterized by high rates of extinction, smaller values for metapopulation growth and larger fluctuations in population size and growth rate. Dispersal effects on metapopulation persistence were related to the size of the populations and to the sexes that were capable of dispersing. Male-biased dispersal had no noticeable effects on metapopulation extinction dynamics, whereas scenarios modelling dispersal by both sexes positively affected metapopulation dynamics through higher growth rates, smaller fluctuations in growth rate, larger final metapopulation sizes and lower probabilities of extinction. The present study highlights the complex relationships between metapopulation size, population subdivision, habitat fragmentation, rate of inter-patch dispersal and sex-biased dispersal and indicates the importance of gaining a better understanding of dispersal and its interactions with correlations between disturbance events.     

Homogenization of dispersal ability across bird species in response to landscape change

Human land use is known to homogenize biotic communities, increasing similarity in their genetic, taxonomic and functional diversity. Explanations have focused almost exclusively on human‐mediated extinction and range expansion. However, homogenization could also be produced by land use driving selection for similar traits across species. We propose a novel hypothesis to explain how human land use homogenizes dispersal ability across species. With habitat loss and increasing human land use intensities there should be larger increases in the costs of dispersal for dispersive than sedentary species, because dispersive species interact with non‐habitat more frequently. In contrast, the benefits of dispersal should increase more for sedentary than dispersive species, because sedentary species are at greater risk from inbreeding depression, predation and competition associated with habitat loss. Therefore we predict that sedentary species become more dispersive in a human‐altered landscape, and dispersive species more sedentary. We tested this prediction using wing pointedness to estimate the initial dispersal ability and change in dispersal ability for 21 North American passerines over the 20th century. More pointed wings are associated with stronger dispersal ability. Thus our prediction would be supported by a negative cross‐species relationship between these two measurements. We found a strong, negative relationship, as predicted. This resulted in declines in the variability in wing pointedness among species over time. Although other things can cause wing shape to change, including changes in habitat availability, none of these explained the observed relationship. Our result provides the first evidence that human landscape alteration is homogenizing bird communities, driving selection for intermediate dispersal ability across species. It also implies that more dispersive species are more at‐risk from human landscape use because, when rates of landscape alteration are faster than a species’ ability to adapt to that change, the costs of dispersal increase more for dispersive than sedentary species.     

Metapopulation models for seasonally migratory animals

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

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.     

Habitat loss-induced tipping points in metapopulations with facilitation

Habitat loss is known to pervade extinction thresholds in metapopulations. Such thresholds result from a loss of stability that can eventually lead to collapse. Several models have been developed to understand the nature of these transitions and how they are affected by the locality of interactions, fluctuations or external drivers. Most models consider the impact of grazing or aridity as a control parameter that can trigger sudden shifts, once critical values are reached. Others explore instead the role played by habitat loss and fragmentation. Here we consider a minimal model incorporating facilitation between the individuals of the same species along with habitat destruction, with the aim of understanding how local cooperation and habitat loss interact with each other. A mathematical model incorporating facilitation and habitat destruction is derived, along with a spatially explicit simulation model. It is found that a catastrophic shift is expected for increasing levels of habitat loss, but the bifurcation becomes continuous when dispersal is local. Under these conditions, spatial patchiness is found and the qualitative change from discontinuous to continuous results are in agreement with previous studies on ecological systems. Our results suggest that species exhibiting facilitation and displaying short-range dispersal will be markedly more capable of avoiding catastrophic tipping points.     

Low dispersal ability and habitat specificity promote extinctions in rare but not in widespread species: the Orthoptera of Germany

Local extinctions are often non‐randomly associated with range size, dispersal ability and habitat specificity, as well as body size, sexual dimorphism and phylogeny. We used a large data set of the Orthoptera species (bush crickets, crickets, grasshoppers) occurring in Germany and compared the number of occupied grid cells before 1980 to those occupied after 1980, corrected for monitoring intensity. The number of grid cells in which a species went extinct was non‐linearly related to the number of occupied grid cells per species. Using generalized linear modelling we analysed extinction in relation to national distribution (the number of occupied grid cells before 1980), dispersal ability (derived from a large body of literature concerning wing development, colonization dynamics and within‐habitat mobility), habitat specificity (moisture specialists versus generalists), potential reproduction (the number of ovarioles), the degree of sexual size dimorphism and phylogeny (twelve clades). Species with a large global range size also had a large national range size. Species with a large range experienced more total extinction events than species with smaller ranges but relatively fewer compared to range size. The latter relationship was largely shaped by the dispersal ability of the species: the interactions of range size×dispersal ability and range size×habitat specificity explained almost one third of the variation in the number of extinction events. Species with high dispersal ability went extinct in a similar number of grid cells irrespective of their range size. By contrast, species with low dispersal ability went extinct in proportion to their range size. Therefore, comparing the speed of extinction across species in the conventional way of extinction rates (that is the percentage of range contraction) might be flawed because it only applies to species with low dispersal ability. Sexual size dimorphism was not a significant predictor of extinction. Extinction was not concentrated on particular clades.