Metapopulation moments: coupling, stochasticity and persistence

1.  Spatial heterogeneity has long been viewed as a reliable means of increasing persistence. Here, an analytical model is developed to consider the variation and, hence, the persistence of stochastic metapopulations. This model relies on a novel moment closure technique, which is equivalent to assuming log-normal distributions for the population sizes.
2.  Single-species models show the greatest persistence when the mixing between subpopulations is large, so spatial heterogeneity is of no benefit. This result is confirmed by stochastic simulation of the full metapopulation.
3.  In contrast, natural-enemy models exhibit the greatest persistence for intermediate levels of coupling. When the coupling is too low, there are insufficient rescue effects between the subpopulations to sustain the dynamics, whereas when the coupling is too high all spatial heterogeneity is lost.
4.  The difference in behaviour between the one- and two-species models can be attributed to the oscillatory nature of the natural-enemy system.     

Metapopulation persistence in dynamic landscapes: the role of dispersal distance

Species associated with transient habitats need efficient dispersal strategies to ensure their regional survival. Using a spatially explicit metapopulation model, we studied the effect of the dispersal range on the persistence of a metapopulation as a function of the local population and landscape dynamics (including habitat patch destruction and subsequent regeneration). Our results show that the impact of the dispersal range depends on both the local population and patch growth. This is due to interactions between dispersal and the dynamics of patches and populations via the number of potential dispersers. In general, long-range dispersal had a positive effect on persistence in a dynamic landscape compared to short-range dispersal. Long-range dispersal increases the number of couplings between the patches and thus the colonisation of regenerated patches. However, long-range dispersal lost its advantage for long-term persistence when the number of potential dispersers was low due to small population growth rates and/or small patch growth rates. Its advantage also disappeared with complex local population dynamics and in a landscape with clumped patch distribution.     

Metapopulation persistence in fragmented landscapes: significant interactions between genetic and demographic processes

We formulated a mathematical model in order to study the joint influence of demographic and genetic processes on metapopulation viability. Moreover, we explored the influence of habitat structure, matrix quality and disturbance on the interplay of these processes. We showed that the conditions that allow metapopulation persistence under the synergistic action of genetic and demographic processes depart significantly from predictions based on a mere superposition of the effects of each process separately. Moreover, an optimal dispersal rate exists that maximizes the range of survival rates of dispersers under which metapopulation persists and at the same time allows the largest sustainable patch removal and patch‐size reduction. The relative impact of patch removal and patch‐size reduction depends both on matrix quality and the dispersal strategy of the species: metapopulation persistence is more affected by patch‐size reduction (patch removal) for low (high)‐dispersing species, in presence of a low (high) quality matrix. Avoidance of inbreeding, through increased dispersal when the rate of inbreeding in a population is large, has positive effects on low‐dispersing species, but impairs the persistence of high‐dispersing species. Finally, size heterogeneity between patches largely influences metapopulation dynamics; the presence of large patches, even at the expense of other patches being smaller, can have positive effects on persistence in particular for species of low dispersing ability.     

Demographic stochasticity and resource autocorrelation control biological invasions in heterogeneous landscapes

Mounting theoretical evidence suggests that demographic stochasticity, environmental heterogeneity and biased movement of organisms individually affect the dynamics of biological invasions and range expansions. Studies of species spread in heterogeneous landscapes have traditionally characterized invasion velocities as functions of the mean resource density throughout the landscape, thus neglecting higher‐order moments of the spatial resource distribution. Here, we show theoretically that different spatial arrangements of resources lead to different spread velocities even if the mean resource density throughout the landscape is kept constant. Specifically, we find that increasing the resource autocorrelation length causes a reduction in the speed of species spread. The model shows that demographic stochasticity plays a key role in the slowdown, which is strengthened when individuals can actively move towards resources. We then experimentally corroborated the theoretically predicted reduction in propagation speed in microcosm experiments with the protist Euglena gracilis by comparing spread in landscapes with different resource autocorrelation lengths. Our work identifies the resource autocorrelation length as a key modulator and a simple measure of landscape susceptibility to biological invasions, which needs to be considered for predicting invasion dynamics within naturally heterogeneous environmental corridors.     

Spatial coherence and the persistence of high diversity in spatially heterogeneous landscapes

Our planet hosts a variety of highly diverse ecosystems. The persistence of high diversity is generally attributed to factors such as the structure of interactions among species and the dispersal of species in metacommunities. Here, we show that large contiguous landscapes—that are characterized by high dispersal—facilitate high species richness due to the spatial heterogeneity in interspecies interactions. We base our analysis on metacommunities under high dispersal where species densities become equal across habitats (spatially coherent). We find that the spatially coherent metacommunity can be represented by an effective species interaction‐web that has a significantly lower complexity than the constituent habitats. Our framework also explains how spatial heterogeneity eliminates differences in the effective interaction‐web, providing a basis for deviations from the area‐heterogeneity tradeoff. These results highlight the often‐overlooked case of high dispersal where spatial coherence provides a novel mechanism for supporting high diversity in large heterogeneous landscapes.     

Metapopulation persistence and species spread in river networks

River networks define ecological corridors characterised by unidirectional streamflow, which may impose downstream drift to aquatic organisms or affect their movement. Animals and plants manage to persist in riverine ecosystems, though, which in fact harbour high biological diversity. Here, we study metapopulation persistence in river networks analysing stage‐structured populations that exploit different dispersal pathways, both along‐stream and overland. Using stability analysis, we derive a novel criterion for metapopulation persistence in arbitrarily complex landscapes described as spatial networks. We show how dendritic geometry and overland dispersal can promote population persistence, and that their synergism provides an explanation of the so‐called `drift paradox’. We also study the geography of the initial spread of a species and place it in the context of biological invasions. Applications concerning the persistence of stream salamanders in the Shenandoah river, and the spread of two invasive species in the Mississippi‐Missouri are also discussed.     

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.     

Metapopulation processes and persistence in remnant water vole populations

We examined the spatial distribution of water vole populations in four consecutive years and investigated whether the regional population processes of extinction, recolonisation and migration influence distribution and persistence. We examined how such regional processes are influenced by spatial variation in habitat quality. In addition, we assessed the relevance of metapopulation concepts for understanding the dynamics of species that deviate from classical metapopulation assumptions and developing conservation measures for them. Populations were patchy and discrete, and the patchy distribution was not static between years. Population turnover occurred even in the absence of predatory mink, which only influenced the network of populations at the end of the study. Most populations were clustered close together in the upper tributaries. Local population persistence was predominantly influenced by population size: large populations were more persistent. Recolonisation rates were influenced by isolation and habitat quality. The isolation estimates which best explained the distribution of water vole populations incorporated straight‐line distances, suggesting water voles disperse overland. The distribution of recolonised sites indicated that dispersing voles actively selected habitat on the basis of its quality. Water voles depart from some of the assumptions made by frequently used metapopulation models. In particular there is no clear binary distinction between suitable and non‐suitable habitat. Accounting for variation in habitat quality before investigating temporal changes in population distribution allowed us to demonstrate that the key metapopulation processes were important. The significance of regional population processes relative to local population processes may have increased in declining, fragmented populations compared to pristine regional populations. We hypothesise that although mink predation is likely to eventually cause regional extinction in many areas, metapopulation processes have delayed this decline. Consequently, conservation measures should take into account mink predation rates and regional population processes, before considering aspects of habitat quality.     

Spatially heterogeneous stochasticity and the adaptive diversification of dormancy

Diversified bet‐hedging, a strategy that leads several individuals with the same genotype to express distinct phenotypes in a given generation, is now well established as a common evolutionary response to environmental stochasticity. Life‐history traits defined as diversified bet‐hedging (e.g. germination or diapause strategies) display marked differences between populations in spatial proximity. In order to find out whether such differences can be explained by local adaptations to spatially heterogeneous environmental stochasticity, we explored the evolution of bet‐hedging dormancy strategies in a metapopulation using a two‐patch model with patch differences in stochastic juvenile survival. We found that spatial differences in the level of environmental stochasticity, restricted dispersal, increased fragmentation and intermediate survival during dormancy all favour the adaptive diversification of bet‐hedging dormancy strategies. Density dependency also plays a major role in the diversification of dormancy strategies because: (i) it may interact locally with environmental stochasticity and amplify its effects; however, (ii) it can also generate chaotic population dynamics that may impede diversification. Our work proposes new hypotheses to explain the spatial patterns of bet‐hedging strategies that we hope will encourage new empirical studies of this topic.     

Metapopulation extinction in fragmented landscapes: using bacteria and protozoa communities as model ecosystems

Extinction is notoriously difficult to study because of the long timescales involved and the difficulty in ascertaining that extinction has actually occurred. The effect of habitat subdivision, or fragmentation, on extinction risk is even harder to study, as it requires copious replication of habitat patches on large spatial scales and control of area effects between treatments. I used simple small-scale communities of bacteria and protozoa to study extinction in response to habitat loss and habitat fragmentation. I studied several different community configurations, each with three trophic levels. Unlike most metapopulation studies (experimental as well as theoretical), which have tended to deal with inherently unstable species interactions, I deliberately used community configurations that were persistent in large stock cultures. I recorded the time to extinction of the top predator in single habitat patches of different sizes and in fragmented systems with different degrees of subdivision but the same amount of available habitat. Habitat loss reduced the time to extinction of isolated populations. Fragmented systems went extinct sooner than corresponding unfragmented (continuous) systems of the same overall size. Unfragmented populations persisted longer than fragmented systems (metapopulations) with or without dispersal corridors between subpopulations. In fact, fragmented systems where the fragments were linked by dispersal corridors went extinctly significantly sooner than those where subpopulations were completely isolated from each other. If these results extend to more "natural" systems, it suggests a need for caution in management programs that emphasize widespread establishment of wildlife corridors in fragmented landscapes.     

Host-parasitoid spatial dynamics in heterogeneous landscapes

This paper explores the effect of spatial processes in a heterogeneous environment on the dynamics of a host-parasitoid interaction. The environment consists of a lattice of favourable (habitat) and hostile (matrix) hexagonal cells, whose spatial distribution is measured by habitat proportion and spatial autocorrelation (inverse of fragmentation). At each time step, a fixed fraction of both populations disperses to the adjacent cells where it reproduces following the Nicholson-Bailey model. Aspects of the dynamics analysed include extinction, stability, cycle period and amplitude, and the spatial patterns emerging from the dynamics.
We find that, depending primarily on the fraction of the host population that disperses in each generation and on the landscape geometry, five classes of spatio-temporal dynamics can be objectively distinguished: spatial chaos, spirals, metapopulation, mainland-island and spiral fragments. The first two are commonly found in theoretical studies of homogeneous landscapes. The other three are direct consequences of the heterogeneity and have strong similarities to dynamic patterns observed in real systems (e.g. extinction-recolonisation, source-sink, outbreaks, spreading waves).
We discuss the processes that generate these patterns and allow the system to persist. The importance of these results is threefold: first, our model merges into a same theoretical framework dynamics commonly observed in the field that are usually modelled independently. Second, these dynamics and patterns are explained by dispersal rate and common landscape statistics, thus linking in a practical way population ecology to landscape ecology. Third, we show that the landscape geometry has a qualitative effect on the length of the cycles and, in particular, we demonstrate how very long periods can be produced by spatial processes.     

Sustainable management of planted landscapes: lessons from Japan

In Japan, 42?% of forests are planted forests, and most of them were established after World War II (1950–1980) to meet increased wood demands. Although Japanese planted forests are now reaching their planned harvest age, they have not been managed, and their restoration is now being discussed. Japanese foresters have not cut their own forests, and the country’s high wood demands have been met by imports during recent decades. The decline of young forests due to the stagnation of forestry activity is suggested to be partly responsible for the nation-wide decline in early-successional species, which is referred to as the “second crisis of biodiversity.” As a timber-importing nation, it is suggested that Japan has underused the nation’s own forests and has overused forests elsewhere. A revival of Japanese plantation forestry may contribute to the restoration of early-successional species because young planted forests are likely to provide suitable habitats. Furthermore, only 30?% of the current planted forests in Japan will be needed to meet the expected future domestic demand for lumber and plywood without imports. The remaining 70?% of the current planted forests may be restored to natural forests with or without harvesting. The history of Japanese planted forests suggests that some natural trees/forests should be retained, even in the landscapes that specialize in wood production, because part of the planted forests may be economically marginalized in the future, and their restoration to natural forests would then be needed.     

Initial conditions and their effect on invasion velocity across heterogeneous landscapes

Accurate, time dependent control options are required to halt biological invasions prior to equilibrium establishment, beyond which control efforts are often impractical. Although invasions have been successfully modeled using diffusion theory, diffusion models are typically confined to providing simple range expansion estimates. In this work, we use a Susceptible/Infected cellular automaton (CA) to simulate diffusion. The CA model is coupled with a network model to track the speed and direction of simulated invasions across heterogeneous landscapes, allowing for identification of locations for targeted control in both time and space. We evaluated the role of the location of initial establishment insofar as it affected the pattern and rate of spread and how these are influenced by patch attributes such as size. Our results show that the location of initial establishment can significantly affect the temporal dynamics of an invasion. Traditional network metrics such as degree and measures of topological distance were insufficient for predicting the direction and speed of the invasion. Our coupled models allow the dynamic tracking of invasions across fragmented landscapes for both theoretical and practical applications.     

Phenology of Lymantria dispar (Lepidoptera: Lymantriidae), male flight and the effect of moth dispersal in heterogeneous landscapes

 A model of Lymantria dispar development was assembled from the published literature and used to predict the period of male moth flight in the United States. Model predictions were compared with observations made with pheromone traps in several locations throughout the United States but especially in Virginia, West Virginia and North Carolina between 1995 and 1996. The model was found to provide accurate and unbiased forecasts of the dates of 5%, 50% and 95% cumulative trap catch, particularly at lower elevations. In areas of high topographic diversity (such as West Virginia), deviations between model output and observations were minimized by basing predictions of 5% and 50% cumulative catch on minimum elevation within neighborhoods of 25–81 km². This model of L. dispar male flight phenology can be used to time the deployment and retrieval of pheromone traps in intensive or extensive monitoring programs. However, a better understanding of moth movement is needed to fully explain the patterns of local trap catch. Received: 9 October 1997/Accepted: 8 December 1997     

异质城市景观中苔藓植物群落多样性的研究

苔藓植物是一类敏感的环境指示植物。通过对上海市市区及市郊5种景观类型中苔藓植物群落的取样调查,从丰富性、均匀性、相似性等方面进行了多种α和β多样性指数分析。结果表明,5种生境中的苔藓群落多样性指数呈现出明显的梯度变化,对景观异质性有较好指示作用;同时苔藓植物平均株高和大型藓类比例在不同景观中也出现规律性变化.     

Persistence and spread of stage-structured populations in heterogeneous landscapes

Journal of Mathematical Biology - Conditions for population persistence in heterogeneous landscapes and formulas for population spread rates are important tools for conservation ecology and...