Are spatially correlated or uncorrelated disturbance regimes better for the survival of species?

The survival of species in dynamic landscapes (characterised by patch destruction and subsequent regeneration) depends on both the species' attributes and the disturbance pattern. Using a spatially explicit model we explored how the mean time to extinction of a metapopulation depends on the spatial correlation of patch destruction in relation to the population growth and dispersal abilities of species. Two contrasting answers are possible. On the one hand, increasing spatial correlation of patch destruction increases the spatial correlation of population growth and this is known to decrease metapopulation persistence. On the other hand, spatially correlated patch destruction and regeneration can lead to clustered habitat patches and this is known to increase metapopulation persistence. Therefore, we hypothesised that some species are better off under spatially correlated and alternatively uncorrelated disturbance regimes. However, contrary to this hypothesis, in all kinds of cases spatial correlation reduced metapopulation persistence. We found this to be due to the fact that the spatial correlation of patch destruction causes increasing temporal fluctuations in the regional carrying capacity of the metapopulation and is hence generally disadvantageous for long-term persistence. The main consequence for conservation biology is that reducing spatial correlation in disturbances is likely to be a reliable strategy in a dynamic landscape that will benefit practically all species with a low risk of adverse side effects .     

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.     

A spatially structured metapopulation model with patch dynamics

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

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.     

Competitive coexistence in a dynamic landscape

This paper investigates the effect of a dynamic landscape on the persistence of many interacting species. We develop a multi-species community model with an evolving landscape in which the creation and destruction of habitat are dynamic and local in space. Species interactions are also local involving hierarchical competitive trade-offs. We show that dynamic landscapes can reverse the trend of increasing species richness with higher fragmentation observed in static landscapes. The increase in the species-area exponent from a homogeneous to a fragmented landscape does not occur when dynamics are turned on. Thus, temporal aspects of the processes that generate and destroy habitat appear dominant relative to spatial characteristics. We also demonstrate, however, that temporal and spatial aspects interact to influence the persistence time of individual species, and therefore, rank-abundance curves. Specifically, persistence in the model increases in habitats with faster local turnover because of the presence of dynamic corridors.     

Experimental beetle metapopulations respond positively to dynamic landscapes and reduced connectivity

Interactive effects of multiple environmental factors on metapopulation dynamics have received scant attention. We designed a laboratory study to test hypotheses regarding interactive effects of factors affecting the metapopulation dynamics of red flour beetle, Tribolium castaneum. Within a four-patch landscape we modified resource level (constant and diminishing), patch connectivity (high and low) and patch configuration (static and dynamic) to conduct a 2(3) factorial experiment, consisting of 8 metapopulations, each with 3 replicates. For comparison, two control populations consisting of isolated and static subpopulations were provided with resources at constant or diminishing levels. Longitudinal data from 22 tri-weekly counts of beetle abundance were analyzed using bayesian Poisson generalized linear mixed models to estimate additive and interactive effects of factors affecting abundance. Constant resource levels, low connectivity and dynamic patches yielded greater levels of adult beetle abundance. For a given resource level, frequency of colonization exceeded extinction in landscapes with dynamic patches when connectivity was low, thereby promoting greater patch occupancy. Negative density dependence of pupae on adults occurred and was stronger in landscapes with low connectivity and constant resources; these metapopulations also demonstrated greatest stability. Metapopulations in control landscapes went extinct quickly, denoting lower persistence than comparable landscapes with low connectivity. When landscape carrying capacity was constant, habitat destruction coupled with low connectivity created asynchronous local dynamics and refugia within which cannibalism of pupae was reduced. Increasing connectivity may be counter-productive and habitat destruction/recreation may be beneficial to species in some contexts.     

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.     

Modelling the spatial dynamics and persistence of the leaf beetle Gonioctena olivacea in dynamic habitats

In dynamic landscapes natural and anthropogenic disturbance as well as succession are responsible for the emergence and subsequent disappearance of suitable habitat patches. Species inhabiting such landscapes are faced with varying number and spatial configuration of patches. A stochastic, spatially explicit simulation model was developed in order to analyse the persistence of the leaf beetle Gonioctena olivacea in a system of dynamic patches of its host plant Cytisus scoparius . The model was parameterized with data from a three-year field study on the spatial configuration, distribution, and turnover of the host plant patches as well as the patch occupancy, extinction, and colonization rates of the beetle. The simulations showed large fluctuations in the occurrence of the beetle in the patches. High levels of occupancy were related to high aggregation of the patches within the landscape. The velocity of patch turnover was found to have a severe effect on the persistence of the beetle metapopulation. Enhancing the turnover rate by only a few patches, the mean time to extinction decreases rapidly. Moreover, the results revealed that not necessarily an effect of connectivity can be detected in the analysis of occupancy patterns in dynamic landscapes, although the colonization of patches is clearly connectivity-dependent. In general, this modelling study demonstrates the importance of detailed information on patch turnover. The amount and spatial distribution of suitable habitat is a major driver of metapopulation dynamics of species in dynamic landscapes.     

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     

Continuum or discrete patch landscape models for savanna birds? Towards a pluralistic approach

Conceptualising landscapes as a mosaic of discrete habitat patches is fundamental to landscape ecology, metapopulation theory and conservation biology. An emerging question in ecology is: when is the discrete patch model more appropriate than alternative and conceptually appealing models such as the continuum model? There is limited empirical testing of the utility of alternative landscape models compared to the discrete patch model for a range of species. In this paper, we constructed three alternative sets of models for testing the effect of landscape structure on diversity and abundance of a suite of woodland birds in a savanna landscape of northern Australia: the null model (only site‐scale habitat variables, landscape context not important), the continuum model, and the discrete patch model. We utilised high‐spatial resolution satellite images to quantify spatial gradients in tree cover density (the continuum model), and to then aggregate the fine‐scale heterogeneity in tree cover into discrete patches of trees, with grass cover forming the “matrix” (the discrete patch‐model). We then evaluated the relative importance of the alternative models using generalised linear models and an information theoretic approach. We found that the importance of the models varied among species, with no single model dominant. Species that move between open grassy areas and woody shelter responded well to the continuum model, reflecting the importance of gradients in density of forage (grasses) and cover (trees), while the discrete model performed best for species that forage in all vegetation strata, and nest predominantly in dense woody vegetation. This finding supports a pluralistic approach, highlighting the need for adopting and testing more than one landscape model in savanna landscapes, and in other landscapes that do not have a well defined patch structure.     

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.     

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.     

Toward ecologically scaled landscape indices

Nature conservation is increasingly based on a landscape approach rather than a species approach. Landscape planning that includes nature conservation goals requires integrated ecological tools. However, species differ widely in their response to landscape change. We propose a framework of ecologically scaled landscape indices that takes into account this variation. Our approach is based on a combination of field studies of spatially structured populations (metapopulations) and model simulations in artificial landscapes. From these, we seek generalities in the relationship among species features, landscape indices, and metapopulation viability. The concept of ecological species profiles is used to group species according to characteristics that are important in metapopulations' response to landscape change: individual area requirements as the dominant characteristic of extinction risk in landscape patches and dispersal distance as the main determinant of the ability to colonize patches. The ecological profiles and landscape indices are then integrated into two ecologically scaled landscape indices (ESLI): average patch carrying capacity and average patch connectivity. The field data show that the fraction of occupied habitat patches is correlated with the two ESLI. To put the ESLI into a perspective of metapopulation persistence, we determine the viability for six ecological profiles at different degrees of habitat fragmentation using a metapopulation model and computer-generated landscapes. The model results show that the fraction of occupied patches is a good indicator for metapopulation viability. We discuss how ecological profiles, ESLI, and the viability threshold can be applied for landscape planning and design in nature conservation.     

Habitat quality of source patches and connectivity in fragmented landscapes

Because spatial connectivity is critical to dispersal success and persistence of species in highly fragmented landscapes, the way that we envision and measure connectivity is consequential for biodiversity conservation. Connectivity metrics used for predictive modeling of spatial turnover and patch occupancy for metapopulations, such as with Incidence Function Models (IFM), incorporate distances to and sizes of possible source populations. Here, our focus is on whether habitat quality of source patches also is considered in these connectivity metrics. We propose that effective areas (weighted by habitat quality) of source patches should be better surrogates for population size and dispersal potential compared to unadjusted patch areas. Our review of a representative sample of the literature revealed that only 12.5% of studies incorporated habitat quality of source patches into IFM-type connectivity metrics. Quality of source patches generally was not taken into account in studies even if habitat quality of focal patches was included in analyses. We provide an empirical example for a metapopulation of a rare wetland species, the round-tailed muskrat (Neofiber alleni), demonstrating that a connectivity metric based on effective areas of source patches better predicts patch colonization and occupancy than a metric that used simple patch areas. The ongoing integration of landscape ecology and metapopulation dynamics could be hastened by incorporating habitat quality of source patches into spatial connectivity metrics applied to species conservation in fragmented landscapes.     

Using connectivity metrics in conservation planning – when does habitat quality matter?

Aim The objective of conservation planning is often to prioritize patches based on their estimated contribution to metapopulation or metacommunity viability. The contribution that an individual patch makes will depend on its intrinsic characteristics, such as habitat quality, as well as its location relative to other patches, its connectivity. Here we systematically evaluate five patch value metrics to determine the importance of including an estimate of habitat quality into the metrics. Location We tested the metrics in landscapes designed to represent different degrees of variability in patch quality and different levels of patch aggregation. Methods In each landscape, we simulated population dynamics using a spatially explicit, continuous time metapopulation model linked to within patch logistic growth models. We tested five metrics that are used to estimate the contribution that a patch makes to metapopulation viability: two versions of the probability of connectivity index, two versions of patch centrality (a graph theory metric) and the metapopulation capacity metric. Results All metrics performed best in environments where patch quality was very variable and high quality patches were aggregated. Metrics that incorporated some measure of patch quality did better in all environments, but did particularly well in environments with high variance of patch quality and spatial aggregation of good quality patches. Main conclusions Including an estimate of patch quality significantly increased the ability of a given connectivity metric to rank correctly habitat patches according to their contribution to metapopulation viability. Incorporating patch quality is particularly important in landscapes where habitat quality is highly variable and good quality patches are spatially aggregated. However, caution should be used when applying patch metrics to homogeneous landscapes, even if good estimates of patch quality are available. Our results demonstrate that landscape structure and the degree of variability in patch quality need to be assessed prior to selecting a suitable method for estimating patch value.     

How does temporal variation in habitat connectivity influence metapopulation dynamics?

Metapopulation persistence depends on connectivity between habitat patches. While emphasis has been placed on the spatial dynamics of connectivity, much less has been placed on its short‐term temporal dynamics. In many terrestrial and aquatic ecosystems, however, transient (short‐term) changes in connectivity occur as habitat patches are connected and disconnected due, for example, to climatic or hydrological variability. We evaluated the implications of transient connectivity using a network‐based metapopulation model and a series of scenarios representing temporal changes in connectivity. The transient loss of connectivity can influence metapopulation persistence, and more strongly autocorrelated temporal dynamics affect metapopulation persistence more severely. Given that many ecosystems experience short‐term and temporary loss of habitat connectivity, it is important that these dynamics are adequately represented in metapopulation models; failing to do so may yield overly optimistic‐estimates of metapopulation persistence in fragmented landscapes.     

The influence of patch demographics on metapopulations, with particular reference to successional landscapes

The classical view of metapopulations relates the regional abundance of a species to the balance between the extinction and colonization dynamics of identical local populations. Species in successional landscapes may represent the most appropriate examples of classical metapopulations. However, Levins‐type metapopulation models do not explicitly separate population loss due to successional habitat change from other causes of extinction. A further complication is that the chance of population loss due to successional habitat change may be related to the age of a patch. I developed simple patch occupancy models to include succession and included consideration of patch age structure to address two related questions: what are the implications of changes in patch demographic rates and when is a move to a structured patch occupancy model justified? Age‐related variation in patch demography could increase or decrease the equilibrium fraction of the available habitat occupied by a species when compared to the predictions of an unstructured model. Metapopulation persistence was enhanced when the age class of patches with the highest species occupancy suffered relatively low losses to habitat succession. Conversely, when the age class of patches with the highest species occupancy also had relatively high successional loss rates, extinction thresholds were higher that would be predicted by a simple unstructured model. Hence age‐related variation in patch successional rate introduces biases into the predictions of simple unstructured models. Such biases can be detected from field surveys of the fraction of occupied and unoccupied patches in each age class. Where a bias is demonstrated, unstructured models will not be adequate for making predictions about the effects of changing parameters on metapopulation size. Thinking in successional terms emphasizes how landscapes might be managed to enhance or reduce the patch occupancy by any particular metapopulation     

Metapopulation Persistence in Random Fragmented Landscapes

Habitat destruction and land use change are making the world in which natural populations live increasingly fragmented, often leading to local extinctions. Although local populations might undergo extinction, a metapopulation may still be viable as long as patches of suitable habitat are connected by dispersal, so that empty patches can be recolonized. Thus far, metapopulations models have either taken a mean-field approach, or have modeled empirically-based, realistic landscapes. Here we show that an intermediate level of complexity between these two extremes is to consider random landscapes, in which the patches of suitable habitat are randomly arranged in an area (or volume). Using methods borrowed from the mathematics of Random Geometric Graphs and Euclidean Random Matrices, we derive a simple, analytic criterion for the persistence of the metapopulation in random fragmented landscapes. Our results show how the density of patches, the variability in their value, the shape of the dispersal kernel, and the dimensionality of the landscape all contribute to determining the fate of the metapopulation. Using this framework, we derive sufficient conditions for the population to be spatially localized, such that spatially confined clusters of patches act as a source of dispersal for the whole landscape. Finally, we show that a regular arrangement of the patches is always detrimental for persistence, compared to the random arrangement of the patches. Given the strong parallel between metapopulation models and contact processes, our results are also applicable to models of disease spread on spatial networks.     

Patch dynamics and metapopulation theory: the case of successional species

We present a mathematical framework that combines extinction-colonization dynamics with the dynamics of patch succession. We draw an analogy between the epidemiological categorization of individuals (infected, susceptible, latent and resistant) and the patch structure of a spatially heterogeneous landscape (occupied-suitable, empty-suitable, occupied-unsuitable and empty-unsuitable). This approach allows one to consider life-history attributes that influence persistence in patchy environments (e.g., longevity, colonization ability) in concert with extrinsic processes (e.g., disturbances, succession) that lead to spatial heterogeneity in patch suitability. It also allows the incorporation of seed banks and other dormant life forms, thus broadening patch occupancy dynamics to include sink habitats. We use the model to investigate how equilibrium patch occupancy is influenced by four critical parameters: colonization rate, extinction rate, disturbance frequency and the rate of habitat succession. This analysis leads to general predictions about how the temporal scaling of patch succession and extinction-colonization dynamics influences long-term persistence. We apply the model to herbaceous, early-successional species that inhabit open patches created by periodic disturbances. We predict the minimum disturbance frequency required for viable management of such species in the Florida scrub ecosystem.     

Colonization–extinction dynamics of epixylic lichens along a decay gradient in a dynamic landscape

Metapopulation models are often used for understanding and predicting species dynamics in fragmented landscapes. Several models have been proposed depending on e.g. the relative importance of patch dynamics on the metapopulation dynamics. Dead wood is a dynamic substrate patch, and species that are confined to such patches have experienced a high degree of habitat loss in managed forests. Little is, however, known about how the population dynamics of epixylic species are affected by the fast dynamics of their substrate patches. We quantified the effect of local patch conditions and metapopulation processes on colonizations and extinctions of epixylic lichen species in a managed boreal forest landscape. This was done by twice surveying seven lichen metapopulations on 293 stumps in 30 stands of ages covering the duration of the dynamic patches (stumps). We also investigated the relative importance of local stochastic extinctions from stumps that remained available, and deterministic extinctions due to stump surface disappearance. We found importance of a decay gradient, surrounding metapopulation size, and local population sizes, in driving the colonization–extinction dynamics of epixylic lichens. The species were sorted along the stump decay gradient. Increasing surrounding metapopulation size was associated with increased colonization rates, and increasing local population size decreased lichen extinction rates. Finally, both local stochastic extinctions and deterministic extinctions due to patch disappearance occur, confirming that the long‐term persistence of epixylic lichens depends on colonization rates that compensate for stochastic population extinctions as well as deterministic extinctions.