Stabilization through spatial pattern formation in metapopulations with long-range dispersal

Many studies of metapopulation models assume that spatially extended populations occupy a network of identical habitat patches, each coupled to its nearest neighbouring patches by density-independent dispersal. Much previous work has focused on the temporal stability of spatially homogeneous equilibrium states of the metapopulation, and one of the main predictions of such models is that the stability of equilibrium states in the local patches in the absence of migration determines the stability of spatially homogeneous equilibrium states of the whole metapopulation when migration is added. Here, we present classes of examples in which deviations from the usual assumptions lead to different predictions. In particular, heterogeneity in local habitat quality in combination with long-range dispersal can induce a stable equilibrium for the metapopulation dynamics, even when within-patch processes would produce very complex behaviour in each patch in the absence of migration. Thus, when spatially homogeneous equilibria become unstable, the system can often shift to a different, spatially inhomogeneous steady state. This new global equilibrium is characterized by a standing spatial wave of population abundances. Such standing spatial waves can also be observed in metapopulations consisting of identical habitat patches, i.e. without heterogeneity in patch quality, provided that dispersal is density dependent. Spatial pattern formation after destabilization of spatially homogeneous equilibrium states is well known in reaction–diffusion systems and has been observed in various ecological models. However, these models typically require the presence of at least two species, e.g. a predator and a prey. Our results imply that stabilization through spatial pattern formation can also occur in single-species models. However, the opposite effect of destabilization can also occur: if dispersal is short range, and if there is heterogeneity in patch quality, then the metapopulation dynamics can be chaotic despite the patches having stable equilibrium dynamics when isolated. We conclude that more general metapopulation models than those commonly studied are necessary to fully understand how spatial structure can affect spatial and temporal variation in population abundance.     

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.     

Population turnover and habitat dynamics in Notonecta (Hemiptera: Notonectidae) metapopulations

Simple metapopulation models assume that local populations occur in patches of uniform quality habitat separated by non-habitat. However field metapopulations tend to show considerable spatial and temporal variation in patch quality, and hence probability of occupancy. This may have implications for the adequacy of simple metapopulation models in describing and predicting regional population dynamics of natural systems. This study investigated the effects of habitat characteristics on landscape-scale occupancy dynamics of two species of backswimmer (Notonecta, Hemiptera: Notonectidae) in small freshwater ponds. The results demonstrated clear links between habitat, pond occupancy and population turnover, particularly local extinction. There were considerable changes in the habitat of individual ponds between years, but local changes were not spatially correlated and the frequency distribution of habitat conditions at the landscape level remained similar in different years. Stable occupancy levels of Notonecta species appears to result from a balance of the rates of creation and loss of suitable habitat due to spatially uncorrelated habitat change. Systems such as this, where turnover is driven by habitat dynamics, demonstrate the potential value of incorporating the dynamics of habitat change into metapopulation models. Such developments are likely to improve predictions of landscape-scale occupancy dynamics, whilst also allowing patch-level predictions of occupancy, based on local habitat conditions. Received: 18 August 1999 / Accepted: 3 December 1999     

Spatial population structure in the banner-tailed kangaroo rat,Dipodomys spectabilis

I attempted to characterize spatial units of local dynamics and dispersal in banner-tailed kangaroo rats (Dipodomys spectabilis), to determine if spatial structure influenced population dynamics in the way predicted by current metapopulation models. D. spectabilis exhibited a hierarchical spatial structure. Local populations that appeared as discrete entities on a scale of kilometers were subdivided into clusters of mounds on a scale of meters. This structure, however, cannot be characyerized in terms of the discrete habitat patches envisioned by the metapopulation models. Occupied areas were statistically distinguishable from the surrounding matrix, but this difference was only quantitative. There were no discrete boundaries between occupied areas and the matrix. Habitat within occupied areas was heterogeneous, and occupied areas in different locations were statistically distinguishable from each other. High heterogeneity within occupied areas, and high contrast among them, make it difficult to define what is a suitable habitat patch for D. spectabilis. On a smaller spatial scale, there was significant aggregation of resident mounds within occupied areas. These aggregations, however, do not correspond to discrete habitat patches. Rather, they appear to result from an interaction between fine-scale habitat heterogeneity and limited dispersal due to natal philopatry and low adult vagility. These complications make it difficult to identify habitat patches independent of the species' distribution. For species like D. spectabilis that are patchily distributed but do not occupy discrete habitat patches, a patch occupancy approach does not seem appropriate for describing spatial structure. Hierarchical spatial structure underscores the need for a framework that incorporates multiple scales of spatial structure, rather than one that pre-imposes a single spatial scale as being important for population dynamics. A framework that (i) considers patchiness as a combination of both habitat heterogeneity, and life-history and behavioral characteristics, and (ii) incorporates hierarchical spatial structure, appears to be the most suitable for conceptualizing spatial dynamics of behaviorally complex vertebrates such as D. spectabilis.     

Colonization and extinction dynamics of an annual plant metapopulation in an urban environment

The metapopulation framework considers that the spatiotemporal distribution of organisms results from a balance between the colonization and extinction of populations in a suitable and discrete habitat network. Recent spatially realistic metapopulation models have allowed patch dynamics to be investigated in natural populations but such models have rarely been applied to plants. Using a simple urban fragmented population system in which favourable habitat can be easily mapped, we studied patch dynamics in the annual plant Crepis sancta (Asteraceae). Using stochastic patch occupancy models (SPOMs) and multi‐year occupancy data we dissected extinction and colonization patterns in our system. Overall, our data were consistent with two distinct metapopulation scenarios. A metapopulation (sensu stricto) dynamic in which colonization occurs over a short distance and extinction is lowered by nearby occupied patches (rescue effect) was found in a set of patches close to the city centre, while a propagule rain model in which colonization occurs from a large external population was most consistent with data from other networks. Overall, the study highlights the importance of external seed sources in urban patch dynamics. Our analysis emphasizes the fact that plant distributions are governed not only by habitat properties but also by the intrinsic properties of colonization and dispersal of species. The metapopulation approach provides a valuable tool for understanding how colonization and extinction shape occupancy patterns in highly fragmented plant populations. Finally, this study points to the potential utility of more complex plant metapopulation models than traditionally used for analysing ecological and evolutionary processes in natural metapopulations.     

Spatial heterogeneity, source-sink dynamics, and the local coexistence of competing species

Patch occupancy theory predicts that a trade-off between competition and dispersal should lead to regional coexistence of competing species. Empirical investigations, however, find local coexistence of superior and inferior competitors, an outcome that cannot be explained within the patch occupancy framework because of the decoupling of local and spatial dynamics. We develop two-patch metapopulation models that explicitly consider the interaction between competition and dispersal. We show that a dispersal-competition trade-off can lead to local coexistence provided the inferior competitor is superior at colonizing empty patches as well as immigrating among occupied patches. Immigration from patches that the superior competitor cannot colonize rescues the inferior competitor from extinction in patches that both species colonize. Too much immigration, however, can be detrimental to coexistence. When competitive asymmetry between species is high, local coexistence is possible only if the dispersal rate of the inferior competitor occurs below a critical threshold. If competing species have comparable colonization abilities and the environment is otherwise spatially homogeneous, a superior ability to immigrate among occupied patches cannot prevent exclusion of the inferior competitor. If, however, biotic or abiotic factors create spatial heterogeneity in competitive rankings across the landscape, local coexistence can occur even in the absence of a dispersal-competition trade-off. In fact, coexistence requires that the dispersal rate of the overall inferior competitor not exceed a critical threshold. Explicit consideration of how dispersal modifies local competitive interactions shifts the focus from the patch occupancy approach with its emphasis on extinction-colonization dynamics to the realm of source-sink dynamics. The key to coexistence in this framework is spatial variance in fitness. Unlike in the patch occupancy framework, high rates of dispersal can undermine coexistence, and hence diversity, by reducing spatial variance in fitness.     

Heterogeneity in patch quality buffers metapopulations from pathogen impacts

Many wildlife species persist on a network of ephemerally occupied habitat patches connected by dispersal. Provisioning of food and other resources for conservation management or recreation is frequently used to improve local habitat quality and attract wildlife. Resource improvement can also facilitate local pathogen transmission, but the landscape-level consequences of provisioning for pathogen spread and habitat occupancy are poorly understood. Here, we develop a simple metapopulation model to investigate how heterogeneity in patch quality resulting from resource improvement influences long-term metapopulation occupancy in the presence of a virulent pathogen. We derive expressions for equilibrium host–pathogen outcomes in terms of provisioning effects on individual patches (through decreased patch extinction rates) and at the landscape level (the fraction of high-quality, provisioned patches), and highlight two cases of practical concern. First, if occupancy in the unprovisioned metapopulation is sufficiently low, a local maximum in occupancy occurs for mixtures of high- and low-quality patches, such that further increasing the number of high-quality patches both lowers occupancy and allows pathogen invasion. Second, if the pathogen persists in the unprovisioned metapopulation, further provisioning can result in all patches becoming infected and in a global minimum in occupancy. This work highlights the need for more empirical research on landscape-level impacts of local resource provisioning on pathogen dynamics.     

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     

Effects of matrix heterogeneity on animal dispersal: from individual behavior to metapopulation-level parameters

Mounting theoretical and empirical evidence shows that matrix heterogeneity may have contrasting effects on metapopulation dynamics by contributing to patch isolation in nontrivial ways. We analyze the movement properties during interpatch dispersal in a metapopulation of Iberian lynx (Lynx pardinus). On a daily temporal scale, lynx habitat selection defines two types of matrix habitats where individuals may move: open and dispersal habitats (avoided and used as available, respectively). There was a strong and complex impact of matrix heterogeneity on movement properties at several temporal scales (hourly and daily radiolocations and the entire dispersal event). We use the movement properties on the hourly temporal scale to build a simulation model to reconstruct individual dispersal events. The two most important parameters affecting model predictions at both the individual (daily) and metapopulation scales were related to the movement capacity (number of movement steps per day and autocorrelation in dispersal habitat) followed by the parameters representing the habitat selection in the matrix. The model adequately reproduced field estimates of population-level parameters (e.g., interpatch connectivity, maximum and final dispersal distances), and its performance was clearly improved when including the effect of matrix heterogeneity on movement properties. To assume there is a homogeneous matrix results in large errors in the estimate of interpatch connectivity, especially for close patches separated by open habitat or corridors of dispersal habitat, showing how important it is to consider matrix heterogeneity when it is present. Movement properties affect the interaction of dispersing individuals with the landscape and can be used as a mechanistic representation of dispersal at the metapopulation level. This is so when the effect of matrix heterogeneity on movement properties is evaluated under biologically meaningful spatial and temporal scales.     

Host–parasitoid dynamics in a fragmented landscape: Holly trees,holly leaf miners and their parasitoids

Many species inhabit fragmented landscapes, where units of resource have a patchy spatial distribution. While numerous studies have investigated how the incidence and dynamics of individual species are affected by the spatial configuration and landscape context of habitat patches, fewer studies have investigated the dynamics of multiple interacting resource and consumer species in patchy landscapes. We describe a model system for investigating host–parasitoid dynamics in a patchy landscape: a network of 166 holly trees, a specialised herbivore of holly (the leaf miner, Phytomyza ilicis (Curtis, 1948)), and its suite of parasitoids. We documented patch occupancy by P. ilicis, its density within patches, and levels of parasitism over a 6-year period, and manipulated patch occupancy by creating artificially vacant habitat patches. Essentially all patches were occupied by the herbivore in each year, suggesting that metapopulation dynamics are unlikely to occur in this system. The main determinants of densities for P. ilicis and its parasitoids were resource availability (patch size and host density, respectively). While P. ilicis is apparently not restricted by the spatial distribution of resources, densities of its parasitoids showed a weaker positive relationship with host density in more isolated patches. In patches where local extinctions were generated experimentally, P. ilicis densities and levels of parasitism recovered to pre-manipulation levels within a single generation. Furthermore, patch isolation did not significantly affect re-colonisation by hosts or parasitoids. Analysing the data at a variety of spatial scales indicates that the balance between local demography and dispersal may vary depending on the scale at which patches are defined. Taken together, our results suggest that the host and its parasitoids have dispersal abilities that exceed typical inter-patch distances. Patch dynamics are thus largely governed by dispersal rather than within-patch demography, although the role of demography is higher in larger patches.     

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.     

用空间直观模型是否足以从斑块占据性资料中推断集合种群的动态过程?

在集合种群的研究中,经常要根据空间占据性数据应用斑块模型来推断种群的动态过程,在保护生物学应用中,斑块占据性模型的参数估测对于阐释集合种群动态和预测种群对生境破坏的反应极为重要。我们探讨了一种广泛应用的空间直观模型——率函数模型(Incidence function model)中参数估测的不确定性问题,通过构建由50个斑块组成的网络和两个假想的已知参数的集合种群,应用模拟模型产生集合种群随时间变化的斑块占据性数据系列：即快照(snapshot)。然后,根据这些快照,应用率函数模型和最大似然法估测种群动态参数。此外,我们还给出了传统的率函数模型的一个变形,这个变形包含了目标区效应(Target area effect)：即一个斑块的占据概率不但取决于空间隔离度,也取决于斑块本身面积的大小。结果表明：根据同一个集合种群不同的快照所估测的参数可以有很大差异,一个快照得出的参数提示的是占据性强但存活率低的集合种群,而另一个快照可能反映的是一个占据性弱但存活率高的集合种群。应用传统的率函数模型于一个包含了目标区效应的集合种群,导致斑块大小相关的灭绝率参数估测的正偏差。因此,仅根据一个快照的空间占据性数据来推测集合种群的过程有很大的不确定性[动物学报49(6)：787～794,2003]。     

Long-term dynamics in a metapopulation of the American pika

A 20-yr study of a metapopulation of the American pika revealed a regional decline in occupancy in one part of a large network of habitat patches. We analyze the possible causes of this decline using a spatially realistic metapopulation model, the incidence function model. The pika metapopulation is the best-known mammalian example of a classical metapopulation with significant population turnover, and it satisfies closely the assumptions of the incidence function model, which was parameterized with data on patch occupancy. The model-predicted incidences of patch occupancy are consistent with observed incidences, and the model predicts well the observed turnover rate between four metapopulation censuses. According to model predictions, the part of the metapopulation where the decline has been observed is relatively unstable and prone to large oscillations in patch occupancy, whereas the other part of the metapopulation is predicted to be persistent. These results demonstrate how extinction-colonization dynamics may produce spatially correlated patterns of patch occupancy without any spatially correlated processes in local dynamics or extinction rate. The unstable part of the metapopulation gives an empirical example of multiple quasi equilibria in metapopulation dynamics. Phenomena similar to those observed here may cause fluctuations in species' range limits.     

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.     

Generalizing Levins metapopulation model in explicit space: models of intermediate complexity

A recent study [Harding and McNamara, 2002. A unifying framework for metapopulation dynamics. Am. Nat. 160, 173-185] presented a unifying framework for the classic Levins metapopulation model by incorporating several realistic biological processes, such as the Allee effect, the Rescue effect and the Anti-rescue effect, via appropriate modifications of the two basic functions of colonization and extinction rates. Here we embed these model extensions on a spatially explicit framework. We consider population dynamics on a regular grid, each site of which represents a patch that is either occupied or empty, and with spatial coupling by neighborhood dispersal. While broad qualitative similarities exist between the spatially explicit models and their spatially implicit (mean-field) counterparts, there are also important differences that result from the details of local processes. Because of localized dispersal, spatial correlation develops among the dynamics of neighboring populations that decays with distance between patches. The extent of this correlation at equilibrium differs among the metapopulation types, depending on which processes prevail in the colonization and extinction dynamics. These differences among dynamical processes become manifest in the spatial pattern and distribution of “clusters” of occupied patches. Moreover, metapopulation dynamics along a smooth gradient of habitat availability show significant differences in the spatial pattern at the range limit. The relevance of these results to the dynamics of disease spread in metapopulations is discussed.     

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.     

Evolutionary branching of dispersal strategies in structured metapopulations

 Dispersal polymorphism and evolutionary branching of dispersal strategies has been found in several metapopulation models. The mechanism behind those findings has been temporal variation caused by cyclic or chaotic local dynamics, or temporally and spatially varying carrying capacities. We present a new mechanism: spatial heterogeneity in the sense of different patch types with sufficient proportions, and temporal variation caused by catastrophes. The model where this occurs is a generalization of the model by Gyllenberg and Metz (2001). Their model is a size-structured metapopulation model with infinitely many identical patches. We present a generalized version of their metapopulation model allowing for different types of patches. In structured population models, defining and computing fitness in polymorphic situations is, in general, difficult. We present an efficient method, which can be applied also to other structured population or metapopulation models. Received: 6 March 2001 / Revised version: 12 February 2002 / Published online: 17 July 2002     

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.     

Variability in primary productivity determines metapopulation dynamics

Temporal variability in primary productivity can change habitat quality for consumer species by affecting the energy levels available as food resources. However, it remains unclear how habitat-quality fluctuations may determine the dynamics of spatially structured populations, where the effects of habitat size, quality and isolation have been customarily assessed assuming static habitats. We present the first empirical evaluation on the effects of stochastic fluctuations in primary productivity—a major outcome of ecosystem functions—on the metapopulation dynamics of a primary consumer. A unique 13-year dataset from an herbivore rodent was used to test the hypothesis that inter-annual variations in primary productivity determine spatiotemporal habitat occupancy patterns and colonization and extinction processes. Inter-annual variability in productivity and in the growing season phenology significantly influenced habitat colonization patterns and occupancy dynamics. These effects lead to changes in connectivity to other potentially occupied habitat patches, which then feed back into occupancy dynamics. According to the results, the dynamics of primary productivity accounted for more than 50% of the variation in occupancy probability, depending on patch size and landscape configuration. Evidence connecting primary productivity dynamics and spatiotemporal population processes has broad implications for metapopulation persistence in fluctuating and changing environments.     

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.