The effective size of a metapopulation living in a heterogeneous patch network

I analyze stochastic patch occupancy models (SPOMs), which record habitat patches as empty or occupied. A problem with SPOMs has been that if the spatial structure of a heterogeneous habitat patch network is taken into account, the computational effort needed to analyze a SPOM grows as a power of 2n, where n is the number of habitat patches. I propose a computationally feasible approximation method, which approximates the behavior of a heterogeneous SPOM by an "ideal" metapopulation inhabiting a network of identical and equally connected habitat patches. The transformation to the ideal metapopulation is based on weighting the individual patch occupancies by the dynamic values of the habitat patches, which may be calculated from the deterministic mean-field approximation of the original SPOM. Conceptually, the method resembles the calculation of the effective size of a population in the context of population genetics. I demonstrate how the method may be applied to SPOMs with flexible structural assumptions and with spatially correlated and temporally varying parameter values. I apply the method to a real habitat patch network inhabited by the Glanville fritillary butterfly, illustrating that the metapopulation dynamics of this species are essentially driven by temporal variability in the environmental conditions.     

Metapopulation-level adaptation of insect host plant preference and extinction-colonization dynamics in heterogeneous landscapes

Species living in highly fragmented landscapes typically occur as metapopulations with frequent turnover of local populations. The turnover rate depends on population sizes and connectivities, but it may also depend on the phenotypic and genotypic composition of populations. The Glanville fritillary butterfly (Melitaea cinxia) in Finland uses two host plant species, which show variation in their relative abundances at two spatial scales: locally among individual habitat patches and regionally among networks of patches. Female butterflies in turn exhibit spatial variation in genetically determined host plant preference within and among patch networks. Emigration, immigration and establishment of new populations have all been shown to be strongly influenced by the match between the host plant composition of otherwise suitable habitat patches and the host plant preference of migrating butterflies. The evolutionary consequences of such biased migration and colonization with respect to butterfly phenotypes might differ depending on spatial configuration and plant species composition of the patches in heterogeneous patch networks. Using a spatially realistic individual-based model we show that the model-predicted evolution of host plant preference due to biased migration explains a significant amount of the observed variation in host plant use among metapopulations living in dissimilar networks. This example illustrates how the ecological extinction-colonization dynamics may be linked with the evolutionary dynamics of life history traits in metapopulations.     

Molecular-level variation affects population growth in a butterfly metapopulation

The dynamics of natural populations are thought to be dominated by demographic and environmental processes with little influence of intraspecific genetic variation and natural selection, apart from inbreeding depression possibly reducing population growth in small populations. Here we analyse hundreds of well-characterised local populations in a large metapopulation of the Glanville fritillary butterfly (Melitaea cinxia), which persists in a balance between stochastic local extinctions and recolonisations in a network of 4,000 discrete habitat patches. We show that the allelic composition of the glycolytic enzyme phosphoglucose isomerase (Pgi) has a significant effect on the growth of local populations, consistent with previously reported effects of allelic variation on flight metabolic performance and fecundity in the Glanville fritillary and Colias butterflies. The strength and the sign of the molecular effect on population growth are sensitive to the ecological context (the area and spatial connectivity of the habitat patches), which affects genotype-specific gene flow and the influence of migration on the dynamics of local populations. The biological significance of the results for Pgi is underscored by lack of any association between population growth and allelic variation at six other loci typed in the same material. In demonstrating, to our knowledge for the first time, that molecular variation in a candidate gene affects population growth, this study challenges the perception that differential performance of individual genotypes, leading to differential fitness, is irrelevant to population dynamics. These results also demonstrate that the spatial configuration of habitat and spatial dynamics of populations contribute to maintenance of Pgi polymorphism in this species.     

A candidate locus for variation in dispersal rate in a butterfly metapopulation

Frequent extinctions of local populations in metapopulations create opportunities for migrant females to establish new populations. In a metapopulation of the Glanville fritillary butterfly (Melitaea cinxia), more mobile individuals are more likely to establish new populations, especially in habitat patches that are poorly connected to existing populations. Here we show that flight metabolic rate and the frequency of a specific allele of the metabolic enzyme phosphoglucose isomerase (pgi) were both highest in newly established, isolated populations. Furthermore, genotypes with this pgi allele had elevated flight metabolic rates. These results suggest that genetic variation in pgi or a closely linked locus has a direct effect on flight metabolism, dispersal rate, and thereby on metapopulation dynamics in this species. These results also contribute to an emerging understanding of the mechanisms by which population turnover in heterogeneous landscapes may maintain genetic and phenotypic variation across populations.     

Size and genetic composition of the colonizing propagules in a butterfly metapopulation

The amount and spatial distribution of genetic variation that is maintained in a metapopulation depends critically on the colonization process. Here, we use molecular markers to determine the number and genetic relatedness of individuals establishing new local populations in a large metapopulation of the Glanville fritillary butterfly Melitaea cinxia. The empirical results are compared with the predictions of a dispersal model based on a diffusion approximation of correlated random walk, which serves as a base‐line hypothesis about the rate and pattern of colonization. The results show that half of the new local populations consisted of a single larval group of full sibs and hence necessarily of the offspring of a single female. If the colonization involved two or more larval groups, these were usually oviposited by two different females that were unrelated to each other. The pattern of colonizations is thus intermediate between the propagule pool and the migrant pool models. These results elucidate the generation of genetic stochasticity, which may influence the dynamics of small populations. The dispersal model predicted well the pattern of habitat occupancy and the pattern of colonizations in relation to landscape structure, though which particular habitat patches became colonized was influenced also by measures of habitat quality not included in the model.     

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

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

Correlated extinctions, colonizations and population fluctuations in a highly connected ringlet butterfly metapopulation

 The persistence of metapopulations is likely to be highly dependent on whether population dynamics are correlated among habitat patches as a result of migration between patches and spatially-correlated environmental stochasticity (weather effects). We examined whether population dynamics of the ringlet butterfly, Aphantopus hyperantus, were synchronous in an area of approximately 0.5 km², with respect to extinction, colonization and population fluctuations. Monks Wood Butterfly Monitoring Scheme transect count data from 1973 to 1995, revealed (A) a major environmental perturbation, the drought of 1976, which caused synchronized extinctions of A. hyperantus in subsequent years, (B) synchronized recolonization in years following the large number of apparent extinctions, and (C) population changes by A. hyperantus were highly correlated in many of the 14 sections of the transect, presumably reflecting similar responses to environmental stochasticity, and the exchange of individuals among sections. However, extinction and population synchrony depended on habitat type. Following the 1976 drought, A. hyperantus apparently became extinct from the most open and most shady habitats it occupied, with some persistence in habitats of intermediate shading, thus showing retraction to core populations in central parts of an environmental gradient, albeit with an average shift to relatively open habitat. Populations at extreme ends of the environmental gradient occupied by A. hyperantus fluctuated least synchronously, suggesting a potential buffering effect of habitat heterogeneity, but this was not crucial to survival after the 1976 drought. Thus, not all habitats are equally important to persistence. Correlated temporal dynamics, variation in habitat quality and the interaction between habitat quality and temporal environmental stochasticity are important determinants of metapopulation persistence and should be incorporated in metapopulation models. Received: 26 April 1996 / Accepted: 17 July 1996     

Area-dependent migration by ringlet butterflies generates a mixture of patchy population and metapopulation attributes

Interpretation of spatially structured population systems is critically dependent on levels of migration between habitat patches. If there is considerable movement, with each individual visiting several patches, there is one ”patchy population”; if there is intermediate movement, with most individuals staying within their natal patch, there is a metapopulation; and if (virtually) no movement occurs, then the populations are separate (Harrison 1991, 1994). These population types actually represent points along a continuum of much to no mobility in relation to patch structure. Therefore, interpretation of the effects of spatial structure on the dynamics of a population system must be accompanied by information on mobility. We use empirical data on movements by ringlet butterflies, Aphantopus hyperantus, to investigate two key issues that need to be resolved in spatially-structured population systems. First, do local habitat patches contain largely independent local populations (the unit of a metapopulation), or merely aggregations of adult butterflies (as in patchy populations)? Second, what are the effects of patch area on migration in and out of the patches, since patch area varies considerably within most real population systems, and because human landscape modification usually results in changes in habitat patch sizes? Mark-release-recapture (MRR) data from two spatially structured study systems showed that 63% and 79% of recaptures remained in the same patch, and thus it seems reasonable to call both systems metapopulations, with some capacity for separate local dynamics to take place in different local patches. Per capita immigration and emigration rates declined with increasing patch area, while the resident fraction increased. Actual numbers of emigrants either stayed the same or increased with area. The effect of patch area on movement of individuals in the system are exactly what we would have expected if A. hyperantus were responding to habitat geometry. Large patches acted as local populations (metapopulation units) and small patches simply as locations with aggregations (units of patchy populations), all within 0.5 km². Perhaps not unusually, our study system appears to contain a mixture of metapopulation and patchy-population attributes.     

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.     

Dispersal-related life-history trade-offs in a butterfly metapopulation

1. Recent studies on butterflies have documented apparent evolutionary changes in dispersal rate in response to climate change and habitat change. These studies often assume a trade-off between dispersal rate (or flight capacity) and reproduction, which is the rule in wing-dimorphic species but might not occur equally in wing-monomorphic species such as butterflies. 2. To investigate the relationship between dispersal rate and fecundity in the Glanville fritillary butterfly Melitaea cinxia we recorded lifetime individual movements, matings, ovipositions, and maximal life span in a large (32 x 26 m) population cage in the field. Experimental material was obtained from 20 newly established and 20 old local populations within a large metapopulation in the Aland Islands in Finland. 3. Females of the Glanville fritillary from newly established populations are known to be more dispersive in the field, and in the cage they showed significantly greater mobility, mated earlier, and laid more egg clutches than females from old populations. The dispersive females from new populations exhibited no reduced lifetime fecundity in the cage, but they had a shorter maximal life span than old-population females. 4. These results challenge the dispersal-fecundity trade-off for nonmigratory butterflies but instead suggest a physiological trade-off between high metabolic performance and reduced maximal life span. High metabolic performance may explain high rates of dispersal and oviposition in early life. 5. In fragmented landscapes, an ecological trade-off exists between being more dispersive and hence spending more time in the landscape matrix vs. having more time for reproduction in the habitat. We estimate with a dispersal model parameterized for the Glanville fritillary that the lifetime egg production is 4% smaller on average in the more dispersive butterflies in a representative landscape, with much variation depending on landscape structure in the neighbourhood of the natal patch, from--26 to 45% in the landscape analysed in this paper.     

Using surrogate data in population viability analysis: the case of the critically endangered cranberry fritillary butterfly

Population viability analyses (PVA) are central tools for the management of threatened populations. However, the parameterisation of effective PVA models is very demanding in high quality data, which are often impossible to collect on endangered populations. Here we propose the use of a generalisation strategy to bypass this limitation: management measures for an endangered metapopulation of the cranberry fritillary butterfly in the Netherlands are evaluated with RAMAS/GIS by using parameters estimated from a healthier metapopulation in Belgium. The Belgian metapopulation seems viable, with stable abundance and number of local populations, despite their erratic dynamics, whereas the Dutch metapopulation shows a continuous decline in the course of time, with many vacant habitat patches. Simulations of various scenarios indicated that (1) large scale restoration of habitat patches would be necessary to ensure long-term survival of the species in the Netherlands as not enough suitable habitats are currently remaining; and that (2) global warming is expected to put a major threat on both metapopulations by reducing the growth rate of this glacial relict species, and/or increasing environmental stochasticity (amplified climatic variations).     

Metapopulation dynamics of the bog fritillary butterfly: movements between habitat patches

Recent studies on metapopulation dynamics have emphasized the need for improved methods for quantifying individual movements between local populations and habitat patches. In this paper, we report on a 6-yr study in which a network of 12 habitat patches occupied by the bog fritillary, Proclossiana eunomia , was surveyed, with special focus on quantifying movements between the habitat patches. We applied the Virtual Migration model which has been designed to estimate survival and migration parameters in a metapopulation of several connected local populations. The model was parameterized using mark-release-recapture data collected during 6 yr. Generally, the estimated parameter values indicated a high level of movements, with roughly half of butterfly-days spent outside the natal patch. Mortality within patches was higher in males than in females. Females tended to be more mobile and spent more time outside their natal patch than males. Further analysis of the MRR data shows that in this protandrous species males tend to move very little between habitat patches before substantial numbers of females have emerged.     

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.     

Long-term demographic surveys reveal a consistent relationship between average occupancy and abundance within local populations of a butterfly metapopulation

Species distribution models are the tool of choice for large-scale population monitoring, environmental association studies and predictions of range shifts under future environmental conditions. Available data and familiarity of the tools rather than the underlying population dynamics often dictate the choice of specific method – especially for the case of presence–absence data. Yet, for predictive purposes, the relationship between occupancy and abundance embodied in the models should reflect the actual population dynamics of the modelled species. To understand the relationship of occupancy and abundance in a heterogeneous landscape at the scale of local populations, we built a spatio-temporal regression model of populations of the Glanville fritillary butterfly Melitaea cinxia in a Baltic Sea archipelago. Our data comprised nineteen years of habitat surveys and snapshot data of land use in the region. We used variance partitioning to quantify relative contributions of land use, habitat quality and metapopulation covariates. The model revealed a consistent and positive, but noisy relationship between average occupancy and mean abundance in local populations. Patterns of abundance were highly variable across years, with large uncorrelated random variation and strong local population stochasticity. In contrast, the spatio-temporal random effect, habitat quality, population connectivity and patch size explained variation in occupancy, vindicating metapopulation theory as the basis for modelling occupancy patterns in fragmented landscapes. Previous abundance was an important predictor in the occupancy model, which points to a spillover of abundance into occupancy dynamics. While occupancy models can successfully model large-scale population structure and average occupancy, extinction probability estimates for local populations derived from occupancy-only models are overconfident, as extinction risk is dependent on actual, not average, abundance.     

Single-species metapopulation dynamics: concepts, models and observations

This paper outlines a conceptual and theoretical framework for single-species metapopulation dynamics based on the Levins model and its variants. The significance of the following factors to metapopulation dynamics are explored: evolutionary changes in colonization ability; habitat patch size and isolation; compensatory effects between colonization and extinction rates; the effect of immigration on local dynamics (the rescue effect); and heterogeneity among habitat patches. The rescue effect may lead to alternative stable equilibria in metapopulation dynamics. Heterogeneity among habitat patches may give rise to a bimodal equilibrium distribution of the fraction of patches occupied in an assemblage of species (the core-satellite distribution). A new model of incidence functions is described, which allows one to estimate species' colonization and extinction rates on islands colonized from mainland. Four distinct kinds of stochasticity affecting metapopulation dynamics are discussed with examples. The concluding section describes four possible scenarios of metapopulation extinction.     

Functional genomics of life history variation in a butterfly metapopulation

In fragmented landscapes, small populations frequently go extinct and new ones are established with poorly understood consequences for genetic diversity and evolution of life history traits. Here, we apply functional genomic tools to an ecological model system, the well-studied metapopulation of the Glanville fritillary butterfly. We investigate how dispersal and colonization select upon existing genetic variation affecting life history traits by comparing common-garden reared 2-day adult females from new populations with those from established older populations. New-population females had higher expression of abdomen genes involved in egg provisioning and thorax genes involved in the maintenance of flight muscle proteins. Physiological studies confirmed that new-population butterflies have accelerated egg maturation, apparently regulated by higher juvenile hormone titer and angiotensin converting enzyme mRNA, as well as enhanced flight metabolism. Gene expression varied between allelic forms of two metabolic genes (Pgi and Sdhd), which themselves were associated with differences in flight metabolic rate, population age and population growth rate. These results identify likely molecular mechanisms underpinning life history variation that is maintained by extinction-colonization dynamics in metapopulations.     

Butterfly abundance and movements among prairie patches: the roles of habitat quality, edge, and forest matrix permeability

The spatial distribution of patchy insect populations is partly caused by behavioral patterns of insect movement that are influenced by habitat quality, isolation, and the permeability of the surrounding matrix. We recorded insect movements, abundance, and edge behaviors in two species of butterflies, the great-spangled fritillary (Speyeria cybele F., Lepidoptera: Nymphalidae) and the pearl crescent (Phyciodes tharos Drury, Lepidoptera: Nymphalidae), inhabiting remnant prairies surrounded by a forest matrix in south-central Ohio. We also determined the number of forest matrix types present and recorded the permeability of the different types to butterfly movement. The great-spangled fritillary exhibited a relatively high number of interpatch movements, a higher abundance at patch edges, and a propensity to cross the prairie-forest edges, and the forest matrix had a high permeability to butterfly movement. The pearl crescent, in contrast, rarely crossed edge boundaries, moved infrequently among patches, and was more abundant within the patch interior and in patches with high host-plant and flower densities. There were three structurally different forest matrix types separating habitat patches, which in previous studies would have been classified as a single deciduous forest matrix. Butterfly movement and edge behaviors mechanistically interact with patch quality, isolation, and the matrix permeability to determine the spatial structure of these populations in fragmented habitats.     

Habitat destruction, environmental catastrophes, and metapopulation extinction

The extinction process of fragmented populations, characterized by a small number of conspecifics inhabiting each patch, is heavily affected by natural and human disturbance. To evaluate the risk of extinction we consider a network of identical patches connected by passive or active dispersal and hosting a finite, discrete number of individuals. We discuss three types of disturbance affecting the metapopulation: permanent loss of habitat patches, erosion of existing patches, and random catastrophes that wipe out the entire population of a patch. Starting from an infinite-dimensional Markov model that fully accounts for demographic stochasticity, we reduce it to finite dimension via moment closure with negative-binomial approximation. The compact models obtained in this way account for the dynamics of the fraction of empty patches, the average number of individuals in occupied patches, and the variance of their distribution. After comparing the performance of these compact models with that of the infinite-dimensional model in the case of no disturbances, we then proceed to computing persistence-extinction boundaries as bifurcation lines of the compact models in the space of demographic and disturbance parameters. We consider bifurcations with respect to demographic and environmental parameters and contrast our results with those of previous theories. We find out that environmental catastrophes increase the risk of extinction for both frequent and infrequent dispersers, while the random loss of patches has a much larger influence on frequent dispersers. This influence can be counterbalanced by active dispersal. Local erosion of habitat fragments has a larger influence on infrequent than on frequent dispersers. We finally discuss the important synergistic effects of disturbances acting simultaneously.     

Variation in migration propensity among individuals maintained by landscape structure

Metapopulation dynamics lead to predictable patterns of habitat occupancy, population density and trophic structure in relation to landscape features such as habitat patch size and isolation. Comparable patterns may occur in behavioural, physiological and life‐history traits but remain little studied. In the Glanville fritillary butterfly, females in newly established populations were more mobile than females in old populations. Among females from new populations, mobility decreased with increasing connectivity (decreasing isolation), but in females from old populations mobility increased with connectivity. The [ATP]/[ADP] ratio of flight muscles following controlled activity showed the same pattern as mobility in relation to population age and connectivity, suggesting that physiological differences in flight metabolic performance contribute to the observed variation in mobility. We demonstrate with an evolutionary metapopulation model parameterised for the Glanville fritillary that increasing spatial variation in landscape structure increases variance in mobility among individuals in a metapopulation, supporting the general notion that complex landscape structure maintains life‐history variation.