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.     

Analyses of spatial patterns and population processes of clonal plants

The nonrandom spatial structure of terrestrial plants is formed by ecological interactions and reproduction with a limited dispersal range, and in turn this may strongly affect population dynamics and population genetics. The traditional method of modelling in population ecology is either to neglect spatial pattern (e.g. in transition matrix models) or to do straightforward computer simulation. We review here three analytical mothods to deal with plant populations in a lattice-structured habitat, which propagate both by seeds that scatter over the whole habitat and by vegetative reproduction (producing runners, rhizomes, etc.) to neighboring vacant sites. [1]Dynamics of global and local densities: Dynamical equations of population density considering nearest-neighbor correlation (spatial clumping) are developed as the joint dynamics of global average density and local density (comparable to mean crowding) based onpair approximation. If there is a linear trade-off between seed production and vegetative reproduction, the equilibrium abundance of the population may be maximized by engaging both means of reproduction. This result is accurately predicted by the pair approximation method, but not by mean-field approximation (neglect of spatial structure). [2]Cluster size distributions: Using global and local densities obtained by pair approximation, we predicted cluster size distribution, i.e. the number of clusters of occupied sites of various sizes. [3]Clonal identity probability decreasing with distance: Multi-locus measurement of allozymes or other neutral molecular markers tells us whether or not a given pair of individuals belong to the same clone. From the pattern of clonal identity probability decreasing with the distance between ramets, we can estimate the relative importance of two modes of reproduction: vegetative propagation and sexual seed production.     

Restricted dispersal reduces the strength of spatial density dependence in a tropical bird population

Spatial processes could play an important role in density-dependent population regulation because the disproportionate use of poor quality habitats as population size increases is widespread in animal populations-the so-called buffer effect. While the buffer effect patterns and their demographic consequences have been described in a number of wild populations, much less is known about how dispersal affects distribution patterns and ultimately density dependence. Here, we investigated the role of dispersal in spatial density dependence using an extraordinarily detailed dataset from a reintroduced Mauritius kestrel (Falco punctatus) population with a territorial (despotic) breeding system. We show that recruitment rates varied significantly between territories, and that territory occupancy was related to its recruitment rate, both of which are consistent with the buffer effect theory. However, we also show that restricted dispersal affects the patterns of territory occupancy with the territories close to release sites being occupied sooner and for longer as the population has grown than the territories further away. As a result of these dispersal patterns, the strength of spatial density dependence is significantly reduced. We conclude that restricted dispersal can modify spatial density dependence in the wild, which has implications for the way population dynamics are likely to be impacted by environmental change.     

Limited seed dispersal shapes fine-scale spatial genetic structure in a Neotropical dioecious large-seeded palm

Seed and pollen dispersal contribute to gene flow and shape the genetic patterns of plants over fine spatial scales. We inferred fine-scale spatial genetic structure (FSGS) and estimated realized dispersal distances in Phytelephas aequatorialis, a Neotropical dioecious large-seeded palm. We aimed to explore how seed and pollen dispersal shape this genetic pattern in a focal population. For this purpose, we genotyped 138 seedlings and 99 adults with 20 newly developed microsatellite markers. We tested if rodent-mediated seed dispersal has a stronger influence than insect-mediated pollen dispersal in shaping FSGS. We also tested if pollen dispersal was influenced by the density of male palms around mother palms in order to further explore this ecological process in large-seeded plants. Rodent-mediated dispersal of these large seeds occurred mostly over short distances (mean 34.76 ± 34.06 m) while pollen dispersal distances were two times higher (mean 67.91 ± 38.29 m). The spatial extent of FSGS up to 35 m and the fact that seed dispersal did not increase the distance at which male alleles disperse suggest that spatially limited seed dispersal is the main factor shaping FSGS and contributes only marginally to gene flow within the population. Pollen dispersal distances depended on the density of male palms, decreasing when individuals show a clumped distribution and increasing when they are scattered. Our results show that limited seed dispersal mediated by rodents shapes FSGS in P. aequatorialis, while more extensive pollen dispersal accounts for a larger contribution to gene flow and may maintain high genetic diversity. Abstract in Spanish is available with online material.     

Spatially autocorrelated disturbances and patterns in population synchrony

Spatially synchronous population dynamics have been documented in many taxa. The prevailing view is that the most plausible candidates to explain this pattern are extrinsic disturbances (the Moran effect) and dispersal. In most cases disentangling these factors is difficult. Theoretical studies have shown that dispersal between subpopulations is more likely to produce a negative relationship between population synchrony and distance between the patches than perturbations. As analyses of empirical data frequently show this negative relationship between the level of synchrony and distance between populations, this has emphasized the importance of dispersal as a synchronizing agent. However, several weather patterns show spatial autocorrelation, which could potentially produce patterns in population synchrony similar to those caused by dispersal. By using spatially extended versions of several population dynamic models, we show that this is indeed the case. Our results show that, especially when both factors (spatially autocorrelated perturbations and distance-dependent dispersal) act together, there may exist groups of local populations in synchrony together but fluctuating asynchronously with some other groups of local populations. We also show, by analysing 56 long-term population data sets, that patterns of population synchrony similar to those found in our simulations are found in natural populations as well. This finding highlights the subtlety in the interactions of dispersal and noise in organizing spatial patterns in population fluctuations.     

Forecasting spatially structured populations: the role of dispersal and scale

We forecasted spatially structured population models with complex dynamics, focusing on the effect of dispersal and spatial scale on the predictive capability of nonlinear forecasting (NLF). Dispersal influences NLF ability by its influence on population dynamics. For simple 2-cell models, when dispersal is small, our ability to predict abundance in subpopulations decreased and then increased with increasing dispersal. Spatial heterogeneity, dispersal manner, and environmental noise did not qualitatively change this result. But results are not clear for complex spatial configurations because of complicated dispersal interactions across subpopulations. Populations undergoing periodic fluctuations could be forecasted perfectly for all deterministic cases that we studied, but less reliably when environmental noise was incorporated. More importantly, for all models that we have examined, NLF was much worse at larger spatial scales as a consequence of the asynchronous dynamics of subpopulations when the dispersal rate was below some critical value. The only difference among models was the critical value of dispersal rate, which varied with growth rate, carrying capacity, mode of dispersal, and spatial configuration. These results were robust even when environmental noise was incorporated. Intermittency, common in the dynamics of spatially structured populations, lowered the predictive capability of NLF. Forecasting population behaviour is of obvious value in resource exploitation and conservation. We suggest that forecasting at local scales holds promise, whereas forecasting abundance at regional scales may yield poor results. Improved understanding of dispersal can enhance the management and conservation of natural resources, and may help us to understand resource-exploitation strategies employed by local indigenous humans.     

DISPERSAL AND GENETIC STRUCTURE IN KANGAROO RATS

We used spatial autocorrelation of allele frequencies to examine local structure in a population of bannertailed kangaroo rats for which Wright's isolation-by-distance model seems applicable, and for which we can estimate neighborhood size based on 10 years of data on demography and dispersal. The uniform dispersion and strong philopatric tendencies of this species provide a test case for the idea that restricted dispersal can lead to local genetic structure in small mammals. Whether we considered such complications as nonnormal dispersal distances, variation in lifetime reproductive success, fluctuating population density, and adult as well as juvenile dispersal, our estimate of effective population size was fewer than 15 animals. Nevertheless, data from four polymorphic allozyme loci analyzed over a range of separations between 50 m (approximately one home range diameter) and 1,000 m detected no evidence for spatial clustering of alleles. One resolution of this apparent paradox is that “gamete dispersal,” caused by the movements of males away from their residences during the breeding season, may be a significant (and unmeasured) component of gene dispersal. Our analyses also demonstrate that a decline in population density may actually increase neighborhood size. A more general implication is that even extremely philopatric mammals have effective population sizes large enough to prevent the development of local genetic structure.     

Spatial genetic structure of a small rodent in a heterogeneous landscape

Gene flow in natural populations may be strongly influenced by landscape features. The integration of landscape characteristics in population genetic studies may thus improve our understanding of population functioning. In this study, we investigated the population genetic structure and gene flow pattern for the common vole, Microtus arvalis, in a heterogeneous landscape characterised by strong spatial and temporal variation. The studied area is an intensive agricultural zone of approximately 500 km² crossed by a motorway. We used individual-based Bayesian methods to define the number of population units and their spatial borders without prior delimitation of such units. Unexpectedly, we determined a single genetic unit that covered the entire area studied. In particular, the motorway considered as a likely barrier to dispersal was not associated with any spatial genetic discontinuity. Using computer simulations, we demonstrated that recent anthropogenic barriers to effective dispersal are difficult to detect through analysis of genetic variation for species with large effective population sizes. We observed a slight, but significant, pattern of isolation by distance over the whole study site. Spatial autocorrelation analyses detected genetic structuring on a local scale, most probably due to the social organisation of the study species. Overall, our analysis suggests intense small-scale dispersal associated with a large effective population size. High dispersal rates may be imposed by the strong spatio-temporal heterogeneity of habitat quality, which characterises intensive agroecosystems.     

Contemporary pollen and seed dispersal in a Prunus mahaleb population: patterns in distance and direction

Pollination and seed dispersal determine the spatial pattern of gene flow in plant populations and, for those species relying on pollinators and frugivores as dispersal vectors, animal activity plays a key role in determining this spatial pattern. For these plant species, reported dispersal patterns are dominated by short-distance movements with a significant amount of immigration. However, the contribution of seed and pollen to the overall contemporary gene immigration is still poorly documented for most plant populations. In this study we investigated pollination and seed dispersal at two spatial scales in a local population of Prunus mahaleb (L.), a species pollinated by insects and dispersed by frugivorous vertebrates. First, we dissected the relative contribution of pollen and seed dispersal to gene immigration from other parts of the metapopulation. We found high levels of gene immigration (18.50%), due to frequent long distance seed dispersal events. Second, we assessed the distance and directionality for pollen and seed dispersal events within the local population. Pollen and seed movement patterns were non-random, with skewed distance distributions: pollen tended moved up to 548 m along an axis approaching the N-S direction, and seeds were dispersed up to 990 m, frequently along the SW and SE axes. Animal-mediated dispersal contributed significantly towards gene immigration into the local population and had a markedly nonrandom pattern within the local population. Our data suggest that animals can impose distinct spatial signatures in contemporary gene flow, with the potential to induce significant genetic structure at a local level.     

Reid's paradox revisited: the evolution of dispersal kernels during range expansion

Current approaches to modeling range advance assume that the distribution describing dispersal distances in the population (the "dispersal kernel") is a static entity. We argue here that dispersal kernels are in fact highly dynamic during periods of range advance because density effects and spatial assortment by dispersal ability ("spatial selection") drive the evolution of increased dispersal on the expanding front. Using a spatially explicit individual-based model, we demonstrate this effect under a wide variety of population growth rates and dispersal costs. We then test the possibility of an evolved shift in dispersal kernels by measuring dispersal rates in individual cane toads (Bufo marinus) from invasive populations in Australia (historically, toads advanced their range at 10 km/year, but now they achieve >55 km/year in the northern part of their range). Under a common-garden design, we found a steady increase in dispersal tendency with distance from the invasion origin. Dispersal kernels on the invading front were less kurtotic and less skewed than those from origin populations. Thus, toads have increased their rate of range expansion partly through increased dispersal on the expanding front. For accurate long-range forecasts of range advance, we need to take into account the potential for dispersal kernels to be evolutionarily dynamic.     

Evolution of Pathogen Specialisation in a Host Metapopulation: Joint Effects of Host and Pathogen Dispersal

Metapopulation processes are important determinants of epidemiological and evolutionary dynamics in host-pathogen systems, and are therefore central to explaining observed patterns of disease or genetic diversity. In particular, the spatial scale of interactions between pathogens and their hosts is of primary importance because migration rates of one species can affect both spatial and temporal heterogeneity of selection on the other. In this study we developed a stochastic and discrete time simulation model to specifically examine the joint effects of host and pathogen dispersal on the evolution of pathogen specialisation in a spatially explicit metapopulation. We consider a plant-pathogen system in which the host metapopulation is composed of two plant genotypes. The pathogen is dispersed by air-borne spores on the host metapopulation. The pathogen population is characterised by a single life-history trait under selection, the infection efficacy. We found that restricted host dispersal can lead to high amount of pathogen diversity and that the extent of pathogen specialisation varied according to the spatial scale of host-pathogen dispersal. We also discuss the role of population asynchrony in determining pathogen evolutionary outcomes.     

Community-driven dispersal in an individual-based predator–prey model

We present a spatial, individual-based predator–prey model in which dispersal is dependent on the local community. We determine species suitability to the biotic conditions of their local environment through a time and space varying fitness measure. Dispersal of individuals to nearby communities occurs whenever their fitness falls below a predefined tolerance threshold. The spatiotemporal dynamics of the model is described in terms of this threshold. We compare this dynamics with the one obtained through density-independent dispersal and find marked differences. In the community-driven scenario, the spatial correlations in the population density do not vary in a linear fashion as we increase the tolerance threshold. Instead we find the system to cross different dynamical regimes as the threshold is raised. Spatial patterns evolve from disordered, to scale-free complex patterns, to finally becoming well-organized domains. This model therefore predicts that natural populations, the dispersal strategies of which are likely to be influenced by their local environment, might be subject to complex spatiotemporal dynamics.     

The intermediate dispersal principle in spatially explicit metapopulations

Aim of this paper is to assess the fate of metapopulations described by spatially explicit models. To this end, we first present an interacting particle system (IPS) where individuals of a single species compete logistically at the local scale and can move among patches according to various dispersal kernels. As the IPS is a complex stochastic system, it is impossible to determine the persistence-extinction boundaries in any relevant parameter space with analytical methods or numerical continuation techniques. We thus resort to a heuristic method that lets us determine the boundaries as space-time percolation thresholds with a relatively modest computational effort. Such boundaries are qualitatively consistent with those we obtained with spatial implicit modelling. In particular, we find that the intermediate dispersal principle, namely that globally persistent metapopulations correspond to dispersal rates that are neither too low nor too high, turns out to be very robust even in this explicit context. However, the quantification of the boundaries strongly depends upon the number of patches, the dispersal kernels and the border conditions. Finally, we show that there exists a scaling law that relates the number of species lost in a fragmented landscape to the number of patches. Thus, the law allows a rough estimation of the cost of destroying a patch.     

Dispersal, Environmental Correlation, and Spatial Synchrony in Population Dynamics

Many species exhibit widespread spatial synchrony in population fluctuations. This pattern is of great ecological interest and can be a source of concern when the species is rare or endangered. Both dispersal and spatial correlations in the environment have been implicated as possible causes of this pattern, but these two factors have rarely been studied in combination. We develop a spatially structured population model, simple enough to obtain analytic solutions for the population correlation, that incorporates both dispersal and environmental correlation. We ask whether these two synchronizing factors contribute additively to the total spatial population covariance. We find that there is always an interaction between these two factors and that this interaction is small only when one or both of the environmental correlation and the dispersal rate are small. The interaction is opposite in sign to the environmental correlation; so, in the normal case of positive environmental correlation across sites, the population synchrony will be lower than predicted by simply adding the effects of dispersal and environmental correlation. We also find that population synchrony declines as the strength of population regulation increases. These results indicate that dispersal and environmental correlation need to be considered in combination as explanations for observed patterns of population synchrony.     

Do landscape processes predict phylogeographic patterns in the wood frog?

Understanding factors that influence population connectivity and the spatial distribution of genetic variation is a major goal in molecular ecology. Improvements in the availability of high-resolution geographic data have made it increasingly possible to quantify the effects of landscape features on dispersal and genetic structure. However, most studies examining such landscape effects have been conducted at very fine (e.g. landscape genetics) or broad (e.g. phylogeography) spatial scales. Thus, the extent to which processes operating at fine spatial scales are linked to patterns at larger scales remains unclear. Here, we test whether factors impacting wood frog dispersal at fine spatial scales are correlated with genetic structure at regional scales. Using recently developed methods borrowed from electrical circuit theory, we generated landscape resistance matrices among wood frog populations in eastern North America based on slope, a wetness index, land cover and absolute barriers to wood frog dispersal. We then determined whether these matrices are correlated with genetic structure based on six microsatellite markers and whether such correlations outperform a landscape-free model of isolation by resistance. We observed significant genetic structure at regional spatial scales. However, topography and landscape variables associated with the intervening habitat between sites provide little explanation for patterns of genetic structure. Instead, absolute dispersal barriers appear to be the best predictor of regional genetic structure in this species. Our results suggest that landscape variables that influence dispersal, microhabitat selection and population structure at fine spatial scales do not necessarily explain patterns of genetic structure at broader scales.     

Species diversity and population density affect genetic structure and gene dispersal in a subtropical understory shrub

Aims The dispersal of pollen and seeds is spatially restricted and may vary among plant populations because of varying biotic interactions, population histories or abiotic conditions. Because gene dispersal is spatially restricted, it will eventually result in the development of spatial genetic structure (SGS), which in turn can allow insights into gene dispersal processes. Here, we assessed the effect of habitat characteristics like population density and community structure on small-scale SGS and estimate historical gene dispersal at different spatial scales.Methods In a set of 12 populations of the subtropical understory shrub Ardisia crenata, we assessed genetic variation at 7 microsatellite loci within and among populations. We investigated small-scale genetic structure with spatial genetic autocorrelation statistics and heterogeneity tests and estimated gene dispersal distances based on population differentiation and on within-population SGS. SGS was related to habitat characteristics by multiple regression.Important findings The populations showed high genetic diversity (H e = 0.64) within populations and rather strong genetic differentiation (F ′ ST = 0.208) among populations, following an isolation-by-distance pattern, which suggests that populations are in gene flow–drift equilibrium. Significant SGS was present within populations (mean Sp = 0.027). Population density and species diversity had a joint effect on SGS with low population density and high species diversity leading to stronger small-scale SGS. Estimates of historical gene dispersal from between-population differentiation and from within-population SGS resulted in similar values between 4.8 and 22.9 m. The results indicate that local-ranged pollen dispersal and inefficient long-distance seed dispersal, both affected by population density and species diversity, contributed to the genetic population structure of the species. We suggest that SGS in shrubs is more similar to that of herbs than to trees and that in communities with high species diversity gene flow is more restricted than at low species diversity. This may represent a process that retards the development of a positive species diversity–genetic diversity relationship.     

Similarity in temporal variation in sex‐biased dispersal over short and long distances in the dark‐eyed junco,Junco hyemalis

Patterns of sex‐biased dispersal (SBD) are typically consistent within taxa, for example female‐biased in birds and male‐biased in mammals, leading to theories about the evolutionary pressures that lead to SBD. However, generalizations about the evolution of sex biases tend to overlook that dispersal is mediated by ecological factors that vary over time. We examined potential temporal variation in between‐ and within‐population dispersal over an 11‐year period in a bird, the dark‐eyed junco (Junco hyemalis). We measured between‐population dispersal patterns using genetic assignment indices and found yearly variation in which sex was more likely to have immigrated. When we measured within‐population spatial genetic structure and mark–recapture dispersal distances, we typically found yearly SBD patterns that mirrored between‐population dispersal, indicating common eco‐evolutionary causes despite expected differences due to the scale of dispersal. However, in years without detectable between‐population sex biases, we found genetic similarity between nearby males within our population. This suggests that, in certain circumstances, ecological pressures may act on within‐population dispersal without affecting dispersal between populations. Alternatively, current analytical tools may be better able to detect within‐population SBD. Future work will investigate potential causes of the observed temporal variation in dispersal patterns and whether they have greater effects on within‐population dispersal.     

Density-dependent dispersal in host-parasitoid assemblages

Most spatial population models assume constant rates of dispersal. However, in a given community, dispersal may not only depend on the density of conspecifics, i.e. density‐dependent dispersal, but also on the density of other species, a phenomenon we term ‘community‐dependent dispersal’. We co‐vary the densities of both the beetle host Callosobruchus chinensis and its parasitoid wasp, Anisopteromalus calandrae, in a laboratory study and record the proportions of each species that disperse within a two‐hour period. The parasitoid in these systems exhibits community‐dependent dispersal – dispersing more frequently when parasitoid density is high and larval host density is low. This supported our prediction that individuals should disperse according to competition for available resources. However, in this study the host's dispersal was independent of density. We suggest that this may be due to less intense selection acting on host dispersal strategies than on the parasitoid. We consider some possible consequences of community‐dependent dispersal for a number of spatial population processes. A well‐known host‐parasitoid metapopulation model is expanded so that it includes a greater range of dispersal functions. When the model is parameterised with the parasitoid community‐dependent dispersal function observed in the empirical study, similar population dynamics are obtained as when fixed‐rate dispersal functions are applied. The importance of dispersal functions for invasions of both competitive and host‐parasitoid systems is also considered. The model results demonstrate that understanding how individuals disperse in response to different species’ population densities is important in determining the rate of spread of an invasion. We suggest that more empirical studies are needed to establish what determines dispersal rate and distance in a range of species, combined with theoretical studies investigating the role of the dispersal function in determining spatial population processes.     

Evolution of conditional dispersal: evolutionarily stable strategies in spatial models

We consider a two-species competition model in which the species have the same population dynamics but different dispersal strategies. Both species disperse by a combination of random diffusion and advection along environmental gradients, with the same random dispersal rates but different advection coefficients. Regarding these advection coefficients as movement strategies of the species, we investigate their course of evolution. By applying invasion analysis we find that if the spatial environmental variation is less than a critical value, there is a unique evolutionarily singular strategy, which is also evolutionarily stable. If the spatial environmental variation exceeds the critical value, there can be three or more evolutionarily singular strategies, one of which is not evolutionarily stable. Our results suggest that the evolution of conditional dispersal of organisms depends upon the spatial heterogeneity of the environment in a subtle way.