A metapopulation paradox: partial improvement of habitat may reduce metapopulation persistence

The adverse influence of habitat degradation on the survival of populations may sometimes be amplified by rapid evolution over ecological timescales. This phenomenon of evolutionary suicide has been described in theoretical as well as empirical studies. However, no studies have suggested that habitat improvement could possibly also trigger an evolutionary response that would result in a decline in population size. We use individual-based simulations to demonstrate the potential for such a paradoxical response. An increase in the quality, size, or stability of only a fraction of the habitat patches in a metapopulation may result in an evolutionary decline in the dispersal propensity of individuals, followed by a decrease in recolonization, a reduction in the number of patches occupied, a decline in overall population size, and even extinction. Thus, well-intended conservation efforts that ignore potential evolutionary consequences of habitat management may increase the extinction risk of populations.     

How patch configuration affects the impact of disturbances on metapopulation persistence

Disturbances affect metapopulations directly through reductions in population size and indirectly through habitat modification. We consider how metapopulation persistence is affected by different disturbance regimes and the way in which disturbances spread, when metapopulations are compact or elongated, using a stochastic spatially explicit model which includes metapopulation and habitat dynamics. We discover that the risk of population extinction is larger for spatially aggregated disturbances than for spatially random disturbances. By changing the spatial configuration of the patches in the system--leading to different proportions of edge and interior patches--we demonstrate that the probability of metapopulation extinction is smaller when the metapopulation is more compact. Both of these results become more pronounced when colonization connectivity decreases. Our results have important management implication as edge patches, which are invariably considered to be less important, may play an important role as disturbance refugia.     

The effects of connectivity on metapopulation persistence: network symmetry and degree correlations

A spatial metapopulation is a mosaic of interconnected patch populations. The complex routes of colonization between the patches are governed by the metapopulation''s dispersal network. Over the past two decades, there has been considerable interest in uncovering the effects of dispersal network topology and its symmetry on metapopulation persistence. While most studies find that the level of symmetry in dispersal pattern enhances persistence, some have reached the conclusion that symmetry has at most a minor effect. In this work, we present a new perspective on the debate. We study properties of the in- and out-degree distribution of patches in the metapopulation which define the number of dispersal routes into and out of a particular patch, respectively. By analysing the spectral radius of the dispersal matrices, we confirm that a higher level of symmetry has only a marginal impact on persistence. We continue to analyse different properties of the in–out degree distribution, namely the ‘in–out degree correlation’ (IODC) and degree heterogeneity, and find their relationship to metapopulation persistence. Our analysis shows that, in contrast to symmetry, the in–out degree distribution and particularly, the IODC are dominant factors controlling persistence.     

Threshold parameters and metapopulation persistence

A method is presented to estimate the minimum viable metapopulation size based on the basic reproductive number R ₀ and the expected time to extinction τ _E for epidemiological models. We exemplify our approach with two simple deterministic metapopulation models of the patch occupancy type and then proceed to stochastic versions that permit the estimation of the minimum viable metapopulation size.     

Effects of colonization asymmetries on metapopulation persistence

Ocean currents, prevailing winds, and the hierarchical structures of river networks are known to create asymmetries in re-colonization between habitat patches. The impacts of such asymmetries on metapopulation persistence are seldom considered, especially rarely in theoretical studies. Considering three classical models (the island, the stepping stone and the distance-dependent model), we explore how metapopulation persistence is affected by (i) asymmetry in dispersal strength, in which the colonization rate between two patches differs in direction, and (ii) asymmetry in connectivity, in which the overall colonization pattern displays asymmetry (circulating or dendritic networks). Viability can be drastically reduced when directional bias in dispersal strength is higher than 25%. Re-colonization patterns that allow for strong local connectivity provide the highest persistence compared to systems that allow circulation. Finally, asymmetry has relatively weak effects when metapopulations maintain strong general connectivity.     

The effects of habitat destruction in finite landscapes: a chain-binomial metapopulation model

We present a stochastic model for metapopulations in landscapes with a finite but arbitrary number of patches. The model, similar in form to the chain-binomial epidemic models, is an absorbing Markov chain that describes changes in the number of occupied patches as a sequence of binomial probabilities. It predicts the quasi-equilibrium distribution of occupied patches, the expected extinction time (τ¯), and the probability of persistence (l¯(x)) to time x as a function of the number N of patches in the landscape and the number S of those patches that are suitable for the population. For a given value of N , the model shows that: (1) τ¯ and l¯(x) are highly sensitive to changes in S and (2) there is a threshold value of S at which τ¯ declines abruptly from extremely large to very small values. We also describe a statistical method for estimating model parameters from time series data in order to evaluate metapopulation viability in real landscapes. An example is presented using published data on the Glanville fritillary butterfly, Meltiaea cinxia , and its specialist parasitoid Cotesia melitaearum . We calculate the expected extinction time of M. cinxia as a function of the frequency of parasite outbreaks, and are able to predict the minimum number of years between outbreaks required to ensure long-term persistence of M. cinxia . The chain-binomial model provides a simple but powerful method for assessing the effects of human and natural disturbances on extinction times and persistence probabilities in finite landscapes.     

Conserving extirpated sites: using habitat quality to manage unoccupied patches for metapopulation persistence

Conservation of metapopulations requires managing extirpated sites, particularly with current threats of increased fragmentation and displacement from global warming. Determining the habitat requirements of threatened species and how they relate to defining characteristics of occupied and unoccupied sites is key to managing suitable habitat in extirpated patches. Due to habitat destruction and degradation, the endangered Ohlone tiger beetle (Cicindela ohlone) is found in only five sites of a once more extensive metapopulation in Santa Cruz County, California. To determine the role of habitat quality in classifying sites, I measured vegetation and ground cover as well as plant and soil composition in sites in which C. ohlone are present, extirpated, and absent. I used conditional inference trees to determine what habitat factors significantly predicted the different sites types. I also analyzed habitat characteristics within present sites to determine factors that predicted egg-laying habitat. As isolation has been shown to be an important driver of metapopulation patch extirpation, I tested the spatial autocorrelation of C. ohlone occupancy to determine if extirpated patches were significantly isolated. Habitat characteristics successfully differentiated nearly 90 % of extirpated plots, which were not isolated from occupied sites. Sites in which C. ohlone are currently present were classified as having at least 10 % cover of bare ground, high forb cover, low litter cover and depth, and high soil bulk density, characteristics that extirpated sites lacked. I illustrate how the defining characteristics could be used to manage habitat in extirpated and absents sites for potential recolonization or translocation, which is vital for metapopulation persistence.     

Spatial network structure and metapopulation persistence

We explore the relationship between network structure and dynamics by relating the topology of spatial networks with its underlying metapopulation abundance. Metapopulation abundance is largely affected by the architecture of the spatial network, although this effect depends on demographic parameters here represented by the extinction-to-colonization ratio (e/c). Thus, for moderate to large e/c-values, regional abundance grows with the heterogeneity of the network, with uniform or random networks having the lowest regional abundances, and scale-free networks having the largest abundance. However, the ranking is reversed for low extinction probabilities, with heterogeneous networks showing the lowest relative abundance. We further explore the mechanisms underlying such results by relating a node's incidence (average number of time steps the node is occupied) with its degree, and with the average degree of the nodes it interacts with. These results demonstrate the importance of spatial network structure to understanding metapopulation abundance, and serve to determine under what circumstances information on network structure should be complemented with information on the species life-history traits to understand persistence in heterogeneous environments.     

The role of landscape-dependent disturbance and dispersal in metapopulation persistence

The fundamental processes that influence metapopulation dynamics (extinction and recolonization) will often depend on landscape structure. Disturbances that increase patch extinction rates will frequently be landscape dependent such that they are spatially aggregated and have an increased likelihood of occurring in some areas. Similarly, landscape structure can influence organism movement, producing asymmetric dispersal between patches. Using a stochastic, spatially explicit model, we examine how landscape-dependent correlations between dispersal and disturbance rates influence metapopulation dynamics. Habitat patches that are situated in areas where the likelihood of disturbance is low will experience lower extinction rates and will function as partial refuges. We discovered that the presence of partial refuges increases metapopulation viability and that the value of partial refuges was contingent on whether dispersal was also landscape dependent. Somewhat counterintuitively, metapopulation viability was reduced when individuals had a preponderance to disperse away from refuges and was highest when there was biased dispersal toward refuges. Our work demonstrates that landscape structure needs to be incorporated into metapopulation models when there is either empirical data or ecological rationale for extinction and/or dispersal rates being landscape dependent.     

The effects of spatial habitat configuration on recruitment, growth and population structure in arctic Collembola

The population density and demography of five species of arctic Collembola were studied in a naturally patchy habitat, consisting of Carex ursinae tussocks with varying degrees of isolation. Focal predictor variables were those describing the spatial configuration of tussocks, including tussock size and isolation and the amount of habitat (cover) at a 1-m² scale surrounding each tussock population. The Collembola populations were heavily influenced by environmental stochasticity in the form of winter mortality and summer drought, and the influence of patchiness on population characteristics was evaluated in this context. The five species showed very different responses to the structuring effect of the habitat, depending on life history characteristics, mobility and habitat requirements. Population density was highly variable in both time and space. Spring densities indicated larger winter mortality compared to observations from a previous study, and the snow- and ice-free season from June to August only resulted in population growth for Folsomia sexoculata. In the other species, adult mortality must have been high as there was no net population growth despite observed reproduction. The exception was Hypogastrura viatica, whose population decline was more likely to have been the result of migration out of the study area. Cover was the most important variable explaining density. No pure area or isolation effects at the tussock level were detected, even in areas with very low habitat cover. Drought was probably an important mortality factor, as July was particularly warm and dry. Due to qualitative differences in the tussocks and the matrix substrate, desiccation risk would be higher during dispersal between tussocks. We suggest that increased dispersal mortality gave the observed pattern of increased density in relation to cover, both in general and in F. quadrioculata, an opportunistic species otherwise known for rapid population growth. Onychiurus groenlandicus, which had a similar density response to cover, may also be influenced by a rescue effect sustaining densities in areas with high cover. The cover effect can be viewed as a large-scale factor which encompasses the general spatial neighbourhood of each tussock, where inter-population processes are important, as opposed to internal patch dynamics. Received: 15 March 1999 / Accepted: 22 March 2000     

Potential metapopulation structure and the effects of habitat quality on population size of the endangered False Ringlet butterfly

The False Ringlet (Coenonympha oedippus) is a European butterfly species, endangered due to the severe loss and fragmentation of its habitat. In Hungary, two remaining populations of the butterfly occur in lowland Purple Moorgrass meadows. We studied a metapopulation occupying twelve habitat patches in Central Hungary. Our aim was to reveal what measures of habitat quality affect population size and density of this metapopulation, estimate dispersal parameters and describe phenology of subpopulations. Local population sizes and dispersal parameters were estimated from an extensive mark–release–recapture dataset, while habitat quality was characterized by groundwater level, cover of grass tussocks, bush cover, height of vegetation and grass litter at each habitat patch. The estimated size of the metapopulation was more than 3,000 individuals. We estimated a low dispersal capacity, especially for females, indicating a very low probability of (re)colonization. Butterfly abundance and density in local populations increased with higher grass litter, lower groundwater level and larger area covered by tussocks. We suppose that these environmental factors affect butterfly abundance by determining the microclimatic conditions for both larvae and adult butterflies. Our results suggest that the long-term preservation of the studied metapopulation needs the maintenance of high quality habitat patches by appropriate mowing regime and water regulation. Management also should facilitate dispersal to strengthen metapopulation structure with creating stepping-stones or gradually increase habitat quality in present matrix.     

On optimal size and number of reserves for metapopulation persistence

Habitat fragmentation is generally considered to be detrimental to the persistence of natural populations. In nature management, one therefore tends to prefer few large nature reserves over many small nature reserves having equal total area. This paper examines whether this preference is warranted in a metapopulation framework with circular reserves (patches) by formulating the dependence of metapopulation persistence on the size and number of reserves, both of which depend on reserve radius if the total area is kept constant. Two measures of metapopulation persistence are used: R(0), the number of patches colonized by an occupied patch during its lifetime as an occupied patch, and T(e), the expected time to extinction. These two measures are functions of the extinction and colonization rates of the metapopulation. Several mechanisms for the extinction and colonization processes are formulated from which the dependence of these rates on reserve radius is calculated. It turns out that T(e)generally increases with reserve radius for all mechanisms, which supports the preference of few large reserves. However, R(0)supports this preference only in the case of some special, rather unrealistic, mechanisms. In many other, more realistic, cases an intermediate reserve size exists for which metapopulation persistence measured by R(0)is optimal.     

Exact asymptotic analysis for metapopulation dynamics on correlated dynamic landscapes

We compute the mean patch occupancy for a stochastic, spatially explicit patch-occupancy metapopulation model on a dynamic, correlated landscape, using a mathematically exact perturbation expansion about a mean-field limit that applies when dispersal range is large. Stochasticity in the metapopulation and landscape dynamics gives negative contributions to patch occupancy, the former being more important at high occupancy and the latter at low occupancy. Positive landscape correlations always benefit the metapopulation, but are only significant when the correlation length is comparable to, or smaller than, the dispersal range. Our analytical results allow us to consider the importance of spatial kernels in all generality. We find that the shape of the landscape correlation function is typically unimportant, and that the variance is overwhelmingly the most important property of the colonisation kernel. However, short-range singularities in either the colonisation kernel or landscape correlations can give rise to qualitatively different behaviour.     

Extinction dynamics and the regional persistence of a tree frog metapopulation

The concept of a metapopulation acknowledges local extinctions as a natural part of the dynamics of a patchily distributed population. However, if extinctions are not balanced by recolonizations or if there is a high degree of spatial synchrony of local extinctions, this poses a threat to and will reduce the metapopulation persistence time. Here we show that, in a metapopulation network of 378 pond patches used by the tree frog (Hyla arborea), even though extinctions are frequent (mean extinction probability p(e) = 0.24) they pose no threat to the metapopulation as they are balanced by recolonizations (p(c) = 0.33). In any one year there was a pattern of large populations tending to persist while small populations became extinct. The total number of individuals belonging to populations that went extinct was small (< 5%) compared with those populations that persisted. A spatial autocorrelation analysis indicated no clustering of local extinctions. The tree frog metapopulation studied consisted of a set of larger, persistent populations mixed with smaller populations characterized by high turnover dynamics.     

The genetic architecture of ecological specialization: correlated gene effects on host use and habitat choice in pea aphids

Genetic correlations among phenotypic characters result when two traits are influenced by the same genes or sets of genes. By reducing the degree to which traits in two environments can evolve independently (e.g., Lande 1979; Via and Lande 1985), such correlations are likely to play a central role in both the evolution of ecological specialization and in its link to speciation. For example, negative genetic correlations between fitness traits in different environments (i.e., genetic trade-offs) are thought to influence the evolution of specialization, while positive genetic correlations between performance and characters influencing assortative mating can accelerate the evolution of reproductive isolation between ecologically specialized populations. We first discuss how the genetic architecture of a suite of traits may affect the evolutionary role of genetic correlations among them and review how the mechanisms of correlations can be analyzed using quantitative trait locus (QTL) mapping. We then consider the implications of such data for understanding the evolution of specialization and its link to speciation. We illustrate this approach with a QTL analysis of key characters in two races of pea aphids that are highly specialized on different host plants and partially reproductively isolated. Our results suggest that antagonism among QTL effects on performance in the two environments leads to a genetic trade-off in this system. We also found evidence for parallel QTL effects on host-plant acceptance and fecundity on the accepted host, which could produce assortative mating. These results suggest that the genetic architecture of traits associated with host use may have played a central role in the evolution of specialization and reproductive isolation in pea aphids.     

The effects of habitat fragmentation on persistence of source-sink metapopulations in systems with predators and prey or apparent competitors.

We consider systems with one predator and one prey, or a common predator and two prey species (apparent competitors) in source and sink habitats. In both models, the predator species is vulnerable to extinction, if productivity in the source is insufficient to rescue demographically deficient sink populations. Conversely, in the model with two prey species, if the source is too rich, one of the prey species may be driven extinct by apparent competition, since the predator can maintain a large population because of the alternative prey. Increasing the rate of predator movement from the source population has opposite effects on prey and predator persistence. High emigration rate exposes the predator population to danger of extinction, reducing the number of individuals that breed and produce offspring in the source habitat. This may promote coexistence of prey by relaxing predation pressure and apparent competition between the two prey species. The number of sinks and spatial arrangement of patches, or connectivity between patches, also influence persistence of the species. More sinks favor the prey and fewer sinks are advantageous to the predator. A linear pattern with the source at one end is profitable for the predator, and a centrifugal pattern in which the source is surrounded by sinks is advantageous to the prey. When the dispersal rate is low, effects of the spatial structure may exceed those of the number of sinks. In brief, productivity in patches and patterns of connectivity between patches differentially influence persistence of populations in different trophic levels.     

The effect of the spatial configuration of habitat fragmentation on invasive spread

To address how the spatial configuration of habitat fragmentation influences the persistence and the rate of spread of an invasive species, we consider three simple periodically fragmented environments, a lattice-like corridor environment, an island-like environment and a striped environment. By numerically analyzing Fisher’s equation with a spatially varying diffusion coefficient and the intrinsic growth rate, we find the following. (1) When the scale of fragmentation is sufficiently large, the minimum favorable area needed for successful invasion reduces in the following order: lattice-like corridor, striped and island-like environments. (2) When the scale of fragmentation and the fraction of favorable area are sufficiently large, the spreading speeds along contiguous favorable habitats in the lattice-like corridor and striped environments are faster than the speeds across isolated favorable habitats in the island-like environment and the striped environment. (3) When the periodicity of fragmentation is relaxed by stochastically shifting the boundaries between favorable and unfavorable habitats, the average speed increases with increases in the irregularity of fragmentation.     

Effects of demographic parameters on metapopulation size and persistence: an analytical stochastic model

An analytical stochastic metapopulation model is developed. It describes how individuals will be distributed among patches as a function of density-dependent birth, death and emigration rates, and the probability of successful dispersal. The model includes demographic stochasticity, but not catastrophes, environmental stochasticity or variation in patch size and suitability. All patches are equally likely to be colonized by migrants. The model predicts: (a) mean and variance of the number of individuals per patch; (b) probability distribution of individuals per patch; (c) mean number of individuals in transit; and (d) turn-over rate and expected persistence time of a single patch. The model shows that (a) dispersal rates must be intermediate in order to ensure metapopulation persistence; (b) the mean number of individuals per patch is often well below the carrying capacity; (c) long transit times and/or high mortality during dispersal reduce the mean number of individuals per patch; (d) density-dependent emigration responses will usually increase metapopulation size and persistence compared with density-independent dispersal; (e) an increase in the per capita net growth rate can both increase and decrease metapopulation size and persistence depending on whether dispersal rates are high or low; (f) density-independent birth, death, and emigration rates lead to a spatial pattern described by the negative binomial distribution.