Metapopulation Dynamics of the Froghopper Neophilaenus albipennis (F., 1798) (Homoptera, Cercopidae) – What is the Minimum Viable Metapopulation Size?

The occurrence of the froghopper Neophilaenus albipennis was surveyed in a network of 506 patches of its host plant Brachypodium pinnatum. The occupancy pattern largely depends on the size and isolation of the habitat patches. Together with the observed turnover this indicates a metapopulation structure. In order to simulate the dynamics of the metapopulation the incidence function model was used. The model was successfully fitted to the field data. Impacts on the metapopulation were simulated and the probability of survival of the whole metapopulation was estimated. Implications for conservation, especially the minimum viable metapopulation size, are discussed.     

Approximate Bayesian estimation of extinction rate in the Finnish Daphnia magna metapopulation

Approximate Bayesian computation (ABC) is useful for parameterizing complex models in population genetics. In this study, ABC was applied to simultaneously estimate parameter values for a model of metapopulation coalescence and test two alternatives to a strict metapopulation model in the well‐studied network of Daphnia magna populations in Finland. The models shared four free parameters: the subpopulation genetic diversity (θ_S), the rate of gene flow among patches (4Nm), the founding population size (N₀) and the metapopulation extinction rate (e) but differed in the distribution of extinction rates across habitat patches in the system. The three models had either a constant extinction rate in all populations (strict metapopulation), one population that was protected from local extinction (i.e. a persistent source), or habitat‐specific extinction rates drawn from a distribution with specified mean and variance. Our model selection analysis favoured the model including a persistent source population over the two alternative models. Of the closest 750 000 data sets in Euclidean space, 78% were simulated under the persistent source model (estimated posterior probability = 0.769). This fraction increased to more than 85% when only the closest 150 000 data sets were considered (estimated posterior probability = 0.774). Approximate Bayesian computation was then used to estimate parameter values that might produce the observed set of summary statistics. Our analysis provided posterior distributions for e that included the point estimate obtained from previous data from the Finnish D. magna metapopulation. Our results support the use of ABC and population genetic data for testing the strict metapopulation model and parameterizing complex models of demography.     

NEUTRAL GENETIC DIVERSITY IN A METAPOPULATION WITH RECURRENT LOCAL EXTINCTION AND RECOLONIZATION

Many species exist as metapopulations in balance between local population extinction and recolonization, processes that may strongly affect the distribution of neutral genetic diversity within demes and in the metapopulation as a whole. In this paper we use both the infinite-alleles and the infinite-sites models to reframe Slatkin's propagulepool and migrant-pool models in terms of mean within-deme and among-deme genetic diversity; the infinite-sites model is particularly relevant to DNA sequence data. Population turnover causes a major reduction in neutral genetic diversity within demes, π_S, and in the metapopulation as a whole, π_t. This effect is particularly strong for propagulepool colonization, in which colonists are drawn from a single extant deme. Because metapopulation dynamics affect both within-deme and total metapopulation diversity similarly, comparisons between species with different ecologies on the basis of ratios such as F_ST are difficult to interpret and absolute measures of divergence between populations should be used as well. Although the value of F_ST in a metapopulation with local extinction depends strongly on the mode of colonization, this has almost no effect on the numerator of the F_ST ratio, π_t – π_S, so that F_ST is influenced mainly by the effect of the colonization mode on the denominator (π_t). Our results also indicate that it is inappropriate to use measures of average within-deme diversity in species with population turnover to estimate the scaled mutation rate, θ, because extinction can greatly reduce π_S. Finally, we discuss the effect of population turnover on the effective size of a metapopulation.     

Metapopulation viability of an endangered holoparasitic plant in a dynamic landscape

By creating transient patch mosaics, disturbance can influence the dynamics of interacting populations in many ecosystems. In European heathland, traditional land use created such dynamic systems favourable for both early and later successional species. Little empirical evidence is, however, available on the impact of current management on metapopulations occurring in such landscapes. This paper looks at the metapopulation viability of the endangered holoparasite Cuscuta epithymum, a species that typically occurs in early successional stages of recently managed heathlands. We used both observational and experimental data from a 4‐yr study to parameterise a spatially explicit metapopulation model. This model explores the impact of demographic characteristics and spatiotemporal landscape patterns created by management events on metapopulation viability. Both occasional long‐distance dispersal and dormant seeds are shown to be critical for the long‐term survival of C. epithymum in a dynamic heathland landscape subjected to a fixed rotational mowing of 15 yr. A relatively high management frequency (<15 yr between two consecutive mowing events) appeared to be necessary to sustain a viable C. epithymum metapopulation. When there is a longer interval between management events, grazing can counterbalance the negative effects of vegetation succession. Our results indicate that small‐scale cyclical management events combined with extensive grazing are the most appropriate management strategy to maintain viable populations of C. epithymum instead of the current large‐scale management events. Our results further emphasise the importance of incorporating both spatiotemporal patch availability and key demographic characteristics, especially seed banks, for a realistic view of metapopulation dynamics in disturbed landscapes. This study clearly demonstrates the usefulness of metapopulation models to understand the impact of management events and to provide new ecological insights into processes acting at a landscape scale.     

A Stochastic Metapopulation Model with Variability in Patch Size and Position

Analytically tractable metapopulation models usually assume that every patch is identical, which limits their application to real metapopulations. We describe a new single species model of metapopulation dynamics that allows variation in patch size and position. The state of the metapopulation is defined by the presence or absence of the species in each patch. For a system of n patches, this gives 2ⁿ possible states. We show how to construct and analyse a matrix describing transitions between all possible states by first constructing separate extinction and colonisation matrices. We illustrate the model′s application to metapopulations by considering an example of malleefowl, Leipoa ocellata, in southern Australia, and calculate extinction probabilities and quasi-stationary distributions. We investigate the relative importance of modelling the particular arrangement of patches and the variation in patch sizes for this metapopulation and we use the model to examine the effects of further habitat loss on extinction probabilities.     

Effective size of an Atlantic salmon (Salmo salar L.) metapopulation in Northern Spain

The genetic diversity of metapopulations is influenced not only by the effective sizes (N _e ) of individual subpopulations, but also by the total effective size of the metapopulation (meta-N _e ). We estimated meta-N _e of four neighbouring Atlantic salmon populations connected by gene flow using genetic estimates of subpopulation N _e s and migration rates derived from capture–recapture data. The meta-[^(N)]_e meta{\hbox{-}}\hat{N}_{e} was lower than the sum of [^(N)]_e \hat{N}_{e} s of the subpopulations, suggesting that genetic diversity harboured by the four river salmon metapopulation is lower than what would have been expected by viewing individual subpopulations separately. In addition, meta-[^(N)]_e meta{\hbox{-}}\hat{N}_{e} was found to be sensitive to changes in [^(N)]_e \hat{N}_{e} of the subpopulation from which net emigration rate was largest, so as that the genetic diversity of the metapopulation would be best preserved by avoiding any reductions in N _e of this subpopulation. Yet, this subpopulation is the one that has historically—and still is—experiencing the highest exploitation rate in the metapopulation system.     

Extinction times for closed epidemics: the effects of host spatial structure

Although of practical importance, the relationship between the duration of an epidemic and host spatial structure is poorly understood. Here we use a stochastic metapopulation model for the transmission of infection in a spatially structured host population. There are three qualitatively different regimes for the extinction time, which depend on patch population size, the within‐patch basic reproductive number and the strength of coupling between patches. In the first regime, the extinction time for the metapopulation (i.e. from all patches) is approximately equal to the extinction time for a single patch. In the second regime, the metapopulation extinction time is maximal but also highly variable. In the third regime, the extinction time for the metapopulation (T_E) is given by T_E = a + bn^1/2 where a is the local extinction time (i.e. from last patch), b is the transit time (i.e. the time taken for infection to spread from one patch to another) and n is the total number of patches.     

Effects of population characteristics and structure on estimates of effective population size in a house sparrow metapopulation

Effective population size (N_e) is a key parameter to understand evolutionary processes and the viability of endangered populations as it determines the rate of genetic drift and inbreeding. Low N_e can lead to inbreeding depression and reduced population adaptability. In this study, we estimated contemporary N_e using genetic estimators (LDNE, ONeSAMP, MLNE and CoNe) as well as a demographic estimator in a natural insular house sparrow metapopulation. We investigated whether population characteristics (population size, sex ratio, immigration rate, variance in population size and population growth rate) explained variation within and among populations in the ratio of effective to census population size (N_e/N_c). In general, N_e/N_c ratios increased with immigration rates. Genetic N_e was much larger than demographic N_e, probably due to a greater effect of immigration on genetic than demographic processes in local populations. Moreover, although estimates of genetic N_e seemed to track N_c quite well, the genetic N_e‐estimates were often larger than N_c within populations. Estimates of genetic N_e for the metapopulation were however within the expected range (<N_c). Our results suggest that in fragmented populations, even low levels of gene flow may have important consequences for the interpretation of genetic estimates of N_e. Consequently, further studies are needed to understand how N_e estimated in local populations or the total metapopulation relates to actual rates of genetic drift and inbreeding.     

Evolution of complex life cycles of amphibians: bridging the gap between metapopulation dynamics and life history evolution

Current evolutionary models for amphibian life cycles reflect tradeoffs in size-specific growth and mortality rates between the aquatic and terrestrial stages. A limitation of these models is that they do not incorporate evolutionary phenomena that are associated with metapopulation structure. In this work I address components of the evolution of complex life cycles (CLCs) that are tied to the metapopulation dynamics of amphibians that use seasonal wetlands that vary in hydroperiod. In particular, I describe how selection for the minimum length of the larval period affects metapopulation viability and the selection/migration equilibrium. Selection to increase the minimum length of the larval period functionally reduces the number of viable breeding sites on the landscape, increases the average distance between neighboring sites, and increases the risk of metapopulation extinction. Within a metapopulation, asymmetric gene flow between populations that are adapted to different hydroperiods tends to swamp local selection for long larval periods at sites with long hydroperiods. The evolutionary stability of CLCs of many species with metapopulation structure may reflect the fact that extremely small metamorphs cannot survive on land, while lineages with long larval periods incur a high risk of metapopulation extinction. I encourage theorists to more carefully consider how life history traits and metapopulation viability are related for these and other taxa.     

Metapopulation genetic structure of two coexisting parasitoids of the Glanville fritillary butterfly

We investigated the metapopulation genetic structure of two specialist parasitoids, Cotesia melitaearum and Hyposoter horticola, attacking the Glanville fritillary butterfly (Melitaea cinxia) in the Åland Islands south-western Finland. The host butterfly persists as a classic metapopulation in a network of 4,000 small habitat patches within an area of 50 by 70 km . The two parasitoids are known to differ greatly in their population dynamics and spatial pattern of occupancy in local host populations. Analysis of genetic population structure using F_ST and clustering of multilocus genotypes revealed a distinct large-scale spatial structure in C. melitaearum but a very weak pattern in H. horticola. This result is consistent with the known difference in the dispersal range (much longer in H. horticola) and population size (much greater in H. horticola) of the two parasitoids.     

Extinction dynamics in mainland-island metapopulations: an N-patch stochastic model

A generalization of the well-known Levins’ model of metapopulations is studied. The generalization consists of (i) the introduction of immigration from a mainland, and (ii) assuming the dynamics is stochastic, rather than deterministic. A master equation, for the probability that n of the patches are occupied, is derived and the stationary probability P _s (n), together with the mean and higher moments in the stationary state, determined. The time-dependence of the probability distribution is also studied: through a Gaussian approximation for general n when the boundary at n = 0 has little effect, and by calculating P(0, t), the probability that no patches are occupied at time t, by using a linearization procedure. These analytic calculations are supplemented by carrying out numerical solutions of the master equation and simulations of the stochastic process. The various approaches are in very good agreement with each other. This allows us to use the forms for P _s 0) and P(0, t) in the linearization approximation as a basis for calculating the mean time for a metapopulation to become extinct. We give an analytical expression for the mean time to extinction derived within a mean field approach. We devise a simple method to apply our mean field approach even to complex patch networks in realistic model metapopulations. After studying two spatially extended versions of this nonspatial metapopulation model—a lattice metapopulation model and a spatially realistic model—we conclude that our analytical formula for the mean extinction time is generally applicable to those metapopulations which are really endangered, where extinction dynamics dominates over local colonization processes. The time evolution and, in particular, the scope of our analytical results, are studied by comparing these different models with the analytical approach for various values of the parameters: the rates of immigration from the mainland, the rates of colonization and extinction, and the number of patches making up the metapopulation.     

Habitat Deterioration, Habitat Destruction, and Metapopulation Persistence in a Heterogenous Landscape

Levins's unstructured metapopulation model predicts that the equilibrium fraction of empty habitat patches is a constant function of the fractionhof suitable patches in the landscape and that this constant equals the threshold value for metapopulation persistence. Levins's model thus suggests that the minimum amount of suitable habitat necessary for metapopulation persistence can be estimated from the fraction of empty patches at steady state. In this paper we construct several more realistic structured metapopulation models that include variation in patch quality and the rescue effect. These models predict both positive and negative correlations between the fractions of suitable patches and empty patches. The type of correlation depends in an intricate manner on the strength of the rescue effect and on the quality distribution of the patches to be destroyed. Empty patches can be considered as the resource limiting metapopulation growth. Our results demonstrate that the correlation between the fractions of suitable patches and empty patches is positive if and only if the average value of the resource decreases as the number of patches increases.     

Variance effective population size is affected by census size in sub-structured populations

Measurement of allele frequency shifts between temporally spaced samples has long been used for assessment of effective population size (N_e), and this ‘temporal method’ provides estimates of N_e referred to as variance effective size (N_eV). We show that N_eV of a local population that belongs to a sub-structured population (a metapopulation) is determined not only by genetic drift and migration rate (m), but also by the census size (N_c). The realized N_eV of a local population can either increase or decrease with increasing m, depending on the relationship between N_e and N_c in isolation. This is shown by explicit mathematical expressions for the factors affecting N_eV derived for an island model of migration. We verify analytical results using high-resolution computer simulations, and show that the phenomenon is not restricted to the island model migration pattern. The effect of N_c on the realized N_eV of a local subpopulation is most pronounced at high migration rates. We show that N_c only affects local N_eV, whereas N_eV for the metapopulation as a whole, inbreeding (N_eI), and linkage disequilibrium (N_eLD) effective size are all independent of N_c. Our results provide a possible explanation to the large variation of N_e/N_c ratios reported in the literature, where N_e is frequently estimated by N_eV. They are also important for the interpretation of empirical N_e estimates in genetic management where local N_eV is often used as a substitute for inbreeding effective size, and we suggest an increased focus on metapopulation N_eV as a proxy for N_eI.     

The evolution of generation time in metapopulations of monocarpic perennial plants: some theoretical considerations and the example of the rare thistle Carlina vulgaris

Life-history models for populations in a single patch, in which density dependence occurs through competition between seedlings for safe-sites, suggest that timing of flowering in monocarpic perennials is such that expected lifetime reproductive success (R ₀) is maximised. We discuss metapopulation models in which local populations go extinct either (1) because all rosettes die locally, or (2) because seedling recruitment is limited to restricted periods in time. In both cases there is selection for shorter optimal generation times than suggested by the single-patch model. The mechanism is that in young populations competition between seedlings for safe sites is relaxed for some years. This mostly benefits types with short generation times. Carlina vulgaris flowers earlier than the single-patch model suggests. The metapopulation effect is sufficiently strong to account for the differences but other factors cannot be outruled. Data on other monocarpic perennials are discussed. Flowering in Cirsium vulgare is also earlier than suggested by the single-patch model, but for other species the picture is far from clear. This revised version was published online in July 2006 with corrections to the Cover Date.     

Asynchronization of local population dynamics and persistence of a metapopulation: a lesson from an endangered composite plant, Aster kantoensis

Fragmentation of a large habitat makes local populations less linked to others, and a whole population structure changes to a metapopulation. The smaller a local population is, the more strengthened extinction factors become. Then, frequent extinctions of local populations threaten persistence of the metapopulation unless recolonizations occur rapidly enough after local extinctions. Spatially structured models have been more widely used for predicting future population dynamics and for assessing the extinction risk of a metapopulation. In this article, we first review such spatially structured models that have been applied to conservation biology, focusing on effects of asynchronization among local population dynamics on persistence of the whole metapopulation. Second, we introduce our ongoing project on extinction risk assessment of an endangered composite biennial plant, Aster kantoensis, in the riverside habitat, based on a lattice model for describing its spatiotemporal population dynamics. The model predicted that the extinction risk of A. kantoensis depends on both the frequency of flood occurrence and the time to coverage of a local habitat by other competitively stronger perennials. Finally, we present a measure (Hassell and Pacala's CV ²) for quantifying the effect of asynchronization among local population dynamics on the persistence of a whole metapopulation in conservation ecology. Received: January 12, 2000 / Accepted: February 8, 2000     

Human‐facilitated metapopulation dynamics in an emerging pest species,Cimex lectularius

The number and demographic history of colonists can have dramatic consequences for the way in which genetic diversity is distributed and maintained in a metapopulation. The bed bug (Cimex lectularius) is a re‐emerging pest species whose close association with humans has led to frequent local extinction and colonization, that is, to metapopulation dynamics. Pest control limits the lifespan of subpopulations, causing frequent local extinctions, and human‐facilitated dispersal allows the colonization of empty patches. Founder events often result in drastic reductions in diversity and an increased influence of genetic drift. Coupled with restricted migration, this can lead to rapid population differentiation. We therefore predicted strong population structuring. Here, using 21 newly characterized microsatellite markers and approximate Bayesian computation (ABC), we investigate simplified versions of two classical models of metapopulation dynamics, in a coalescent framework, to estimate the number and genetic composition of founders in the common bed bug. We found very limited diversity within infestations but high degrees of structuring across the city of London, with extreme levels of genetic differentiation between infestations (F_ST = 0.59). ABC results suggest a common origin of all founders of a given subpopulation and that the numbers of colonists were low, implying that even a single mated female is enough to found a new infestation successfully. These patterns of colonization are close to the predictions of the propagule pool model, where all founders originate from the same parental infestation. These results show that aspects of metapopulation dynamics can be captured in simple models and provide insights that are valuable for the future targeted control of bed bug infestations.     

Population dynamics can be more important than physiological limits for determining range shifts under climate change

Evidence is accumulating that species' responses to climate changes are best predicted by modelling the interaction of physiological limits, biotic processes and the effects of dispersal‐limitation. Using commercially harvested blacklip (Haliotis rubra) and greenlip abalone (Haliotis laevigata) as case studies, we determine the relative importance of accounting for interactions among physiology, metapopulation dynamics and exploitation in predictions of range (geographical occupancy) and abundance (spatially explicit density) under various climate change scenarios. Traditional correlative ecological niche models (ENM) predict that climate change will benefit the commercial exploitation of abalone by promoting increased abundances without any reduction in range size. However, models that account simultaneously for demographic processes and physiological responses to climate‐related factors result in future (and present) estimates of area of occupancy (AOO) and abundance that differ from those generated by ENMs alone. Range expansion and population growth are unlikely for blacklip abalone because of important interactions between climate‐dependent mortality and metapopulation processes; in contrast, greenlip abalone should increase in abundance despite a contraction in AOO. The strongly non‐linear relationship between abalone population size and AOO has important ramifications for the use of ENM predictions that rely on metrics describing change in habitat area as proxies for extinction risk. These results show that predicting species' responses to climate change often require physiological information to understand climatic range determinants, and a metapopulation model that can make full use of this data to more realistically account for processes such as local extirpation, demographic rescue, source‐sink dynamics and dispersal‐limitation.     

Stochastic models for mainland-island metapopulations in static and dynamic landscapes

This paper has three primary aims: to establish an effective means for modelling mainland-island metapopulations inhabiting a dynamic landscape; to investigate the effect of immigration and dynamic changes in habitat on metapopulation patch occupancy dynamics; and to illustrate the implications of our results for decision-making and population management. We first extend the mainland-island metapopulation model of Alonso and McKane [Bull. Math. Biol. 64:913–958, 2002] to incorporate a dynamic landscape. It is shown, for both the static and the dynamic landscape models, that a suitably scaled version of the process converges to a unique deterministic model as the size of the system becomes large. We also establish that, under quite general conditions, the density of occupied patches, and the densities of suitable and occupied patches, for the respective models, have approximate normal distributions. Our results not only provide us with estimates for the means and variances that are valid at all stages in the evolution of the population, but also provide a tool for fitting the models to real metapopulations. We discuss the effect of immigration and habitat dynamics on metapopulations, showing thatmainland-like patches heavily influence metapopulation persistence, and we argue for adopting measures to increase connectivity between this large patch and the other island-like patches. We illustrate our results with specific reference to examples of populations of butterfly and the grasshopperBryodema tuberculata.     

The association between pollen size and Renner complex in Oenothera villaricae and O. picensis ssp. picensis and their hybrids: evidence for preanthesis pollen competition

In both Oenothera villaricae Dietrich and O. picensis ssp. picensis, chromosomes are transmitted as two Renner complexes. Reciprocal combinations of the Renner complexes produce eight different F₁ hybrids, but only seven are viable. Each species, and each F₁ hybrid, produces three sizes of pollen, approximately 50% small sterile grains, 15% medium-sized viable grains and 35% large viable grains. Medium- and large-sized grains were separated manually and subjected to random amplified polymorphic DNAs (RAPDs) analysis. A pattern of RAPD amplifications was obtained which indicates that, for each species and F₁ hybrid, one specific Renner complex characterizes the medium- and another the large-sized viable pollen. The results indicate that pollen size is determined in part by the pollen genotype and in part by the genotype of the other pollen grains developing within the same anther.     

The contribution of patch topology and demographic parameters to population viability analysis predictions: the case of the European tree frog

Population viability analyses (PVA) are increasingly used in metapopulation conservation plans. Two major types of models are commonly used to assess vulnerability and to rank management options: population-based stochastic simulation models (PSM such as RAMAS or VORTEX) and stochastic patch occupancy models (SPOM). While the first set of models relies on explicit intrapatch dynamics and interpatch dispersal to predict population levels in space and time, the latter is based on spatially explicit metapopulation theory where the probability of patch occupation is predicted given the patch area and isolation (patch topology). We applied both approaches to a European tree frog (Hyla arborea) metapopulation in western Switzerland in order to evaluate the concordances of both models and their applications to conservation. Although some quantitative discrepancies appeared in terms of network occupancy and equilibrium population size, the two approaches were largely concordant regarding the ranking of patch values and sensitivities to parameters, which is encouraging given the differences in the underlying paradigms and input data.