Impact of Directed Movement on Invasive Spread in Periodic Patchy Environments

To address the effect of taxis of invasive animals on their spreading speed in heterogeneous environments, we deal with an advection-diffusion-reaction equation (ADR) in a periodic patchy environment. Two-types of advection that spatially vary depending on environmental heterogeneity are taken into consideration: a stepwise taxis function and a saw-like taxis function. We first analyze the ADR with the stepwise taxis advection, and derive an invasion criterion. When the invasion criterion holds, an initially localized population evolves to a traveling periodic wave (TPW). The asymptotic speed of the TPW is found to be equal to the minimal speed of the TPW analytically derived. Thus, we examine how the minimal speed is influenced by the taxis. The major results are: (1)?As the magnitude of the taxis toward favorable patches increases, invasion becomes more feasible. However, the spreading speed increases at first, and then decreases to show a one-humped curve against the magnitude of the taxis; (2)?As the scale of fragmentation in the patchy environment is increased, the spreading speed increases when the magnitude of the taxis is small, while it decreases when the magnitude of the taxis becomes sufficiently large. These characteristic features qualitatively apply to the ADR model with the saw-like taxis function.     

Metapopulation persistence in dynamic landscapes: the role of dispersal distance

Species associated with transient habitats need efficient dispersal strategies to ensure their regional survival. Using a spatially explicit metapopulation model, we studied the effect of the dispersal range on the persistence of a metapopulation as a function of the local population and landscape dynamics (including habitat patch destruction and subsequent regeneration). Our results show that the impact of the dispersal range depends on both the local population and patch growth. This is due to interactions between dispersal and the dynamics of patches and populations via the number of potential dispersers. In general, long-range dispersal had a positive effect on persistence in a dynamic landscape compared to short-range dispersal. Long-range dispersal increases the number of couplings between the patches and thus the colonisation of regenerated patches. However, long-range dispersal lost its advantage for long-term persistence when the number of potential dispersers was low due to small population growth rates and/or small patch growth rates. Its advantage also disappeared with complex local population dynamics and in a landscape with clumped patch distribution.     

Integrodifference models for persistence in fragmented habitats

Integrodifference models of growth and dispersal are analyzed on finite domains to investigate the effects of emigration, local growth dynamics and habitat heterogeneity on population persistence. We derive the bifurcation structure for a range of population dynamics and present an approximation that allows straighforward calculation of the equilibrium populations in terms of local growth dynamics and dispersal success rates. We show how population persistence in a heterogeneous environment depends on the scale of the heterogeneity relative to the organism's characteristic dispersal distance. When organisms tend to disperse only a short distance, population persistence is dominated by local conditions in high quality patches, but when dispersal distance is relatively large, poor quality habitat exerts a greater influence.     

From individual behavior to metapopulation dynamics: unifying the patchy population and classic metapopulation models

Spatially structured populations in patchy habitats show much variation in migration rate, from patchy populations in which individuals move repeatedly among habitat patches to classic metapopulations with infrequent migration among discrete populations. To establish a common framework for population dynamics in patchy habitats, we describe an individual-based model (IBM) involving a diffusion approximation of correlated random walk of individual movements. As an example, we apply the model to the Glanville fritillary butterfly (Melitaea cinxia) inhabiting a highly fragmented landscape. We derive stochastic patch occupancy model (SPOM) approximations for the IBMs assuming pure demographic stochasticity, uncorrelated environmental stochasticity, or completely correlated environmental stochasticity in local dynamics. Using realistic parameter values for the Glanville fritillary, we show that the SPOMs mimic the behavior of the IBMs well. The SPOMs derived from IBMs have parameters that relate directly to the life history and behavior of individuals, which is an advantage for model interpretation and parameter estimation. The modeling approach that we describe here provides a unified framework for patchy populations with much movements among habitat patches and classic metapopulations with infrequent movements.     

Temporal autocorrelation can enhance the persistence and abundance of metapopulations comprised of coupled sinks

In spatially heterogeneous landscapes, some habitats may be persistent sources, providing immigrants to sustain populations in unfavorable sink habitats (where extinction is inevitable without immigration). Recent theoretical and empirical studies of source-sink systems demonstrate that temporally variable local growth rates in sinks can substantially increase average abundance of a persisting population, provided that the variation is positively autocorrelated--in effect, temporal variation inflates average abundance. Here we extend these results to a metapopulation in which all habitat patches are sinks. Using numerical studies of a population with discrete generations (buttressed by analytic results), we show that temporal variation and moderate dispersal can jointly permit indefinite persistence of the metapopulation and that positive autocorrelation both lowers the magnitude of variation required for persistence and increases the average abundance of persisting metapopulations. These effects are weakened--but not destroyed--if variation in local growth rates is spatially synchronized and dispersal is localized. We show that the inflationary effect is robust to a number of extensions of the basic model, including demographic stochasticity and density dependence. Because ecological and environmental processes contributing to temporally variable growth rates in natural populations are typically autocorrelated, these observations may have important implications for species persistence.     

Lasting effects of maternal behaviour on the distribution of a dispersive stream insect

1. Predicting population dynamics at large spatial scales requires integrating information about spatial distribution patterns, inter-patch movement rates and within-patch processes. Advective dispersal of aquatic species by water movement is considered paramount to understanding their population dynamics. Rivers are model advective systems, and the larvae of baetid mayflies are considered quintessential dispersers. Egg laying of baetids along channels is patchy and reflects the distribution of oviposition sites, but larvae are assumed to drift frequently and far, thereby erasing patterns created during oviposition. Dispersal kernels are often overestimated, however, and empirical tests of such assumptions are warranted because of the pivotal role distribution patterns can have on populations. 2. We tested empirically whether the egg distribution patterns arising from oviposition behaviours persisted and were reflected in the distribution patterns of larval Baetis rhodani. In field surveys, we tested for associations between egg mass and larval densities over 1 km lengths of four streams. A control species, the mayfly Ephemerella ignita, was employed to test for covarying environmental factors. We estimated drift rates directly to test whether larvae dispersed between riffles (patches of high egg mass density) and whether drift rates were density-dependent or density-related - expected outcomes if drift erases patterns established by maternal behaviours. 3. Positive associations between egg masses and larval benthic densities were found for neonate and mid-stage larvae of Baetis, but not the control species, suggesting persistence of the patchy distribution patterns established at oviposition. Drift rates were high, and riffles were net exporters of neonate and mid-stage larvae, but drift rates were unrelated to benthic densities and few drifters reached the next riffle. Riffles were sinks for large larvae, suggesting ontogenetic shifts in habitat use, but little long-distance dispersal. 4. Overall, the results suggest that most neonate and mid-stage larvae of B. rhodani remain close to the natal riffle, and late-stage larvae disperse shorter distances than routinely assumed. The persistence of maternal effects on distribution patterns well into juvenile life of an allegedly iconic disperser suggests that traditional models of how dispersal influences the population dynamics of many lotic invertebrates may be incorrect.     

Regional and local scale metapopulation dynamics in the interaction between Callosobruchus maculatus and Anisopteromalus calandrae

Habitat structure increases the persistence of many extinction‐prone resource–consumer interactions. Metapopulation theory is one of the leading approaches currently used to explain why local, ephemeral populations persist at a regional scale. Central to the metapopulation concept is the amount of dispersal occurring between patches, too much or too little can result in regional extinction. In this study, the role of dispersal on the metapopulation dynamics of an over‐exploitative host–parasitoid interaction is assessed. In the absence of the parasitoid the highly vagile bruchid, Callosobruchus maculatus, can maintain a similar population size regardless of the permeability of the inter‐patch matrix and exhibits strong negative density‐dependence. After the introduction of the parasitoid the size of the bruchid population decreases with a corresponding increase in the occurrence of empty patches. In this case, limiting the dispersal of both species decouples the interaction to a greater extent and results in larger regional bruchid populations. Given the disparity between the dispersal rates of the two species, it is proposed that the more dispersive host benefits from the reduction in landscape permeability by increasing the opportunity to colonise empty patches and rescue extinction prone populations. Associated with the introduction of the parasitoid is a shift in the strength of density‐dependence as the population moves from bottom–up towards top–down regulation. The importance of local and regional scale measurements is apparent when the role of individual patches on regional dynamics is considered. By only taking regional dynamics into account the importance of dispersal regime on local dynamics is overlooked. Similarly, when local dynamics were examined, patches were found to have different influences on regional dynamics depending on dispersal regime and patch location.     

Dances with fire: Tracking metapopulation dynamics of<Emphasis Type="Italic">polygonella basiramia</Emphasis> in Florida scrub (USA)

The regional persistence of species subject to local population colonization and extinction necessarily depends on how landscape features and disturbance affect metapopulation dynamics. Here, we characterize the metapopulation structure and short-term dynamics ofPolygonella basiramia. This rare, short-lived perennial herb is endemic to Florida scrublands and lacks a seed bank. Fires create the open sand gaps within a shrub matrix that support this species but also kill established plants. Thus, persistence depends on frequent colonization of unoccupied gaps. We are monitoring population dynamics within and among 1204 gaps distributed among 19 shrub patches. Considerable subpopulation turnover is evident at the gap level with rates of gap extinction exceeding rates of colonization in the first year. Whether declines in overall abundance continue is likely to depend on patterns of disturbance and regional stochasticity in this dynamic landscape.Polygonella is more likely to occupy larger and less isolated gaps, demonstrating that landscape features and disturbance strongly affect metapopulation dynamics. BecausePolygonella basiramia displays characteristics, occupancy patterns, and turnover dynamics consistent with metapopulation theory, it represents a model system for studying plant metapopulations.     

Migration of the clouded Apollo butterfly Parnassius mnemosyne in a network of suitable habitats – effects of patch characteristics

The clouded Apollo Parnassius mnemosyne is a food plant specialist with short but frequent movements between habitat patches. The short average dispersal distances suggest that the probability of colonisation of vacant patches decreases rapidly as the distance between the source and target patches increases, which means that a dense habitat network is needed for the conservation of the species. Both emigration rate and the number of immigrants varied among patches and were not affected only by isolation but also by several other patch characteristics. The model that explained most of the variation in emigration rates among patches included patch area and the number of conspecifics. The area and the population density of the target patch had significant effects on the number of arriving immigrants. Thus, the colonisation of vacant patches is dependent on these patch characteristics. Generally, emigration rates were lower and residence times longer in large patches with many conspecifics. Butterfly density was the most important single factor explaining the variation in the number of immigrants among patches, although the positive effect of the area of the target patch was also significant. As a consequence of the marked positive density dependence caused by conspecific attraction, small patches with higher than average butterfly density, receive more immigrants than could be expected based on the patch area only. Due to conspecific attraction, per capita immigration rates are higher in small than large patches. Thus, immigration may have a more significant effect on the local dynamics of small than large populations.     

Impact of dispersal on population growth: the role of inter-patch distance

Dispersal can play a key role in the dynamics of patchy populations through patch colonization, and generally this leads to distance-dependent colonization. Less recognised are the roles of dispersal and inter-patch distance on the growth of a population after colonization. We use a laboratory mite model system in which both juveniles and adults can disperse to explore the impact of dispersal, and particularly inter-patch distance, on population dynamics. We examine the dynamics of patches after colonization by manipulating the presence of a dispersal corridor to a source patch at two inter-patch distances. Consistent with many field studies, the results show colonization was slower in more distant patches. Following colonization, the effect of the dispersal corridor on dynamics was dependent on inter-patch distance. In patches near the source, the number of adults tended to increase at a faster rate, and juveniles at a slower rate when connected with a dispersal corridor. In contrast, adult numbers grew slower and juveniles tended to grow faster when connected with a corridor in more distant patches. In the long-term, equilibrium adult numbers were lower in patches connected to the source patch at both distances. These results are likely to be driven by the effects of inter-patch distance on dispersal mortality, and the effects of dispersal on patch abundance and within-patch competition. These results confirm that distance is important for patch colonization and also show that distance can affect population density after colonization. The effects of dispersal and distance on local dynamics could be important in the dynamics of patchy populations in increasingly fragmented landscapes.     

Structured models of metapopulation dynamics

I develop models of metapopulation dynamics that describe changes in the numbers of individuals within patches. These models are analogous to structured population models, with patches playing the role of individuals. Single species models which do not include the effect of immigration on local population dynamics of occupied patches typically lead to a unique equilibrium. The models can be used to study the distributions of numbers of individuals among patches, showing that both metapopulations with local outbreaks and metapopulations without outbreaks can occur in systems with no underlying environmental variability. Distributions of local population sizes (in occupied patches) can vary independently of the total population size, so both patterns of distributions of local population sizes are compatible with either rare or common species. Models which include the effect of immigration on local population dynamics can lead to two positive equilibria, one stable and one unstable, the latter representing a threshold between regional extinction and persistence.     

Metapopulation dynamics: Does it help to have more of the same?

With the interest in conservation biology shifting towards processes from patterns, and to populations from communities, the theory of metapopulation dynamics is replacing the equilibrium theory of island biogeography as the population ecology paradigm in conservation biology. The simplest models of metapopulation dynamics make predictions about the effects of habitat fragmentation - size and isolation of habitat patches - on metapopulation persistence. The simple models may be enriched by considerations of the effects of demographic and environmental stochasticity on the size and extinction probability of local populations. Environmental stochasticity affects populations at two levels: it makes local extinctions more probable, and it also decreases metapopulation persistence time by increasing the correlation of extinction events across populations. Some controversy has arisen over the significance of correlated extinctions, and how they may affect the optimal subdivision of metapopulations to maximize their persistence time.     

Effects of asymmetric dispersal and environmental gradients on the stability of host–parasitoid systems

We consider host–parasitoid systems spatially distributed on a row of patches connected by dispersal. We analyze the effects of dispersal frequency, dispersal asymmetry, number of patches and environmental gradients on the stability of the host–parasitoid interactions. To take into account dispersal frequency, the hosts and parasitoids are allowed to move from one patch to a neighboring patch a certain number of times within a generation. When this number is high, aggregation methods can be used to simplify the proposed initial model into an aggregated model describing the dynamics of both the total host and parasitoid populations. We show that as the number of patches increases less asymmetric parasitoid dispersal rates are required for stability. We found that the 'CV²>1 rule' is a valid approximation for stability if host growth rate is low, otherwise the general condition of stability we establish should be preferred. Environmental variability along the row of patches is introduced as gradients on host growth rate and parasitoid searching efficiency. We show that stability is more likely when parasitoids move preferentially towards patches where they have high searching efficiency or when hosts go mainly to patches where they have a low growth rate.     

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     

Divide and conquer? Persistence of infectious agents in spatial metapopulations of hosts

Persistence of an infectious agent in a population is an important issue in epidemiology. It is assumed that spatially fragmenting a population of hosts increases the probability of persistence of an infectious agent and that movement of hosts between the patches is vital for that. The influence of migration on persistence is however often studied in mean-field models, whereas in reality the actual distance travelled can be limited and influence the movement dynamics. We use a stochastic model, where within- and between-patch dynamics are coupled and movement is modelled explicitly, to show that explicit consideration of movement distance makes the relation between persistence of infectious agents and the metapopulation structure of its hosts less straightforward than previously thought. We show that the probability of persistence is largest at an intermediate movement distance of the host and that spatially fragmenting a population of hosts is not necessarily beneficial for persistence.     

Fire-mediated effects of shrubs, lichens and herbs on the demography of Hypericum cumulicola in patchy Florida scrub

Understanding the effect of disturbance and interspecific interactions on population dynamics and availability of suitable habitats for colonization and growth is critical for conservation and management of endangered species. Hypericum cumulicola is a narrowly endemic, small perennial herb virtually restricted to open areas of well-drained white sand in Florida rosemary scrub, a naturally patchy community that burns about every 20–80 years. Over 1 year (September 1994 to September 1995) we evaluated variation in survival, growth and fecundity among 1214 individuals in 14 rosemary scrub patches of different sizes (0.09–1.85 ha) and fire histories (2, 8–10, and >20 years since the last fire). Fire kills aboveground individuals of H. cumulicola, but new individuals were present a year after fire. Recruitment decreased in patches more than a decade post-fire. Survival, annual height growth rate, and fecundity (number of flowers and fruits) were higher in recently burned patches. Scrub patch size did not affect these demographic variables. Survival was positively associated with the presence of conspecifics and negatively related to proximity to the dominant shrub Florida rosemary (Ceratiola ericoides), prior reproductive output, and ground lichen cover. Since H. cumulicola and other herbaceous species in the rosemary scrub depend on sporadic fires to decrease interference of shrubs and ground lichens, its persistence may be threatened by fire suppression. Received: 4 December 1996 / Accepted: 5 June 1997     

Scramble in behaviour and ecology

Nicholson's distinction between 'scramble' and 'contest' modes of competition has received widespread attention in ecology and in behaviour, though the emphasis has been different between the two disciplines. In ecology the focus has been on the effects on population; in behavioural ecology the focus has been on the consequences at the individual level. This paper reviews and develops a theory of scramble competition at the individual level, deriving a general evolutionarily stable strategy (ESS) for individual scramble expenditure in a patchy habitat in which individuals compete in local groups for available resources, and examines two population consequences. The critical parameter determining the relationship between individual scramble expenditure and the number of competitors in a patch is the expected resource per capita. If resource input, R, to a patch is constant and independent of the number of competitors, n, then as the number of competitors increases, the per-capita resources declines as R/n, and the ESS scramble level declines (in proportion to (n-1)/n2). However, if the resource input to a patch is positively related to the number of competitors in the patch, scramble expenditure may increase with the number of competitors. In the case where the per-capita resource input stays constant (i.e. R(n) = Rn), the scramble level increases with competitor number (in proportion to (n-1) /n). There are plausible ecological reasons why either of these extreme limits may be approached in nature, making it important to ascertain the relationship between R and n before predicting individual scramble expenditure. For example, resource input may be constant when groups of competitors are constrained to remain together in given patches, and constant per-capita resources may be approached when ideal-free foraging rules apply. However, in the latter case, scramble expenditure must be accounted for in determining the ideal-free distribution. An analysis shows that this leads to 'undermatching', i.e. the ratio of numbers of competitors for good/bad patches becomes progressively less than the ratio of input rates for good/bad patches as the difference between the good and bad patches increases. A second population consequence of the scramble ESS relates to the fact that scrambles may dramatically affect fitness. The per-capita gain in energy can be reduced by a factor of up to 1/n as a result of scramble expenditure, potentially reducing realized population size to as little as the square root of the maximum potential carrying capacity, though reasons are given why such large reductions are unlikely.     

Variable reproductive success in fragmented populations

Marine habitats are naturally patchy and anthropogenic disturbance can further fragment them. Many marine animals are sessile as adults or obligate inhabitants of particular habitats, so populations living in isolated patches of habitat are linked largely by dispersal of planktonic larvae. Theoretically, larvae are more likely to find and settle into large patches of habitat than small patches, thus small habitat patches may experience a more discontinuous supply of recruits resulting in small populations with unusual size- or age-structures or odd sex ratios — conditions where Allee effects on reproductive success are likely. We tested this hypothesis for the Caribbean spotted spiny lobster (Panulirus guttatus), an obligate inhabitant of coral patch reefs whose mating dynamics are size-dependent. We found that P. guttatus were less abundant on small reefs where their size structure and per capita reproductive success were significantly more variable, particularly among large females that are susceptible to sperm limitation that diminishes fertilization rates. These results are indicative of Allee effects and provide a mechanistic understanding of how size-dependent mating dynamics influence reproductive success in ways that alter population dynamics in patchy habitats.