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.     

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.     

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.     

Generalizing Levins metapopulation model in explicit space: models of intermediate complexity

A recent study [Harding and McNamara, 2002. A unifying framework for metapopulation dynamics. Am. Nat. 160, 173-185] presented a unifying framework for the classic Levins metapopulation model by incorporating several realistic biological processes, such as the Allee effect, the Rescue effect and the Anti-rescue effect, via appropriate modifications of the two basic functions of colonization and extinction rates. Here we embed these model extensions on a spatially explicit framework. We consider population dynamics on a regular grid, each site of which represents a patch that is either occupied or empty, and with spatial coupling by neighborhood dispersal. While broad qualitative similarities exist between the spatially explicit models and their spatially implicit (mean-field) counterparts, there are also important differences that result from the details of local processes. Because of localized dispersal, spatial correlation develops among the dynamics of neighboring populations that decays with distance between patches. The extent of this correlation at equilibrium differs among the metapopulation types, depending on which processes prevail in the colonization and extinction dynamics. These differences among dynamical processes become manifest in the spatial pattern and distribution of “clusters” of occupied patches. Moreover, metapopulation dynamics along a smooth gradient of habitat availability show significant differences in the spatial pattern at the range limit. The relevance of these results to the dynamics of disease spread in metapopulations is discussed.     

Density dependent dispersal decisions and the Allee effect

The decision to move between patches in the environment is among the most important life history choices an organism can make. I derive a new density dependent dispersal rule, and examine how dispersal decisions based on avoiding fitness loss associated with an Allee effect or competitive effects impact upon population dynamics in spatially structured populations with qualitatively different dynamics. I also investigate the effects of the number of patches in the system and a limit to the patch sampling time available to dispersers. Dispersing to avoid competitive pressures can destabilise otherwise stable population dynamics, and stabilise chaotic dynamics. Dispersing to avoid an Allee effect does not qualitatively change local population dynamics until eventually driving unstable populations to global extinction with a sufficiently high fitness threshold. A time limit for sampling can stabilise dynamics if dispersal is based on escaping the Allee effect, and rescue populations from global extinction. The results are sensitive to the number of patches available in the environment and suggest that dispersal to avoid an Allee effect will only arise under biologically plausible conditions, i.e. where there is a limit to the number of dispersal attempts that can be made between generations.     

Discrete consumers,small scale resource heterogeneity,and population stability

We present a consumer-resource model in which individual consumers subsist on a continuum of resource distributed over a very large number of small “bite-sized” patches, each patch being sufficiently small that all its resource is eaten whenever a consumer visits. This form of consumer–resource interaction forces a heterogeneous distribution of resource among the patches, and may dampen out the large amplitude, consumer-resource cycles that are predicted by traditional models of well-mixed, spatially homogeneous systems. The resource equilibrium does not increase with enrichment, a prediction that distinguishes this model from models that invoke direct or indirect consumer density dependence as a stabilizing mechanism.     

Body size mediated coexistence of consumers competing for resources in space

Body size is a major phenotypic trait of individuals that commonly differentiates co-occurring species. We analyzed inter-specific competitive interactions between a large consumer and smaller competitors, whose energetics, selection and giving-up behaviour on identical resource patches scaled with individual body size. The aim was to investigate whether pure metabolic constraints on patch behaviour of vagile species can determine coexistence conditions consistent with existing theoretical and experimental evidence. We used an individual-based spatially explicit simulation model at a spatial scale defined by the home range of the large consumer, which was assumed to be parthenogenic and semelparous. Under exploitative conditions, competitive coexistence occurred in a range of body size ratios between 2 and 10. Asymmetrical competition and the mechanism underlying asymmetry, determined by the scaling of energetics and patch behaviour with consumer body size, were the proximate determinant of inter-specific coexistence. The small consumer exploited patches more efficiently, but searched for profitable patches less effectively than the larger competitor. Therefore, body-size related constraints induced niche partitioning, allowing competitive coexistence within a set of conditions where the large consumer maintained control over the small consumer and resource dynamics. The model summarises and extends the existing evidence of species coexistence on a limiting resource, and provides a mechanistic explanation for decoding the size-abundance distribution patterns commonly observed at guild and community levels.     

Host–parasitoid dynamics in a fragmented landscape: Holly trees,holly leaf miners and their parasitoids

Many species inhabit fragmented landscapes, where units of resource have a patchy spatial distribution. While numerous studies have investigated how the incidence and dynamics of individual species are affected by the spatial configuration and landscape context of habitat patches, fewer studies have investigated the dynamics of multiple interacting resource and consumer species in patchy landscapes. We describe a model system for investigating host–parasitoid dynamics in a patchy landscape: a network of 166 holly trees, a specialised herbivore of holly (the leaf miner, Phytomyza ilicis (Curtis, 1948)), and its suite of parasitoids. We documented patch occupancy by P. ilicis, its density within patches, and levels of parasitism over a 6-year period, and manipulated patch occupancy by creating artificially vacant habitat patches. Essentially all patches were occupied by the herbivore in each year, suggesting that metapopulation dynamics are unlikely to occur in this system. The main determinants of densities for P. ilicis and its parasitoids were resource availability (patch size and host density, respectively). While P. ilicis is apparently not restricted by the spatial distribution of resources, densities of its parasitoids showed a weaker positive relationship with host density in more isolated patches. In patches where local extinctions were generated experimentally, P. ilicis densities and levels of parasitism recovered to pre-manipulation levels within a single generation. Furthermore, patch isolation did not significantly affect re-colonisation by hosts or parasitoids. Analysing the data at a variety of spatial scales indicates that the balance between local demography and dispersal may vary depending on the scale at which patches are defined. Taken together, our results suggest that the host and its parasitoids have dispersal abilities that exceed typical inter-patch distances. Patch dynamics are thus largely governed by dispersal rather than within-patch demography, although the role of demography is higher in larger patches.     

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.     

Spatial and temporal variation in patch occupancy and population density in a model system of an arctic Collembola species assemblage

We employed an experimental model system to investigate the mechanisms underlying patterns of patch occupancy and population density in a high arctic assemblage of Collembola species inhabiting a sedge tussock landscape on Svalbard. The replicate model systems consisted of 5 cores of the tussocks (habitat patches) imbedded in a barren matrix. Four of the patches were open so that animals could migrate between them, while there was one closed patch per system to test the effect of migration on extinction rate. There were model systems of two types: one with long and one with short inter‐patch distances to test the effect of patch isolation on colonisation and extinction rates. Each of the four most common collembolan species at the field site were introduced to two open patches per system (source patches), with the other two functioning as colonisation patches for the species. The experiment was run in an ecotrone over three identical, simulated arctic summers separated by winters of 3 weeks. Six replicates of systems with short and long inter‐patch distances were sampled at the end of each summer. The species varied markedly in their performance in both open arenas and closed patches, indicating differential responses to patch humidity, consistent with their differential distribution along the moisture gradient in the field site. The extinction – colonisation dynamics differed markedly between species as predicted from our field studies. This could partly be ascribed to differential dispersal and colonisation ability, but also to different tolerance to spatially variable patch quality and/or tendency for aggregative behaviour. Three of the species exhibited dynamics that superficially resemble what could be expected from classical metapopulation dynamics. However, there was a striking discrepancy between what would be expected from the effect of migration on the extinction rate of isolated patches (in particular closed patches) and the observed rates. Thus, metapopulation processes, such as stochastic colonisation and extinction events due to demographic stochasticity, were relatively unimportant compared to other sources of spatial variability among which subtle differences in patch quality are probably most important. We discuss the value of combining field studies with model system experiments, in particular when habitat quality cannot easily be measured in the field. However, our field and laboratory studies also emphasise the need for a thorough knowledge of species‐specific life history traits for making biologically sound interpretations based on both observational and experimental data.     

Does colonization asymmetry matter in metapopulations?

Despite the considerable evidence showing that dispersal between habitat patches is often asymmetric, most of the metapopulation models assume symmetric dispersal. In this paper, we develop a Monte Carlo simulation model to quantify the effect of asymmetric dispersal on metapopulation persistence. Our results suggest that metapopulation extinctions are more likely when dispersal is asymmetric. Metapopulation viability in systems with symmetric dispersal mirrors results from a mean field approximation, where the system persists if the expected per patch colonization probability exceeds the expected per patch local extinction rate. For asymmetric cases, the mean field approximation underestimates the number of patches necessary for maintaining population persistence. If we use a model assuming symmetric dispersal when dispersal is actually asymmetric, the estimation of metapopulation persistence is wrong in more than 50% of the cases. Metapopulation viability depends on patch connectivity in symmetric systems, whereas in the asymmetric case the number of patches is more important. These results have important implications for managing spatially structured populations, when asymmetric dispersal may occur. Future metapopulation models should account for asymmetric dispersal, while empirical work is needed to quantify the patterns and the consequences of asymmetric dispersal in natural metapopulations.     

Stabilizing effects in spatial parasitoid-host and predator-prey models: a review

We review the literature on spatial host-parasitoid and predator-prey models. Dispersal on its own is not stabilizing and can destabilize a stable local equilibrium. We identify three mechanisms whereby limited dispersal of hosts and parasitoids combined with other features, such as spatial and temporal heterogeneity, can promote increased persistence and stability. The first mechanisms, "statistical stabilization", is simply the statistical effect that summing a number of out-of-phase population trajectories results in a relatively constant total population density. The second mechanism involves decoupling of immigration from local density, such that limited dispersal between asynchronous patches results in an effect that mimics density-dependence at the local patch level. The third mechanism involves altering spatially averaged parameter values resulting from spatial heterogeneity in density combined with non-linear responses to density. Persistence in spatially explicit models with local dispersal frequently associated with self-organized spatial patterning.     

Rapid evolution of a consumer stoichiometric trait destabilizes consumer–producer dynamics

Recent studies have shown that adaptive evolution can be rapid enough to affect contemporary ecological dynamics in nature (i.e. ‘rapid evolution’). These studies tend to focus on trait functions relating to interspecific interactions; however, the importance of rapid evolution of stoichiometric traits has been relatively overlooked. Various traits can affect the balance of elements (carbon, nitrogen, and phosphorus) of organisms, and rapid evolution of such stoichiometric traits will not only alter population and community dynamics but also influence ecosystem functions such as nutrient cycling. Multiple environmental changes may exert a selection pressure leading to adaptation of stoichiometrically important traits, such as an organism's growth rate. In this paper, we use theoretical approaches to explore the connections between rapid evolution and ecological stoichiometry at both the population and ecosystem level. First, we incorporate rapid evolution into an ecological stoichiometry model to investigate the effects of rapid evolution of a consumer's stoichiometric phosphorus:carbon ratio on consumer–producer population dynamics. We took two complementary approaches, an asexual clonal genotype model and a quantitative genetic model. Next, we extended these models to explicitly track nutrients in order to evaluate the effect of rapid evolution at the ecosystem level. Our model results indicate rapid evolution of the consumer stoichiometric trait can cause complex dynamics where rapid evolution destabilizes population dynamics and rescues the consumer population from extinction (evolutionary rescue). The model results also show that rapid evolution may influence the level of nutrients available in the environment and the flux of nutrients across trophic levels. Our study represents an important step for theoretical integration of rapid evolution and ecological stoichiometry.     

Habitat destruction in mutualistic metacommunities

We investigate a mutualistic metacommunity where the strength of the mutualistic interaction between species is measured by the extent to which the presence of one species on a patch either reduces the extinction rate of the others present on the same patch or increases their ability to colonize other patches. In both cases, a strong enough mutualism enables all species to persist at habitat densities where they would all be extinct in the absence of the interaction. However, a mutualistic interaction that enhances colonization enables the species to persist at lower habitat density than one that suppresses extinction. All species abruptly go extinct (catastrophe) when the habitat density is decreased infinitesimally below a critical value. A comparison of the mean field or spatially implicit case with unrestricted dispersal and colonization to all patches in the system with a spatially explicit case where dispersal is restricted to the immediate neighbours of the original patch leads to the intriguing conclusion that restricted dispersal can be favourable for species that have a beneficial effect on each other when habitat conditions are adverse. When the mutualistic interaction is strong enough, the extinction threshold or critical amount of habitat required for the persistence of all species is lower when the dispersal is locally restricted than when unrestricted ! The persistence advantage for all species created by the mutualistic interaction increases substantially with the number of species in the metacommunity, as does the advantage for restricted dispersal over global dispersal.     

Spatial heterogeneity, source-sink dynamics, and the local coexistence of competing species

Patch occupancy theory predicts that a trade-off between competition and dispersal should lead to regional coexistence of competing species. Empirical investigations, however, find local coexistence of superior and inferior competitors, an outcome that cannot be explained within the patch occupancy framework because of the decoupling of local and spatial dynamics. We develop two-patch metapopulation models that explicitly consider the interaction between competition and dispersal. We show that a dispersal-competition trade-off can lead to local coexistence provided the inferior competitor is superior at colonizing empty patches as well as immigrating among occupied patches. Immigration from patches that the superior competitor cannot colonize rescues the inferior competitor from extinction in patches that both species colonize. Too much immigration, however, can be detrimental to coexistence. When competitive asymmetry between species is high, local coexistence is possible only if the dispersal rate of the inferior competitor occurs below a critical threshold. If competing species have comparable colonization abilities and the environment is otherwise spatially homogeneous, a superior ability to immigrate among occupied patches cannot prevent exclusion of the inferior competitor. If, however, biotic or abiotic factors create spatial heterogeneity in competitive rankings across the landscape, local coexistence can occur even in the absence of a dispersal-competition trade-off. In fact, coexistence requires that the dispersal rate of the overall inferior competitor not exceed a critical threshold. Explicit consideration of how dispersal modifies local competitive interactions shifts the focus from the patch occupancy approach with its emphasis on extinction-colonization dynamics to the realm of source-sink dynamics. The key to coexistence in this framework is spatial variance in fitness. Unlike in the patch occupancy framework, high rates of dispersal can undermine coexistence, and hence diversity, by reducing spatial variance in fitness.     

Coexistence of competitors in metacommunities due to spatial variation in resource growth rates; does R * predict the outcome of competition?

Simple mathematical models are used to investigate the coexistence of two consumers using a single limiting resource that is distributed over distinct patches, and that has unequal growth rates in the different patches. Relatively low movement rates or high demographic rates of an inefficient resource exploiter allow it to coexist at a stable equilibrium with a more efficient species whose ratio of movement to demographic rates is lower. The range of conditions allowing coexistence depends on the between‐patch heterogeneity in resource growth rates, but this range can be quite broad. The between‐patch movement of the more efficient consumer turns patches with high resource growth rates into sources, while low‐growth‐rate patches effectively become sinks. A less efficient species can coexist with or even exclude the more efficient species from the global environment if it is better able to bias its spatial distribution towards the source patches. This can be accomplished with density independent dispersal if the less efficient species has a lower ratio of per capita between‐patch movement rate to demographic rates. Conditions that maximize the range of efficiencies allowing coexistence of two species are: a relatively high level of heterogeneity in resource growth conditions; high dispersal (or low demographic rates) of the superior competitor; and low dispersal (or high demographic rates) of the inferior competitor. Global exclusion of the more efficient competitor requires that the inferior competitor have sufficient movement to also produce a source‐sink environment.     

Colonization and extinction dynamics of an annual plant metapopulation in an urban environment

The metapopulation framework considers that the spatiotemporal distribution of organisms results from a balance between the colonization and extinction of populations in a suitable and discrete habitat network. Recent spatially realistic metapopulation models have allowed patch dynamics to be investigated in natural populations but such models have rarely been applied to plants. Using a simple urban fragmented population system in which favourable habitat can be easily mapped, we studied patch dynamics in the annual plant Crepis sancta (Asteraceae). Using stochastic patch occupancy models (SPOMs) and multi‐year occupancy data we dissected extinction and colonization patterns in our system. Overall, our data were consistent with two distinct metapopulation scenarios. A metapopulation (sensu stricto) dynamic in which colonization occurs over a short distance and extinction is lowered by nearby occupied patches (rescue effect) was found in a set of patches close to the city centre, while a propagule rain model in which colonization occurs from a large external population was most consistent with data from other networks. Overall, the study highlights the importance of external seed sources in urban patch dynamics. Our analysis emphasizes the fact that plant distributions are governed not only by habitat properties but also by the intrinsic properties of colonization and dispersal of species. The metapopulation approach provides a valuable tool for understanding how colonization and extinction shape occupancy patterns in highly fragmented plant populations. Finally, this study points to the potential utility of more complex plant metapopulation models than traditionally used for analysing ecological and evolutionary processes in natural metapopulations.     

Effective dispersal rate is a function of habitat size and corridor shape: mechanistic formulation of a two‐patch compartment model for spatially continuous systems

Two‐patch compartment models have been explored to understand the spatial processes that promote species coexistence. However, a phenomenological definition of the inter‐patch ‘dispersal rate’ has limited the quantitative predictability of these models to community dynamics in spatially continuous habitats. Here, we mechanistically rederived a two‐patch Lotka–Volterra competition model for a spatially continuous reaction‐diffusion system where a narrow corridor connects two large habitats. We provide a mathematical formula of the dispersal rate appearing in the two‐patch compartment model as a function of habitat size, corridor shape (ratio of its width to its length), and organism diffusion coefficients. For most reasonable settings, the two‐patch compartment model successfully approximated not only the steady states, but also the transient dynamics of the reaction–diffusion model. Further numerical simulations indicated the general applicability of our formula to other types of community dynamics, e.g. driven by resource‐competition, in spatially homogeneous and heterogeneous environments. Our results suggest that the spatial configuration of habitats plays a central role in community dynamics in space. Furthermore, our new framework will help to improve experimental designs for quantitative test of metacommunity theories and reduce the gaps among modeling, empirical studies, and their application to landscape management.     

用空间直观模型是否足以从斑块占据性资料中推断集合种群的动态过程?

在集合种群的研究中,经常要根据空间占据性数据应用斑块模型来推断种群的动态过程,在保护生物学应用中,斑块占据性模型的参数估测对于阐释集合种群动态和预测种群对生境破坏的反应极为重要。我们探讨了一种广泛应用的空间直观模型——率函数模型(Incidence function model)中参数估测的不确定性问题,通过构建由50个斑块组成的网络和两个假想的已知参数的集合种群,应用模拟模型产生集合种群随时间变化的斑块占据性数据系列：即快照(snapshot)。然后,根据这些快照,应用率函数模型和最大似然法估测种群动态参数。此外,我们还给出了传统的率函数模型的一个变形,这个变形包含了目标区效应(Target area effect)：即一个斑块的占据概率不但取决于空间隔离度,也取决于斑块本身面积的大小。结果表明：根据同一个集合种群不同的快照所估测的参数可以有很大差异,一个快照得出的参数提示的是占据性强但存活率低的集合种群,而另一个快照可能反映的是一个占据性弱但存活率高的集合种群。应用传统的率函数模型于一个包含了目标区效应的集合种群,导致斑块大小相关的灭绝率参数估测的正偏差。因此,仅根据一个快照的空间占据性数据来推测集合种群的过程有很大的不确定性[动物学报49(6)：787～794,2003]。