A sharp threshold for disease persistence in host metapopulations

A sharp threshold is established that separates disease persistence from the extinction of small disease outbreaks in an S→E→I→R→S type metapopulation model. The travel rates between patches depend on disease prevalence. The threshold is formulated in terms of a basic replacement ratio (disease reproduction number), ?(0), and, equivalently, in terms of the spectral bound of a transmission and travel matrix. Since frequency-dependent (standard) incidence is assumed, the threshold results do not require knowledge of a disease-free equilibrium. As a trade-off, for ?(0)>1, only uniform weak disease persistence is shown in general, while uniform strong persistence is proved for the special case of constant recruitment of susceptibles into the patch populations. For ?(0)<1, Lyapunov's direct stability method shows that small disease outbreaks do not spread much and eventually die out.     

Fitness-dependent dispersal in metapopulations and its consequences for persistence and synchrony

1. We present a novel metapopulation model where dispersal is fitness dependent: the strength of migration from a site is dependent on the expected reproductive fitness of individuals there. Furthermore, individuals continue to migrate until they reach a suitable habitat where their expected fitness is above a threshold value.
2. Fitness-dependent dispersal has a very strong stabilizing effect on population dynamics, even when the intrinsic dynamics of populations in the absence of dispersal exhibit complex high-amplitude oscillations. This stabilizing effect is much stronger than that of the density-independent dispersal normally considered in metapopulation models.
3. Even when fitness-dependent dispersal does not stabilize the dynamics in a formal sense, it generally leads to simplification, with complex or even chaotic fluctuations being reduced to simple cycles.
4. This form of dispersal also has a strong tendency to synchronize local population dynamics across the spatial extent of the metapopulation.
5. These conclusions are robust to the addition of strong stochasticity in the migration threshold.     

The persistence of vertically transmitted fungi in grass metapopulations

Theory predicts that (i) vertical transmission of parasites (i.e. when they are passed directly from a host to its offspring) selects for benign association with the host and that (ii) vertically transmitted parasites that lower their hosts' fitness cannot persist if they are not able to infect horizontally (i.e. contagiously) other host individuals in the population. In this paper, we develop a mathematical model to examine whether mutualism is a prerequisite for persistence of exclusively vertically transmitted (from maternal plant to offspring via seeds) fungal endophytes in structured grass metapopulations. Interestingly, endophyte survival does not require plant mutualism, even in a metapopulation consisting of qualitatively identical patches, if vertical transmission of the fungus is perfect, i.e. if all established seedlings in offspring of the endophyte-infected plant are infected. In more realistic situations, when the metapopulation consists of qualitatively different patches, endophyte-infected plants may persist at the metapopulation level even if the vertical transmission is imperfect (due to hyphae inviability or failure to grow into all seeds) and the endophyte decreases the host grass fitness in certain environments. These results have biological importance because they (i) question the requirement of a mutualistic nature in exclusively vertically transmitted symbionts and (ii) emphasize the importance of habitat diversity in relation to symbiont success in vertical transmission.     

Indirect effects and spatial scaling affect the persistence of multispecies metapopulations

Quantifying the role of space and spatial scale on the population dynamics of ecological assemblages is a contemporary challenge in ecology. Here, we evaluate the role of metapopulation dynamics on the persistence and dynamics of a multispecies predator-prey assemblage where two prey species shared a common natural enemy (apparent competition). By partitioning the effects of increased resource availability from the effects of metapopulation structure on regional population persistence we show that space has a marked impact on the dynamics of apparent competition in multispecies predator-prey assemblages. Further, the role of habitat size and stochasticity are also shown to influence the dynamics and persistence of this multispecies interaction. The broader consequences of these processes are discussed.     

Periodic local disturbance in host-parasitoid metapopulations: host suppression and parasitoid persistence

Within many agricultural systems, insect pests and their natural enemies are forced to persist as a metapopulation, continuously recolonizing patches following disturbance through harvesting or spraying with insecticides. Despite the need to understand factors influencing biocontrol success, few theoretical studies of host-parasitoid interactions have examined the potential impact of local disturbance within a metapopulation framework. Here, we add periodic local mortality to series of classical host-parasitoid models to examine its effect on host suppression and parasitoid persistence. Using a deterministic lattice model, we show that despite the wide range of complex dynamics generated at the patch level, the region wide pattern of disturbance is the key factor influencing host suppression. The level of host suppression achieved can be understood in terms of both the strength of density dependent parasitism, and the relative amounts of host and parasitoid mixing amongst patches of different ages. Local dispersal among patches is sufficient to ensure coexistence of the host and parasitoid, though persistence is not necessarily associated with the formation of self-organized spatial structures reported in previous studies. Finally, a stochastic version of the model is developed, in order to highlight how the effects of demographic stochasticity may influence biocontrol success in highly disturbed agricultural systems.     

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.     

Maintenance of the sexes and persistence of a clonal organism in spatially complex metapopulations

Clonal organisms persist at a range of population sex ratios, from equal numbers of males and females to single-sex systems. When intersexual competition is strong enough to drive one sex locally extinct, the maintenance of the sexes is facilitated by the semi-independent dynamics of populations within a metapopulation. These semi-independent dynamics are influenced by dispersal and recolonization rates, which are affected by the spatial arrangement of populations. To establish the quantitative relationship between spatially complex metapopulations and the maintenance of the sexes, we used a mathematical model of the liverwort Marchantia inflexa. This clonal organism is found in discrete patches on rocks and along the banks of streams, which form single-sex and two-sex metapopulations. In this system, asexual propagules mainly disperse short distances. Long-distance between-patch dispersal and recolonization mainly occurs via sexual propagules, which require both sexes to be present. Dispersal of these two types of propagules could interact with the spatial arrangement of populations to affect the maintenance of the sexes. With our mathematical model, we found that at intermediate distances between populations, metapopulations maintained both sexes, and the spatial arrangement of populations changed the threshold at which one sex was lost. On the other hand, when populations were close to one another, one sex was lost and the single-sex metapopulation persisted through dispersal of asexual propagules. When populations were far apart, one sex was lost, and the metapopulation either went extinct due to lack of recolonization by asexual propagules or persisted because clumped populations facilitated recolonization. These idealized spatial arrangements help clarify the effects of the spatial arrangement on the maintenance of the sexes and the persistence of metapopulations of clonal organisms, which can help explain geographic parthenogenesis and the distribution of asexual populations, the persistence of asexual species, and inform the conservation of clonal organisms.     

Anticarnosine activity of staphylococci as a criterion for assessment of their persistence potential

The analysis on clinical material and the use of experimental models allowed to prove the role of anticarnosine activity of staphylococci in their persistence. Light and electronic microscopy revealed large destruction of ultrastructural eukaryote components and decreased proliferative activity in animals challenged with strains characterized by high anticarnosine activity. Adaptive mechanisms, providing dynamic equilibrium in "eukaryote--prokaryote" system, are described.     

A formula for the mean lifetime of metapopulations in heterogeneous landscapes

We present a formula for the mean lifetime of metapopulations in heterogeneous landscapes. This formula provides new insights into the effect of the spatial structure of habitat networks on metapopulation survival, with consequences for modeling, landscape evaluation, and metapopulation management. In the whole study, the spatially realistic metapopulation model of Frank and Wissel is taken as a basis. First, as a key result on the way toward the desired formula, it is shown that a simple nonspatial (Levins-type) model is able to reproduce the behavior of the complex spatial model considered regarding the mean lifetime, provided its parameters appropriately summarize all the relevant details of spatial heterogeneity. Second, the formula presented reveals how data from species and landscape have to be combined to estimate the survival chance of a metapopulation without having to run any simulation or to solve numerically any model equation. Third, by taking the formula as a basis, landscape measures are derived that allow dissimilar habitat networks to be evaluated, compared, and ranked in terms of their effect on metapopulation survival. Fourth, a combination of analytical, nonlinear regression as well as aggregation techniques was used to deduce the formula presented. The potential of these techniques for simplifying (meta)population models that are complex due to spatial heterogeneity is discussed.     

Resource allocation for epidemic control in metapopulations

Deployment of limited resources is an issue of major importance for decision-making in crisis events. This is especially true for large-scale outbreaks of infectious diseases. Little is known when it comes to identifying the most efficient way of deploying scarce resources for control when disease outbreaks occur in different but interconnected regions. The policy maker is frequently faced with the challenge of optimizing efficiency (e.g. minimizing the burden of infection) while accounting for social equity (e.g. equal opportunity for infected individuals to access treatment). For a large range of diseases described by a simple SIRS model, we consider strategies that should be used to minimize the discounted number of infected individuals during the course of an epidemic. We show that when faced with the dilemma of choosing between socially equitable and purely efficient strategies, the choice of the control strategy should be informed by key measurable epidemiological factors such as the basic reproductive number and the efficiency of the treatment measure. Our model provides new insights for policy makers in the optimal deployment of limited resources for control in the event of epidemic outbreaks at the landscape scale.     

A movement criterion for running

The adjustment of the leg during running was addressed using a spring-mass model with a fixed landing angle of attack. The objective was to obtain periodic movement patterns. Spring-like running was monitored by a one-dimensional stride-to-stride mapping of the apex height to identify mechanically stable fixed points. We found that for certain angles of attack, the system becomes self-stabilized if the leg stiffness was properly adjusted and a minimum running speed was exceeded. At a given speed, running techniques fulfilling a stable movement pattern are characterized by an almost constant maximum leg force. With increasing speed, the leg adjustment becomes less critical. The techniques predicted for stable running are in agreement with experimental studies. Mechanically self-stabilized running requires a spring-like leg operation, a minimum running speed and a proper adjustment of leg stiffness and angle of attack. These conditions can be considered as a movement criterion for running.     

Interspecific competition in metapopulations

The assumptions and predictions of metapopulation models for competing species are discussed in relation to empirical studies of colonization and extinction in metapopulations. In three species of Daphnia in rockpools, interspecific competition increased local extinction rates, while no effects on colonization rates were detected. Distributional patterns were consistent with several predictions of the competition model; for example, the number of species on an island increased with the number of pools and the proportion of pools occupied by each species decreased with increasing species number. It is concluded that interspecific competition is important for the distributional dynamics of Daphnia species in rockpools, but the question whether the coexistence of these species depends on metapopulation dynamics is still unresolved. Other studies on the effects of interspecific competition on colonization and extinction rates are discussed.     

Seabird metapopulations: searching for alternative breeding habitats

Today, many seabird species nest in port areas, which are also necessary for human economic activity. In this paper, we evaluate, using a metapopulation model, the possibilities for creating alternative breeding sites for the Common Tern (Sterna hirundo) in the Rhine–Meuse–Scheldt estuary. We explore 22 scenarios that differ with respect to (1) loss of breeding habitat in port areas, (2) location and size of newly created habitat, and (3) coexistence of old and new habitat. Results indicate that loss of port area habitats results in a serious 41% decline in the breeding population. When the loss in ports is compensated for within the ports, the decline was negligible. Fourteen scenarios result in an increase of the Common Tern metapopulation. In these, extra breeding habitat is created outside the ports in fish-rich waters, resulting in a potential metapopulation increase of 25%. However, the period of overlap between lost and newly created habitat strongly affects the results. A gap between the removal of old and the creation of new breeding areas might cause a drop in the metapopulation level of 30%. The population recovery from this drop might take more than 100 years due to slow recolonization. Our results suggest that conservation of seabird species should be evaluated on a metapopulation scale and that the creation of new habitat may help to compensate for habitat loss in other areas. Furthermore, the results indicate that overlap between the existence of old and newly created breeding habitats is crucial for the success of compensation efforts. However, new locations should be carefully selected, because not only is the suitability of the breeding grounds important, but ample fish availability nearby is also key. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

The meta-Allee effect: A generalization from intermittent metapopulations

Intermittent population trajectories are likely to emerge in almost any population that faces a predator yet has a refuge from that predator. Using the well-known model of Pomeau and Manneville for intermittent populations, a collection of a group of inherently unstable subpopulations can survive through the balance of extinction and migration rates, which is a metapopulation. This formulation also generates a meta-Allee point, which is to say a minimal number of subpopulations that must exist to sustain the population over the long term.     

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.     

Evidence for positive density-dependent emigration in butterfly metapopulations

A positive effect of (meta)population density on emigration has been predicted by many theoretical models and confirmed empirically in various organisms. However, in butterflies, the most popular species for dispersal studies, the evidence for its existence has so far been equivocal, with negative relationships between density and emigration being reported more frequently. We analysed dispersal in sympatric metapopulations of two Maculinea butterflies, intensively surveyed with mark–release–recapture methods for 7 years. Dispersal parameters, derived using the virtual migration model, were assessed against butterfly densities, which fluctuated strongly over the study period. Emigration was positively correlated with density, and this effect was particularly strong at densities above carrying capacity, when emigration increased up to threefold in females and twofold in males compared with the normal levels. In turn, density had little impact on other dispersal parameters analysed. Our findings provide good evidence for positive density-dependence of emigration in butterflies. Emigrating at high densities is particularly beneficial for females, because it gives them a chance to lay part of their egg-load in less crowded patches, where offspring survival is higher due to lower intraspecific competition. Even though the rise in emigration becomes considerable at densities exceeding carrying capacity, i.e. relatively infrequently, it still has serious implications for many ecological phenomena, such as species range expansions, gene flow, and metapopulation persistence. Consequently, instead of treating emigration as a fixed trait, it is worth allowing for its density-dependence in applications such as population viability analyses, genetic models or metapopulation models.     

Dispersal and connectivity in metapopulations

This paper reviews characteristics of dispersal that influence metapopulation functioning, such as releasing factors, density dependence, timing and types and health of dispersers. Economic thresholds, intraspecific conflicts and avoidance of inbreeding arc often regarded as the key ultimate or proximate (or both) causes of dispersal, but there is no consensus about the most important mechanisms. Dispersing individuals arc often considered to differ genetically from the residents but good supporting evidence has only been presented for some insect species. Sex and age differences in dispersal rates are most common in polygamous species and in long-lived species with many litters per female. A bimodal distribution of dispersal distances, earlier thought to be a common pattern, is probably an artifact, caused by habitat heterogeneity and varying survival of settled individuals. Dispersal distances are longer in poor environments. Habitat specialists are more affected by boundaries during dispersal than generalists. Dispersal just before or during the early reproductive season is common in certain species occupying early successional habitats. Dispersal increased both population and metapopulation size and persistence in plants, insects and small mammals.     

A new criterion for confounder selection

Summary We propose a new criterion for confounder selection when the underlying causal structure is unknown and only limited knowledge is available. We assume all covariates being considered are pretreatment variables and that for each covariate it is known (i) whether the covariate is a cause of treatment, and (ii) whether the covariate is a cause of the outcome. The causal relationships the covariates have with one another is assumed unknown. We propose that control be made for any covariate that is either a cause of treatment or of the outcome or both. We show that irrespective of the actual underlying causal structure, if any subset of the observed covariates suffices to control for confounding then the set of covariates chosen by our criterion will also suffice. We show that other, commonly used, criteria for confounding control do not have this property. We use formal theory concerning causal diagrams to prove our result but the application of the result does not rely on familiarity with causal diagrams. An investigator simply need ask, “Is the covariate a cause of the treatment?” and “Is the covariate a cause of the outcome?” If the answer to either question is “yes” then the covariate is included for confounder control. We discuss some additional covariate selection results that preserve unconfoundedness and that may be of interest when used with our criterion.     

On fitness in structured metapopulations

In this paper we derive a general expression measuring fitness in general structured metapopulation models. We apply the theory to a model structured by local population size and in which local dynamics is explicitly modelled. In particular, we calculate the evolutionarily stable dispersal strategy for individuals that can assess the local population density in the case where only dispersal is subject to evolutionary control but all other model ingredients are assumed fixed. We show that there exists a threshold size such that at ESS everyone should stay as long as the population size is below the threshold and everyone should disperse immediately as the population size reaches the threshold. Received: 13 August 1999 / Revised version: 2 May 2001 / Published online: 12 October 2001     

A dispersal-induced paradox: synchrony and stability in stochastic metapopulations

Understanding how dispersal influences the dynamics of spatially distributed populations is a major priority of both basic and applied ecologists. Two well-known effects of dispersal are spatial synchrony (positively correlated population dynamics at different points in space) and dispersal-induced stability (the phenomenon whereby populations have simpler or less extinction-prone dynamics when they are linked by dispersal than when they are isolated). Although both these effects of dispersal should occur simultaneously, they have primarily been studied separately. Herein, I summarise evidence from the literature that these effects are expected to interact, and I use a series of models to characterise that interaction. In particular, I explore the observation that although dispersal can promote both synchrony and stability singly, it is widely held that synchrony paradoxically prevents dispersal-induced stability. I show here that in many realistic scenarios, dispersal is expected to promote both synchrony and stability at once despite this apparent destabilising influence of synchrony. This work demonstrates that studying the spatial and temporal impacts of dispersal together will be vital for the conservation and management of the many communities for which human activities are altering natural dispersal rates.