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AbstractReproductive mode may strongly impact adaptation in spatially varying populations linked by dispersal, especially when sexual and clonal offspring differ in dispersal. We determined how spatial structure affects adaptation in populations with mixed clonal and sexual reproduction. In a source-sink quantitative genetic deterministic model (with stabilizing selection around different optima), greater clonal reproduction or parent-offspring association (a measure of the part of the parent's phenotype other than the additive genetic component inherited by clonal offspring) increased the selective difference (difference between phenotypic optima) allowing sink populations to adapt. Given dispersal differences between clonally and sexually produced juveniles, adaptation increased with an increasing fraction of clonal dispersers. When considering migrational meltdown, partially clonal reproduction reduced cases where dispersal caused habitat loss. Stochastic individual-based simulations support these results, although the effect of differential dispersal was reversed, with decreased clonal dispersal allowing greater adaptation. These results parallel earlier findings that for an instantaneous shift in phenotypic optimum, increasing clonality allowed population persistence for a greater shift; here, selective change is spatial rather than temporal. These results may help explain the success of many partially clonal organisms in invading new habitats, complementing traditional explanations based on avoiding Allee effects.

AbstractCommunity structure depends jointly on species' responses to, and effects on, environmental factors. Many such factors, including detritus, are studied in ecosystem ecology. Detritus in terrestrial ecosystems is dominated by plant litter (nonliving organic material), which, in addition to its role in material cycling, can act as a niche factor modulating interactions among plants. Litter thus links traditional community and ecosystem processes, which are often studied separately. We explore this connection using population dynamics models of two plant species and a litter pool. We first find conditions determining the outcome of interactions between these species, highlighting the role that litter plays and the role of broader ecosystem parameters, such as decomposition rate. Species trade-offs in tolerance to direct competition and litter-based interference competition allow for coexistence, provided the litter-tolerant species produces more litter at the population level; otherwise, priority effects may result. When species coexist, litter-mediated interactions between plants disrupt the traditional relationship between biomass accumulation and decomposition. Increasing decomposition rate may have no effect on standing litter density and, in some cases, may even increase litter load. These results illustrate how ecosystem variables can influence community outcomes that then feed back to influence the ecosystem.

AbstractUnderstanding Batesian mimicry is a classic problem in evolutionary biology. In Batesian mimicry, a defended species (the model) is mimicked by an undefended species (the mimic). Prior theories have emphasized the role of predator behavior and learning as well as evolution in model-mimic complexes but have not examined the role of population dynamics in potentially governing the relative abundances and even persistence of model-mimic systems. Here, we examined the effect of the population dynamics of predators and alternative prey on the prevalence of warning-signaling prey composed of models and mimics. Using optimal foraging theory and signal detection theory, we found that the inclusion of predator and alternative prey population dynamics could reverse traditional theoretical predictions: as alternative prey increase in numbers, mimics suffer because larger populations of predators are maintained, resulting in apparent competition. Under some circumstances, apparent competition affects model populations as well, although not as severely as it affects mimics. Our results bear on the intriguing puzzle that in nature warning signals are relatively scarce, yet experiments suggest that such signals can be highly advantageous. The availability of alternative prey and numerical responses by predators can overwhelm advantages observed in experiments to keep warning signals in model-mimic systems relatively scarce.

AbstractHyperparasitism denotes the natural phenomenon where a parasite infecting a host is in turn infected by its own parasite. Hyperparasites can shape the dynamics of host-parasite interactions and often have a deleterious impact on pathogens, an important class of parasites, causing a reduction in their virulence and transmission rate. Hyperparasitism thus could be an important tool of biological control. However, host-parasite-hyperparasite systems have so far been outside the mainstream of modeling studies, especially those dealing with eco-evolutionary aspects of species interactions. Here, we theoretically explore the evolution of life-history traits in a generic host-parasite-hyperparasite system, focusing on parasite virulence and the positive impact that hyperparasitism has on the host population. We also explore the coevolution of life-history traits of the parasite and hyperparasite, using adaptive dynamics and quantitative genetics frameworks to identify evolutionarily singular strategies. We find that in the presence of hyperparasites, the evolutionarily optimal pathogen virulence generally shifts toward more virulent strains. However, even in this case the use of hyperparasites in biocontrol could be justified, since overall host mortality decreases. An intriguing possible outcome of the evolution of the hyperparasite can be its evolutionary suicide.

In nature, rates of dispersal vary greatly over time, yet most theoretical explorations of ecological and evolutionary dynamics to date have assumed constant movement rates. Here we examine how a particular pattern of temporal variation-periodic pulses of immigration-influences adaptation to a harsh environment, in which a species experiences conditions outside its niche requirements. Using both deterministic models and stochastic individual-based simulations, we show that for many ecological and genetic scenarios, temporally spacing out immigration events increases the probability that local adaptation is sufficient for persistence (i.e., niche evolution). When immigration events are too frequent, gene flow can hamper local adaptation in sexual species, but sufficiently infrequent pulses of immigration allow for repeated opportunities for adaptation with temporary escapes from gene flow during which local selection is unleashed. We develop versions of our models with and without density dependence for three different assumptions about the genetics underlying fitness (haploid, diploid, and quantitative genetic variation) so that our results may be applicable to a wide range of natural systems. Our study adds to a growing body of literature showing that temporal variation in migration rates can have significant effects on local adaptation and is among the first to show how such variation affects niche evolution.

Evolutionary lag-the difference between mean and optimal phenotype in the current environment-is of keen interest in light of rapid environmental change. Many ecologically important organisms have life histories that include stage structure and both sexual and clonal reproduction, yet how stage structure and clonality interplay to govern a population's rate of evolution and evolutionary lag is unknown. Effects of clonal reproduction on mean phenotype partition into two portions: one that is phenotype dependent, and another that is genotype dependent. This partitioning is governed by the association between the nonadditive genetic plus random environmental component of phenotype of clonal offspring and their parents. While clonality slows phenotypic evolution toward an optimum, it can dramatically increase population survival after a sudden step change in optimal phenotype. Increased adult survival slows phenotypic evolution but facilitates population survival after a step change; this positive effect can, however, be lost given survival-fecundity trade-offs. Simulations indicate that the benefits of increased clonality under environmental change greatly depend on the nature of that change: increasing population persistence under a step change while decreasing population persistence under a continuous linear change requiring de novo variation. The impact of clonality on the probability of persistence for species in a changing world is thus inexorably linked to the temporal texture of the change they experience.

Plastic changes in organisms' phenotypes can result from either abiotic or biotic effectors. Biotic effectors create the potential for a coevolutionary dynamic. Through the use of individual-based simulations, we examined the coevolutionary dynamic of two species that are phenotypically plastic. We explored two modes of biotic and abiotic interactions: ecological interactions that determine the form of natural selection and developmental interactions that determine phenotypes. Overall, coevolution had a larger effect on the evolution of phenotypic plasticity than plasticity had on the outcome of coevolution. Effects on the evolution of plasticity were greater when the fitness-maximizing coevolutionary outcomes were antagonistic between the species pair (predator-prey interactions) than when those outcomes were augmenting (competitive or mutualistic). Overall, evolution in the context of biotic interactions reduced selection for plasticity even when trait development was responding to just the abiotic environment. Thus, the evolution of phenotypic plasticity must always be interpreted in the full context of a species' ecology. Our results show how the merging of two theory domains--coevolution and phenotypic plasticity--can deepen our understanding of both and point to new empirical research.

Gene flow that hampers local adaptation can constrain species distributions and slow invasions. Predation as an ecological factor mainly limits prey species ranges, but a richer array of possibilities arises once one accounts for how predation alters the interplay of gene flow and selection. We extend previous single-species theory on the interplay of demography, gene flow, and selection by investigating how predation modifies the coupled demographic-evolutionary dynamics of the range and habitat use of prey. We consider a model for two discrete patches and a complementary model for species along continuous environmental gradients. We show that predation can strongly influence the evolutionary stability of prey habitat specialization and range limits. Predators can permit prey to expand in habitat or geographical range or, conversely, cause range collapses. Transient increases in predation can induce shifts in prey ranges that persist even if the predator itself later becomes extinct. Whether a predator tightens or loosens evolutionary constraints on the invasion speed and ultimate size of a prey range depends on the predator effectiveness, its mobility relative to its prey, and the prey's intraspecific density dependence, as well as the magnitude of environmental heterogeneity. Our results potentially provide a novel explanation for lags and reversals in invasions.

Understanding range limits is a fundamental problem in ecology and evolutionary biology. In 1963, Mayr argued that "contaminating" gene flow from central populations constrained adaptation in marginal populations, preventing range expansion, while in 1984, Bradshaw suggested that absence of genetic variation prevented species from occurring everywhere. Understanding stability of range boundaries requires unraveling the interplay of demography, gene flow, and evolution of populations in concrete landscape settings. We walk through a set of interrelated spatial scenarios that illustrate interesting complexities of this interplay. To motivate our individual-based model results, we consider a hypothetical zooplankter in a landscape of discrete water bodies coupled by dispersal. We examine how patterns of dispersal influence adaptation in sink habitats where conditions are outside the species' niche. The likelihood of observing niche evolution (and thus range expansion) over any given timescale depends on (1) the degree of initial maladaptation; (2) pattern (pulsed vs. continuous, uni- vs. bidirectional), timing (juvenile vs. adult), and rate of dispersal (and hence population size); (3) mutation rate; (4) sexuality; and (5) the degree of heterogeneity in the occupied range. We also show how the genetic architecture of polygenic adaptation is influenced by the interplay of selection and dispersal in heterogeneous landscapes.

For many organisms, stage is a better predictor of demographic rates than age. Yet no general theoretical framework exists for understanding or predicting evolution in stage-structured populations. Here, we provide a general modeling approach that can be used to predict evolution and demography of stage-structured populations. This advances our ability to understand evolution in stage-structured populations to a level previously available only for populations structured by age. We use this framework to provide the first rigorous proof that Lande's theorem, which relates adaptive evolution to population growth, applies to stage-classified populations, assuming only normality and that evolution is slow relative to population dynamics. We extend this theorem to allow for different means or variances among stages. Our next major result is the formulation of Price's theorem, a fundamental law of evolution, for stage-structured populations. In addition, we use data from Trillium grandiflorum to demonstrate how our models can be applied to a real-world population and thereby show their practical potential to generate accurate projections of evolutionary and population dynamics. Finally, we use our framework to compare rates of evolution in age- versus stage-structured populations, which shows how our methods can yield biological insights about evolution in stage-structured populations.

Multiple hypotheses have been proposed to explain the annual migration of the Serengeti wildebeest, but few studies have compared distribution patterns with environmental drivers. We used a rainfall-driven model of grass dynamics and wildebeest movement to generate simulated monthly wildebeest distributions, with wildebeest movement decisions depending on 14 candidate models of adaptive movement in response to resource availability. We used information-theoretic approaches to compare the fits of simulated and observed monthly distribution patterns at two spatial scales over a 3-year period. Models that included the intake rate and nitrogen (N) concentration of green grass and the suppressive effect of tree cover on grass biomass provided the best model fits at both spatial scales tested, suggesting that digestive constraints and protein requirements may play key roles in driving migratory behavior. The emergence of a migration was predicted to be dependent on the ability of the wildebeest to track changes in resource abundance at relatively large scales (>80-100 km). When movement decisions are based solely on local resource availability, the wildebeest fail to migrate across the ecosystem. Our study highlights the potentially key role of strong and countervailing seasonally driven rainfall and fertility gradients--a consistent feature of African savanna ecosystems--as drivers of long-distance seasonal migrations in ungulates.

Evolution by natural selection improves fitness and may therefore influence population trajectories. Demographic matrix models are often employed in conservation studies to project population dynamics, but such analyses have not incorporated evolutionary dynamics. We project evolutionarily informed population trajectories for a population of the perennial plant Trillium grandiflorum, which is declining due to high levels of herbivory by white-tailed deer. Individuals with later flowering times are less often consumed, so there is selection on this trait. We first incorporated selection analyses into a deterministic matrix model in three ways (corresponding to different methods that have been used for analyzing evolution in structured populations). Because it is not clear which of these methods works best for stage-structured models, we compared each with a more realistic, individual-based model. Deterministic models using fitness averaged over the phenotypic distribution gave trajectories that were similar to those of the individual-based model, whereas the deterministic model using fitness at the mean phenotype gave a much faster rate of evolution than that which was observed. This illustrates that subtle differences in the way in which one splices evolution into demographic models can have a large effect on expected outcomes. This study demonstrates that, by combining demographic and selection analyses, one can gauge the potential relevance of evolution to population dynamics and persistence.

Prior studies of the evolution of species' niches and ranges have identified the importance of within-population genetic variance, migration rate, and environmental heterogeneity in determining evolutionarily stable patterns of species' range and habitat use. Different combinations of these variables can produce either habitat specialists or generalists and cause either stable range limits or unbounded expansion. We examine the effect of density regulation on a species' range and habitat use within a landscape comprised of two discrete habitats and along continuous environmental gradients. Using the theta-logistic formulation, we demonstrate the following. (1) Spatially uniform density regulation generally weakens gene swamping and opposes habitat specialization and range limitation. (2) The form of density regulation should play an important role in determining whether the equilibrium species' range is limited by gene flow. (3) Even when no long-term limited-range equilibrium occurs, quasi-stable (or even contracting) range limits may be maintained for a long period during the initial phases of an invasion; the length of this period depends on the form of density regulation. (4) The steady state invasion speed in heterogeneous environments depends on the form of density regulation. Implications for the study of biological invasions are discussed, and directions for further exploration are sketched.

Many host-pathogen interactions are embedded in a web of other interspecific interactions. Recent theoretical studies have suggested that reductions in predator abundance can indirectly lead to upsurges in infectious diseases harbored by prey populations. In this note, we use simple models to show that in some circumstances, predation can actually increase the equilibrial prevalence of infection in a host, where prevalence is defined as the fraction of host population that is infected. Our results show that there is no complete generalization possible about how shifts in predation pressure translate into shifts in infection levels, without some understanding of host population regulation and the role of acquired immunity. Our results further highlight the importance of understanding the dynamics of nonregulatory pathogens in reservoir host populations and the understudied effects of demographic costs incurred by individuals that survive infection and develop acquired immunity.

Understanding the process of adaptation to novel environments may help to elucidate several ecological phenomena, from the stability of species range margins to host-pathogen specificity and persistence in degraded habitats. We study evolution in one type of novel environment: a sink habitat where populations cannot persist without recurrent immigration from a source population. Previous studies on source-sink evolution have focused on how extrinsic environmental factors influence adaptation to a sink, but few studies have examined how intrinsic genetic factors influence adaptation. We use an individual-based model to explore how genetic canalization that evolves in gene regulation networks influences the adaptation of a population to a sink. We find that as canalization in the regulation network increases, the probability of adaptation to the novel habitat decreases. When adaptation to the habitat does occur, it is usually preceded by a breakdown of canalization. As evolution continues in the novel habitat, canalization reemerges, but a legacy of the breakdown may remain, even after several generations. We also find that environmental noise tends to increase the probability of adaptation to the novel habitat. Our results suggest that the details of genetic architecture can significantly influence the likelihood of niche evolution in novel environments.

Viruses can occasionally emerge by infecting new host species. However, the early phases of emergence can hinge upon ecological sustainability of the virus population, which is a product of both within-host population growth and between-host transmission. Insufficient growth or transmission can force virus extinction before the latter phases of emergence, where genetic adaptations that improve host use may occur. We examined the early phase of emergence by studying the population dynamics of RNA phages in replicated laboratory environments containing native and novel host bacteria. To predict the breadth of transmission rates allowing viral persistence on each species, we developed a simple model based on in vitro data for phage growth rate over a range of initial population densities on both hosts. Validation of these predictions using serial passage experiments revealed a range of transmission rates for which the native host was a source and the novel host was a sink. In this critical range of transmission rates, periodic exposure to the native host was sufficient for the maintenance of the viral population on the novel host. We argue that this effect should facilitate adaptation by the virus to utilize the novel host--often crucial in subsequent phases of emergence.

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.

We examine the impact of temporal variation on adaptive evolution in "sink" environments, where a species encounters conditions outside its niche. Sink populations persist because of recurrent immigration from sources. Prior studies have highlighted the importance of demographic constraints on adaptive evolution in sinks and revealed that adaptation is less likely in harsher sinks. We examine two complementary models of population and evolutionary dynamics in sinks: a continuous-state quantitative-genetics model and an individual-based model. In the former, genetic variance is fixed; in the latter, genetic variance varies because of mutation, drift, and sampling. In both models, a population in a constant harsh sink environment can exist in alternative states: local maladaptation (phenotype comparable to immigrants from the source) or adaptation (phenotype near the local optimum). Temporal variation permits transitions between these states. We show that moderate amounts of temporal variation can facilitate adaptive evolution in sinks, permitting niche evolution, particularly for slow or autocorrelated variation. Such patterns of temporal variation may particularly pertain to sinks caused by biotic interactions (e.g., predation). Our results are relevant to the evolutionary dynamics of species' ranges, the fate of exotic invasive species, and the evolutionary emergence of infectious diseases into novel hosts.

Spatial flows of materials and organisms across ecosystem boundaries are ubiquitous. Understanding the consequences of these flows should be a basic goal of ecosystem science, and yet it has received scant theoretical treatment to date. Here, using a simple, open, nutrient-limited ecosystem model with trophic interactions, we explore theoretically how spatial flows affect the functioning of local ecosystems, how physical mass-balance constraints interact with biological demographic constraints in the regulation of this functioning, and how failure to consider these constraints explicitly can lead to models that are ecologically inconsistent. In particular, we show that standard prey-dependent models for trophic interactions may lead to implausible outcomes when embedded in an ecosystem context with appropriate mass flows and mass-balance constraints. Our analysis emphasizes the need for integration of population, community, and ecosystem perspectives in ecology and the critical consequences of assuming closed versus open systems.

Theoretical studies of adaptation to sink environments (with conditions outside the niche requirements of a species) have shown that immigration from source habitats can either facilitate or inhibit local adaptation. Here, we examine the influence of immigration on the evolution of local adaptation, given an Allee effect (i.e., at low densities, absolute fitness increases with population density). We consider a deterministic model for evolution at a haploid locus, and a stochastic individual-based model for evolution of a quantitative trait, and several kinds of Allee effects. We demonstrate that increased immigration can greatly facilitate adaptive evolution in the sink; with greater immigration, local population sizes rise, and because of the Allee effect, there is a positive indirect effect of immigration on local fitness. This makes it easier for alleles of modest effect to be captured by natural selection, transforming the sink into a locally adapted population that can persist without immigration.

In the absence of other limiting factors, assemblages in which species share a common, effective natural enemy are not expected to persist. Although a variety of mechanisms have been postulated to explain the coexistence of species that share natural enemies, the role of productivity gradients has not been explored in detail. Here, we examine how enrichment can affect the outcome of apparent competition. We develop a structured resource/consumer/natural enemy model in which the prey are exposed to attacks during a vulnerable life phase, the length of which depends on resource availability. With a single prey species, the model exhibits the "paradox of enrichment," with unstable dynamics at high levels of resource productivity. We extend this model to consider two prey species linked by a shared predator, each with their own distinct resource base. We derive invasion and stability conditions and examine how enrichment influences prey species exclusion and coexistence. Contrary to expectations from simpler, prey-dependent models, apparent competition is not necessarily strong at high productivity, and prey species coexistence may thus be more likely in enriched environments. Further, the coexistence of apparent competitors may be facilitated by unstable dynamics. These results contrast with the standard theory that apparent competition in productive environments leads to nonpersistent interactions and that coexistence of multispecies interactions is more likely under equilibrial conditions.

This article develops a theoretical framework to link dynamical and population genetic models of persistent viral infection. This linkage is useful because, while the dynamical and population genetic theories have developed independently, the biological processes they describe are completely interrelated. Parameters of the dynamical models are important determinants of evolutionary processes such as natural selection and genetic drift. We develop analytical methods, based on coupled differential equations and Markov chain theory, to predict the accumulation of genetic diversity within the viral population as a function of dynamical parameters. These methods are first applied to the standard model of viral dynamics and then generalized to consider the infection of multiple host cell types by the viral population. Each cell type is characterized by specific parameter values. Inclusion of multiple cell types increases the likelihood of persistent infection and can increase the amount of genetic diversity within the viral population. However, the overall rate of gene sequence evolution may actually be reduced.

We study the consequences of asymmetric dispersal rates (e.g., due to wind or current) for adaptive evolution in a system of two habitat patches. Asymmetric dispersal rates can lead to overcrowding of the "downstream" habitat, resulting in a source-sink population structure in the absence of intrinsic quality differences between habitats or can even cause an intrinsically better habitat to function as a sink. Source-sink population structure due to asymmetric dispersal rates has similar consequences for adaptive evolution as a source-sink structure due to habitat quality differences: natural selection tends to be biased toward the source habitat. We demonstrate this for two models of adaptive evolution: invasion of a rare allele that improves fitness in one habitat but reduces it in the other and antagonistic selection on a quantitative trait determined by five additive loci. If a habitat can sustain a population without immigration, the conditions for adaptation to that habitat are most favorable if there is little or no immigration from the other habitat; the influence of emigration depends on the magnitude of the allelic effects involved and other parameters. If, however, the population is initially unable to persist in a given habitat without immigration, our model predicts that the population will be most likely to adapt to that habitat if the dispersal rates in both directions are high. Our results highlight the general message that the effect of gene flow upon local adaptation should depend profoundly on the demographic context of selection.

All species' ranges are the result of successful past invasions. Thus, models of species' invasions and their failure can provide insight into the formation of a species' geographic range. Here, we study the properties of invasion models when a species cannot persist below a critical population density known as an "Allee threshold." In both spatially continuous reaction-diffusion models and spatially discrete coupled ordinary-differential-equation models, the Allee effect can cause an invasion to fail. In patchy landscapes (with dynamics described by the spatially discrete model), range limits caused by propagation failure (pinning) are stable over a wide range of parameters, whereas, in an uninterrupted habitat (with dynamics described by a spatially continuous model), the zero velocity solution is structurally unstable and thus unlikely to persist in nature. We derive conditions under which invasion waves are pinned in the discrete space model and discuss their implications for spatially complex dynamics, including critical phenomena, in ecological landscapes. Our results suggest caution when interpreting abrupt range limits as stemming either from competition between species or a hard environmental limit that cannot be crossed: under a wide range of plausible ecological conditions, species' ranges may be limited by an Allee effect. Several example systems appear to fit our general model.

Species interactions commonly coevolve as complex geographic mosaics of populations shaped by differences in local selection and gene flow. We use a haploid matching-alleles model for coevolution to evaluate how a pair of species coevolves when fitness interactions are reciprocal in some locations ("hot spots") but not in others ("cold spots"). Our analyses consider mutualistic and antagonistic interspecific interactions and a variety of gene flow patterns between hot and cold spots. We found that hot and cold spots together with gene flow influence coevolutionary dynamics in four important ways. First, hot spots need not be ubiquitous to have a global influence on evolution, although rare hot spots will not have a disproportionate impact unless selection is relatively strong there. Second, asymmetries in gene flow can influence local adaptation, sometimes creating stable equilibria at which species experience minimal fitness in hot spots and maximal fitness in cold spots, or vice versa. Third, asymmetries in gene flow are no more important than asymmetries in population regulation for determining the maintenance of local polymorphisms through coevolution. Fourth, intraspecific allele frequency differences among hot and cold spot populations evolve under some, but not all, conditions. That is, selection mosaics are indeed capable of producing spatially variable coevolutionary outcomes across the landscapes over which species interact. Altogether, our analyses indicate that coevolutionary trajectories can be strongly shaped by the geographic distribution of coevolutionary hot and cold spots, and by the pattern of gene flow among populations.

Apparent competition is indirect competition between two or more victim species that share a natural enemy, caused by that enemy's numerical response. We review empirical examples of apparent competition in phytophagous insect hosts attacked by polyphagous parasitoids and develop models of apparent competition in host-parasitoid systems. Apparent competition is particularly likely in insect assemblages because parasitoids can limit their hosts to levels at which resource competition is unimportant. A consideration of both equilibrium and nonequilibrium models in which polyphagous parasitoids impose significant mortality on their hosts suggests that the most common outcome is the exclusion of all but one host species, which generates dynamic monophagy (i.e., a single host species persisting with a potentially polyphagous parasitoid). A crisp criterion for dominance in apparent competition is that the winning host supports the highest parasitoid density. We conclude that it is difficult for alternative hosts to coexist when the sole regulatory factor is a shared parasitoid. Yet in nature, coexisting hosts frequently do share parasitoids. We examine several mechanisms promoting host coexistence, including donor-controlled parasitoid dynamics, additional sources of host density dependence (e.g., resource limitation), spatial and temporal refuges, trophic web structure, and labile parasitoid behavior. Elucidating the mechanisms permitting the coexistence of host species confronted by effective polyphagous parasitoids deserves more attention from experimental field ecologists.

Predation may generate patterns in the structure of communities similar to those produced by competition. The potential role of spatial heterogeneity in promoting the coexistence of prey species is explored with both analytical and graphical models. In these models, prey interact indirectly through their effect on predator numbers: an interaction that leads to "apparent competition" and a problem in species coexistence. A model of prey coexistence in a homogeneous habitat is explored. If prey grow logistically, prey abundance is measured by the effect prey have on predator growth, and the predator consumes prey in a finegrained manner, the criterion for species k to remain in the community takes a simple form: its sensitivity to predation (a k /r k ) cannot exceed the average sensitivity to predation of the entire community, ( $$\overline {a/r}$$ ), divided by a measure of the intensity of predation on the community (Δ). At high Δ, species must have very similar values for a i /r i to coexist. This suggests that in spatially homogeneous environments, prey coexistence is difficult to achieve at high intensities of predation. There are two distinct ways in which spatial segregation may promote prey coexistence. First, habitat selection by the predator may provide each prey with an implicit refuge in the presence of the alternative prey, because predators will tend to leave a habitat in which their foraging yields are relatively low. If predators can select their habitats optimally without cost, and without interference from other predators, it is shown that at equilibrium no prey suffers a reduction in density because other prey are present in the diet. Nonoptimal habitat selection or interference between predators makes prey that have either low intrinsic growth rates (r i ) or high rates of predator attack (a i ) vulnerable to density reductions or extinction, as a result of predator "spillover" between patches. Second, if prey are spatially segregated, the predator population may be broken into two, partially independent subpopulations coupled by random predator movement. If each prey grows exponentially in the absence of predation, the permissible difference in their sensitivities to predation (a i /r i ) is bounded by a measure of spatial coupling; the more tightly the two patches are linked by predator movement, the more similar the values for a i /r i must be if the prey are to continue to coexist. This model also provides a simple illustration of how spatial heterogeneity may stabilize an otherwise unstable predator-prey system. The evolutionary stability of segregation between prey is briefly discussed. Even if habitat partitioning relaxes apparent competition between prey occupying separate patches, the segregational pattern itself may persist because of apparent competition within each patch. Several examples from field studies suggest that habitat partitioning and the movement behavior of both predators and prey are important factors affecting coexistence in prey communities.