Predator-prey interactions in a nonequilibrium context: the metapopulation approach to modeling "hide-and-seek" dynamics in a spatially explicit tri-trophic system

Predators and prey are usually heterogeneously distributed in space so that the ability of the predators to respond to the distribution of their prey may have a profound influence on the stability and persistence of a predator‐prey system. A special type of dynamics is “hide‐and‐seek” characterized by a high turnover rate of local populations of prey and predators, because once the predators have found a patch of prey they quickly overexploit it, whereupon the starving predators either should move to better places or die. Continued persistence of prey and predators thus hinges on a long‐term balance between local extinctions and founding of new subpopulations. The colonization rate depends on the rate of emigration from occupied patches and the likelihood of successfully arriving at a suitable new patch, while extinction rate depends on the local population dynamics. Since extinctions and colonizations are both discrete probabilistic events, these phenomena are most adequately modeled by means of a stochastic model. In order to demonstrate the qualitative differences between a deterministic and stochastic approach to population dynamics, a spatially explicit tritrophic predator‐prey model is developed in a deterministic and a stochastic version. The model is parameterized using data for the two‐spotted spider mite (Tetranychus urticae) and the phytoseiid mite predator Phytoseiulus persimilis inhabiting greenhouse cucumbers.
Simulations show that the deterministic and stochastic approaches yield different results. The deterministic version predicts that the populations will exhibit violent fluctuations, implying that the system is fundamentally unstable. In contrast, the stochastic version predicts that the two species will be able to coexist in spite of frequent local extinctions of both species, provided the system consists of a sufficiently large number of local populations. This finding is in agreement with experimental results. It is therefore concluded that demographic stochasticity in combination with dispersal is capable of producing and maintaining sufficient asynchrony between local populations to ensure long‐term regional (metapopulation) persistence.     

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.     

Introduced species provide a novel temporal resource that facilitates native predator population growth

Non-native species are recognized as important components of change to food web structure. Non-native prey may increase native predator populations by providing an additional food source and simultaneously decrease native prey populations by outcompeting them for a limited resource. This pattern of apparent competition may be important for plants and sessile marine invertebrate suspension feeders as they often compete for space and their immobile state make them readily accessible to predators. Reported studies on apparent competition have rarely been examined in biological invasions and no study has linked seasonal patterns of native and non-native prey abundance to increasing native predator populations. Here, we evaluate the effects of non-native colonial ascidians (Diplosoma listerianum and Didemnum vexillum) on population growth of a native predator (bloodstar, Henricia sanguinolenta) and native sponges through long-term surveys of abundance, prey choice and growth experiments. We show non-native species facilitate native predator population growth by providing a novel temporal resource that prevents loss of predator biomass when its native prey species are rare. We expect that by incorporating native and non-native prey seasonal abundance patterns, ecologists will gain a more comprehensive understanding of the mechanisms underlying the effects of non-native prey species on native predator and prey population dynamics.     

The role of sink to source re-colonisation in the population dynamics of insects living in unstable habitats: an example of terrestrial chironomids

Certain species of terrestrial chironomids (Diptera) are specialised on open patches in initial stages of primary or secondary succession (early fallow, lichens and mosses on rocks, etc.). These "source" habitats provide good quality food for their larvae and most offspring are produced here, but they are sensitive to summer desiccation. This often results in extinction of the summer larval population, followed in winter by re-colonisation from less suitable, but more stable "sink" habitats in the surrounding landscape. Soil dwelling and long-lived larvae are poor migrants; short-lived, winged adult females select patches for their development. Proper choice of oviposition sites and consequent distribution of eggs among individual habitats is thus critical for the success of these species. A mathematical model was developed in order to find out whether this re-colonisation strategy could ensure population persistence at the landscape level. The model was verified using long-term data on Smittia atterima abundance in old fields. The results indicate that even a small proportion of eggs laid in a sink habitat can ensure a successful re-colonisation of the source habitat. Thus, re-colonisation of source habitats from sink habitats is concluded to be one of the reasons for persistence of the latter. The model indicates that this re-colonisation may ensure population persistence even in conditions when exclusive use of only one habitat leads to population extinction either due to environmental stress or to a negative growth rate.     

Metapopulation dynamics for spatially extended predator–prey interactions

Traditional metapopulation theory classifies a metapopulation as a spatially homogeneous population that persists on neighboring habitat patches. The fate of each population on a habitat patch is a function of a balance between births and deaths via establishment of new populations through migration to neighboring patches. In this study, we expand upon traditional metapopulation models by incorporating spatial heterogeneity into a previously studied two-patch nonlinear ordinary differential equation metapopulation model, in which the growth of a general prey species is logistic and growth of a general predator species displays a Holling type II functional response. The model described in this work assumes that migration by generalist predator and prey populations between habitat patches occurs via a migratory corridor. Thus, persistence of species is a function of local population dynamics and migration between spatially heterogeneous habitat patches. Numerical results generated by our model demonstrate that population densities exhibit periodic plane-wave phenomena, which appear to be functions of differences in migration rates between generalist predator and prey populations. We compare results generated from our model to results generated by similar, but less ecologically realistic work, and to observed population dynamics in natural metapopulations.     

Experimental demonstration of accelerated extinction in source‐sink metapopulations

Population extinction is a fundamental ecological process which may be aggravated by the exchange of organisms between productive (source) and unproductive (sink) habitat patches. The extent to which such source‐sink exchange affects extinction rates is unknown. We conducted an experiment in which metapopulation effects could be distinguished from source‐sink effects in laboratory populations of Daphnia magna. Time‐to‐extinction in this experiment was maximized at intermediate levels of habitat fragmentation, which is consistent with a minority of theoretical models. These results provided a baseline for comparison with experimental treatments designed to detect effects of concentrating resources in source patches. These treatments showed that source‐sink configurations increased population variability (the coefficient of variation in abundance) and extinction hazard compared with homogeneous environments. These results suggest that where environments are spatially heterogeneous, accurate assessments of extinction risk will require understanding the exchange of organisms among population sources and sinks. Such heterogeneity may be the norm rather than the exception because of both the intrinsic heterogeneity naturally exhibited by ecosystems and increasing habitat fragmentation by human activity.     

Large‐scale predator control increases population viability of a rare New Zealand riverine duck

The introduction of mammalian predators to oceanic islands has led to dramatic declines in the abundance of many native species. Conservation management of these species often relies on low‐cost predator control techniques that can be implemented over large scales. Assessing the effectiveness of such management techniques is difficult, but using population viability analyses (PVA), which identify the population growth rate (λ) and extinction risk of threatened species, may offer a solution. PVA provide the opportunity to compare the relative effectiveness of various management options and can identify knowledge gaps to prioritize research efforts. We used PVA to assess the population viability of whio (Hymenolaimus malacorhynchos), a rare riverine duck endemic to New Zealand. Current populations are threatened by introduced mammalian predators and are rapidly declining in both distribution and abundance. Whio conservation management is dominated by large‐scale, low‐intensity predator control, targeting introduced stoats (Mustela erminea). There is evidence that such control increases whio productivity but it is unknown if this increase is sufficient for long‐term population persistence. We undertook a stochastic PVA to assess the viability of whio populations under different management scenarios using data obtained from a 6‐year study of whio demographic responses to predator control. Populations with no predator control and low productivity will rapidly decline to extinction. Increasing productivity through predator control increased population viability but populations still showed a declining trajectory. A perturbation analysis showed that the growth rate of whio populations was largely driven by adult survival. Therefore, future research should target obtaining more robust estimates of adult survival, particularly how it is affected by predator control. Overall, our analysis indicated that large‐scale predator control increases the short‐term viability of whio populations but is insufficient for long‐term population persistence.     

Habitat subdivision causes changes in food web structure

Theory suggests that the response of communities to habitat subdivision depends on both species' characteristics and the extent to which species interact. For species with dynamics that are independent of other species, subdivision is expected to promote regional extinction as populations become small and isolated. By contrast, intermediate levels of subdivision can facilitate persistence of strongly interacting species. Consistent with this prediction, experimental subdivision lengthened persistence of some species, altering the extent of food web collapse through extinction. Extended persistence was associated with immigration rescuing a basal prey species from local extinction. As predicted by food web theory, habitat subdivision reduced population density of a top predator. Removal of this top predator from undivided microcosms increased the abundance of two other predator species, and these changes paralleled those produced by habitat subdivision. These results show that species interactions structured this community, and illustrate the need for investigations of other communities.     

Dynamics of a intraguild predation model with generalist or specialist predator

Intraguild predation (IGP) is a combination of competition and predation which is the most basic system in food webs that contains three species where two species that are involved in a predator/prey relationship are also competing for a shared resource or prey. We formulate two intraguild predation (IGP: resource, IG prey and IG predator) models: one has generalist predator while the other one has specialist predator. Both models have Holling-Type I functional response between resource-IG prey and resource-IG predator; Holling-Type III functional response between IG prey and IG predator. We provide sufficient conditions of the persistence and extinction of all possible scenarios for these two models, which give us a complete picture on their global dynamics. In addition, we show that both IGP models can have multiple interior equilibria under certain parameters range. These analytical results indicate that IGP model with generalist predator has “top down” regulation by comparing to IGP model with specialist predator. Our analysis and numerical simulations suggest that: (1) Both IGP models can have multiple attractors with complicated dynamical patterns; (2) Only IGP model with specialist predator can have both boundary attractor and interior attractor, i.e., whether the system has the extinction of one species or the coexistence of three species depending on initial conditions; (3) IGP model with generalist predator is prone to have coexistence of three species.     

Effects of an attractive sink leading into maladaptive habitat selection

Habitat sinks can attract dispersing animals if high mortality or breeding failure are difficult to detect (e.g., when due to human hunting or pollution). Using a simple deterministic model, we explore the dynamics of such source-sink systems considering three scenarios: an avoided sink, no habitat preference, and an attractive sink. In the second two scenarios, there is a threshold proportion of sink habitat above which the whole population decreases to extinction, but this extinction threshold varies with habitat preference and the relative qualities of the two habitat types. Hence, it would be necessary to know the habitat preferences of any species in a source-sink system to interpret data on population increases and declines. In the attractive sink scenario, small changes in the proportion of sink habitat may have disproportionate effects on the population persistence. Also, small changes in growth rates at the source and the sink severely affect the threshold and the time of extinction. For some combinations of demographic parameters and proportion of habitat sink, the decline affects the source first; thus, during some time, it will be hidden to population monitoring at the sink, where numbers can even increase. The extinction threshold is also very sensitive to the initial population sizes relative to carrying capacity. Attractive sinks represent a novel aspect of source-sink dynamics with important conservation and management implications.     

The influence of generalist predators in spatially extended predator–prey systems

The presence of generalist predators is known to have important ecological impacts in several fields. They have wide applicability in the field of biological control. However, their role in the spatial distribution of predator and prey populations is still not clear. In this paper, the spatial dynamics of a predator–prey system is investigated by considering two different types of generalist predators. In one case, it is considered that the predator population has an additional food source and can survive in the absence of the prey population. In the other case, the predator population is involved in intraguild predation, i.e., the source of the additional food of the predator coincides with the food source of the prey population and thus both prey and predator populations compete for the same resource. The conditions for linear stability and Turing instability are analyzed for both the cases. In the presence of generalist predators, the system shows different pattern formations and spatiotemporal chaos which has important implications for ecosystem functioning not only in terms of their predictability, but also in influencing species persistence and ecosystem stability in response to abrupt environmental changes. This study establishes the importance of the consideration of spatial dynamics while determining optimal strategies for biological control through generalist predators.     

Strength of asymmetric competition between predators in food webs ruled by fluctuating prey: the case of foxes in tundra

In food webs heavily influenced by multi‐annual population fluctuations of key herbivores, predator species may differ in their functional and numerical responses as well as their competitive ability. Focusing on red and arctic fox in tundra with cyclic populations of rodents as key prey, we develop a model to predict how population dynamics of a dominant and versatile predator (red fox) impacted long‐term growth rate of a subdominant and less versatile predator (arctic fox). We compare three realistic scenarios of red fox performance: (1) a numerical response scenario where red fox acted as a resident rodent specialist exhibiting population cycles lagging one year after the rodent cycle, (2) an aggregative response scenario where red fox shifted between tundra and a nearby ecosystem (i.e. boreal forest) so as to track rodent peaks in tundra without delay, and (3) a constant subsidy scenario in which the red fox population was stabilized at the same mean density as in the other two scenarios. For all three scenarios it is assumed that the arctic fox responded numerically as a rodent specialist and that the mechanisms of competition is of a interference type for space, in which the arctic fox is excluded from the most resource rich patches in tundra. Arctic fox is impacted most by the constant subsidy scenario and least by the numerical response scenario. The differential effects of the scenarios stemmed from cyclic phase‐dependent sensitivity to competition mediated by changes in temporal mean and variance of available prey to the subdominant predator. A general implication from our result is that external resource subsidies (prey or habitats), monopolized by the dominant competitor, can significantly reduce the likelihood for co‐existence within the predator guild. In terms of conservation of vulnerable arctic fox populations this means that the likelihood of extinction increases with increasing amount of subsidies (e.g. carcasses of large herbivores or marine resources) in tundra and nearby forest areas, since it will act to both increase and stabilize populations of red fox.     

A discrete time stochastic model of a two prey, one predator species interaction

A stochastic discrete time model of a two prey, one predator interaction, an extension of one and two species models proposed by Leslie (1958) and Leslie and Gower, 1958, Leslie and Gower, 1960, is studied. Monte Carlo simulations and the stability properties of the analogous continuous time deterministic model suggest the following hypotheses. (1) The two prey, one predator interaction is in general unstable. The range of parameters allowing coexistence of all three species is small. (2) Deterministically the predator always survives. (3) If the parameters defining the effects of density on the rates of population growth are large, the simulations lead to the rapid extinction of all three species or all but one of the prey species even if the interaction is deterministically stable. (4) The outcome of this three species interaction is largely probabilistic over a wide range of parameters. (5) A prey species with a competitive advantage over a second prey species may still find it difficult to invade and displace the second prey species if the density of the second prey species is high. Increasing the density of the predator offsets this numerical advantage somewhat. (6) The introduction of a predator common to two noncompeting species of prey usually leads to the extinction of one of the prey species. (7) In a stable two prey, one predator interaction the fluctuations of the two prey species are nonperiodic and erratic. The fluctuations of the rarer prey species are damped relative to the commoner species and the fluctuations of the rarer prey species behave as if the series has no fixed mean abundance. The predator population fluctuates with a remarkably constant period. The relevance of these hypotheses to the problem of relating population stability and persistence with the number of species in a community is discussed.     

Antagonistic coevolution over productivity gradients

This study addresses the question of how spatial heterogeneity in prey productivity and migration act to determine geographic patterns in antagonistic coevolution with a predator. We develop and analyze a quantitative coevolutionary model for a predator-prey interaction. If the model is modified appropriately, the results could broadly apply to multispecies communities and to herbivore-plant, parasite-host, and parasitoid-host associations. Model populations are distributed over a gradient in prey birth rate (as a measure of productivity). Each population, in each patch, is made up of a suite of strains. Each strain of the predator has a certain ability to successfully attack each strain of the prey. We consider scenarios of isolated patches, global migration, and stepping-stone (i.e., local) migration over a linear string of patches. The most pervasive patterns are the following: investments in predator offense and prey defense are both maximal in the patches of highest prey productivity; when there are no constraints on maximal investment, mean predation evolves to highest levels in the most productive patches; similarly, the predator has a greater impact (measured as the percentage reduction in prey density) on the prey population in high productivity patches as compared with low productivity ones-in spite (even after evolution) of prey abundance being highest in the most productive patches; and migration has the net effect of shunting relatively offensive and defensive strains from productive patches to nonproductive ones, potentially resulting in the elimination of otherwise rare, low-investment clones. A modification of the model to gene-for-gene type interactions predicts that generalist strains (in terms of the range of strains the predator can exploit or the prey can fend off) dominate in productive areas of the prey, whereas specialists prevail in marginal habitats. Assuming a wide range of productivities over the prey's geographical distribution, the greatest strain diversity should be found in habitats of intermediate productivity. We discuss the implications of our study for adaptation and conservation. Empirical studies are in broad accord with our findings.     

The role of density-dependent dispersal in source-sink dynamics

I investigate two aspects of source-sink theory that have hitherto received little attention: density-dependent dispersal and the cost of dispersal to sources. The cost arises because emigration reduces the per capita growth rate of sources, thus predisposing them to extinction. I show that source-sink persistence depends critically on the interplay between these two factors. When the emigration rate increases with abundance at an accelerating rate, dispersal costs to sources is the lowest and risk of source-sink extinction the least. When the emigration rate increases with abundance at a decelerating rate, dispersal costs to sources is the highest and the risk of source-sink extinction the greatest. Density-independent emigration has an intermediate effect. Thus, density-dependent dispersal per se does not increase or decrease source-sink persistence relative to density-independent dispersal. The exact mode of dispersal is crucial. A key point to appreciate is that these effects of dispersal on source-sink extinction arise from the temporal density-dependence that dispersal induces in the per capita growth rates of source and sink populations. Temporal density-dependence due to dispersal is beneficial at low abundances because it rescues sinks from extinction, and detrimental at high abundances because it drives otherwise viable sources to extinction. These results are robust to the nature of population dynamics in the sink, whether exponential or logistic. They provide a means of assessing the relative costs and benefits of preserving sink habitats given three biological parameters.     

Prey persistence and abundance in systems with intraguild predation and type-2 functional responses

The apparent prevalence of intraguild predation in productive environments has been regarded as puzzling because some simple models suggest that the intraguild prey species is often either reduced in abundance or driven extinct at high resource productivity. While various theoretical mechanisms that avoid this prediction have been uncovered, they have often been viewed as being narrowly applicable. This article examines the fate of the intraguild prey in models in which consumer species may have type-2 functional responses; these are usually characterized by sustained fluctuations in population density at high enough resource productivities. The models also include adaptive, but imperfect diet choice by the top predator. We concentrate on two situations: (1) the prey exhibits less saturation in its functional response to the resource than does the predator and (2) the predator is unable to persist on the basal resource alone. The reasons given by previous studies for discounting these cases are re-examined. The present analysis shows that prey abundance often increases with increasing productivity in both cases, as does the range of prey parameters that allows prey persistence. It is also possible for the prey to coexist with the predator in spite of having a larger equilibrium requirement for the resource. Different assumptions about the dynamics of diet choice can have a large impact on population responses to enrichment. We argue that the persistence and/or increase in abundance of intraguild prey at higher productivity should not be regarded as puzzling because observations are consistent with a range of theoretical models that reflect commonly observed mechanisms.     

Successful invasion of a food web in a chemostat

A food web in a chemostat is considered in which an arbitrary number of competitor populations compete for a single, essential, nonreproducing, growth-limiting substrate, and an arbitrary number of predator populations prey on some or all of the competitor populations. Although any number of predator populations may prey on the same competitor population, each predator population preys on only one competitor population. The dynamics of substrate uptake is modeled by Lotka-Volterra or Michaelis-Menten (Holling type I or II), but the dynamics of competitor uptake is restricted to Lotka-Volterra. Based on certain parameters, the model predicts the asymptotic survival or extinction of each of the different populations and suggests how competitor and/or predator populations could successfully invade the chemostat with or without causing a diverse ecosystem to crash. Similarly, it suggests how the elimination of certain populations could result in a more diverse or less diverse system.     

The role of variability and risk on the persistence of shared-enemy,predator-prey assemblages

The role of indirect effects such as apparent competition in structuring predator-prey assemblages has recently received empirical attention. That one prey species can be excluded by the impact of a shared-enemy contrasts with the known diversity of multispecies predator-prey interactions. Here, the role of predator foraging among patches of two different prey species is examined as a mechanism that can mediate coexistence in multispecies prey-predator assemblages. Specifically, models of host-parasitoid interactions are constructed to analyse how different types of aggregative behaviour (generated by host-dependent and host-independent responses) affect persistence of the assemblage. How the distribution of hosts and the response of the parasitoid to these distributions can influence coexistence is shown. A generic explanation for coexistence suggests that it is the variability rather than the precise functional relationship that is critical for coexistence under shared-enemy interactions.     

Influence of predator‐specific defense adaptation on intraguild predation

The persistence of intraguild predation (IGP), the prey–predator interaction between competing species, is puzzling because simple IGP models readily predict species extinction. In this study, we explored a mathematical model incorporating predator‐specific defense adaptation of basal prey against intraguild prey and intraguild predator. The model explicitly described the dynamics of the defense effort against each predator under the assumption that anti‐predator defense was associated with reducing effort allocated to reproduction. The model predicted that defense adaptation (i.e. the ability to reallocate defense effort) would facilitate coexistence, particularly when system productivity is high; at low productivity, coexistence would be facilitated or inhibited depending on initial effort allocation prior to defense adaptation. In addition, we found that three‐species dynamics became more stable at higher adaptation rates. The results suggest that common behavioral changes, such as predator‐specific defense adaptation, have significant implications for the community structure and dynamics of IGP systems.     

Paradox of marine protected areas: suppression of fishing may cause species loss

A number of fish and invertebrate stocks have been depleted by overexploitation in recent years. To address this, marine protected areas (MPAs) are often established to protect biodiversity and recover stocks. We analyzed the potential impact of establishing MPAs on marine ecosystems using mathematical models. We demonstrate that establishment of an MPA can sometimes result in a considerable decline, or even extinction, of a species. We focus on a prey–predator system in two patches, one exposed to fishing activity and the other protected (MPA). Our analyses reveal that the establishment of the MPA can cause a reduction in prey abundance, and even extinction of the prey. Such unintended consequences are more likely to occur if the predator species is a generalist and if the MPA is intended to protect only the predatory species. Further, a mobile predator that migrates adaptively rather than randomly is associated with a greater reduction in prey abundance.