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.     

Impact of Allee effect on an eco-epidemiological system

In this paper, we propose a general ratio-dependent prey-predator model with disease in predator subject to the strong Allee effect in prey. We obtain the complete dynamics of both models: (a) full model with Allee effect; (b) full model without Allee effect. Model (a) may have more than one interior equilibrium point, but model (b) has only one interior equilibrium point. Numerical results reveal that the coexistence of all the populations at the endemic state is possible for both the models. But for the model with Allee effect, the coexistence can be destroyed by an increased supply of alternative food for the predators. It can also be proved that for the full model with Allee effect, the disease can be suppressed under certain parametric conditions. Also by comparing models (a) and (b), we conclude that Allee effect can create or destroy the interior attractor. Finally, we have studied the disease free-submodel (prey and susceptible predator model) with and without Allee effect. The comparative study between these two submodels leads to the following conclusions: 1) In the presence of Allee effect, the number of interior equilibrium points can change from zero to two whereas the submodel without Allee effect has unique interior equilibrium point; 2) Both with and without Allee effect, initial conditions play an important role on the survival and extinction of prey as well as its corresponding predator; 3) In the presence of Allee effect, bi-stability occurs with stable or periodic coexistence of prey and susceptible predator and the extinction of prey and susceptible predator; 4) Allee effect can generate or destroy the interior equilibrium points.     

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.     

Not attackable or not crackable—How pre‐ and post‐attack defenses with different competition costs affect prey coexistence and population dynamics

It is well‐known that prey species often face trade‐offs between defense against predation and competitiveness, enabling predator‐mediated coexistence. However, we lack an understanding of how the large variety of different defense traits with different competition costs affects coexistence and population dynamics. Our study focusses on two general defense mechanisms, that is, pre‐attack (e.g., camouflage) and post‐attack defenses (e.g., weaponry) that act at different phases of the predator—prey interaction. We consider a food web model with one predator, two prey types and one resource. One prey type is undefended, while the other one is pre‐ or post‐attack defended paying costs either by a higher half‐saturation constant for resource uptake or a lower maximum growth rate. We show that post‐attack defenses promote prey coexistence and stabilize the population dynamics more strongly than pre‐attack defenses by interfering with the predator's functional response: Because the predator spends time handling “noncrackable” prey, the undefended prey is indirectly facilitated. A high half‐saturation constant as defense costs promotes coexistence more and stabilizes the dynamics less than a low maximum growth rate. The former imposes high costs at low resource concentrations but allows for temporally high growth rates at predator‐induced resource peaks preventing the extinction of the defended prey. We evaluate the effects of the different defense mechanisms and costs on coexistence under different enrichment levels in order to vary the importance of bottom‐up and top‐down control of the prey community.     

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.     

Theoretical dynamics of competitors under predation

Summary Continuous population models of two prey species and a predator were explored by isocline analysis. When predator satiation and substitution between prey (with or without switching) are introduced in the models, many qualitatively different kinds of dynamic behaviour become possible. These depend in a complex but predictable way on competitive relations between prey and on predator feeding behaviour and efficiency. Under constant predation many cases of threshold responses between two or more alternate stable states are possibly; the numerical response of the predator population reduces some of the possibilities.Apparently contradictory community phenomena previously proposed, e.g. prey coexistence versus exclusion by addition of predator, exclusion versus stabilization by addition of alternate prey, are all possible as special cases. A prey which is relatively tolerant to predation can act as a keystone species, on which the existence of other prey species in the community depends, in either a positive or a negative sense. In certain conditions predator-induced obligatory mutualism between two prey species is theoretically possible.To Michael Evenari, pioneer, teacher and friend     

Transient dynamics limit the effectiveness of keystone predation in bringing about coexistence

We analyze the transient dynamics of simple models of keystone predation, in which a predator preferentially consumes the dominant of two (or more) competing prey species. We show that coexistence is unlikely in many systems characterized both by successful invasion of either prey species into the food web that lacks it and by a stable equilibrium with high densities of all species. Invasion of the predator-resistant consumer species often causes the resident, more vulnerable prey to crash to such low densities that extinction would occur for many realistic population sizes. Subsequent transient cycles may entail very low densities of the predator or of the initially successful invader, which may also preclude coexistence of finite populations. Factors causing particularly low minimum densities during the transient cycles include biotic limiting resources for the prey, limited resource partitioning between the prey, a highly efficient predator with relatively slow dynamics, and a vulnerable prey whose population dynamics are rapid relative to the less vulnerable prey. Under these conditions, coexistence of competing prey via keystone predation often requires that the prey's competitive or antipredator characteristics fall within very narrow ranges. Similar transient crashes are likely to occur in other food webs and food web models.     

The influence of vigilance on intraguild predation

Theoretical work on intraguild predation suggests that if a top predator and an intermediate predator share prey, the system will be stable only if the intermediate predator is better at exploiting the prey, and the top predator gains significantly from consuming the intermediate predator. In mammalian carnivore systems, however, there are examples of top predator species that attack intermediate predator species, but rarely or never consume the intermediate predator. We suggest that top predators attacking intermediate predators without consuming them may not only reduce competition with the intermediate predators, but may also increase the vigilance of the intermediate predators or alter the vigilance of their shared prey, and that this behavioral response may help to maintain the stability of the system. We examine two models of intraguild predation, one that incorporates prey vigilance, and a second that incorporates intermediate predator vigilance. We find that stable coexistence can occur when the top predator has a very low consumption rate on the intermediate predator, as long as the attack rate on the intermediate predator is relatively large. However, the system is stable when the top predator never consumes the intermediate predator only if the two predators share more than one prey species. If the predators do share two prey species, and those prey are vigilant, increasing top predator attack rates on the intermediate predator reduces competition with the intermediate predator and reduces vigilance by the prey, thereby leading to higher top predator densities. These results suggest that predator and prey behavior may play an important dynamical role in systems with intraguild predation.     

Trophic supplements to intraguild predation

Intraguild predation (IGP) is a dominant community module in terrestrial food webs that occurs when multiple consumers feed both on each other and on a shared prey. This specific form of omnivory is common in terrestrial communities and is of particular interest for conservation biology and biological control given its potential to disrupt management of threatened or pest species. Extensive theory exists to describe the dynamics of three-species IGP, but these models have largely overlooked the potential for other, exterior interactions, to alter the dynamics within the IGP module. We investigated how three forms of feeding outside of the IGP module by intraguild predators (i.e. trophic supplementation) affect the dynamics of the predators (both IG predator and IG prey) and their shared resource. Specifically, we examined how the provision of a constant donor-controlled resource, the availability of an alternative prey species, and predator plant-feeding affect the dynamics of IGP models. All three forms of trophic supplements modified the basic expectations of IGP theory in two important ways, and their effects were similar. First, coexistence was possible without the IG prey being a superior competitor for the original shared resource if the IG prey could effectively exploit one of the types of trophic supplements. However, supplements to the IG predator restricted the potential for coexistence. Second, supplements to the IG prey ameliorated the disruptive effects of the IG predator on the suppression of the shared resource, promoting effective control of the resource in the presence of both predators. Consideration of these three forms of trophic supplementation, all well documented in natural communities, adds substantial realism and predictive power to intraguild predation theory.     

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.     

High reproductive rates result in high predation risks: a mechanism promoting the coexistence of competing prey in spatially structured populations

I tested the hypothesis that spatial structure provides a trade-off between reproduction and predation risk and thereby facilitates predator-mediated coexistence of competing prey species. I compared a cellular automata model to a mean-field model of two prey species and their common predator. In the mean-field model, the prey species with the higher reproductive rate (the superior competitor) always outcompeted the other species (the inferior competitor), both in the presence of and the absence of the predator. In the cellular automata model, both prey species, which differed only in their reproductive rates, coexisted for a long time in the presence of their common predator at intermediate levels of predation. At low predation rates, the superior competitor dominated, while high predation rates favored the inferior competitor. This discrepancy in the results of the different models was due to a trade-off that spontaneously emerged in spatially structured populations; that is, the more clustered distribution of the superior competitor made it more susceptible to predation. In addition, coexistence of competing prey species declined with increasing dispersal ranges of either prey or predator, which suggests that the trade-off that results from spatial structure becomes less important as either prey or predator disperse over a broader range.     

Existence and bifurcation of stable equilibrium in two-prey,one-predator communities

In this paper, stability of two-prey, one-predator communities is investigated by Lyapunov's direct method and Hopf's bifurcation theory. Three patterns of three-species coexistence are possible. A globally stable non-negative equilibrium exists for the system even if two competing prey species without a predator cannot coexist. The stable equilibrium bifurcates to a periodic motion with a small amplitude when the predation rate increases. It is also shown that a chaotic motion emerges from the periodic motion when one of two prey has greater competitive abilities than the other. This predator-mediated coexistence can be realized by the intimate relationship between preferences of a predator and competitive abilities of two prey.     

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.     

Effects of habitat destruction and resource supplementation in a predator-prey metapopulation model

We developed a mean field, metapopulation model to study the consequences of habitat destruction on a predator-prey interaction. The model complements and extends earlier work published by Bascompte and Solé (1998, J. theor. Biol.195, 383-393) in that it also permits use of alternative prey (i.e., resource supplementation) by predators. The current model is stable whenever coexistence occurs, whereas the earlier model is not stable over the entire domain of coexistence. More importantly, the current model permits an assessment of the effect of a generalist predator on the trophic interaction. Habitat destruction negatively affects the equilibrium fraction of patches occupied by predators, but the effect is most pronounced for specialists. The effect of habitat destruction on prey coexisting with predators is dependent on the ratio of extinction risk due to predation and prey colonization rate. When this ratio is less than unity, equilibrial prey occupancy of patches declines as habitat destruction increases. When the ratio exceeds one, equilibrial prey occupancy increases even as habitat destruction increases; i.e., prey "escape" from predation is facilitated by habitat loss. Resource supplementation reduces the threshold colonization rate of predators necessary for their regional persistence, and the benefit derived from resource supplementation increases in a nonlinear fashion as habitat destruction increases. We also compared the analytical results to those from a stochastic, spatially explicit simulation model. The simulation model was a discrete time analog of our analytical model, with one exception. Colonization was restricted locally in the simulation, whereas colonization was a global process in the analytical model. After correcting for differences between nominal and effective colonization rates, most of the main conclusions of the two types of models were similar. Some important differences did emerge, however, and we discuss these in relation to the need to develop fully spatially explicit analytical models. Finally, we comment on the implications of our results for community structure and for the conservation of prey species interacting with generalist predators.     

An eco-epidemiological system with infected prey and predator subject to the weak Allee effect

In this article, we propose a general prey–predator model with disease in prey and predator subject to the weak Allee effects. We make the following assumptions: (i) infected prey competes for resources but does not contribute to reproduction; and (ii) in comparison to the consumption of the susceptible prey, consumption of infected prey would contribute less or negatively to the growth of predator. Based on these assumptions, we provide basic dynamic properties for the full model and corresponding submodels with and without the Allee effects. By comparing the disease free submodels (susceptible prey–predator model) with and without the Allee effects, we conclude that the Allee effects can create or destroy the interior attractors. This enables us to obtain the complete dynamics of the full model and conclude that the model has only one attractor (only susceptible prey survives or susceptible-infected coexist), or two attractors (bi-stability with only susceptible prey and susceptible prey–predator coexist or susceptible prey-infected prey coexists and susceptible prey–predator coexist). This model does not support the coexistence of susceptible-infected-predator, which is caused by the assumption that infected population contributes less or are harmful to the growth of predator in comparison to the consumption of susceptible prey.     

Predator selectivity alters the effect of dispersal on coexistence among apparent competitors

While the majority of studies on dispersal effects on patterns of coexistence among species in a metacommunity have focused on resource competitors, dispersal in systems with predator–prey interactions may provide very different results. Here, we use an analytical model to study the effect of dispersal rates on coexistence of two prey species sharing a predator (apparent competition), when the traits of that predator vary. Specifically, we explore the range in immigration rates where apparent competitors are able to coexist, and how that range changes with predator selectivity and efficiency. We find that if the inferior apparent competitor has a higher probability of being consumed, it will require less immigration to invade and to exclude the superior prey as the predator becomes more opportunistic. However, if the inferior apparent competitor has a lower probability of being consumed (and lower growth rates), higher immigration is required for the inferior prey to invade and exclude the superior prey as the predator becomes more opportunistic. We further find that the largest range of immigration rates where prey coexist occurs when predator selectivity is intermediate (i.e. they do not show much bias towards consuming one species or the other). Increasing predator efficiency generally reduces the immigration rates necessary for the inferior apparent competitor to invade and exclude the superior apparent competitor, but also reduces the range of immigration rates where the two apparent competitors can coexist. However, when the superior apparent competitor has a higher probability of being consumed, increased predator efficiency can increase the range of parameters where the species can coexist. Our results are consistent with some of the variation observed in the effect of dispersal on prey species richness in empirical systems with top predators.     

Multiple predator effects result in risk reduction for prey across multiple prey densities

Investigating how prey density influences a prey’s combined predation risk from multiple predator species is critical for understanding the widespread importance of multiple predator effects. We conducted experiments that crossed six treatments consisting of zero, one, or two predator species (hellgrammites, greenside darters, and creek chubs) with three treatments in which we varied the density of mayfly prey. None of the multiple predator effects in our system were independent, and instead, the presence of multiple predator species resulted in risk reduction for the prey across both multiple predator combinations and all three levels of prey density. Risk reduction is likely to have population-level consequences for the prey, resulting in larger prey populations than would be predicted if the effects of multiple predator species were independent. For one of the two multiple predator combinations, the magnitude of risk reduction marginally increased with prey density. As a result, models predicting the combined risk from multiple predator species in this system will sometimes need to account for prey density as a factor influencing per-capita prey death rates.     

Prey: predator ratio dependence in the functional response of a freshwater amphipod

1. First known for their shredding activity, freshwater amphipods also behave as active predators with consequences for prey population regulation and amphipod coexistence in the context of biological invasions. 2. A way to quantify predation is to determine the average consumption rate per predator, also known as its functional response (FR). 3. Although amphipods are gregarious and can display social interactions that can alter per capita consumption rates, previous studies using the FR approach to investigate amphipod predation ignored such potential mutual interference because they did not consider variations in predator density. 4. We investigated the FR of Echinogammarus berilloni feeding on dipteran larvae with joint variations in prey and predator densities. This bivariate experimental design allowed us to estimate interference and to compare the fits of the three main classes of theoretical FR models, in which the predation rate is a function of prey density alone (prey‐dependent models), of both prey and predator densities (predator‐dependent models) or of the prey‐to‐predator ratio (ratio‐dependent models). 5. The Arditi–Ginzburg ratio‐dependent FR model provided the best representation of the FR of E. berilloni, whose predation rate showed a decelerating rise to a horizontal asymptote as prey abundance increased. 6. Ratio dependence means that mutual interference between amphipods leads to prey sharing. Mutual interference is likely to vary between amphipod species, depending on their level of aggressiveness.     

Evolutionary Consequences of Predation for Pathogens in Prey

This article investigates the impact of predation on the coexistence and competitive exclusion of pathogen strains in the prey. Two types of predator are considered—a generalist and a specialist. For each type of predator, we assume that the predator can discriminate among susceptible and infected with each strain prey. The two strains will competitively exclude each other in the absence of predation with the strain with the larger reproduction number persisting. If a generalist predator preys discriminantly and the disease is fatal, then depending on the predation level, a switch in the dominant pathogen may occur. Thus, for some predation levels, the first strain may persist while for other predation levels the second strain may persist. Furthermore, a specialist predator preying discriminantly may mediate the coexistence of the two strains. Although in most cases increasing predation reduces the disease load in the prey, when predation leads to coexistence, it may also lead to increase in the disease load.     

The storage effect due to frequency-dependent predation in multispecies plant communities

Frequency-dependent seed predation (FDP) has been shown to be a powerful coexistence mechanism in models of annual plant communities. However, FDP undermines the competition-based coexistence mechanism called the storage effect (SEc), which relies on temporal environmental fluctuations that drive fluctuations in competition. Although environmental fluctuations also drive fluctuations in predation, a storage effect due to predation (SEp) may not arise due to a time lag between a change in the environment and the resulting change in the predation rate. Here we show how SEp can arise with multispecies FDP, and in a two-species setting with density-dependent frequency-dependence, partially compensating for the reduction in SEc, in the presence of predation. These outcomes occur when predatory behavior is flexible, and can accommodate to changes in prey abundances on a within-year time scale, leading to changes in predator preferences in response to prey abundances in a given year. When predator preferences are determined by average prey abundances over several years, FDP is still a strong coexistence mechanism but undermines SEc without creating SEp.