Influence of prey reserve capacity on predator–prey dynamics

In this article the dynamics of a predator and prey population has been modelled when a reserve is created to protect a certain number of prey population from predation. This investigation is essential to derive some guiding principles to conserve the prey population and also to understand the behaviour and dependence of predator population on the reserve capacity. The present study concerns analysis of a fairly general model and hence some of the existing results based on specific explicit models, like Lotka–Volterra model and Rosenzweig–MacArthur model, can be derived from this work. In this study, conditions have been derived for coexistence of predator and prey, and extinction of predators. Results are obtained for global stability of required equilibrium of the model. Also, a method is suggested to compute reserve capacity in order to drive the ecosystem state to a required level. The key results developed in this article have been illustrated using numerical simulation. These results can be interpreted in different contexts like resource conservation, pest management, bio-economics of a renewable resource, etc.     

Prey–predator dynamics with predator switching regulated by a catabolic repression control mode

Since many predators can live under certain circumstances as saprophytes or consume more than one prey, and different enzymes are generally required for each prey or nutrient digestion, the predator must be sufficiently adaptive for effective utilization of the prey mass. Control modes as induction and repression, however, act at the level of genes and cause changes in the biosynthesis rate of these enzymes. In this work, an extension of the catabolic repression control mode from the level of genes to the level of the behavior of the predator is proposed, in order to model the balanced attack of the predator on the prey. It is demonstrated that, when the prey population has the competitive advantage over the predator (in using the common substrate), the catabolic repression mechanism favors the prey population, which dominates over the predator even at low specific dilution rate values, whereas, the stable steady or periodic coexistence state is not favored. When the predator has the competitive advantage at low substrate concentrations and the prey at high substrate concentrations, the introduction of the catabolic repression mechanism in the model again favors the stable steady state of the prey, while the coexistence region is dramatically reduced. Conversely, when the prey population has the competitive advantage at low and the predator at high substrate concentrations, dominance of prey and coexistence steady state could be favored by the catabolic repression mechanism. It is concluded that the catabolic repression control favors dominance of the prey population and, under certain circumstances, coexistence of both prey and predator populations.     

Dynamics of a two-prey–one-predator system with predator switching regulated by a catabolic repression control-like mode

The strategy of alternative prey (switching), regulated by a catabolic repression control-like (CRCL) mode, in which the desirable prey acts as repressor on the predator's attack on the alternative prey, was studied in a two-prey–one-predator chemostat system. In this system, alternative prey has to survive predation and competition for nutrients from the desirable prey. Therefore, when the alternative prey has no competitive advantage for the common substrate over the desirable prey, its survival depends on the protection offered by the desirable prey via CRCL. In this case, CRCL allows the coexistence of both desirable and alternative prey and predator populations. However, when the alternative prey has the competitive advantage over the desirable prey, CRCL negatively affects both the state of survival of the desirable prey and the coexistence state.     

The effects of opportunistic and intentional predators on the herding behavior of prey

In this article, we study how predator behavior influences the aggregation of prey into herds. Game-theoretic models of herd formation are developed based on different survival probabilities of solitary prey and prey that join the herd and on the predator's preference of what type of prey to search for. For an intentional predator that will only pursue its preferred type of prey, a single herd with no solitaries cannot emerge unless the herd acts as a prey refuge. If neither prey choice provides a refuge, it is shown that an equilibrium always exists where there are both types of prey and the predator does not always search for the same type of prey (i.e., a mixed equilibrium exists). On the other hand, if the predator is opportunistic in that it sometimes shifts to pursue the type of prey that is observed first, there may be a single herd equilibrium that does not act as a prey refuge when there is a high level of opportunistic behavior. For low opportunistic levels, a mixed equilibrium is again the only outcome. The evolutionary stability of each equilibrium is tested to see if it predicts the eventual herding behavior of prey in its corresponding model. Our analysis confirms that both predator and prey preferences (for herd or solitary) have strong effects on why prey aggregate. In particular, in our models, only the opportunistic predator can maintain all prey in a single herd that is under predation risk.     

Local interactions between predators and prey call into question commonly used functional responses

Commonly used functional response models (Holling’s type I and type II models) assume that the encounter rate of a predator increases linearly with prey density, provided that the predator is searching for prey. In other other words, aN (a is the baseline encounter rate and N is prey density) describes the encounter rate. This study examined whether the models are adequate when predators and prey interact locally by using a spatially explicit individual based model because local interactions affect the spatial distribution of predators and prey, which also affects the encounter rate. Predators were assumed to possess a spatial perception range that influenced their foraging behavior (e.g., if a prey is in the perception range, the predator moves towards the prey). The effect of antipredator behavior by prey was also examined. The results suggest that prey and predator densities as well as handling time affect the baseline rate (i.e., parameter a) as opposed to the common assumption that the parameter is constant. The nature of model deviations depended on both the antipredator behavior and the predators’ perception range. Understanding these deviations is important as they qualitatively affect community dynamics.     

Consumptive and nonconsumptive effects of predators on metacommunities of competing prey

Although predators affect prey both via consumption and by changing prey migration behavior, the interplay between these two effects is rarely incorporated into spatial models of predator-prey dynamics and competition among prey. We develop a model where generalist predators have consumptive effects (i.e., altering the likelihood of local prey extinction) as well as nonconsumptive effects (altering the likelihood of colonization) on spatially separated prey populations (metapopulations). We then extend this model to explore the effects of predators on competition among prey. We find that generalist predators can promote persistence of prey metapopulations by promoting prey colonization, but predators can also hasten system-wide extinction by either increasing local extinction or reducing prey migration. By altering rates of prey migration, predators in one location can exert remote control over prey dynamics in another location via predator-mediated changes in prey flux. Thus, the effect of predators may extend well beyond the proportion of patches they visit. In the context of prey metacommunities, predator-mediated shifts in prey migration and mortality can shift the competition-colonization trade-off among competing prey, leading to changes in the prey community as well as changes in the susceptibility of prey species to habitat loss. Consequently, native prey communities may be susceptible to invasion not only by exotic prey species that experience reduced amounts of mortality from resident predators, but also by exotic prey species that exhibit strong dispersal in response to generalist native predators. Ultimately, our work suggests that the consumptive and nonconsumptive effects of generalist predators may have strong, yet potentially cryptic, effects on competing prey capable of mediating coexistence, fostering invasion, and interacting with anthropogenic habitat alteration.     

A predator-prey model with satiation and intraspecific competition

We present a new predator-prey model where, except for the prey growth, assumed to be logistic, we endeavor to give some behavioral justification to all elements of the predator-prey interaction. The functional response takes account of predator satiation and predator competition. It is supported by some experimental evidence. We distinguish two contributions to the numerical response: the positive part, proportional to the functional response, is the birth rate of predators; the negative part is the death rate due to hunger.Two outcomes are possible. If the prey are unable to grow fast enough to replace the amount killed by the predators, both species become extinct. In the opposite case, both populations stabilize at a constant population. At this equilibrium level, the prey are not abundant enough to satiate the predators.The predation rate that allows the highest predator population is one half of the ideal prey growth rate. A higher exploitation rate can allow higher populations only temporarily. Evolved predator behavior, reguges for the prey, or other mechanisms can explain this regulation.Two more population behaviors (cycles and predator extinction) can be obtained with a time-lag in one of the responses. This is shown in a separate paper.The model is structurally stable. It can thus withstand small environmental perturbations.     

How population dynamics shape the functional response in a one-predator-two-prey system

The type III functional response has historically been associated with switching predators; when there is a choice of prey the predator favors the more abundant prey type. Although this functional response has been found in experiments where both prey densities are manipulated, in real world studies the type II functional response is more commonly found. In modeling, the type III functional response is often used in systems where the second prey type is, implicitly, assumed to be constant. Here we define a functional response that takes into account both prey densities. This causes the functional response to show both type II and type III behavior, dependent on the interaction between the two prey densities. If we take into account population dynamics, we find a type II functional response in most cases, because predation regulates the relative prey densities. This explains why type III functional responses are found in experiments where both prey densities are manipulated, but type II functional responses occur when the feedback of population dynamics on the functional response is important. Furthermore, the results show that switching can have a stabilizing or destabilizing effect and can even lead to predator extinction.     

The community effects of phenotypic and genetic variation within a predator population

Natural populations are heterogeneous mixtures of individuals differing in physiology, morphology, and behavior. Despite the ubiquity of phenotypic variation within natural populations, its effects on the dynamics of ecological communities are not well understood. Here, we use a quantitative genetics framework to examine how phenotypic variation in a predator affects the outcome of apparent competition between its two prey species. Classical apparent competition theory predicts that prey have reciprocally negative effects on each other. The addition of phenotypic trait variation in predation can marginalize these negative effects, mediate coexistence, or generate positive indirect effects between the prey species. Long-term coexistence or facilitation, however, can be preceded by long transients of extinction risk whenever the heritability of phenotypic variation is low. Greater heritability can circumvent these ecological transients but also can generate oscillatory and chaotic dynamics. These dramatic changes in ecological outcomes, in the sign of indirect effects, and in stability suggest that studies which ignore intraspecific trait variation may reach fundamentally incorrect conclusions regarding ecological dynamics.     

The interaction of cannibalism and omnivory: consequences for community dynamics

Although cannibalism is ubiquitous in food webs and frequent in systems where a predator and its prey also share a common resource (intraguild predation, IGP), its impacts on species interactions and the dynamics and structure of communities are still poorly understood. In addition, the few existing studies on cannibalism have generally focused on cannibalism in the top-predator, ignoring that it is frequent at intermediate trophic levels. A set of structured models shows that cannibalism can completely alter the dynamics and structure of three-species IGP systems depending on the trophic position where cannibalism occurs. Contrary to the expectations of simple models, the IG predator can exploit the resources more efficiently when it is cannibalistic, enabling the predator to persist at lower resource densities than the IG prey. Cannibalism in the IG predator can also alter the effect of enrichment, preventing predator-mediated extinction of the IG prey at high productivities predicted by simple models. Cannibalism in the IG prey can reverse the effect of top-down cascades, leading to an increase in the resource with decreasing IG predator density. These predictions are consistent with current data. Overall, cannibalism promotes the coexistence of the IG predator and IG prey. These results indicate that including cannibalism in current models can overcome the discrepancy between theory and empirical data. Thus, we need to measure and account for cannibalistic interactions to reliably predict the structure and dynamics of communities.     

Behavioral games involving a clever prey avoiding a clever predator: An individual-based model of dusky dolphins and killer whales

Faced with an intermittent but potent threat, animals exhibit behavior that allows them to balance foraging needs and avoid predators and over time, these behaviors can become hard-wired adaptations with both species trying to maximize their own fitness. In systems where both predator and prey share similar sensory modalities and cognitive abilities, such as with marine mammals, the dynamic nature of predator-prey interactions is poorly understood. The costs and benefits of these anti-predator adaptations need to be evaluated and quantified based on the dynamic engagement of predator and prey. Many theoretic models have addressed the complexity of predator-prey relationships, but few have translated into testable mechanistic models. In this study, we developed a spatially-explicit, geo-referenced, individual-based model of a prototypical adult dusky dolphin off Kaikoura, New Zealand facing a more powerful, yet infrequent predator, the killer whale. We were interested in two primary objectives, (1) to capture the varying behavioral game between a clever prey and clever predator based on our current understanding of the Kaikoura system, (2) to compare evolutionary costs vs. benefits (foraging time and number of predator encounters) for an adult non-maternal dusky dolphin at various levels of killer whale-avoidance behaviors and no avoidance rules. We conducted Monte Carlo simulations to address model performance and parametric uncertainty. Mantel tests revealed an 88% correlation (426 × 426 distance matrix, km²) between observed field sightings of dusky dolphins with model generated sightings for non-maternal adult dusky dolphin groups. Simulation results indicated that dusky dolphins incur a 2.7% loss in feeding time by evolving the anti-predator behavior of moving to and from the feeding grounds. Further, each evolutionary strategy we explored resulted in dolphins incurring an additional loss of foraging time. At low killer whale densities (appearing less than once every 3 days), each evolutionary strategy simulated converged towards the evolutionary cost of foraging, that is, the loss in foraging time approached the 2.7% loss experienced by evolving near shore-offshore movement behavior. However, the highest level of killer whale presence resulted in 38% decreases in foraging time. The biological significance of these losses potentially incurred by a dusky dolphin is dependent on various factors from dolphin group foraging behavior and individual energy needs to dolphin prey availability and behavior.     

Connected fragmented habitats facilitate stable coexistence dynamics

In this paper we endeavor to test the controversial ideas that exist about the role of fragmentation in a conservation context. In line with earlier understanding, we find that habitat fragmentation alone results in a strong detrimental effect (especially for the predator population). Connecting the fragmented habitats facilitates predator survival and hence prey survival as compared to the unconnected fragmented case. Our main result is counterintuitive: in the presence of a high quality predator, connected fragmented habitats ensure a better chance for coexistence than does even the unfragmented case. We explain why a connected fragmented habitat might thus be beneficial for the stabilization of the system, and how connections between sub-habitats are able to protect prey population from over-exploitation. In the model, habitat fragmentation is separated from the effects of habitat destruction, in order to better understand how populations react to habitat transformation.     

Cost-Effective Suppression and Eradication of Invasive Predators

Abstract: Introduced predators can have pronounced effects on naïve prey species; thus, predator control is often essential for conservation of threatened native species. Complete eradication of the predator, although desirable, may be elusive in budget‐limited situations, whereas predator suppression is more feasible and may still achieve conservation goals. We used a stochastic predator–prey model based on a Lotka‐Volterra system to investigate the cost‐effectiveness of predator control to achieve prey conservation. We compared five control strategies: immediate eradication, removal of a constant number of predators (fixed‐number control), removal of a constant proportion of predators (fixed‐rate control), removal of predators that exceed a predetermined threshold (upper‐trigger harvest), and removal of predators whenever their population falls below a lower predetermined threshold (lower‐trigger harvest). We looked at the performance of these strategies when managers could always remove the full number of predators targeted by each strategy, subject to budget availability. Under this assumption immediate eradication reduced the threat to the prey population the most. We then examined the effect of reduced management success in meeting removal targets, assuming removal is more difficult at low predator densities. In this case there was a pronounced reduction in performance of the immediate eradication, fixed‐number, and lower‐trigger strategies. Although immediate eradication still yielded the highest expected minimum prey population size, upper‐trigger harvest yielded the lowest probability of prey extinction and the greatest return on investment (as measured by improvement in expected minimum population size per amount spent). Upper‐trigger harvest was relatively successful because it operated when predator density was highest, which is when predator removal targets can be more easily met and the effect of predators on the prey is most damaging. This suggests that controlling predators only when they are most abundant is the “best” strategy when financial resources are limited and eradication is unlikely.     

Effects of combining an intraguild predator with a cannibalistic intermediate predator on a species-level trophic cascade

A greater diversity of natural enemies can in some cases disrupt prey suppression, particularly when natural enemies engage in intraguild predation, where natural enemies compete with and prey upon each other. However, empirical studies have often demonstrated enhanced prey suppression despite intraguild predation. A recent theoretical study proposed the hypothesis that, when the intermediate predator is cannibalistic, intraguild predation can reduce cannibalism within the intermediate predator population, leading to little change in intermediate predator mortality and thus enhanced prey suppression. The goal of this study was to examine this hypothesis empirically. Two summer-long field enclosure experiments were conducted in cotton fields. We investigated the effects of adding an intraguild predator, Zelus renardii, on (1) the abundance of a cannibalistic intermediate predator, Geocoris pallens, (2) the abundance of a herbivore, Lygus hesperus, and (3) cotton plant performance. G. pallens adult abundance did not increase, even when food availability was high and natural enemies were absent, suggesting that density-dependent cannibalism imposes an upper limit on its densities. Furthermore, although Z. renardii is an intraguild predator of G. pallens, G. pallens long-term densities were unaffected by Z. renardii. In the presence of the intermediate predator, the addition of the intraguild predator Z. renardii enhanced suppression of L. hesperus, and there were suggestions that Z. renardii and G. pallens partitioned the L. hesperus population. Effects of herbivore suppression cascaded to the plant level, improving plant performance. In conclusion, we provide empirical support for the hypothesis that the addition of an intraguild predator may enhance prey suppression if the intermediate predator expresses density-dependent cannibalism. Intraguild predation and cannibalism co-occur in many communities; thus their joint effects may be broadly important in shaping predator effects on herbivores and plant performance.     

A comparison of models for predicting population persistence

We consider a range of models that may be used to predict the future persistence of populations, particularly those based on discrete-state Markov processes. While the mathematical theory of such processes is very well-developed, they may be difficult to work with when attempting to estimate parameters or expected times to extinction. Hence, we focus on diffusion and other approximations to these models, presenting new and recent developments in parameter estimation for density dependent processes, and the calculation of extinction times for processes subject to catastrophes. We illustrate these and other methods using data from simulated and real time series. We give particular attention to a procedure, due to Ross et al. [Ross, J.V., Taimre, T., Pollett, P.K. On parameter estimation in population models, Theor. Popul. Biol., in press], for estimating the parameters of the stochastic SIS logistic model, and demonstrate ways in which these parameters may be used to estimate expected extinction times. Although the stochastic SIS logistic model is strictly density dependent and allows only for birth and death events, it nonetheless may be used to predict extinction times with some accuracy even for populations that are only weakly density dependent, or that are subject to catastrophes.     

Transient dynamics and the destabilizing effects of prey heterogeneity

The presence of prey heterogeneity and weakly interacting prey species is frequently viewed as a stabilizer of predator-prey dynamics, countering the destabilizing effects of enrichment and reducing the amplitude of population cycles. However, prior model explorations have largely focused on long-term, dynamic attractors rather than transient dynamics. Recent theoretical work shows that the presence of prey that are defended from predation can have strongly divergent effects on dynamics depending on time scale: prey heterogeneity can counteract the destabilizing effects of enrichment on predator-prey dynamics at long time scales but strongly destabilize systems during transient phases by creating long periods of low predator/prey abundance and increasing extinction probability (an effect that is amplified with increasing enrichment). We tested these general predictions using a planktonic system composed of a zooplankton predator and multiple algal prey. We first parameterized a model of our system to generate predictions and tested these experimentally. Our results qualitatively supported several model predictions. During transient phases, presence of defended algal prey increased predator extinctions at low and high enrichment levels compared to systems with only a single edible prey. This destabilizing effect was moderated at higher dilution rates, as predicted by our model. When examining dynamics beyond initial oscillations, presence of the defended prey increased predator-prey temporal variability at high nutrient enrichment but had no effect at low nutrient levels. Our results highlight the importance of considering transient dynamics when assessing the role of stabilizing factors on the dynamics of food webs.     

An individual-based numerical model of medusa swimming behavior

Scyphomedusae are ubiquitous in marine and estuarine systems, where they frequently play an important role in trophodynamics. Many scyphomedusae are cruising predators, and feeding rates depend, in part, on swimming behavior. Yet, no model of medusa swimming exists. An individual-based correlated random walk (CRW) model of medusa swimming behavior in three dimensions was developed. The model was validated using a previously published dataset of the swimming of 19 Chrysaora quinquecirrha (Desor, 1848) medusae that were observed in the presence or absence of zooplankton prey in laboratory mesocosms in August–October 1998 (Matanoski et al. in Mar Biol 139:191–200, 2001). In the presence of prey, medusae swam at a constant moderate rate in looping trajectories. In the absence of prey, medusae alternated periods of slow and fast swimming in more linear trajectories. In the model, looping trajectories were reproduced only when changes in movement by a medusa were oriented to its current position and orientation; more linear trajectories were reproduced by movement oriented to a fixed framework. This suggests that medusae change from swimming behavior oriented to local stimuli (e.g., contact with prey) to long-range stimuli (e.g., gravity) depending on the availability of prey. The model reproduced cyclical changes in swimming speeds by medusae in the absence of prey by simulating switching in the behavior controlling the strength of swimming bell pulsations using a probabilistic function. Model results also demonstrated that medusae tend to swim toward the surface, avoid contact with the bottom, increase time spent in prey patches if they alter swimming patterns in the presence of prey, and exhibit significant periodicities in swimming patterns that are the result of deterministic behavior. The model will permit the simulation of the complex behavior of medusae.     

Behavioral resource depression and decaying perceived risk of predation in two species of coexisting gerbils

Summary Behavioral resource depression occurs when the behavior of prey individuals changes in response to the presence of a predator, resulting in a reduction of the encounter rate of the predator with its prey. Here I present experimental evidence on the response of two species of gerbils (Gerbillus allenbyi and G. pyramidum) to the presence of barn owls. I conducted the experiments in a large aviary. Both gerbils responded to the presence of barn owl predators by foraging in fewer resource patches (seed trays) and by quitting foraged resource patches at a higher resource harvest rate (giving-up density of resource; GUD). This reduced the amount of time gerbils were exposed to owl predation, and hence the encounter rate of owls with gerbils, i.e., behavioral resource depression. Thus, the presence of owls imposes a foraging cost on gerbils due to risk of predation, and also on the owls themselves due to resource depression. I then examined how resource depression relaxed over time following exposure to owls. In the days following an encounter with the predator, the reduction in foraging activity for both gerbil species eased. Increasing numbers of trays were foraged each day, and GUDs in seed trays declined. The two gerbils differed in their rate of recovery, with G. pyramidum returning to prepredator levels of foraging after 1 or 2 nights and G. allenbyi taking 5 nights or longer. Interspecific differences in recovery rates may be based on differences between the species in vulnerability to predation and/or ability to detect the presence of predators. The differences in recovery rates may be due to optimal memory windows or decay rates, where differences between species are based on risk of predation or on how perceived risk changes with time since a predator was last encountered. Finally, differences between or among competitors in recovery from resource depression may provide foraging opportunities in time for the species which recover most quickly and may have implications for species coexistence.     

Role of predator switching in an eco-epidemiological model with disease in the prey

In the present paper we propose a modification of a basic eco-epidemiological model by incorporating predator switching among susceptible and infected prey population. A local and global study of the basic model is performed around the disease-free boundary equilibrium and the interior equilibrium to estimate important parameter thresholds that control disease eradication and species coexistence. Next we analyze the switching model from the same perspective in order to elucidate the role of switching on disease dynamics. Numerical simulations are carried out to justify analytical results.     

Validity of the Prey‐Trap Hypothesis for Carnivore‐Ungulate Interactions at Wildlife‐Crossing Structures

Abstract: Wildlife‐exclusion fencing and wildlife‐crossing structures (e.g., underpasses and overpasses) are becoming increasingly common features of highway projects around the world. The prey‐trap hypothesis posits that predators exploit crossing structures to detect and capture prey. The hypothesis predicts that predation events occur closer to a highway after the construction of fences and crossing structures and that prey species’ use of crossings increases the probability that predators will attack prey. We examined interactions between ungulates and large carnivores at 28 wildlife crossing structures along 45 km of the Trans‐Canada Highway in Banff National Park, Alberta. We obtained long‐term records of locations where ungulates were killed (kill sites) before and after crossing structures were built. We also placed remote, motion‐triggered cameras at two crossing structures to monitor predator behavior following ungulate passage through the structure. The proximity of ungulate kill sites to the highway was similar before and after construction of fencing and crossing structures. We found only five kill sites near crossing structures after more than 32,000 visits over 13 years. We found no evidence that predator behavior at crossing structures is affected by prey movement. Our results suggest that interactions between large mammals and their prey at wildlife‐crossing structures in Banff National Park are not explained by the prey‐trap hypothesis.