Stochastic Predation Research Articles

Stochastic predation exposes prey to predator pits and local extinction

Understanding how predators affect prey populations is a fundamental goal for ecologists and wildlife managers. A well‐known example of regulation by predators is the predator pit, where two alternative stable states exist and prey can be held at a low density equilibrium by predation if they are unable to pass the threshold needed to attain a high density equilibrium. While empirical evidence for predator pits exists, deterministic models of predator–prey dynamics with realistic parameters suggest they should not occur in these systems. Because stochasticity can fundamentally change the dynamics of deterministic models, we investigated if incorporating stochasticity in predation rates would change the dynamics of deterministic models and allow predator pits to emerge. Based on realistic parameters from an elk–wolf system, we found predator pits were predicted only when stochasticity was included in the model. Predator pits emerged in systems with highly stochastic predation and high carrying capacities, but as carrying capacity decreased, low density equilibria with a high likelihood of extinction became more prevalent. We found that incorporating stochasticity is essential to fully understand alternative stable states in ecological systems, and due to the interaction between top–down and bottom–up effects on prey populations, habitat management and predator control could help prey to be resilient to predation stochasticity.

Dynamics of a Stochastic Intraguild Predation Model

Intraguild predation (IGP) is a widespread ecological phenomenon which occurs when one predator species attacks another predator species with which it competes for a shared prey species. The objective of this paper is to study the dynamical properties of a stochastic intraguild predation model. We analyze stochastic persistence and extinction of the stochastic IGP model containing five cases and establish the sufficient criteria for global asymptotic stability of the positive solutions. This study shows that it is possible for the coexistence of three species under the influence of environmental noise, and that the noise may have a positive effect for IGP species. A stationary distribution of the stochastic IGP model is established and it has the ergodic property, suggesting that the time average of population size with the development of time is equal to the stationary distribution in space. Finally, we show that our results may be extended to two well-known biological systems: food chains and exploitative competition.

Global gradients of avian longevity support the classic evolutionary theory of ageing

Senescence, the process of physiological deterioration associated with growing old, is a shared characteristic of a wide range of animals. Yet, lifespan varies dramatically among species. To explain this variation, the evolutionary theory of ageing has been proposed more than 50 yr ago. Although the theory has been tested experimentally and through comparative analyses, there remains debate whether its fundamental prediction is empirically supported. Here, we use a comprehensive database on avian life history traits to test the evolutionary theory of ageing at a global scale. We show that pronounced geographical gradients of maximum longevity exist, that they are predicted by measures of predator diversity and only partly depend on correlated life‐history traits. The results are consistent with species‐level analyses and can be replicated across bio‐geographical regions. Our analyses suggest that stochastic predation is an important driver of the evolution of lifespan, at least in birds.

Incorporating preferential prey selection and stochastic predation into population viability analysis for rare prey species

There is increasing evidence that predation can cause the decline and extinction of small populations of prey, and that stochastic predation resulting from variation in prey selection by individual predators can have significant consequences for population persistence. Modelling approaches that ignore variation in prey selection exhibited by individual predators may inaccurately predict the effect of predation on prey populations, especially over longer time scales. We assess the impacts of variation in prey selection by building PVA models for endangered huemul deer Hippocamelus bisulcus that sequentially include and exclude observed stochasticity in predation among individual pumas Puma concolor. Our results indicated that huemul are at risk of extinction in all scenarios modelled, although the immediacy of this risk differed based on model structure and time period considered. Specifically, modelling predation as a random effect based on an interrupted Poisson process rather than as a directional and continuous change in survival rates, resulted in significantly longer estimates of time to extinction independent of the assumed intensity of predation. Our results highlight the importance of determining whether specialist predators are driving predation on rare prey, and when they are, incorporating said stochastic predation when attempting to predict persistence probabilities of rare prey using PVA models. Since results of PVA models are commonly used to develop conservation strategies, we advocate for the inclusion of stochastic predation in future PVA models where warranted to more accurately inform strategies for the conservation of rare prey and their predators.

Size-mediated non-trophic interactions and stochastic predation drive assembly and dynamics in a seabird community

Theoretical and empirical evidence suggests that body size is a major life-history trait impacting on the structure and functioning of complex food webs. However, long-term analyses of size-dependent interactions within simpler network modules, for instance, competitive guilds, are scant. Here, we model the assembly dynamics of the largest breeding seabird community in the Mediterranean basin during the last 30 years. This unique data set allowed us to test, through a "natural experiment," whether body size drove the assembly and dynamics of an ecological guild growing from very low numbers after habitat protection. Although environmental stochasticity accounted for most of community variability, the population variance explained by interspecific interactions, albeit small, decreased sharply with increasing body size. Since we found a demographic gradient along a body size continuum, in which population density and stability increase with increasing body size, the numerical effects of interspecific interactions were proportionally higher on smaller species than on larger ones. Moreover, we found that the per capita interaction coefficients were larger the higher the size ratio among competing species, but only for the set of interactions in which the species exerting the effect was greater. This provides empirical evidence for long-term asymmetric interspecific competition, which ultimately prompted the local extinction of two small species during the study period. During the assembly process stochastic predation by generalist carnivores further triggered community reorganizations and global decays in population synchrony, which disrupted the pattern of interspecific interactions. These results suggest that the major patterns detected in complex food webs can hold as well for simpler sub-modules of these networks involving non-trophic interactions, and highlight the shifting ecological processes impacting on assembling vs. asymptotic communities.

Restoring a keystone predator may endanger a prey species in a human‐altered ecosystem: the return of the snow leopard to Sagarmatha National Park

AbstractTwenty‐five years ago, the snow leopardUncia uncia, an endangered large cat, was eliminated from what is now Sagarmatha National Park (SNP). Heavy hunting pressure depleted that area of most medium–large mammals, before it became a park. After three decades of protection, the cessation of hunting and the recovery of wild ungulate populations, snow leopards have recently returned (four individuals). We have documented the effects of the return of the snow leopard on the population of its main wild prey, the Himalayan tahrHemitragus jemlahicus, a ‘near‐threatened’ caprin. Signs of snow leopard presence were recorded and scats were collected along a fixed trail (130 km) to assess the presence and food habits of the snow leopard in the Park, from 2004 to 2006. Himalayan tahr, the staple of the diet, had a relative occurrence of 48% in summer and 37% in autumn, compared with the next most frequent prey, musk deerMoschus chrysogaster(summer: 20%; autumn: 15%) and cattle (summer: 15%; autumn: 27%). In early summer, the birth rate of tahr (young‐to‐female ratio: 0.8–0.9) was high. The decrease of this ratio to 0.1–0.2 in autumn implied that summer predation concentrated on young tahr, eventually altering the population by removing the kid cohort. Small populations of wildCaprinae, for example the Himalayan tahr population in SNP, are sensitive to stochastic predation events and may be led to almost local extinction. If predation on livestock keeps growing, together with the decrease of Himalayan tahr, retaliatory killing of snow leopards by local people may be expected, and the snow leopard could again be at risk of local extinction. Restoration of biodiversity through the return of a large predator has to be monitored carefully, especially in areas affected by humans, where the lack of important environmental components, for example key prey species, may make the return of a predator a challenging event.

Size‐spectra dynamics from stochastic predation and growth of individuals

In aquatic ecosystems, where organisms typically feed and grow by eating smaller individuals, a characteristic size spectrum emerges, such that large organisms are much more rare than small ones. Here, a stochastic individual-based model for the dynamics of size spectra is described, based on birth, growth, and death of individuals, using simple assumptions about feeding behavior. It is shown that the deterministic limit derived from the stochastic process is a partial differential equation previously used to describe the dynamics of size spectra. The equation has two classes of dynamics in the long term. The first is a steady state. A derivation under simple mass-balance assumptions shows that, at steady state, the linear size spectrum relating log abundance to log mass has a slope of approximately -1, similar to that often observed in natural size spectra. The second class of dynamics, not previously described, is a traveling-wave solution in which waves move along the size spectrum from small to large body size. Traveling waves become more likely when predators prefer prey much smaller than themselves and when they are specialized in the range of prey body sizes consumed. Wavelength depends on the size of prey relative to the size of predator, and wave speed depends on how fast mass moves through the spectrum.

Quantifying stochastic and deterministic threats to island seabirds: last endemic prions face extinction from falcon peregrinations

AbstractUnderstanding how anthropically induced interacting factors may compromise the viability of a particular species or population necessitates expressing them in terms of quantitative effects on population dynamics. The use of mechanistic models to assess these effects is especially helpful to management plans when the causes of species decline are multi‐factorial and potentially interacting. Here, we took the opportunity of observed predation by a vagrant falcon on a rare and endemic seabird to develop a population dynamics model encompassing multiple deterministic and stochastic threats. The Macgillivray's prion Pachyptila macgillivrayi, with a world breeding population of c. 540 individuals confined to one rat‐free islet off Saint‐Paul Island (Southern Indian Ocean), faces high extinction risk from vagrant falcon predation. Extinction is predicted to occur within 200 years if one falcon preys on prions every 5 years, with predation occurring either on breeders only or also on non‐breeders. The minimum initial prion population size ensuring a low extinction risk increased linearly with the annual probability of predator occurrence. Therefore, increasing the initial population size is a useful management option to help the prion face stochastic predation. Recent rat eradication on Saint‐Paul Island helps the prion to face this threat as it released the carrying capacity of the colony, but the earlier population size might never be recovered if falcons carry on preying on prions frequently. This rare burrowing petrel provides a remarkable case study of an endemic insular species threatened with predation by alien mammals, which reduced historical population size dramatically, and by genuine vagrants as catastrophic events that reduce population growth and increase its temporal variance, and might cause the extinction.

Stochastic predation events and population persistence in bighorn sheep.

Many studies have reported temporal changes in the relative importance of density-dependence and environmental stochasticity in affecting population growth rates, but they typically assume that the predominant factor limiting growth remains constant over long periods of time. Stochastic switches in limiting factors that persist for multiple time-steps have received little attention, but most wild populations may periodically experience such switches. Here, we consider the dynamics of three populations of individually marked bighorn sheep (Ovis canadensis) monitored for 24-28 years. Each population experienced one or two distinct cougar (Puma concolor) predation events leading to population declines. The onset and duration of predation events were stochastic and consistent with predation by specialist individuals. A realistic Markov chain model confirms that predation by specialist cougars can cause extinction of isolated populations. We suggest that such processes may be common. In such cases, predator-prey equilibria may only occur at large geographical and temporal scales, and are unlikely with increasing habitat fragmentation.

Reinforcement learning for a stochastic automaton modelling predation in stationary model-mimic environments

In this paper we propose a mathematical learning model for the feeding behaviour of a specialist predator operating in a random environment occupied by two types of prey, palatable mimics and unpalatable models, and a generalist predator with additional alternative prey at its disposal. A well known linear reinforcement learning algorithm and its special cases are considered for updating the probabilities of the two actions, eat prey or ignore prey. Each action elicits a probabilistic response from the environment that can be favorable or unfavourable. To assess the performance of the predator a payoff function is constructed that captures the energetic benefit from consuming acceptable prey, the energetic cost from consuming unacceptable prey, and lost benefit from ignoring acceptable prey. Conditions for an improving predator payoff are also explicitly formulated.

Stationary probability distributions of some lotka-volterra types of stochastic predation systems

This paper provides exact solutions to the stationary probability distributions in some stochastic predation systems. These are derived by solving the Fokker-Planck equations for: (i) a generalized stochastic Lotka-Volterra predator-prey system, and (ii) a generalised stochastic Lotka-Volterra food chain. In all these systems the growth dynamics of all levels of species are subject to stochastic shocks. Since stationary probability distributions provide the most comprehensive characterization of a stochastic system in a steady state, system stability can be analysed accordingly

A stochastic predation model: Application to largemouth bass observations

Predation by largemouth bass ( Micropterus salmoides L.) is modeled as a Poisson renewal process, except for a modification to include diurnal variations in the likelihood of predation. The model simulates the distribution of numbers of prey in largemouth bass stomachs and the ‘apparent’ distribution of prey intercapture intervals for bass captured in 1980 and is validated against 1982 data. The apparent distribution of prey intercapture times, based on measurements of the length of time decomposing prey had been in largemouth bass stomachs, utilizes bass that have two or more prey in their stomach. Because most bass have zero or one prey in their stomach, this calculation errs seriously in biasing the predicted distribution toward short intercapture times. The simulation model, by allowing sampling regimes that are impractical in the field, estimates the true prey intercapture time distribution.