A stochastic foraging model with predator training effects: I. Functional response,switching, and run lengths

Training effects are changes in a predator's behavior while it is searching for the next prey to eat which are caused by the predator's experience with the last prey encountered. A stochastic foraging model is formulated incorporating several specific types of training effects, and their impact on the functional response shape, switching, and mean prey run lengths is evaluated. The main result is that training effects such as search image formation can cause sigmoid functional responses and switching, and can result in runs of prey captures longer than expected in the absence of training.     

Optimal foraging and predator-prey dynamics, II.

In this paper we consider one-predator-two-prey population dynamics described by a control system. We study and compare conditions for permanence of the system for three types of predator feeding behaviors: (i) specialized feeding on the more profitable prey type, (ii) generalized feeding on both prey types, and (iii) optimal foraging behavior. We show that the region of parameter space leading to permanence for optimal foraging behavior is smaller than that for specialized behavior, but larger than that for generalized behavior. This suggests that optimal foraging behavior of predators may promote coexistence in predator-prey systems. We also study the effects of the above three feeding behaviors on apparent competition between the two prey types.     

Optimal foraging versus shared doom effects: interactive influence of mussel size and epibiosis on predator preference

In the western Baltic Sea, the highly competitive blue mussel Mytilus edulis tends to monopolize shallow water hard substrata. In many habitats, mussel dominance is mainly controlled by the generalist predator Carcinus maenas. These predator-prey interactions seem to be affected by mussel size (relative to crab size) and mussel epibionts.There is a clear relationship between prey size and predator size as suggested by the optimal foraging theory: Each crab size class preferentially preys on a certain mussel size class. Preferred prey size increases with crab size.Epibionts on Mytilus, however, influence this simple pattern of feeding preferences by crabs. When offered similarly sized mussels, crabs prefer Balanus-fouled mussels over clean mussels. There is, however, a hierarchy of factors: the influence of attractive epibiotic barnacles is weaker than the factor ‘mussel size’. Testing small mussels against large mussels, presence or absence of epibiotic barnacles does not significantly alter preferences caused by mussel size. Balanus enhanced crab predation on mussels in two ways: Additional food gain and, probably more important, improvement in handling of the prey. The latter effect is illustrated by the fact that artificial barnacle mimics increased crab predation on mussels to the same extent as do live barnacles.We conclude that crab predation preferences follows the optimal foraging model when prey belong to different size classes, whereas within size classes crab preferences is controlled by epibionts.     

A stochastic model of cellular senescence. II. Concordance with experimental data

This report presents the results of computer simulations of a mathematical model for cell proliferation and senescence. The mathematical model is based on the idea that the in vitro proliferative potential of normal cells is determined by the number of a certain class of self-replicating particles it possesses. In the simulation model these particles are lost by both stochastic and deterministic processes. When all self-replicating particles are lost a cell can divide up to seven times before it irreversibly ceases to replicate. The simulated in vitro lifespans of clones and subclones are shown to be in close agreement with experimental data. We also show that other properties of finitely proliferating cultures can be simulated by this model.     

A functional response model of a predator population foraging in a patchy habitat

1. Functional response models (e.g. Holling's disc equation) that do not take the spatial distributions of prey and predators into account are likely to produce biased estimates of predation rates. 2. To investigate the consequences of ignoring prey distribution and predator aggregation, a general analytical model of a predator population occupying a patchy environment with a single species of prey is developed. 3. The model includes the density and the spatial distribution of the prey population, the aggregative response of the predators and their mutual interference. 4. The model provides explicit solutions to a number of scenarios that can be independently combined: the prey has an even, random or clumped distribution, and the predators show a convex, sigmoid, linear or no aggregative response. 5. The model is parameterized with data from an acarine predator-prey system consisting of Phytoseiulus persimis and Tetranychus urticae inhabiting greenhouse cucumbers. 6. The model fits empirical data quite well and much better than if prey and predators were assumed to be evenly distributed among patches, or if the predators were distributed independently of the prey. 7. The analyses show that if the predators do not show an aggregative response it will always be an advantage to the prey to adopt a patchy distribution. On the other hand, if the predators are capable of responding to the distribution of prey, then it will be an advantage to the prey to be evenly distributed when its density is low and switch to a more patchy distribution when its density increases. The effect of mutual interference is negligible unless predator density is very high. 8. The model shows that prey patchiness and predator aggregation in combination can change the functional response at the population level from type II to type III, indicating that these factors may contribute to stabilization of predator-prey dynamics.     

Optimal foraging in an amphibious mammal. II. A study using principal component analysis

The organization of underwater foraging behaviour by mink (Mustela vison) was examined using multivariate analyses, thus enabling the role of fish density and the effect of cover in shaping the mink's hunting effort to be clarified. The effect of the mink's oxygen limitation was more strongly linked to the availability of cover for the prey than to the density of fish provided. Foraging economics accounted for approximately 51% of the variance in behaviour pattern whilst oxygen constraints took out a further 23%. Open waters are deemed unsuitable hunting grounds for this predator because mink lack the underwater endurance necessary for effective pursuit of detected prey.     

Nonconsumptive effects in a multiple predator system reduce the foraging efficiency of a keystone predator

Many studies have demonstrated that the nonconsumptive effect (NCE) of predators on prey traits can alter prey demographics in ways that are just as strong as the consumptive effect (CE) of predators. Less well studied, however, is how the CE and NCE of multiple predator species can interact to influence the combined effect of multiple predators on prey mortality. We examined the extent to which the NCE of one predator altered the CE of another predator on a shared prey and evaluated whether we can better predict the combined impact of multiple predators on prey when accounting for this influence. We conducted a set of experiments with larval dragonflies, adult newts (a known keystone predator), and their tadpole prey. We quantified the CE and NCE of each predator, the extent to which NCEs from one predator alters the CE of the second predator, and the combined effect of both predators on prey mortality. We then compared the combined effect of both predators on prey mortality to four predictive models. Dragonflies caused more tadpoles to hide under leaf litter (a NCE), where newts spend less time foraging, which reduced the foraging success (CE) of newts. Newts altered tadpole behavior but not in a way that altered the foraging success of dragonflies. Our study suggests that we can better predict the combined effect of multiple predators on prey when we incorporate the influence of interactions between the CE and NCE of multiple predators into a predictive model. In our case, the threat of predation to prey by one predator reduced the foraging efficiency of a keystone predator. Consequently, the ability of a predator to fill a keystone role could be compromised by the presence of other predators.     

Predation-risk effects of predator identity on the foraging behaviors of frugivorous bats

Predators directly and indirectly affect the density and the behavior of prey. These effects may potentially cascade down to lower trophic levels. In this study, we tested the effects of predator calls (playbacks of bird vocalizations: Tyto alba, Speotyto cunicularia, and Vanellus chilensis), predator visual stimuli (stuffed birds) and interactions of visual and auditory cues, on the behavior of frugivore phyllostomid bats in the field. In addition, we tested if the effects of predation risk cascade down to other trophic levels by measuring rates of seed dispersal of the tree Muntingia calabura. Using video recording, we found that bats significantly decreased the foraging frequency on trees when a visual cue of T. alba was present. However, no stimuli of potential predatory birds, including vocalization of T. alba, affected bat foraging frequency. There was a change in bat behavior during 7 min, but then their frequency of activity gradually increased. Consequently, the presence of T. alba decreased by up to ten times the rate of seed removal. These results indicate that risk sensitivity of frugivorous phyllostomid bats depends on predator identity and presence. Among the predators used in this study, only T. alba is an effective bat predator in the Neotropics. Sound stimuli of T. alba seem not to be a cue of predation risk, possibly because their vocalizations are used only for intraspecific communication. This study emphasizes the importance of evaluating different predator stimuli on the behavior of vertebrates, as well as the effects of these stimuli on trait-mediated trophic cascades.     

A predator prey model with age structure

A general predator-prey model is considered in which the predator population is assumed to have an age structure which significantly affects its fecundity. The model equations are derived from the general McKendrick equations for age structured populations. The existence, stability and destabilization of equilibria are studied as they depend on the prey's natural carrying capacity and the maturation periodm of the predator. The main result of the paper is that for a broad class of maturation functions positive equilibria are either unstable for smallm or are destabilized asm decreases to zero. This is in contrast to the usual rule of thumb that increasing (not decreasing) delays in growth rate responses cause instabilities.Research supported by National Science Foundation Grant No. MCS-7901307-01Research supported by National Scholarship for Study Abroad No. EDN/S-59/80 from the government of India     

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.     

A stochastic model for in vitro ageing II. A theory of marginotomy

A model for variation in the lifespan of mass cultures and clones of human diploid fibroblasts is analyzed. The model is based on Olovnikov's theory of marginotomy and the following four assumptions: The time between successive divisions of a given cell may be split into a portion of fixed length and a portion of random length; cells divide or lose the ability to divide independently of one another; there is a fixed probability that a cell may lose one of its important parts during DNA synthesis; there is a small but fixed probability that a cell may lose all its important parts and hence the ability to replicate further during DNA synthesis. Samples taken by Monte Carlo means at successive stages in the development of a hypothetical population are compared with clonal survival data derived experimentally. The fit between theoretical and experimental findings is within the range of variation inherent in the experimental method. Applications of the theory and suggestions for further experiments are given.     

The effect of predation pressure and predator adaptive foraging on the relative importance of consumptive and non‐consumptive predator net effects in a freshwater model system

An important challenge in community ecology is identifying the functional characteristics capable of predicting the nature and strength of predator effects on food webs. We developed an individual‐based model, based on a shallow lake model system, to evaluate the total, consumptive, and non‐consumptive indirect effect that predators have on basal resources when the predators differ in their foraging types (active adaptive foraging or sedentary foraging). Overall, both predator types caused similar total indirect effects on lower trophic levels. However, the nature net effects of predators diverged between predator foraging types. Active predators caused larger non‐consumptive effects, relative to the total indirect effect, irrespective of predation pressure levels. On the other hand, sedentary predators caused larger non‐consumptive effects for lower predation pressure levels, but consumptive effects became more important as predation pressure increased. Our simulations showed that the reliance on a particular mechanism driving consumer–resource interactions is altered by predator foraging behavior and highlight the importance of both prey and predator foraging behaviors to predict the causes and consequences of cascading effects observed in food webs.     

A one-compartment model with stochastic parameter

We consider a one-compartment system with stochastic transfer rate characterized either by Gaussian or by two-level jump process and study the time evolution of the (statistical) moments of the (random) amount of the substance present in the system. The effect of the coloured as well as of the white noise is investigated and it is found that the presence of stochasticity in the transfer rate parameter increases the relaxation time of the system. Finally, we obtain the conditions for the stability of the system in the moment sense.     

On the time-dependent reversible stochastic compartmental model—II. A class ofn-compartment systems

This paper discusses the solution of a generaln-compartment system with time dependent transition probabilities utilizing the technique described by Cardenas and Matis (1975) (hereafter abbreviated (CM)). In addition, the cumulant generating function is derived for a special class of reversiblen-compartment systems where the time-dependent intensity coefficients corresponding to the migration and death rates are some multiple of each other. The immigration rates can be any integrable function of time. The moments are also obtained and the solution to the two-compartment system is presented explicitly. The solution is illustrated with a linear and a periodic function which forms have been widely reported in the literature.     

A two-state recurrent stochastic model with time-dependent transition rates.

The two-state recurrent stochastic model with time-independent transition rates is generalized to a model with time-dependent transition rates. The rates can be any general function of external time, that is, any general function of the calendar time in which the process unfolds. Formulas for the state transition probabilities, the proportion of individuals in a particular state at time t, the distribution function, and the expectation of the number of individuals in a particular state at time t are derived.     

Optimal foraging: A case for random movement

Summary The bumblebee, Bombus flavifrons, forages randomly with respect to direction on Polemonium foliosissimum. This foraging pattern is as predicted for a system where there is a low probability of revisiting any given flower upon returning to a patch. This low revisitation probability is a function of the floral resource arrangement. It is further shown that B. flavifrons is using the resource distribution to direct its movements. A large percentage of all movements are to nearest neighbors with maximal foraging efficiency gained through minimization of flight distances.     

Bayesian birds: A simple example of Oaten's stochastic model of optimal foraging

Allan Oaten (1977, Theor. Pop. Biol.12, 263–285) has argued that stochastic models of optimal foraging may produce results qualitatively different from those of the analogous deterministic models. Oaten's model is very general and difficult to understand intuitively. In this paper a simple, tractable model is considered in which the predator searches each patch systematically (without going over the same area twice) until he exhausts the patch or decides the patch is not very good. It is assumed that each patch contains a fixed number of bits, each of which may contain a prey. The number of prey per patch is assumed to have a binomial distribution with n equal to the number of bits and p being a random variable having a beta distribution. After searching each bit the predator decides whether to leave the patch or not according to how many prey it has found. In this paper the best strategy is determined and the long-term rate of feeding is compared with that of the naive animal that searches each patch completely. The advantage of being a Bayesian is determined for a variety of environmental conditions.