A stochastic foraging model with predator training effects. II. Optimal diets

Standard optimal diet models require that a predator's behavior while searching for food does not change in response to experiences with individual prey. There is evidence for rapid and reversible changes in feeding behavior caused by as few as one or two prey encounters. When these “training effects” occur, a given prey type is more likely to be captured next if it was the last type with which the predator had experience. This is not compatible with the standard foraging model. I present a stochastic model which incorporates predator training effects, and three types of training are explored: training in the ability to detect prey (search image formation), training in the probability of succeeding in an attempted capture, and training in the time to pursue, capture, and eat prey. The main result is that all three types of training can result in optimal diets which do not obey the standard optimal diet rules. Conditions under which these rules will suffice are discussed.     

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.     

Optimal foraging and the traveling salesman

Optimal foraging models are examined that assume animals forage for discrete point resources on a plane and attempt to minimize their travel distance between resources. This problem is similar to the well-known traveling salesman problem: A salesman must choose the shortest path from his home office to all cities on his itinerary and back to his home office again. The traveling salesman problem is in a class of enigmatic problems, called NP-complete, which can be so difficult to solve that animals might be incapable of finding the best solution. Two major results of this analysis are: (1) The simple foraging strategy of always moving to the closest resource site does surprisingly well. More sophisticated strategies of “looking ahead” a small number of steps, choosing the shortest path, then taking a step, do worse if all the resource sites are visited, but do slightly better (less than 10%) if not all the resource sites are visited. (2) Short cyclical foraging routes resulted when resources were allowed to renew. This is suggested as an alternative explanation for “trap-lining” in animals that forage for discrete, widely separated resources.     

Optimal foraging, specialization, and a solution to Liem's paradox

Species that appear highly specialized on the basis of their phenotype (e.g., morphology, behavior, and physiology) also sometimes act as ecological generalists. This apparent paradox has been used to argue against the importance of competition as a diversifying evolutionary force. We provide an alternative explanation based on optimal foraging theory. Some resources are intrinsically easy to use and are widely preferred, while others require specialized phenotypic traits on the part of the consumer. This asymmetry allows optimally foraging consumers to evolve phenotypic specializations on nonpreferred resources without greatly compromising their ability to use preferred resources. The evolution of phenotypic specialization on nonpreferred resources can be driven by competition, but the specialists act as ecological generalists whenever their preferred resources are available. Our model identifies at least three different concepts of specialization that need to be distinguished, based on diet, prey utilization efficiencies, and phenotypic adaptations. The relationships among these concepts are complex and often counterintuitive. Specialists should often reject the very resources that they have evolved traits to use. The most extreme phenotypic specializations should occur in the absence of a trade-off between using preferred and nonpreferred resources. Our model may explain why extreme phenotypic-specializations evolve more often in fish communities than in terrestrial vertebrate communities and provides a mechanism whereby species can coexist in stable communities despite common preferences for some resources.     

Optimal intraguild foraging and population stability

This article explores effects of adaptive intraguild predation on species coexistence and community structure in three species' food webs. Two Lotka-Volterra models that assume a trade-off between competition and predation strength are considered in detail. The first model does not explicitly model resource dynamics and is considered with both nonadaptive and adaptive intraguild predation; in the latter case predators choose their diet in order to maximize their instantaneous population growth rate. The second model includes resource population dynamics. Effects of adaptive intraguild predation on the community structure along a gradient in environment productivity are analyzed and compared with some experimental results of protist food webs. Conditions under which intraguild predation is adaptive are discussed for both models. It is proved that if intraguild predators are perfect optimizers then intraguild predation should decrease with increasing environmental productivity and adaptive intraguild predation is a stabilizing factor provided environmental productivity is high enough.     

Adaptive foraging by predators as a cause of predator-prey cycles

Summary When foraging has costs, it is generally adaptive for foragers to adjust their foraging effort in response to changes in the population density of their food. If effort decreases in response to increased food density, this can result in a type-2 functional response; intake rate increases in a negatively accelerated manner as prey density increases. Unlike other mechanisms for type-2 responses, adaptive foraging usually involves a timelag, because foraging behaviours do not often change instantaneously with changes in food density or risks. This paper investigates predator-prey models in which there are explicit dynamics for the rate of adaptive change. Models appropriate to both behavioural and evolutionary change are considered. Both types of change can produce cycles under similar circumstances, but under some evolutionary models there is not sufficient genetic variability for evolutionary change to produce cycles. If there is sufficient variability, the remaining conditions required for cycles are surprisingly insensitive to the nature of the adaptive process. A predator population that approaches the optimum foraging strategy very slowly usually produces cycles under similar conditions as does a very rapidly adapting population.     

Habitat shape, metapopulation processes and the dynamics of multispecies predator-prey interactions

1. The effects of habitat shape, connectivity and the metapopulation processes of persistence and extinction are explored in a multispecies resource-consumer interaction. 2. The spatial dynamics of the indirect interaction between two prey species (Callosobruchus chinensis, Callosobruchus maculatus) and a predator (Anisopteromalus calandrae) are investigated and we show how the persistence time of this interaction is altered in different habitat configurations by the presence of an apparent competitor. 3. Habitat structure has differential effects on the dynamics of the resource-consumer interaction. Across all habitat types, the pairwise interaction between C. chinensis and A. calandrae is highly prone to extinction, while the interaction between C. maculatus and A. calandrae shows sustained long-term fluctuations. Contrary to expectations from theory, habitat shape has no significant effect on persistence time of the full, three-species resource-consumer assemblage. 4. A stochastic metapopulation model for a range of habitat configurations, incorporating different forms of regulatory processes, highlights that it is the spatially explicit population dynamics rather than the shape of the metapopulation that is the principal determinant of interaction persistence time.     

Plant population dynamics, pollinator foraging, and the selection of self-fertilization

Many flowering plants rely on pollinators, self-fertilization, or both for reproduction. We model the consequences of these features for plant population dynamics and mating system evolution. Our mating systems-based population dynamics model includes an Allee effect. This often leads to an extinction threshold, defined as a density below which population densities decrease. Reliance on generalist pollinators who primarily visit higher density plant species increases the extinction threshold, whereas autonomous modes of selfing decrease and can eliminate the threshold. Generalist pollinators visiting higher density plant species coupled with autonomous selfing may introduce an effect where populations decreasing in density below the extinction threshold may nonetheless persist through selfing. The extinction threshold and selfing at low density result in populations where individuals adopting a single reproductive strategy exhibit mating systems that depend on population density. The ecological and evolutionary analyses provide a mechanism where prior selfing evolves even though inbreeding depression is greater than one-half. Simultaneous consideration of ecological and evolutionary dynamics confirms unusual features (e.g., evolution into extinction or abrupt increases in population density) implicit in our separate consideration of ecological and evolutionary scenarios. Our analysis has consequences for understanding pollen limitation, reproductive assurance, and the evolution of mating systems.     

Optimal foraging in nonpatchy habitats. I. Bounded one-dimensional resource

We present a model of optimal foraging in habitats where the food has an arbitrary density distribution (continuous or not). The classical models of foraging strategies assume that the food is distributed in patches and that the animal divides its time between the two distinct behaviors of patch exploitation and interpatch travel. This assumption is hard to accept in instances where the food distribution is continuous in space, and where travel and feeding cannot be sharply distinguished. In this paper, the habitat is assumed to be one-dimensional and bounded, and the animal is assumed to have a limited foraging time available. The problem is treated mathematically in the context of the calculus of variations. The optimal solution is to divide the habitat in two subsets according to the food density. In the richer subset, the animal equalizes the density distribution; in the poorer subset, it travels as fast as possible.     

Balancing organization and flexibility in foraging dynamics

Proper pattern organization and reorganization are central problems facing many biological networks which thrive in fluctuating environments. However, in many cases the mechanisms that organize system activity oppose those that support behavioral flexibility. Thus, a balance between pattern organization and pattern flexibility is critically important for overall biological fitness. We study this balance in the foraging strategies of ant colonies exploiting food in dynamic environments. We present discrete time and space simulations of colony activity that uses a pheromone-based recruitment strategy biasing foraging towards a food source. After food relocation, the pheromone must evaporate sufficiently before foraging can shift colony attention to a new food source. The amount of food consumed within the dynamic environment depends non-monotonically on the pheromone evaporation time constant—with maximal consumption occurring at a time constant which balances trail formation and trail flexibility. A deterministic, ‘mean field’ model of pheromone and foragers on trails mimics our colony simulations. This reduced framework captures the essence of the flexibility-organization balance, and relates optimal pheromone evaporation to the timescale of the dynamic environment. We expect that the principles exposed in our study will generalize and motivate novel analysis across a broad range systems biology.     

Spatiotemporal dynamics of two generic predator-prey models

We present the analysis of two reaction-diffusion systems modelling predator-prey interactions, where the predator displays the Holling type II functional response, and in the absence of predators, the prey growth is logistic. The local analysis is based on the application of qualitative theory for ordinary differential equations and dynamical systems, while the global well-posedness depends on invariant sets and differential inequalities. The key result is an L (∞)-stability estimate, which depends on a polynomial growth condition for the kinetics. The existence of an a priori L ( p )-estimate, uniform in time, for all p≥1, implies L (∞)-uniform bounds, given any nonnegative L (∞)-initial data. The applicability of the L (∞)-estimate to general reaction-diffusion systems is discussed, and how the continuous results can be mimicked in the discrete case, leading to stability estimates for a Galerkin finite-element method with piecewise linear continuous basis functions. In order to verify the biological wave phenomena of solutions, numerical results are presented in two-space dimensions, which have interesting ecological implications as they demonstrate that solutions can be 'trapped' in an invariant region of phase space.     

Unique coevolutionary dynamics in a predator-prey system

In this paper, we study the predator-prey coevolutionary dynamics when a prey's defense and a predator's offense change in an adaptive manner, either by genetic evolution or phenotypic plasticity, or by behavioral choice. Results are: (1) The coevolutionary dynamics are more likely to be stable if the predator adapts faster than the prey. (2) The prey population size can be nearly constant but the predator population can show very large amplitude fluctuations. (3) Both populations may oscillate in antiphase. All of these are not observed when the handling time is short and the prey's density dependence is weak. (4) The population dynamics and the trait dynamics show resonance: the amplitude of the population fluctuation is the largest when the speed of adaptation is intermediate. These results may explain experimental studies with microorganisms.     

Global dynamics of a ratio-dependent predator-prey system

Recently, ratio-dependent predator-prey systems have been regarded by some researchers to be more appropriate for predator-prey interactions where predation involves serious searching processes. However, such models have set up a challenging issue regarding their dynamics near the origin since these models are not well-defined there. In this paper, the qualitative behavior of a class of ratio-dependent predator-prey system at the origin in the interior of the first quadrant is studied. It is shown that the origin is indeed a critical point of higher order. There can exist numerous kinds of topological structures in a neighborhood of the origin including the parabolic orbits, the elliptic orbits, the hyperbolic orbits, and any combination of them. These structures have important implications for the global behavior of the model. Global qualitative analysis of the model depending on all parameters is carried out, and conditions of existence and non-existence of limit cycles for the model are given. Computer simulations are presented to illustrate the conclusions.     

Phytoseiid life-histories,local predator-prey dynamics,and strategies for control of tetranychid mites

Numerous studies have been devoted to estimating the intrinsic rates of increase, r_m, of phytoseiid and tetranychid mites. Intrinsic rates of increase may be helpful for biological control purposes, but how exactly is still unclear. In this paper, we show how r_ms can be used to this end, by using a simple model for the local dynamics of predator and prey populations. The application of this model critically depends on what is meant by the term local. Here, we define it as a spatial scale at which predator and prey dynamics are strongly coupled.Furthermore, it is shown that the r_m of phytoseiid and tetranychid mites are correlated with mean and peak oviposition rates. Since peak oviposition rates are easy to determine, the regression equation provides a quick and simple way toestimate r_m. Subsequently, it is possible to calculate appropriate predator/prey ratios for biological control by using the model and the estimated r_m.     

Qualitative dynamics of three species predator-prey systems

Summary A qualitative analysis of some two and three species predator-prey models is achieved by application of the method of averaging in conjunction with a Lyapunov function constructed from the appropriate Volterra-Lotka model. We calculate the limit cycle solution for a two-species model with a Holling type functional response of the predator to its prey by means of a time-scaled transformation. The existence of a bifurcation of steady states for a community of three species is discussed and the periodic solution around one of the unstable steady states is calculated to the lowest approximation. Several comments are made regarding the behavior of these systems under changes of some control parameters.This work was supported in parts by USERDA, Contract number E(11-1)-3001.     

Evolution of exploitation ecosystems I. Predation,foraging ecology and population dynamics in herbivores

Summary The hypothesis of exploitation ecosystems was reanalysed using the model of Armstrong (1979) which simultaneously deals with population dynamics and evolution. The results indicate that the prediction of Oksanenet al. (1981) of strict predation limitation of herbivores in productive ecosystems does not hold for coevolved systems. Depending on the nature of herbivore-carnivore coevolution, herbivore biomass may level off at a threshold productivity value or increase monotonously with increasing primary productivity, though at a strongly reduced rate in productive ecosystems. Under both circumstances, increasing primary productivity is predicted to be accompanied by gradual replacement of genuine folivores by semi-granivores and true granivores. The dominating guild members are predicted to show some degree of resource-limitation, although only granivores are predicted to be chiefly resource-limited even in the most productive ecosystems. Data on arctic-to-temperate patterns in the community structure of herbivorous vertebrates conform to the implications of the analysis.     

Optimal foraging and fitness in Columbian ground squirrels

Summary Optimal diets were determined for each of 109 individual Columbian ground squirrels (Spermophilus columbianus) at two sites in northwestern Montana. Body mass, daily activity time, and vegetation consumption rates for individuals were measured in the field, along with the average water content of vegetation at each ground squirrel colony. I also measured stomach and caecal capacity and turnover rate of plant food through the digestive tract for individuals in the laboratory to construct regressions of digestive capacity as a function of individual body mass. Finally, I obtained literature estimates of average daily energy requirements as a function of body mass and digestible energy content of vegetation. These data were used to construct a linear programming diet model for each individual. The model for each individual was used to predict the proportion of two food types (monocots and dicots) that maximized daily energy intake, given time and digestive constraints on foraging. Individuals were classified as optimal or deviating, depending on whether their observed diet was significantly different from their predicted optimal diet. I determined the consequences of selecting an optimal diet for energy intake and fitness. As expected, daily energy intake calculated for deviators (based on their observed diet proportion) was less than that for optimal foragers. Deviating foragers do not appear to compensate for their lower calculated energy intake through other factors such as body size or physiological efficiency of processing food. Growth rate, yearly survivorship, and litter size increase with calculated energy intake, and optimal foragers have six times the reproductive success of deviators by age three. Optimal foraging behavior, therefore, appears to confer a considerable fitness advantage.     

Exploitation ecosystems in heterogeneous habitat complexes II: Impact of small-scale heterogeneity on predator-prey dynamics

Summary The model of exploitation ecosystems was re-analysed, assuming that habitat patches are so small that they form only parts of the home range of an individual predator. For habitat complexes where productive patches abound, the results suggested that predation will strongly spill over from productive patches, which set the tune for population dynamics within the whole landscape, to barren ones. This result conforms to the one obtained by T. Oksanen by assuming despotic habitat choice and essentially larger patch sizes. For habitat complexes heavily dominated by the barren habitat, spillover predation was predicted to be weak, as was the case in her large patch model. Unlike in her analysis, however, predation pressure was substantially reduced also within the productive habitat. In habitat complexes where patches are so small that they are exploited in a fine-grained manner, predation pressure was always found to be more intense in the barren habitat, contrary to the predictions of the original model of exploitation ecosystems. This analysis thus suggests that their model is applicable mainly on the landscape level. On the level of individual habitats, the applicability of their results depends on the habitat configuration (at its best for the prevailing habitat of the landscape and for moderate-sized patches of an essentially more productive habitat) and generally decreases with decreasing patch sizes.