Body mass relationships affect the age structure of predation across carnivore–ungulate systems: a review and synthesis

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Cannibalism in an age-structured predator-prey system

Recently, Kohlmeier and Ebenhöh showed that cannibalism can stabilize population cycles in a Lotka-Volterra type predator-prey model. Population cycles in their model are due to the interaction between logistic population growth of the prey and a hyperbolic functional response. In this paper, we consider a predator-prey system where cyclic population fluctuations are due to the age structure in the predator species. It is shown that cannibalism is also a stabilizing mechanism when population oscillations are due to this age structure. We conclude that in predator-prey systems, cannibalism by predators can stabilize both externally generated (consumer-resource) as well as internally generated (agestructure) fluctuations.     

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.     

A mechanistic model for interference and Allee effect in the predator population

We present the results of simulations in an individual-based model describing spatial movement and predator-prey interaction within a closed rectangular habitat. Movement of each individual animal is determined by local conditions only, so any collective behavior emerges owing to self-organization. It is shown that the pursuit of prey by predators entails predator interference, manifesting itself at the population level as the dependency of the trophic function (individual ration) on predator abundance. The stabilizing effect of predator interference on the dynamics of a predator-prey system is discussed. Inclusion of prey evasion induces apparent cooperation of predators and further alters the functional response, giving rise to a strong Allee effect, with extinction of the predator population upon dropping below critical numbers. Thus, we propose a simple mechanistic interpretation of important but still poorly understood behavioral phenomena that underlie the functioning of natural trophic systems.     

Mixed encounters, limited perception and optimal foraging

This article demonstrates how perceptual constraints of predators and the possibility that predators encounter prey both sequentially (one prey type at a time) and simultaneously (two or more prey types at a time) may influence the predator attack decisions, diet composition and functional response of a behavioural predator-prey system. Individuals of a predator species are assumed to forage optimally on two prey types and to have exact knowledge of prey population numbers (or densities) only in a neighbourhood of their actual spatial location. The system characteristics are inspected by means of a discrete-time, discrete-space, individual-based model of the one-predator-two-prey interaction. Model predictions are compared with ones that have been obtained by assuming only sequential encounters of predators with prey and/or omniscient predators aware of prey population densities in the whole environment. It is shown that the zero-one prey choice rule, optimal for sequential encounters and omniscient predators, shifts to abruptly changing partial preferences for both prey types in the case of omniscient predators faced with both types of prey encounters. The latter, in turn, become gradually changing partial preferences when predator omniscience is considered only local.     

Modeling changes in predator functional response to prey across spatial scales

Extrapolation of predator functional responses from laboratory observations to the field is often necessary to predict predation rates and predator-prey dynamics at spatial and temporal scales that are difficult to observe directly. We use a spatially explicit individual-based model to explore mechanisms behind changes in functional responses when the scale of observation is increased. Model parameters were estimated from a predator-prey system consisting of the predator Delphastus catalinae (Coleoptera: Coccinellidae) and Bemisia tabaci biotype B (Hemiptera: Aleyrodidae) on tomato plants. The model explicitly incorporates prey and predator distributions within single plants, the search behavior of predators within plants, and the functional response to prey at the smallest scale of interaction (within leaflets) observed in the laboratory. Validation revealed that the model is useful in scaling up from laboratory observations to predation in whole tomato plants of varying sizes. Comparing predicted predation at the leaflet scale, as observed in laboratory experiments, with predicted predation on whole plants revealed that the predator functional response switches from type II within leaflets to type III within whole plants. We found that the magnitude of predation rates and the type of functional response at the whole plant scale are modulated by (1) the degree of alignment between predator and prey distributions and (2) predator foraging behavior, particularly the effect of area-concentrated search within plants when prey population density is relatively low. The experimental and modeling techniques we present could be applied to other systems in which active predators prey upon sessile or slow-moving species.     

Simulation model of a predator-prey system comprised ofPhytoseiulus persimilis andTetranychus urticae. II. Model sensitivity to variations in the life history parameters of both species and to variations in the functional response and components of the numerical response

A detailed sensitivity analysis of a model of a predator-prey system comprised of Tetranychus urticae and Phytoseiulus persimilis was performed. The aim was to assess the relative importance of the life history parameters of both species, the functional response, and the components of the numerical response. In addition, the impact of the initial predator-prey ratio and the timing of predator introduction were tested. Results indicated that the most important factors in the system were relative rates of predator and prey development, the time of onset of predator oviposition, and the mode of the predator's oviposition curve. The total oviposition of the predator, the effect of prey consumption on predator oviposition, and predator searching were important under some conditions. Factors of moderate importance were the adult female predator's functional response, total prey oviposition, the mode of the prey's oviposition curve, abiotic mortality of the pre-adult predator, and the effect of prey consumption on predator development and on the immature predator's mortality. Factors of least importance were the variances of the predator's and prey's oviposition curves, the abiotic mortality of the adult predator, the abiotic mortality of the pre-adult and adult prey, the functional response of the nymphal and adult male predators, and the effect of prey consumption on adult predator mortality. The sex ratios had little effect, except when the proportion of female predators was very low. The initial predator-prey ratio and time of predator introduction had significant impacts on system behavior, though the patterns of impact were different.     

The nature of predation: prey dependent, ratio dependent or neither?

To describe a predator-prey relationship, it is necessary to specify the rate of prey consumption by an average predator. This functional response largely determines dynamic stability, responses to environmental influences and the nature of indirect effects in the food web containing the predator-prey pair. Nevertheless, measurements of functional responses in nature are quite rare. Recently, much work has been devoted to comparing two idealized forms of the functional response: prey dependent and ratio dependent. Although we agree that predator abundance often affects the consumption rate of individual predators, this phenomenon requires more attention. Disagreement remains over which of the two idealized responses serves as a better starting point in building models when data on predator dependence are absent.     

PREY ADAPTATION AS A CAUSE OF PREDATOR-PREY CYCLES

We analyze simple models of predator-prey systems in which there is adaptive change in a trait of the prey that determines the rate at which it is captured by searching predators. Two models of adaptive change are explored: (1) change within a single reproducing prey population that has genetic variation for vulnerability to capture by the predator; and (2) direct competition between two independently reproducing prey populations that differ in their vulnerability. When an individual predator's consumption increases at a decreasing rate with prey availability, prey adaptation via either of these mechanisms may produce sustained cycles in both species' population densities and in the prey's mean trait value. Sufficiently rapid adaptive change (e.g., behavioral adaptation or evolution of traits with a large additive genetic variance), or sufficiently low predator birth and death rates will produce sustained cycles or chaos, even when the predator-prey dynamics with fixed prey capture rates would have been stable. Adaptive dynamics can also stabilize a system that would exhibit limit cycles if traits were fixed at their equilibrium values. When evolution fails to stabilize inherently unstable population interactions, selection decreases the prey's escape ability, which further destabilizes population dynamics. When the predator has a linear functional response, evolution of prey vulnerability always promotes stability. The relevance of these results to observed predator-prey cycles is discussed.     

Sigmoid functional responses and population stability

Sigmoid functional responses are known to stabilize the differential Lotka-Volterra predator-prey model. However, we have found that they have no such effect in a comparable discrete generation model. The difficulty in stabilizing this model results from the one-generation time delay between changes in predator population density and the level of prey mortality. By contrast, sigmoid functional responses can stabilize the system if the predator population remains relatively constant, as is more likely of generalist predators.     

Energetic conditions promoting top-down control of prey by predators

Humans remove large amounts of biomass from natural ecosystems, and large bodied high trophic level animals are especially sensitive and vulnerable to exploitation. The effects of removing top-predators on food webs are often difficult to predict because of limited information on species interaction strengths. Here we used a three species predator-prey model to explore relationships between energetic properties of trophodynamic linkages and interaction strengths to provide heuristic rules that indicate observable energetic conditions that are most likely to lead to stable and strong top-down control of prey by predator species. We found that strong top-down interaction strengths resulted from low levels of energy flow from prey to predators. Strong interactions are more stable when they are a consequence of low per capita predation and when predators are subsidized by recruitment. Diet composition also affects stability, but the relationship depends on the form of the functional response. Our results imply that for generalist satiating predators, strong top-down control on prey is most likely for prey items that occupy a small portion of the diet and when density dependent recruitment is moderately high.     

Impacts of Foraging Facilitation Among Predators on Predator-prey Dynamics

Whereas impacts of predator interference on predator-prey dynamics have received considerable attention, the “inverse” process—foraging facilitation among predators—have not been explored yet. Here we show, via mathematical models, that impacts of foraging facilitation on predator-prey dynamics depend on the way this process is modeled. In particular, foraging facilitation destabilizes predator-prey dynamics when it affects the encounter rate between predators and prey. By contrast, it might have a stabilizing effect if the predator handling time of prey is affected. Foraging facilitation is an Allee effect mechanism among predators and we show that for many parameters, it gives rise to a demographic Allee effect or a critical predator density in need to be crossed for predators to persist. We explore also the effects of predator interference, to make the picture “symmetric” and complete. Predator interference is shown to stabilize predator-prey dynamics once its strength is not too high, and thus corroborates results of others. On the other hand, there is a wide range of model parameters for which predator interference gives rise to three co-occurring co-existence equilibria. Such a multi-equilibrial regime is rather robust as we observe it for all the functional response types we explore. This is a previously unreported phenomenon which we show cannot occur for the Beddington–DeAngelis functional response. An interesting topic for future research thus might be to seek for general conditions on predator functional responses that would produce multiple co-existence equilibria in a predator-prey model.     

The dynamics of two diffusively coupled predator-prey populations

I analyze the dynamics of predator and prey populations living in two patches. Within a patch the prey grow logistically and the predators have a Holling type II functional response. The two patches are coupled through predator migration. The system can be interpreted as a simple predator-prey metapopulation or as a spatially explicit predator-prey system. Asynchronous local dynamics are presumed by metapopulation theory. The main question I address is when synchronous and when asynchronous dynamics arise. Contrary to biological intuition, for very small migration rates the oscillations always synchronize. For intermediate migration rates the synchronous oscillations are unstable and I found periodic, quasi-periodic, and intermittently chaotic attractors with asynchronous dynamics. For large predator migration rates, attractors in the form of equilibria or limit cycles exist in which one of the patches contains no prey. The dynamical behavior of the system is described using bifurcation diagrams. The model shows that spatial predator-prey populations can be regulated through the interplay of local dynamics and migration.     

Should "handled" prey be considered? Some consequences for functional response, predator-prey dynamics and optimal foraging theory

Predator-prey models consider those prey that are free. They assume that once a prey is captured by a predator it leaves the system. A question arises whether in predator-prey population models the variable describing prey population shall consider only those prey which are free, or both free and handled prey together. In the latter case prey leave the system after they have been handled. The classical Holling type II functional response was derived with respect to free prey. In this article we derive a functional response with respect to prey density which considers also handled prey. This functional response depends on predator density, i.e., it accounts naturally for interference. We study consequences of this functional response for stability of a simple predator-prey model and for optimal foraging theory. We show that, qualitatively, the population dynamics are similar regardless of whether we consider only free or free and handled prey. However, the latter case may change predictions in some other cases. We document this for optimal foraging theory where the functional response which considers both free and handled prey leads to partial preferences which are not observed when only free prey are considered.     

Variation in foraging success among predators and its implications for population dynamics

The effects of the expected predation rate on population dynamics have been studied intensively, but little is known about the effects of predation rate variability (i.e., predator individuals having variable foraging success) on population dynamics. In this study, variation in foraging success among predators was quantified by observing the predation of the wolf spider Pardosa pseudoannulata on the cricket Gryllus bimaculatus in the laboratory. A population model was then developed, and the effect of foraging variability on predator–prey dynamics was examined by incorporating levels of variation comparable to those quantified in the experiment. The variability in the foraging success among spiders was greater than would be expected by chance (i.e., the random allocation of prey to predators). The foraging variation was density‐dependent; it became higher as the predator density increased. A population model that incorporates foraging variation shows that the variation influences population dynamics by affecting the numerical response of predators. In particular, the variation induces negative density‐dependent effects among predators and stabilizes predator–prey dynamics.     

The Effect of Refuge on Dermestes ater (Coleoptera: Dermestidae) Predation on Musca domestica (Diptera: Muscidae): Refuge for Prey or the Predator?

It is believed that habitat heterogeneity can change the extent of predator-prey interactions. Therefore, in this study we examined the effect of habitat heterogeneity (characterized here as an addition of refuge) on D. ater predation on M. domestica. Predation of D. ater on M. domestica larvae was carried out in experimental habitats with and without refuge, and examined at different prey densities. The number of prey eaten by beetles over 24 h of predator-prey interaction was recorded, and we investigated the strength of interaction between prey and predator in both experimental habitats by determining predator functional response. The mean number of prey eaten by beetles in the presence of refuge was significantly higher than in the absence of refuge. Females had greater weight gains than males. Logistic regression analyses revealed the type II functional response for both experimental habitats, even though data did not fit well into the random predator model. Results suggest that the addition of refuge in fact enhanced predation, as prey consumption increased in the presence of refuge. Predators kept in the presence of refuge also consumed more prey at high prey densities. Thus, we concluded that the addition of refuge was an important component mediating D. ater-M. domestica population interactions. Refuge actually acted as a refuge for predators from prey, since prey behaviors detrimental to predators were reduced in this case.     

Variation in the population demographics of <Emphasis Type="Italic">Scolopsis bilineatus</Emphasis> in response to predators

Predatory fishes play critical roles in the trophodynamics of coral reefs, and the biomass of predatory fish can be a strong determinant of the structure of reef fish assemblages. In this study, we used variations in predator biomass between management zones on the Great Barrier Reef to examine how predators influence the biomass, mortality, condition, and reproductive potential of a common prey species Scolopsis bilineatus (bridled monocle bream; Nemipteridae). Despite no numerical differences in biomass or mortality, we found significant differences in a variety of demographic traits for S. bilineatus between multiple areas of high and low predator biomass. The size-at-age, condition, and reproductive potential of fish were reduced in marine reserves where predator biomass was high. The response of fish to predators was highly sex dependent; females suffered the greatest reductions in condition and reproductive potential. This study supports the notion that predators can play important roles in regulating prey dynamics and emphasises the importance of understanding top-down control by predators when considering fisheries management techniques and conservation strategies.     

Food-web formation with recursive evolutionary branching

A reaction-diffusion model describing the evolutionary dynamics of a food-web was constructed. In this model, predator-prey relationships among organisms were determined by their position in a two-dimensional phenotype space defined by two traits: as prey and as predator. The mutation process is expressed with a diffusion process of biomass in the phenotype space. Numerical simulation of this model showed co-evolutionary dynamics of isolated phenotypic clusters, including various types of evolutionary branching, which were classified into branching as prey, branching as predators, and co-evolutionary branching of both prey and predators. A complex food-web develops with recursive evolutionary branching from a single phenotypic cluster. Biodiversity peaks at the medium strength of the predator-prey interaction, where the food-web is maintained at medium biomass by a balanced frequency between evolutionary branching and extinction.     

Stabilizing effects of spatial heterogeneity in predator-prey systems

A general predator is assumed to divide its hunting time between two sub-habitats with different prey species, spending a larger fraction (φ) of search time in an area as the relative prey abundance there increases. This always causes switching in the model, and changes a functional response from one that imposes a risk on the average prey that decreases with prey density in the direction of one that imposes an increasing risk. I discuss the conditions for a response that is density dependent, and those predatory attributes that make such a response more likely. Transit time between subhabitats always increases the density dependent effect, and is necessary for “system stability” in a Lotka-Volterra model with two prey species. Experiments have confirmed the model's basic assumption. General predators do not fit easily into classical predator-prey models of simple “closed” communities, and then the degree of density dependence of the functional response becomes a useful measure of a predator's short-term stabilizing effect on a prey species. The model demonstrates how spatial heterogeneity can be stabilizing.     

Modelling Holling type II functional response in deterministic and stochastic food chain models with mass conservation

The Rosenzweig-MacArthur predator-prey model is the building block in modeling food chain, food webs and ecosystems. There are a number of hidden assumptions involved in the derivation. For instance the prey population growth is logistic without predation but also with predation. In order to reveal these we will start with modelling a resource-predator-prey system in a closed spatially homogeneous environment. This allows us to keep track of the nutrient flow. With an instantaneous remineralisation of the products excreted in the environment by the populations and dead body mass there is conservation of mass. This allows for a model dimension reduction and yields the mass balance predator-prey model. When furthermore the searching and handling processes are much faster that the population changing rates, the trophic interaction is described by a Holling type II functional response, also assumed in the Rosenzweig-MacArthur model. The derivation uses an extended deterministic model with number of searching and handling predators as model variables where the ratio of the predator/prey body masses is used as a mechanistic time-scale parameter. This extended model is also used as a starting point for the derivation of a stochastic model. We will investigate the stochastic effects of random switching between searching and handling of the predators and predator dying. Prey growth by consumption of ambient resources is still deterministic and therefore the stochastic model is hybrid. The transient dynamics is studied by numerical Monte Carlo simulations and also the quasi-equilibrium distribution for the population quantities is calculated. The body mass of the prey individual is the scaling parameter in the stochastic model formulation. This allows for a quantification of the mean-field approximation criterion for the justification of replacement of the stochastic by a deterministic model.