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.     

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.     

Temperature alters food web body-size structure

The increased temperature associated with climate change may have important effects on body size and predator–prey interactions. The consequences of these effects for food web structure are unclear because the relationships between temperature and aspects of food web structure such as predator–prey body-size relationships are unknown. Here, we use the largest reported dataset for marine predator–prey interactions to assess how temperature affects predator–prey body-size relationships among different habitats ranging from the tropics to the poles. We found that prey size selection depends on predator body size, temperature and the interaction between the two. Our results indicate that (i) predator–prey body-size ratios decrease with predator size at below-average temperatures and increase with predator size at above-average temperatures, and (ii) that the effect of temperature on predator–prey body-size structure will be stronger at small and large body sizes and relatively weak at intermediate sizes. This systematic interaction may help to simplify forecasting the potentially complex consequences of warming on interaction strengths and food web stability.     

The influence of the type 3 (sigmoid) functional response upon the stability of predator-prey difference models

Sigmoid functional responses are found to exert a stabilizing influence upon a discrete-generation predator-prey model in a way analogous to that found in continuous predator-prey models. The precise effect depends upon the degree to which a predator's feeding history influences its reproductive success. The time delay intrinsic in difference equation models imposes constraints not found in differential models, however, it is shown that in an otherwise unstable model the inclusion of a sigmoid functional response can result in local stability. With the addition of prey self-regulation the stabilizing influence of the functional response acts in concert with self-regulation, as it does in continuous models. These results show that the effect of the sigmoid response upon stability is not dependent upon the assumption of continuity, and reinforces the view that sigmoid responses could be an important factor stabilizing natural communities.     

Prey and predator density‐dependent interactions under different water volumes

Predation is a critical ecological process that directly and indirectly mediates population stabilities, as well as ecosystem structure and function. The strength of interactions between predators and prey may be mediated by multiple density dependences concerning numbers of predators and prey. In temporary wetland ecosystems in particular, fluctuating water volumes may alter predation rates through differing search space and prey encounter rates. Using a functional response approach, we examined the influence of predator and prey densities on interaction strengths of the temporary pond specialist copepod Lovenula raynerae preying on cladoceran prey, Daphnia pulex, under contrasting water volumes. Further, using a population dynamic modeling approach, we quantified multiple predator effects across differences in prey density and water volume. Predators exhibited type II functional responses under both water volumes, with significant antagonistic multiple predator effects (i.e., antagonisms) exhibited overall. The strengths of antagonistic interactions were, however, enhanced under reduced water volumes and at intermediate prey densities. These findings indicate important biotic and abiotic contexts that mediate predator–prey dynamics, whereby multiple predator effects are contingent on both prey density and search area characteristics. In particular, reduced search areas (i.e., water volumes) under intermediate prey densities could enhance antagonisms by heightening predator–predator interference effects.     

Can size distributions of European lake fish communities be predicted by trophic positions of their fish species?

An organism''s body size plays an important role in ecological interactions such as predator–prey relationships. As predators are typically larger than their prey, this often leads to a strong positive relationship between body size and trophic position in aquatic ecosystems. The distribution of body sizes in a community can thus be an indicator of the strengths of predator–prey interactions. The aim of this study was to gain more insight into the relationship between fish body size distribution and trophic position in a wide range of European lakes. We used quantile regression to examine the relationship between fish species'' trophic position and their log‐transformed maximum body mass for 48 fish species found in 235 European lakes. Subsequently, we examined whether the slopes of the continuous community size distributions, estimated by maximum likelihood, were predicted by trophic position, predator–prey mass ratio (PPMR), or abundance (number per unit effort) of fish communities in these lakes. We found a positive linear relationship between species'' maximum body mass and average trophic position in fishes only for the 75% quantile, contrasting our expectation that species'' trophic position systematically increases with maximum body mass for fish species in European lakes. Consequently, the size spectrum slope was not related to the average community trophic position, but there were negative effects of community PPMR and total fish abundance on the size spectrum slope. We conclude that predator–prey interactions likely do not contribute strongly to shaping community size distributions in these lakes.     

Identifying Predator–Prey Processes from Time-Series

The functional response is a key element in predator–prey models as well as in food chains and food webs. Classical models consider it as a function of prey abundance only. However, many mechanisms can lead to predator dependence, and there is increasing evidence for the importance of this dependence. Identification of the mathematical form of the functional response from real data is therefore a challenging task. In this paper we apply model-fitting to test if typical ecological predator–prey time series data, which contain both observation error and process error, can give some information about the form of the functional response. Working with artificial data (for which the functional response is known) we will show that with moderate noise levels, identification of the model that generated the data is possible. However, the noise levels prevailing in real ecological time-series can give rise to wrong identifications. We will also discuss the quality of parameter estimation by fitting differential equations to such time-series.     

Predator–prey relationships in a Mediterranean vertebrate system: Bonelli’s eagles,rabbits and partridges

How predators impact on prey population dynamics is still an unsolved issue for most wild predator–prey communities. When considering vertebrates, important concerns constrain a comprehensive understanding of the functioning of predator–prey relationships worldwide; e.g. studies simultaneously quantifying ‘functional’ and ‘numerical responses’ (i.e., the ‘total response’) are rare. The functional, the numerical, and the resulting total response (i.e., how the predator per capita intake, the population of predators and the total of prey eaten by the total predators vary with prey densities) are fundamental as they reveal the predator’s ability to regulate prey population dynamics. Here, we used a multi-spatio-temporal scale approach to simultaneously explore the functional and numerical responses of a territorial predator (Bonelli’s eagle Hieraaetus fasciatus) to its two main prey species (the rabbit Oryctolagus cuniculus and the red-legged partridge Alectoris rufa) during the breeding period in a Mediterranean system of south Spain. Bonelli’s eagle responded functionally, but not numerically, to rabbit/partridge density changes. Type II, non-regulatory, functional responses (typical of specialist predators) offered the best fitting models for both prey. In the absence of a numerical response, Bonelli’s eagle role as a regulating factor of rabbit and partridge populations seems to be weak in our study area. Simple (prey density-dependent) functional response models may well describe the short-term variation in a territorial predator’s consumption rate in complex ecosystems.     

Natural selection and population density-feedback II. The evolution of functional response curves

The nature of the functional response may be qualitatively understood as follows. Sigmoid responses to one food type may arise, in the presence of alternate foods, as a result of optimal feeding and foraging behavior. Sigmoid curves resulting from this cause I term class A curves. The same curve may also arise in the absence of alternate foods as a result of learning, individual variations in the level of food density at which predators begin feeding, or training effects. The latter I have termed class B curves. At very high food densities, a drop in food intake per predator might occur because of the tendency for predators to take easily found and captured items first and to become more selective when food is very common. Such “dome-shaped” curves have been found in the laboratory but should be rare in nature. Computer simulation of a three trophic-level system, using the phenotypic selection model of Emlen, indicates that natural selection acting on prey should encourage sigmoidality in the predator's class B functional response, at least in disturbed environments. The opposite force arises from selection acting on predators. However, given the magnitudes of growth efficiencies (see Eq. (8), it appears that at least for terrestrial vertebrates, selection on prey species is more important than selection on predators for determining functional responses. Accordingly, prey-predator systems occupying highly variable environments are expected to show more marked type III (class B) curves than systems in more stable areas. Finally, the role of functional response for prey-predator stability is discussed. Class A (alternate food) responses may result in population control for prey in multiple prey systems. Peterman and Pikitch have modeled systems in which type III functional response by predators, in systems where predation varies independently of prey, may lead to double equilibria. This picture is clouded, however, when predator populations are interactive with their food, though double equilibria are still possible (J. M. Emlen, 1984, “Population Biology: The Coevolution of Population Dynamics and Behavior,” Macmillan, New York, in press).     

Artificial selection for timing of dispersal in predatory mites yields lines that differ in prey exploitation strategies

Dispersal is the main determinant of the dynamics and persistence of predator–prey metapopulations. When defining dispersal as a predator exploitation strategy, theory predicts the existence of a continuum of strategies: from some dispersal throughout the predator–prey interaction (the Milker strategy) to dispersal only after the prey had been exterminated (the Killer strategy). These dispersal strategies relate to differences in prey exploitation at the population level, with more dispersal leading to longer predator–prey interaction times and higher cumulative numbers of dispersing predators. In the predatory mite Phytoseiulus persimilis, empirical studies have shown genetic variation for prey exploitation as well as for the timing of aerial dispersal in the presence of prey. Here, we test whether artificial selection for lines that differ in timing of dispersal also results in these lines differing in prey exploitation. Six rounds of selection for early or late dispersal resulted in predator lines displaying earlier or later dispersal. Moreover, it resulted—at the population level—in predicted differences in the local predator–prey interaction time and in the cumulative numbers of dispersers in a population dynamics experiment. We pose that timing of dispersal is a heritable trait that can be selected in P. persimilis, which results in lines that show quantitative differences in local predator–prey dynamics. This opens ways to experimentally investigate the evolution of alternative prey exploitation strategies and to select for predator strains with prey exploitation strategies resulting in better biological control.     

Comparing functional responses in predator-infected eco-epidemics models

The current paper deals with the mathematical models of predator–prey system where a transmissible disease spreads among the predator species only. Four mathematical models are proposed and analysed with several popular predator functional responses in order to show the influence of functional response on eco-epidemic models. The existence, boundedness, uniqueness of solutions of all the models are established. Mathematical analysis including stability and bifurcation are observed. Comparison among the results of these models allows the general conclusion that relevant behaviour of the eco-epidemic predator–prey system, including switching of stability, extinction, persistence and oscillations for any species depends on four important parameters viz. the rate of infection, predator interspecies competition and the attack rate on susceptible predator. The paper ends with a discussion of the biological implications of the analytical and numerical results.     

When phenology matters: age–size truncation alters population response to trophic mismatch

Climate-induced shifts in the timing of life-history events are a worldwide phenomenon, and these shifts can de-synchronize species interactions such as predator–prey relationships. In order to understand the ecological implications of altered seasonality, we need to consider how shifts in phenology interact with other agents of environmental change such as exploitation and disease spread, which commonly act to erode the demographic structure of wild populations. Using long-term observational data on the phenology and dynamics of a model predator–prey system (fish and zooplankton in Windermere, UK), we show that age–size truncation of the predator population alters the consequences of phenological mismatch for offspring survival and population abundance. Specifically, age–size truncation reduces intraspecific density regulation due to competition and cannibalism, and thereby amplifies the population sensitivity to climate-induced predator–prey asynchrony, which increases variability in predator abundance. High population variability poses major ecological and economic challenges as it can diminish sustainable harvest rates and increase the risk of population collapse. Our results stress the importance of maintaining within-population age–size diversity in order to buffer populations against phenological asynchrony, and highlight the need to consider interactive effects of environmental impacts if we are to understand and project complex ecological outcomes.     

Foraging tactics of a terrestrial salamander: Sustained yield in territories

Territorial red-backed salamanders (Plethodon cinereus) were given a high density of two prey types differing in size and caloric profitability. They chose a diet that approximated optimal foraging when they foraged in areas previously marked with advertisement pheromones. However, when foraging in previously unmarked or conspecific-marked areas they did not forage optimally, in a short time frame. In the latter two situations they evinced a lower rate of net energy due to their failure to specialize on the more profitable prey type and their longer intercapture intervals while time was devoted either to marking behaviour or submissive posturing. The salamanders appeared to opt for a strategy of sacrificing initial caloric yield until they had established marked territories and then switching to a higher sustained caloric yield. The data show that experimental handling of a predator per se can alter its foraging behaviour. Also a predator just initiating a territory may forage quite differently from one that has already established ownership, making the time frame during which observations are made important to understanding the predator's foraging strategy.     

Joint evolution of predator body size and prey-size preference

We studied the joint evolution of predator body size and prey-size preference based on dynamic energy budget theory. The predators’ demography and their functional response are based on general eco-physiological principles involving the size of both predator and prey. While our model can account for qualitatively different predator types by adjusting parameter values, we mainly focused on ‘true’ predators that kill their prey. The resulting model explains various empirical observations, such as the triangular distribution of predator–prey size combinations, the island rule, and the difference in predator–prey size ratios between filter feeders and raptorial feeders. The model also reveals key factors for the evolution of predator–prey size ratios. Capture mechanisms turned out to have a large effect on this ratio, while prey-size availability and competition for resources only help explain variation in predator size, not variation in predator–prey size ratio. Predation among predators is identified as an important factor for deviations from the optimal predator–prey size ratio.     

Rapid prey evolution and the dynamics of two-predator food webs

Traits affecting ecological interactions can evolve on the same time scale as population and community dynamics, creating the potential for feedbacks between evolutionary and ecological dynamics. Theory and experiments have shown in particular that rapid evolution of traits conferring defense against predation can radically change the qualitative dynamics of a predator–prey food chain. Here, we ask whether such dramatic effects are likely to be seen in more complex food webs having two predators rather than one, or whether the greater complexity of the ecological interactions will mask any potential impacts of rapid evolution. If one prey genotype can be well-defended against both predators, the dynamics are like those of a predator–prey food chain. But if defense traits are predator-specific and incompatible, so that each genotype is vulnerable to attack by at least one predator, then rapid evolution produces distinctive behaviors at the population level: population typically oscillate in ways very different from either the food chain or a two-predator food web without rapid prey evolution. When many prey genotypes coexist, chaotic dynamics become likely. The effects of rapid evolution can still be detected by analyzing relationships between prey abundance and predator population growth rates using methods from functional data analysis.     

Microgeographic divergence of functional responses among salamanders under antagonistic selection from apex predators

A predator''s functional response determines predator–prey interactions by describing the relationship between the number of prey available and the number eaten. Its shape and parameters fundamentally govern the dynamic equilibrium of predator–prey interactions and their joint abundances. Yet, estimates of these key parameters generally assume stasis in space and time and ignore the potential for local adaptation to alter feeding responses and the stability of trophic dynamics. Here, we evaluate if functional responses diverge among populations of spotted salamander (Ambystoma maculatum) larvae that face antagonistic selection on feeding strategies based on their own risk of predation. Common garden experiments revealed that spotted salamander from ponds with varying predation risks differed in their functional responses, suggesting an evolutionary response. Applying mechanistic equations, we discovered that the combined changes in attack rates, handling times and shape of the functional response enhanced feeding rate in environments with high densities of gape-limited predators. We suggest how these parameter changes could alter community equilibria and other emergent properties of food webs. Community ecologists might often need to consider how local evolution at fine scales alters key relationships in ways that alter local diversity patterns, food web dynamics, resource gradients and community responses to disturbance.     

Simple order of prey preference technique for modelling the predator functional response

The predator functional response to several prey types and densities may be conceptualized as a multi-dimensional version of the one-dimensional Holling functional-response curves; however, this empirical approach requires inordinate amounts of data to develop and test. A simulation method of modelling this functional response is to consider the behavior of a predator faced with the choice of several prey types. In this model, when all prey are available the predator’s selection will depend on the absolute abundance of the most-preferred prey type, irrespective of the abundances of the less-preferred prey types. Consequently, the predator will consume only the most-preferred prey types while that type is available in sufficient numbers. When abundance of the most-preferred type declines below a certain level, the predator will begin to include in its diet the second-most-preferred prey type along with the most-preferred prey type. This order-of-preference technique holds up well when the model is compared to population data fromOligonychus pratensis (Acarina: Tetranychidae)/Neoseiulus fallacis (Acarina: Phytoseiidae), and is consistent with optimal foraging theory. Implementation is simple, and the data requirements are reduced to determining the predator’s order of preference and normalizing the nutritional values of the prey types to a single type.     

Functional groups in piscivorous fishes

Piscivory is a key ecological function in aquatic ecosystems, mediating energy flow within trophic networks. However, our understanding of the nature of piscivory is limited; we currently lack an empirical assessment of the dynamics of prey capture and how this differs between piscivores. We therefore conducted aquarium‐based performance experiments, to test the feeding abilities of 19 piscivorous fish species. We quantified their feeding morphology, striking, capturing, and processing behavior. We identify two major functional groups: grabbers and engulfers. Grabbers are characterized by horizontal, long‐distance strikes, capturing their prey tailfirst and subsequently processing their prey using their oral jaw teeth. Engulfers strike from short distances, from high angles above or below their prey, engulfing their prey and swallowing their prey whole. Based on a meta‐analysis of 2,209 published in situ predator–prey relationships in marine and freshwater aquatic environments, we show resource partitioning between grabbers and engulfers. Our results provide a functional classification for piscivorous fishes delineating patterns, which transcend habitats, that may help explain size structures in fish communities.     

A spatial theory for characterizing predator–multiprey interactions in heterogeneous landscapes

Trophic interactions in multiprey systems can be largely determined by prey distributions. Yet, classic predator–prey models assume spatially homogeneous interactions between predators and prey. We developed a spatially informed theory that predicts how habitat heterogeneity alters the landscape-scale distribution of mortality risk of prey from predation, and hence the nature of predator interactions in multiprey systems. The theoretical model is a spatially explicit, multiprey functional response in which species-specific advection–diffusion models account for the response of individual prey to habitat edges. The model demonstrates that distinct responses of alternative prey species can alter the consequences of conspecific aggregation, from increasing safety to increasing predation risk. Observations of threatened boreal caribou, moose and grey wolf interacting over 378 181 km² of human-managed boreal forest support this principle. This empirically supported theory demonstrates how distinct responses of apparent competitors to landscape heterogeneity, including to human disturbances, can reverse density dependence in fitness correlates.     

Match and mismatch: Integrating consumptive effects of predators,prey traits,and habitat selection in colonizing aquatic insects

Predators are a particularly critical component of habitat quality, as they affect survival, morphology, behavior, population size, and community structure through both consumptive and non‐consumptive effects. Non‐consumptive effects can often exceed consumptive effects, but their relative importance is undetermined in many systems. Our objective was to determine the consumptive and non‐consumptive effects of a predaceous aquatic insect, Notonecta irrorata, on colonizing aquatic beetles. We tested how N. irrorata affected survival and habitat selection of colonizing aquatic beetles, how beetle traits contributed to their vulnerability to predation by N. irrorata, and how combined consumptive and non‐consumptive effects affected populations and community structure. Predation vulnerabilities ranged from 0% to 95% mortality, with size, swimming, and exoskeleton traits generating species‐specific vulnerabilities. Habitat selection ranged from predator avoidance to preferentially colonizing predator patches. Attraction of Dytiscidae to N. irrorata may be a natural ecological trap given similar cues produced by these taxa. Hence, species‐specific habitat selection by prey can be either predator‐avoidance responses that reduce consumptive effects, or responses that magnify predator effects. Notonecta irrorata had both strong consumptive and non‐consumptive effects on populations and communities, while combined effects predicted even more distinct communities and populations across patches with or without predators. Our results illustrate that an aquatic invertebrate predator can have functionally unique consumptive effects on prey, attracting and repelling prey, while prey have functionally unique responses to predators. Determining species‐specific consumptive and non‐consumptive effects is important to understand patterns of species diversity across landscapes.