ADAPTIVE RESPONSES OF PREDATORS TO PREY AND PREY TO PREDATORS: THE FAILURE OF THE ARMS-RACE ANALOGY

This paper analyzes a number of relatively general models of predator-prey adaptation and coadaptation. The motivation behind this work is, in part, to evaluate the “race analogy” that has been applied in analyzing predator-prey coevolution. The models are based on the assumption that increased investment in predation-related adaptations must be paid for by decreased adaptation to some other factor. Increased investment in predation-related adaptations by the prey lowers the predator's functional response, and increased investment by the predator increases the functional response. The models are used to determine how each species should respond to an increase in the predation-related investment of the other species. Several broad classes of population-dynamics models and several alternatives for the cost of predation-related adaptation are investigated. The results do not support the general applicability of the race analogy. In the type of model analyzed in greatest detail here, predator and prey adaptations combine multiplicatively in determining the predator's capture-rate constant. In such models, prey usually increase investment in predator avoidance or escape when predators increase their investment in capture. However, predators often do not change or decrease their investment in response to an increase in the prey's investment. The direction of the predator's response depends on the particular parameter that pays the cost of increased predation investment, the shape of the cost-benefit functions, and the assumptions about the population dynamics of the predator-prey system. Similar models are used to determine whether increased investment by one species should increase the rate of incorporation of mutations that improve the predation-related adaptations of the other species. The arms-race analogy also fails for this case. The results cast doubt on the usefulness of Dawkins and Krebs (1979) “life-dinner” principle.     

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.     

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.     

Individual‐based models of cod movement and population dynamics

Understanding the strength and diversity of predator‐prey interactions among species is essential to understand ecosystem consequences of population‐level variation. Directly quantifying the predatory behaviour of wild fishes at large spatial scales (>100 m) in the open sea is fraught with difficulties. To date the only empirical approach has been to search for correlations in the abundance of predators and their putative prey. As an example we use this approach to search for predators of the keystone crown‐of‐thorns starfish. We show that this approach is unlikely to detect predator–prey linkages because the theoretical relationship is non‐linear, resulting in multiple possible prey responses for single given predator abundance. Instead we suggest some indication of the strength and ecosystem importance of a predator–prey relationship can be gained by using the abundance of both predators and their putative prey to parameterize functional response models.     

Bioeconomic harvesting of a prey–predator fishery

This paper deals with the problem of non-selective harvesting of a prey–predator system by using a reasonable catch-rate function instead of usual catch-per-unit-efforthypothesis. Here both the prey and the predator species obey the law of logistic growth. We have taken the predator functional response to prey density in such a form that each predator's functional response to the prey density approaches a constant as the prey population increases. Boundedness of the exploited system is examined. The existence of its steady states and their stability (local and global) are studied using Eigenvalue analysis. The existence of bionomic equilibria has been illustrated using a numerical example. The problem of determining the optimal harvesting policy is then solved by using Pontryagin's maximum principle.     

Complex dynamics of a predator–prey–parasite system: An interplay among infection rate,predator's reproductive gain and preference

Parasites are considered as an important factor in regulating their host populations through trait-mediated effects. On the other hand, predation becomes particularly interesting in host–parasite systems because predation can significantly alter the abundance of parasites and their host population. The combined effects of parasites and predator on host population and community structure therefore may have larger effect. Different field experiments confirm that predators consume disproportionately large number of infected prey in comparison to their susceptible counterpart. There are also substantial evidences that predator has the ability to distinguish prey that have been infected by a parasite and avoid such prey to reduce fitness cost. In this paper we study the predator–prey dynamics, where the prey species is infected by some parasites and predators consume both the susceptible and infected prey with some preference. We demonstrate that complexity in such systems largely depends on the predator's selectivity, force of infection and predator's reproductive gain. If the force of infection and predator's reproductive gain are low, parasites and predators both go to extinction whatever be the predator's preference. The story may be totally different in the opposite case. Survival of species in stable, oscillatory or chaotic states, and their extinction largely depend on the predator's preference. The system may also show two coexistence equilibrium points for some parameter values. The equilibrium with lower susceptible prey density is always stable and the equilibrium with higher susceptible prey density is always unstable. These results suggest that understanding the consequences of predator's selectivity or preference may be crucial for community structure involving parasites.     

Merging resource availability with isotope mixing models: the role of neutral interaction assumptions

Background

Bayesian mixing models have allowed for the inclusion of uncertainty and prior information in the analysis of trophic interactions using stable isotopes. Formulating prior distributions is relatively straightforward when incorporating dietary data. However, the use of data that are related, but not directly proportional, to diet (such as prey availability data) is often problematic because such information is not necessarily predictive of diet, and the information required to build a reliable prior distribution for all prey species is often unavailable. Omitting prey availability data impacts the estimation of a predator''s diet and introduces the strong assumption of consumer ultrageneralism (where all prey are consumed in equal proportions), particularly when multiple prey have similar isotope values.

Methodology

We develop a procedure to incorporate prey availability data into Bayesian mixing models conditional on the similarity of isotope values between two prey. If a pair of prey have similar isotope values (resulting in highly uncertain mixing model results), our model increases the weight of availability data in estimating the contribution of prey to a predator''s diet. We test the utility of this method in an intertidal community against independently measured feeding rates.

Conclusions

Our results indicate that our weighting procedure increases the accuracy by which consumer diets can be inferred in situations where multiple prey have similar isotope values. This suggests that the exchange of formalism for predictive power is merited, particularly when the relationship between prey availability and a predator''s diet cannot be assumed for all species in a system.     

The relationship between food density and short term assimilation rates in Potamopyrgus antipodarum and Deleatidiumsp.

Much of the variation in individual growth rates can be attributed to differences in individual feeding rates. Therefore, in order to build predictive models of individual, or population growth, the factors influencing an individual's feeding rate must be described. An important determinant of the feeding rate is the relationship between the local abundance of food and the individual's ingestion rate – otherwise known as the functional response. We determined functional responses for two species of invertebrate grazers: the snail Potamopyrgus antipodarum and the mayfly Deleatidium sp., by measuring their assimilation rate with increasing densities of radiolabelled periphyton. The assimilation rates were consistent with the Holling Type II or Michelis Menten functional response curve. The parameters of the functional response yielded estimates of the search area and handling time for the stream invertebrates. Our functional response data indicate that the half-saturation food density for P. antipodarum and Deleatidium sp. were 980 mg and 3200 mg AFDM m^–2, respectively, suggesting that Deleatidium growth may be subject to food limitation more often than is P. antipodarum – despite the lower assimilation efficiency of the latter species.     

Predator functional response and prey survival: direct and indirect interactions affecting a marked prey population

1. Predation plays an integral role in many community interactions, with the number of predators and the rate at which they consume prey (i.e. their functional response) determining interaction strengths. Owing to the difficulty of directly observing predation events, attempts to determine the functional response of predators in natural systems are limited. Determining the forms that predator functional responses take in complex systems is important in advancing understanding of community interactions. 2. Prey survival has a direct relationship to the functional response of their predators. We employed this relationship to estimate the functional response for bald eagle Haliaeetus leucocepalus predation of Canada goose Branta canadensis nests. We compared models that incorporated eagle abundance, nest abundance and alternative prey presence to determine the form of the functional response that best predicted intra-annual variation in survival of goose nests. 3. Eagle abundance, nest abundance and the availability of alternative prey were all related to predation rates of goose nests by eagles. There was a sigmoidal relationship between predation rate and prey abundance and prey switching occurred when alternative prey was present. In addition, predation by individual eagles increased as eagle abundance increased. 4. A complex set of interactions among the three species examined in this study determined survival rates of goose nests. Results show that eagle predation had both prey- and predator-dependent components with no support for ratio dependence. In addition, indirect interactions resulting from the availability of alternative prey had an important role in mediating the rate at which eagles depredated nests. As a result, much of the within-season variation in nest survival was due to changing availability of alternative prey consumed by eagles. 5. Empirical relationships drawn from ecological theory can be directly integrated into the estimation process to determine the mechanisms responsible for variation in observed survival rates. The relationship between predator functional response and prey survival offers a flexible and robust method to advance our understanding of predator-prey interactions in many complex natural systems where prey populations are marked and regularly visited.     

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.     

Low temperature constrains growth rates but not short-term ingestion rates of Antarctic ciliates

Low environmental temperature is a major factor affecting the feeding activities, growth rates, and growth efficiencies of metazooplankton, but these features are poorly characterized for most protistan species. Laboratory experiments were conducted to examine the growth and ingestion rates of cultured herbivorous Antarctic ciliates. Three ciliates fed several algal species individually at 0 °C exhibited uniformly low growth rates (<0.26 day^?1), but the algae varied substantially in their ability to support ciliate growth. Specific ingestion rate (prey biomass consumed per unit ciliate biomass per unit time) was strongly affected by ciliate physiological state (starved vs. actively growing). Starved cells ingested many more prey than cells in balanced growth during short-term (minutes-to-hours) experiment but did not grow faster, indicating temperature compensation of ingestion rate but not growth rate. Field experiments were also conducted in the Ross Sea, Antarctica, to characterize the feeding rates of ciliates in natural plankton assemblages. Specific ingestion rates of two dominant ciliates were an order of magnitude lower than rates reported for temperate ciliates, but estimated rates were strongly affected by prey abundance. Our data indicate that short-term ingestion rates of Antarctic ciliates were not constrained by low environmental temperature although overall growth rates were, indicating the need for caution when designing experiments to measure the ingestion rates of these species at low environmental temperature. We present evidence that artifacts arising from estimating ingestion in short-term experiments may lead to errors in estimating feeding impact and growth efficiencies that are particularly large for polar protists.     

Evolution towards oscillation or stability in a predator–prey system

We studied a prey–predator system in which both species evolve. We discuss here the conditions that result in coevolution towards a stable equilibrium or towards oscillations. First, we show that a stable equilibrium or population oscillations with small amplitude is likely to occur if the prey''s (host''s) defence is effective when compared with the predator''s (parasite''s) attacking ability at equilibrium, whereas large-amplitude oscillations are likely if the predator''s (parasite''s) attacking ability exceeds the prey''s (host''s) defensive ability. Second, a stable equilibrium is more likely if the prey''s defensive trait evolves faster than the predator''s attack trait, whereas population oscillations are likely if the predator''s trait evolves faster than that of the prey. Third, when the adaptation rates of both species are similar, the amplitude of the fluctuations in their abundances is small when the adaptation rate is either very slow or very fast, but at an intermediate rate of adaptation the fluctuations have a large amplitude. We also show the case in which the prey''s abundance and trait fluctuate greatly, while those of the predator remain almost unchanged. Our results predict that populations and traits in host–parasite systems are more likely than those in prey–predator systems to show large-amplitude oscillations.     

Not attackable or not crackable—How pre‐ and post‐attack defenses with different competition costs affect prey coexistence and population dynamics

It is well‐known that prey species often face trade‐offs between defense against predation and competitiveness, enabling predator‐mediated coexistence. However, we lack an understanding of how the large variety of different defense traits with different competition costs affects coexistence and population dynamics. Our study focusses on two general defense mechanisms, that is, pre‐attack (e.g., camouflage) and post‐attack defenses (e.g., weaponry) that act at different phases of the predator—prey interaction. We consider a food web model with one predator, two prey types and one resource. One prey type is undefended, while the other one is pre‐ or post‐attack defended paying costs either by a higher half‐saturation constant for resource uptake or a lower maximum growth rate. We show that post‐attack defenses promote prey coexistence and stabilize the population dynamics more strongly than pre‐attack defenses by interfering with the predator's functional response: Because the predator spends time handling “noncrackable” prey, the undefended prey is indirectly facilitated. A high half‐saturation constant as defense costs promotes coexistence more and stabilizes the dynamics less than a low maximum growth rate. The former imposes high costs at low resource concentrations but allows for temporally high growth rates at predator‐induced resource peaks preventing the extinction of the defended prey. We evaluate the effects of the different defense mechanisms and costs on coexistence under different enrichment levels in order to vary the importance of bottom‐up and top‐down control of the prey community.     

Habitat heterogeneity and mammalian predator–prey interactions

• 1 In predator–prey theory, habitat heterogeneity can affect the relationship between kill rates and prey or predator density through its effect on the predator's ability to search for, encounter, kill and consume its prey. Many studies of predator–prey interactions include the effect of spatial heterogeneity, but these are mostly based on species with restricted mobility or conducted in experimental settings.
• 2 Here, we aim to identify the patterns through which spatial heterogeneity affects predator–prey dynamics and to review the literature on the effect of spatial heterogeneity on predator–prey interactions in terrestrial mammalian systems, i.e. in freely moving species with high mobility, in non‐experimental settings. We also review current methodologies that allow the study of the predation process within a spatial context.
• 3 When the functional response includes the effect of spatial heterogeneity, it usually takes the form of predator‐dependent or ratio‐dependent models and has wide applicability.
• 4 The analysis of the predation process through its different stages may further contribute towards identifying the spatial scale of interest and the specific spatial mechanism affecting predator–prey interactions.
• 5 Analyzing the predation process based on the functional response theory, but separating the stages of predation and applying a multiscale approach, is likely to increase our insight into how spatial heterogeneity affects predator–prey dynamics. This may increase our ability to forecast the consequences of landscape transformations on predator–prey dynamics.

     

Timing and abundance as key mechanisms affecting trophic interactions in variable environments

Climatic changes are disrupting otherwise tight trophic interactions between predator and prey. Most of the earlier studies have primarily focused on the temporal dimension of the relationship in the framework of the match–mismatch hypothesis. This hypothesis predicts that predator's recruitment will be high if the peak of the prey availability temporally matches the most energy‐demanding period of the predators breeding phenology. However, the match–mismatch hypothesis ignores the level of food abundance while this can compensate small mismatches. Using a novel time‐series model explicitly quantifying both the timing and the abundance component for trophic relationships, we here show that timing and abundance of food affect recruitment differently in a marine (cod/zooplankton), a marine–terrestrial (puffin/herring) and a terrestrial (sheep/vegetation) ecosystem. The quantification of the combined effect of abundance and timing of prey on predator dynamics enables us to come closer to the mechanisms by which environment variability may affect ecological systems.     

Predator density and competition modify the benefits of group formation in a shoaling reef fish

Synthesis Predation risk experienced by individuals living in groups depends on the balance between predator dilution, competition for refuges, and predator interference or synergy. These interactions operate between prey species as well: the benefits of group living decline in the presence of an alternative prey species. We apply a novel model‐fitting approach to data from field experiments to distinguish among competing hypotheses about shifts in predator foraging behavior across a range of predator and prey densities. Our study provides novel analytical tools for analyzing predator foraging behavior and offers insight into the processes driving the dynamics of coral reef fish. Studies of predator foraging behavior typically focus on single prey species and fixed predator densities, ignoring the potential importance of complexities such as predator dilution; predator‐mediated effects of alternative prey; heterospecific competition; or predator–predator interactions. Neglecting the effects of prey density is particularly problematic for prey species that live in mixed species groups, where the beneficial effects of predator dilution may swamp the negative effects of heterospecific competition. Here we use field experiments to investigate how the mortality rates of a shoaling coral reef fish (a wrasse: Thalassoma amblycephalum), change as a result of variation in: 1) conspecific density, 2) density of a predator (a hawkfish: Paracirrhites arcatus), and 3) presence of an alternative prey species that competes for space (a damselfish: Pomacentrus pavo). We quantify changes in prey mortality rates from the predator's perspective, examining the effects of added predators or a second prey species on the predator's functional response. Our analysis highlights a model‐fitting approach that discriminates amongst multiple hypotheses about predator foraging in a community context. Wrasse mortality decreased with increasing conspecific density (i.e. mortality was inversely density‐dependent). The addition of a second predator doubled prey mortality rates, without significantly changing attack rate or handling time – i.e. there was no evidence for predator interference. The presence of a second prey species increased wrasse mortality by 95%; we attribute this increase either to short‐term apparent competition (predator aggregation) or to a decrease in handling time of the predator (e.g. through decreased wrasse vigilance). In this system, 1) prey benefit from intraspecific group living though a reduced predation risk, and 2) the benefit of group living is reduced in the presence of an alternative prey species.     

The complex dynamics of a diffusive prey–predator model with an Allee effect in prey

This paper investigates complex dynamics of a predator–prey interaction model that incorporates: (a) an Allee effect in prey; (b) the Michaelis–Menten type functional response between prey and predator; and (c) diffusion in both prey and predator. We provide rigorous mathematical results of the proposed model including: (1) the stability of non-negative constant steady states; (2) sufficient conditions that lead to Hopf/Turing bifurcations; (3) a prior estimates of positive steady states; (4) the non-existence and existence of non-constant positive steady states when the model is under zero-flux boundary condition. We also perform completed analysis of the corresponding ODE model to obtain a better understanding on effects of diffusion on the stability. Our analytical results show that the small values of the ratio of the prey's diffusion rate to the predator's diffusion rate are more likely to destabilize the system, thus generate Hopf-bifurcation and Turing instability that can lead to different spatial patterns. Through numerical simulations, we observe that our model, with or without Allee effect, can exhibit extremely rich pattern formations that include but not limit to strips, spotted patterns, symmetric patterns. In addition, the strength of Allee effects also plays an important role in generating distinct spatial patterns.     

Feeding by marine fish larvae: developmental and functional responses

Synopsis The relationship between prey consumption rate and prey concentration (functional response), and its change with growth (developmental response) were examined in the laboratory for three species of marine fish larvae: bay anchovy Anchoa mitchilli (Engraulidae), sea bream Archosargus rhomboidalis (Sparidae) and lined sole Achirus lineatus (Soleidae). The major objective was to determine relative predatory abilities of the larvae by fitting feeding rate data to developmental and functional response models. Feeding success, prey capture success, attack rates, handling times and search rates were estimated. Prey consumption rates and attack rates of bay anchovy usually were highest, but at the lowest prey level (50 per liter) first-feeding sea bream larvae had the highest consumption rate. Sea bream could consume prey at near-maximum rates at prey levels lower than those required by the other species. As larvae grew, time searching per attack decreased rapidly for all species, especially at low prey levels. Handling time also decreased, but most rapidly for bay anchovy. Search rates were highest for bay anchovy and lowest for lined sole. Bay anchovy had the best apparent predation ability, but when previous results on larval growth rates, survival rates and growth efficiencies were considered, sea bream larvae were the most efficient predators and the least likely of the three species to be limited by low prey levels.     

Trophic interactions under climate fluctuations: the Atlantic puffin as an example

Co-occurrence in food requirements of offspring and food availability is a key factor determining breeding success. Prey availability is typically dependent on environmental conditions that are different from those influencing the predator''s decision regarding whether or not to initiate breeding, and is not always optimal at the peak of reproduction requirements. We investigated this relationship to understand better what determines the fledging success of the Atlantic puffin (Fratercula arctica). Colony data from Røst (northern Norway) covering a period of 27 years were analysed with parallel data on sea temperature and the size and abundance of the puffins'' main prey (the Norwegian spring-spawning herring, Clupea harengus). By fitting statistical models to the fledging success, we found that one effect of climate on this population of Atlantic puffins is indirect and mediated by sea temperature affecting the availability of first-year herring. The best model also demonstrates that the breeding success of the Røst puffins may be quantitatively predicted from the size of first-year herring and sea temperature.     

Predator population dynamics under a cyclic prey regime: numerical responses,demographic parameters and growth rates

The consequences of cyclic fluctuations in abundance of prey species on predator continue to improve our understanding of the mechanisms behind population regulation. Among predators, vole‐eating raptors usually respond to changes in prey abundance with no apparent time‐lag and therefore contradict predictions from the predator–prey theory. In such systems, the interplay between demographic traits and population growth rate in relation to prey abundance remains poorly studied, yet it is crucial to characterize the link between ecological processes and population changes. Using a mechanistic approach, we assessed the demographic rates associated to the direct and indirect numerical responses of a specialist raptor (Montagu's harrier) to its cyclic prey (common vole), using long term data from two adjacent study sites in France. First‐year survival rates were weakly affected by vole abundance, probably due to the fact that Montagu's harriers are trans‐Saharan migrants and thus escape the vole collapse occurring in autumn–winter. Recruitment of yearling as well as breeding propensity of experienced adult females were strongly affected by vole abundance and at least partially shaped the trajectory of the breeding population. We argued that the strong density dependent signal detected in predator time series was mostly the phenomenological consequence of the positive direct numerical response of harriers to vole abundance. Accounting for this, we proposed a method to assess density dependence in predator relying on a cyclic prey. Finally, the variation in Montagu's harrier population growth rates was best explained by overwinter growth rates of the prey population and to a lesser extent by previous residual predator density.