Disentangling demographic co‐effects of predation and pollution on population dynamics

In nature species react to a variety of endogenous and exogenous ecological factors. Understanding the mechanisms by which these factors interact and drive population dynamics is a need for understanding and managing ecosystems. In this study we assess, using laboratory experiments, the effects that the combinations of two exogenous factors exert on the endogenous structure of the population dynamics of a size‐structured population of Daphnia. One exogenous factor was size‐selective predation, which was applied on experimental populations through simulating: 1) selective predation on small prey, 2) selective predation on large prey and 3) non‐selective predation. The second exogenous factor was pesticide exposure, applied experimentally in a quasi‐continuous regime. Our analysis combined theoretical models and statistical testing of experimental data for analyzing how the density dependence structure of the population dynamics was shifted by the different exogenous factors. Our results showed that pesticide exposure interacted with the mode of predation in determining the endogenous dynamics. Populations exposed to the pesticide and to either selective predation on newborns or selective predation on adults exhibited marked nonlinear effects of pesticide exposure. However, the specific mechanisms behind such nonlinear effects were dependent on the mode of size‐selectivity. In populations under non‐selective predation the pesticide exposure exerted a weak lateral effect. The ways in which endogenous process and exogenous factors may interact determine population dynamics. Increases in equilibrium density results in higher variance of population fluctuations but do not modify the stability properties of the system, while changes in the maximum growth rate induce changes in the dynamic regimes and stability properties of the population. Future consideration for research includes the consequences of the seasonal variation in the composition and activity of the predator assembly in interaction with the seasonal variation in exposure to agrochemicals on freshwater population dynamics.     

Effects of adaptive predatory and anti-predator behaviour in a two-prey—one-predator system

Summary Two prey populations that share a common predator can interact indirectly by causing changes in the predator's foraging behaviour. Previous work suggests that adaptive choice of prey by the predator usually has two related consequences: (i) the predation rate on a particular prey species increases with the relative and/or absolute abundance of that prey; and (ii) increases in either prey population produce a short-term increase in the fitness of the other prey (short-term indirect mutualism between prey). This paper investigates how these two consequences are changed if the prey exhibit adaptive anti-predator behaviour. In this case, the predation rate on a particular prey often decreases as the prey's density increases. The predator then usually exhibits negative switching between prey. However, the presence of adaptive antipredator behaviour does not change the short-term mutualism between prey. In this case, as a prey becomes less common, it achieves a larger growth rate by reducing its anti-predator effort. These results imply that observations of the relationship between prey density and predation rate cannot be used to infer the nature of the behavioural indirect effect between prey that share a predator.     

Predators reverse the direction of density dependence for juvenile salmon mortality

The effect of predators on prey populations depends on how predator-caused mortality changes with prey population density. Predators can enforce density-dependent prey mortality and contribute to population stability, but only if they have a positive numerical or behavioral response to increased prey density. Otherwise, predator saturation can result in inversely density-dependent mortality, destabilizing prey populations and increasing extinction risk. Juvenile salmon and trout provide some of the clearest empirical examples of density-dependent mortality in animal populations. However, although juvenile salmon are very vulnerable to predators, the demographic effects of predators on juvenile salmon are unknown. We tested the interactive effects of predators and population density on the mortality of juvenile Atlantic salmon (Salmo salar) using controlled releases of salmon in natural streams. We introduced newly hatched juvenile salmon at three population density treatments in six study streams, half of which contained slimy sculpin (Cottus cognatus), a common generalist predator (18 release sites in total, repeated over two summers). Sculpin reversed the direction of density dependence for juvenile salmon mortality. Salmon mortality was density dependent in streams with no sculpin, but inversely density dependent in streams where sculpin were abundant. Such predator-mediated inverse density dependence is especially problematic for prey populations suppressed by other factors, thereby presenting a fundamental challenge to persistence of rare populations and restoration of extirpated populations.     

Oscillations in a size-structured prey-predator model

This article introduces a predator–prey model with the prey structured by body size, based on reports in the literature that predation rates are prey-size specific. The model is built on the foundation of the one-species physiologically structured models studied earlier. Three types of equilibria are found: extinction, multiple prey-only equilibria and possibly multiple predator–prey coexistence equilibria. The stabilities of the equilibria are investigated. Comparison is made with the underlying ODE Lotka–Volterra model. It turns out that the ODE model can exhibit sustain oscillations if there is an Allee effect in the net reproduction rate, that is the net reproduction rate grows for some range of the prey’s population size. In contrast, it is shown that the structured PDE model can exhibit sustain oscillations even if the net reproductive rate is strictly declining with prey population size. We find that predation, even size-non-specific linear predation can destabilize a stable prey-only equilibrium, if reproduction is size specific and limited to individuals of large enough size. Furthermore, we show that size-specific predation can also destabilize the predator–prey equilibrium in the PDE model. We surmise that size-specific predation allows for temporary prey escape which is responsible for destabilization in the predator–prey dynamics.     

Mechanisms of coexistence in diverse herbivore–carnivore assemblages: demographic,temporal and spatial heterogeneities affecting prey vulnerability

Simple models coupling the dynamics of single predators to single prey populations tend to generate oscillatory dynamics of both predator and prey, or extirpation of the prey followed by that of the predator. In reality, such oscillatory dynamics may be counteracted by prey refugia or by opportunities for prey switching by the predator in multi‐prey assemblages. How these mechanisms operate depends on relative prey vulnerability, a factor ignored in simple interactive models. I outline how compositional, temporal, demographic and spatial heterogeneities help explain the contrasting effects of top predators on large herbivore abundance and population dynamics in species‐rich African savanna ecosystems compared with less species‐diverse northern temperate or subarctic ecosystems. Demographically, mortality inflicted by predation depends on the relative size and life history stage of the prey. Because all animals eventually die and are consumed by various carnivores, the additive component of the mortality inflicted is somewhat less than the predation rate. Prey vulnerability varies annually and seasonally, and between day and night. Spatial variation in the risk of predation depends on vegetation cover as well as on the availability of food resources. During times of food shortage, herbivores become prompted to occupy more risky habitats retaining more food. Predator concentrations dependent on the abundance of primary prey species may restrict the occurrence of other potential prey species less resistant to predation. The presence of multiple herbivore species of similar size in African savannas allows the top predator, the lion, to shift its prey selection flexibly dependent on changing prey vulnerability. Hence top–down and bottom–up influences on herbivore populations are intrinsically entangled. Models coupling the population dynamics of predators and prey need to accommodate the changing influences of prey demography, temporal variation in environmental conditions, and spatial variation in the relative vulnerability of alternative prey species to predation. Synthesis While re‐established predators have had major impacts on prey populations in northern temperate regions, multiple large herbivore species typically coexist along with diverse carnivores in African savanna ecosystems. In order to explain these contrasting outcomes, certain functional heterogeneities must be recognised, including relative vulnerability of alternative prey, temporal variation in the risk of predation, demographic differences in susceptibility to predation, and spatial contrasts in exposure to predation. Food shortfalls prompt herbivores to exploit more risky habitats, meaning that top–down and bottom–up influences on prey populations are intrinsically entangled. Models coupling the interactive dynamics of predator and prey populations need to incorporate these varying influences on relative prey vulnerability.     

Prey: predator ratio dependence in the functional response of a freshwater amphipod

1. First known for their shredding activity, freshwater amphipods also behave as active predators with consequences for prey population regulation and amphipod coexistence in the context of biological invasions. 2. A way to quantify predation is to determine the average consumption rate per predator, also known as its functional response (FR). 3. Although amphipods are gregarious and can display social interactions that can alter per capita consumption rates, previous studies using the FR approach to investigate amphipod predation ignored such potential mutual interference because they did not consider variations in predator density. 4. We investigated the FR of Echinogammarus berilloni feeding on dipteran larvae with joint variations in prey and predator densities. This bivariate experimental design allowed us to estimate interference and to compare the fits of the three main classes of theoretical FR models, in which the predation rate is a function of prey density alone (prey‐dependent models), of both prey and predator densities (predator‐dependent models) or of the prey‐to‐predator ratio (ratio‐dependent models). 5. The Arditi–Ginzburg ratio‐dependent FR model provided the best representation of the FR of E. berilloni, whose predation rate showed a decelerating rise to a horizontal asymptote as prey abundance increased. 6. Ratio dependence means that mutual interference between amphipods leads to prey sharing. Mutual interference is likely to vary between amphipod species, depending on their level of aggressiveness.     

Adaptive changes in prey vulnerability shape the response of predator populations to mortality

Simple models are used to explore how adaptive changes in prey vulnerability alter the population response of their predator to increased mortality. If the mortality is an imposed harvest, the change in prey vulnerability also influences the relationship between harvest effort and yield of the predator. The models assume that different prey phenotypes share a single resource, but have different vulnerabilities to the predator. Decreased vulnerability is assumed to decrease resource consumption rate. Adaptive change may occur by phenotypic changes in the traits of a single species or by shifts in the abundances of a pair of coexisting species or morphs. The response of the predator population is influenced by the shape of the predator's functional response, the shape of resource density dependence, and the shape of the tradeoff between vulnerability and food intake in the prey. Given a linear predator functional response, adaptive prey defense tends to produce a decelerating decline in predator population size with increased mortality. Prey defense may also greatly increase the range of mortality rates that allow predator persistence. If the predator has a type-2 response with a significant handling time, adaptive prey defense may have a greater variety of effects on the predator's response to mortality, sometimes producing alternative attractors, population cycles, or increased mean predator density. Situations in which there is disruptive selection on prey defense often imply a bimodal change in yield as a function of harvesting effort, with a minimum at intermediate effort. These results argue against using single-species models of density dependent growth to manage predatory species, and illustrate the importance of incorporating anti-predator behavior into models in applied population ecology.     

Evolution of virulence driven by predator-prey interaction: Possible consequences for population dynamics

The evolution of pathogen virulence in natural populations has conventionally been considered as a result of selection caused by the interactions of the host with its pathogen(s). The host population, however, is generally embedded in complex trophic interactions with other populations in the community, in particular, intensive predation on the infected host can increase its mortality, and this can affect the course of virulence evolution. Reciprocally, in the long run, the evolution of virulence within an infected host can affect the patterns of population dynamics of a predator consuming the host (e.g. resulting in large amplitude oscillations, causing a severe drop in the population size, etc.). Surprisingly, neither the effect of predation on the evolution of virulence within a host, nor the influence of the evolution of virulence upon the consumer's dynamics has been addressed in the literature yet. In this paper, we consider a classical S-I ecoepidemiological model in which the infected host is consumed by a predator. We are particularly interested in the evolutionarily stable virulence of the pathogen in the model and its dependence upon ecologically relevant parameters. We show that predation can prominently shift the evolutionarily stable virulence towards more severe strains as compared to the same system without predation. We demonstrate that the evolution of virulence can result in a succession of dynamical regimes and can even lead to the extinction of the predator in the long run. The presence of a predator can indirectly affect the evolution within its prey since the evolutionarily stable virulence becomes a function of the prey growth rate, which would not be the case in a predator-free system. We find that the evolutionarily stable virulence largely depends on the carrying capacity K of the prey in a non-monotonous way. The model also predicts that in an eutrophic environment the shift of virulence towards evolutionarily stable benign strains can cause demographically stochastic evolutionary suicide, resulting in the extinction of both species, thus artificially maintaining severe strains of pathogen can enhance the persistence of both species.     

Stochastic predation exposes prey to predator pits and local extinction

Understanding how predators affect prey populations is a fundamental goal for ecologists and wildlife managers. A well-known example of regulation by predators is the predator pit, where two alternative stable states exist and prey can be held at a low density equilibrium by predation if they are unable to pass the threshold needed to attain a high density equilibrium. While empirical evidence for predator pits exists, deterministic models of predator–prey dynamics with realistic parameters suggest they should not occur in these systems. Because stochasticity can fundamentally change the dynamics of deterministic models, we investigated if incorporating stochasticity in predation rates would change the dynamics of deterministic models and allow predator pits to emerge. Based on realistic parameters from an elk–wolf system, we found predator pits were predicted only when stochasticity was included in the model. Predator pits emerged in systems with highly stochastic predation and high carrying capacities, but as carrying capacity decreased, low density equilibria with a high likelihood of extinction became more prevalent. We found that incorporating stochasticity is essential to fully understand alternative stable states in ecological systems, and due to the interaction between top–down and bottom–up effects on prey populations, habitat management and predator control could help prey to be resilient to predation stochasticity.     

The Effects of Prey Patchiness, Predator Aggregation, and Mutual Interference on the Functional Response of Phytoseiulus persimilis Feeding on Tetranychus urticae (Acari: Phytoseiidae, Tetranychidae)

The spatial distributions of two-spotted spider mites Tetranychus urticae and their natural enemy, the phytoseiid predator Phytoseiulus persimilis, were studied on six full-grown cucumber plants. Both mite species were very patchily distributed and P. persimilis tended to aggregate on leaves with abundant prey. The effects of non-homogenous distributions and degree of spatial overlap between prey and predators on the per capita predation rate were studied by means of a stage-specific predation model that averages the predation rates over all the local populations inhabiting the individual leaves. The empirical predation rates were compared with predictions assuming random predator search and/or an even distribution of prey. The analysis clearly shows that the ability of the predators to search non-randomly increases their predation rate. On the other hand, the prey may gain if it adopts a more even distribution when its density is low and a more patchy distribution when density increases. Mutual interference between searching predators reduces the predation rate, but the effect is negligible. The stage-specific functional response model was compared with two simpler models without explicit stage structure. Both unstructured models yielded predictions that were quite similar to those of the stage-structured model.     

Competition for safe real estate,not food,drives density‐dependent juvenile survival in a large herbivore

Density‐dependent competition for food reduces vital rates, with juvenile survival often the first to decline. A clear prediction of food‐based, density‐dependent competition for large herbivores is decreasing juvenile survival with increasing density. However, competition for enemy‐free space could also be a significant mechanism for density dependence in territorial species. How juvenile survival is predicted to change across density depends critically on the nature of predator–prey dynamics and spatial overlap among predator and prey, especially in multiple‐predator systems. Here, we used a management experiment that reduced densities of a generalist predator, coyotes, and specialist predator, mountain lions, over a 5‐year period to test for spatial density dependence mediated by predation on juvenile mule deer in Idaho, USA. We tested the spatial density‐dependence hypothesis by tracking the fate of 251 juvenile mule deer, estimating cause‐specific mortality, and testing responses to changes in deer density and predator abundance. Overall juvenile mortality did not increase with deer density, but generalist coyote‐caused mortality did, but not when coyote density was reduced experimentally. Mountain lion‐caused mortality did not change with deer density in the reference area in contradiction of the food‐based competition hypothesis, but declined in the treatment area, opposite to the pattern of coyotes. These observations clearly reject the food‐based density‐dependence hypothesis for juvenile mule deer. Instead, our results provide support for the spatial density‐dependence hypothesis that competition for enemy‐free space increases predation by generalist predators on juvenile large herbivores.     

Top–down limits on prey populations may be more severe in larger prey species,despite having fewer predators

Variation in the vulnerability of herbivore prey to predation is linked to body size, yet whether this relationship is size‐nested or size‐partitioned remains debated. If size‐partitioned, predators would be focused on prey within their preferred prey size range. If size‐nested, smaller prey species should become increasingly more vulnerable because increasingly more predators are capable of catching them. Yet, whether either of these strategies manifests in top–down prey population limitation would depend both on the number of potential predator species as well as the total mortality imposed. Here we use a rare ecosystem scale ‘natural experiment’ comparing prey population dynamics between a period of intense predator persecution and hence low predator densities and a period of active predator protection and population recovery. We use three decades of data on herbivore abundance and distribution to test the role of predation as a mechanism of population limitation among prey species that vary widely in body size. Notably, we test this within one of the few remaining systems where a near‐full suite of megaherbivores occur in high density and are thus able to include a thirtyfold range in herbivore body size gradient. We test whether top–down limitation on prey species of particular body size leads to compositional shifts in the mammalian herbivore community. Our results support both size‐nested and size‐partitioning predation but suggest that the relative top–down limiting impact on prey populations may be more severe for intermediate sized species, despite having fewer predators than small species. In addition we show that the gradual recovery of predator populations shifted the herbivore community assemblage towards large‐bodied species and has led to a community that is strongly dominated by large herbivore biomass.     

Keeping the herds healthy and alert: implications of predator control for infectious disease

Predator control programmes are generally implemented in an attempt to increase prey population sizes. However, predator removal could prove harmful to prey populations that are regulated primarily by parasitic infections rather than by predation. We develop models for microparasitic and macroparasitic infection that specify the conditions where predator removal will (a) increase the incidence of parasitic infection, (b) reduce the number of healthy individuals in the prey population and (c) decrease the overall size of the prey population. In general, predator removal is more likely to be harmful when the parasite is highly virulent, macroparasites are highly aggregated in their prey, hosts are long‐lived and the predators select infected prey.     

Producing and scrounging can have stabilizing effects at multiple levels of organization

This study shows, for the first time, that the evolution of a simple behavior, scrounging, at the individual level can have effects on populations, food chains, and community structure. In particular, the addition of scrounging in consumer populations can allow multiple consumers to coexist while exploiting a single prey. Also, scrounging in the top predator of a tritrophic food chain can stabilize interactions between the top predator, its prey, and its prey's prey. This occurs because the payoffs to scrounging for food in a population are negative frequency dependent, allowing scroungers to invade a population and to coexist with producers at a frequency which is density‐dependent. The presence of scroungers, who do not search for resources but simply use those found by others (producers) reduces the total amount of resource acquired by the group. As scrounging increases with group size, this leads to less resource acquired per individual as the group grows. Ultimately, this limits the size of the group, its impact on its prey, and its ability to outcompete other species. These effects can promote stability and thus increase species diversity. I will further suggest that prey may alter their spatial distribution such that scrounging will be profitable among their predators thus reducing predation rate on the prey.     

Predator functional response changed by induced defenses in prey

Functional responses play a central role in the nature and stability of predator-prey population dynamics. Here we investigate how induced defenses affect predator functional responses. In experimental communities, prey (Paramecium) expressed two previously undocumented inducible defenses--a speed reduction and a width increase--in response to nonlethal exposure to predatory Stenostomum. Nonlethal exposure also changed the shape of the predator's functional response from Type II to Type III, consistent with changes in the density dependence of attack rates. Handling times were also affected by prey defenses, increasing at least sixfold. These changes show that induced changes in prey have a real defensive function. At low prey densities, induction led to lower attack success; at high prey densities, attack rates were actually higher for induced prey. However, induction increased handling times sufficiently that consumption rates of defended prey were lower than those of undefended prey. Modification of attack rate and handling time has important potential consequences for population dynamics; Type III functional responses can increase the stability of population dynamics and persistence because predation on small populations is low, allowing a relict population to survive. Simulations of a predator-prey population dynamic model revealed the stabilizing potential of the Type III response.     

Trophic cascades and trophic trickles in pelagic food webs

Prey-dependent models, with the predation rate (per predator) a function of prey numbers alone, predict the existence of a trophic cascade. In a trophic cascade, the addition of a top predator to a two-level food chain to make a three-level food chain will lead to increases in the population size of the primary producers, and the addition of nutrients to three-level chains will lead to increases in the population numbers at only the first and third trophic levels. In contrast, ratio-dependent models, with the predation rate (per predator) dependent on the ratio of predator numbers to prey, predict that additions of top predators will not increase the population sizes of the primary producers, and that the addition of nutrients to a three-level food chain will lead to increases in population numbers at all trophic levels. Surprisingly, recent meta-analyses show that freshwater pelagic food web patterns match neither prey-dependent models (in pelagic webs, ''prey'' are phytoplankton, and ''predators'' are zooplankton), nor ratio-dependent models. In this paper we use a modification of the prey-dependent model, incorporating strong interference within the zooplankton trophic level, that does yield patterns matching those found in nature. This zooplankton interference model corresponds to a more reticulate food web than in the linear, prey-dependent model, which lacks zooplankton interference. We thus reconcile data with a new model, and make the testable prediction that the strength of trophic cascades will depend on the degree of heterogeneity in the zooplankton level of the food chain.     

Impacts of predation on dynamics of age-structured prey: Allee effects and multi-stability

With a series of mathematical models, we explore impacts of predation on a prey population structured into two age classes, juveniles and adults, assuming generalist, age-specific predators. Predation on any age class is either absent, or represented by types II or III functional responses, in various combinations. We look for Allee effects or more generally for multiple stable steady states in the prey population. One of our key findings is the occurrence of a predator pit (low-density ??refuge?? state of prey induced by predation; the chance of escaping predation thus increases both below and above an intermediate prey density) when only one age class is consumed and predators use a type II functional response ??this scenario is known to occur for an unstructured prey consumed via a type III functional response and can never occur for an unstructured prey consumed via a type II one. In the case where both age classes are consumed by type II generalist predators, an Allee effect occurs frequently, but some parameters give also rise to a predator pit and even three stable equilibria (one extinction equilibrium and two positive ones??Allee effect and predator pit combined). Multiple positive stable equilibria are common if one age class is consumed via a type II functional response and the other via a type III functional response??here, in addition to the behaviours mentioned above one may even observe three stable positive equilibria????double?? predator pit. Some of these results are discussed from the perspective of population management.     

Spatial heterogeneity and functional response: an experiment in microcosms with varying obstacle densities

Spatial heterogeneity of the environment has long been recognized as a major factor in ecological dynamics. Its role in predator–prey systems has been of particular interest, where it can affect interactions in two qualitatively different ways: by providing (1) refuges for the prey or (2) obstacles that interfere with the movements of both prey and predators. There have been relatively fewer studies of obstacles than refuges, especially studies on their effect on functional responses. By analogy with reaction–diffusion models for chemical systems in heterogeneous environments, we predict that obstacles are likely to reduce the encounter rate between individuals, leading to a lower attack rate (predator–prey encounters) and a lower interference rate (predator–predator encounters). Here, we test these predictions under controlled conditions using collembolans (springtails) as prey and mites as predators in microcosms. The effect of obstacle density on the functional response was investigated at the scales of individual behavior and of the population. As expected, we found that increasing obstacle density reduces the attack rate and predator interference. Our results show that obstacles, like refuges, can reduce the predation rate because obstacles decrease the attack rate. However, while refuges can increase predator dependence, we suggest that obstacles can decrease it by reducing the rate of encounters between predators. Because of their opposite effect on predator dependence, obstacles and refuges could modify in different ways the stability of predator–prey communities.     

Assessing the influence of prey–predator ratio,prey age structure and packs size on wolf kill rates

Traditional predation theory assumes that prey density is the primary determinant of kill rate. More recently, the ratio of prey‐to‐predator has been shown to be a better predictor of kill rate. However, the selective behavior of many predators also suggests that age structure of the prey population should be an important predictor of kill rate. We compared wolf–moose predation dynamics in two sites, south‐central Scandinavia (SCA) and Isle Royale, Lake Superior, North America (IR), where prey density was similar, but where prey age structure and prey‐to‐predator ratio differed. Per capita kill rates of wolves preying on moose in SCA are three times greater than on IR. Because SCA and IR have similar prey densities differences in kill rate cannot be explained by prey density. Instead, differences in kill rate are explained by differences in the ratio of prey‐to‐predator, pack size and age structure of the prey populations. Although ratio‐dependent functional responses was an important variable for explaining differences in kill rates between SCA and IR, kill rates tended to be higher when calves comprised a greater portion of wolves’ diet (p =0.05). Our study is the first to suggest how age structure of the prey population can affect kill rate for a mammalian predator. Differences in age structure of the SCA and IR prey populations are, in large part, the result of moose and forests being exploited in SCA, but not in IR. While predator conservation is largely motivated by restoring trophic cascades and other top–down influences, our results show how human enterprises can also alter predation through bottom–up processes.     

Dynamics and responses to mortality rates of competing predators undergoing predator-prey cycles

Two or more competing predators can coexist using a single homogeneous prey species if the system containing all three undergoes internally generated fluctuations in density. However, the dynamics of species that coexist via this mechanism have not been extensively explored. Here, we examine both the nature of the dynamics and the responses of the mean densities of each predator to mortality imposed upon it or its competitor. The analysis of dynamics uncovers several previously undescribed behaviors for this model, including chaotic fluctuations, and long-term transients that differ significantly from the ultimate patterns of fluctuations. The limiting dynamics of the system can be loosely classified as synchronous cycles, asynchronous cycles, and chaotic dynamics. Synchronous cycles are simple limit cycles with highly positively correlated densities of the two predator species. Asynchronous cycles are limit cycles, frequently of complex form, including a significant period during which prey density is nearly constant while one predator gradually, monotonically replaces the other. Chaotic dynamics are aperiodic and generally have intermediate correlations between predator densities. Continuous changes in density-independent mortality rates often lead to abrupt transitions in mean population sizes, and increases in the mortality rate of one predator may decrease the population size of the competing predator. Similarly, increases in the immigration rate of one predator may decrease its own density and increase the density of the other predator. Proportional changes in one predator's birth and death rate functions can have significant effects on the dynamics and mean densities of both predator species. All of these responses to environmental change differ from those observed when competitors coexist stably as the result of resource (prey) partitioning. The patterns described here occur in many other competition models in which there are cycles and differences in the linearity of the responses of consumers to their resources.