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Peter A Abrams

Publications and source records attributed to Peter A Abrams.

14 recordsLinked to original sources
PubMed2006

The effects of switching behavior on the evolutionary diversification of generalist consumers.

Mathematical models of consumer-resource systems explore the evolution of a morphological trait that determines two resource acquisition rates in a generalist consumer. The consumer also has the ability to adjust its relative consumption of the two resources via behavioral (or developmental) plasticity subject to a trade-off. The analysis examines both stable systems and those with sustained fluctuations in abundance. In both cases, it seeks to determine how the behavioral choice affects the evolution of the morphological characters. The presence of adaptive switching behavior transforms the shape of the relationship between the morphological character and fitness in a manner that usually leads to evolution of two or more morphological types. As in models without switching, the presence of sustained cycles in resource densities often allows the evolution of a generalist as well as two specialists. However, switching expands and shifts the parameter regions yielding this outcome and in some cases allows the evolution and coexistence of at least two generalists as well as the two specialists. This level of diversity supported by only two resources is not seen in the absence of behavioral choice and resource cycles. The results suggest major roles for both behavior and environmental variation in adaptive radiation.

Adaptation, Physiological↗
PubMed2006

Disruptive selection and then what?

Disruptive selection occurs when extreme phenotypes have a fitness advantage over more intermediate phenotypes. The phenomenon is particularly interesting when selection keeps a population in a disruptive regime. This can lead to increased phenotypic variation while disruptive selection itself is diminished or eliminated. Here, we review processes that increase phenotypic variation in response to disruptive selection and discuss some of the possible outcomes, such as sympatric species pairs, sexual dimorphisms, phenotypic plasticity and altered community assemblages. We also identify factors influencing the likelihoods of these different outcomes.

Adaptation, Physiological↗
PubMed2006

The prerequisites for and likelihood of generalist-specialist coexistence.

Mathematical models of three-consumer-two-resource systems are used to explore the possibility of coexistence when one consumer is a generalist utilizing both resources, and the other two are specialists utilizing only one. Such coexistence requires strongly saturating functional or numerical responses in at least one consumer and the presence of sustained asynchronous variation in resource abundances. Given these conditions, the effects of three dichotomous factors on the range of parameters allowing coexistence are examined: flexible versus inflexible resource choice by the generalist, endogenous or exogenous cause of resource cycles, and location of the two resources in a single habitat versus two habitats. Coexistence of all three species is found to be possible for all combinations of these factors except for inflexible choice in a two-habitat environment. Generalists experience frequency-dependent fitness because, when they are abundant, they synchronize resource cycles and/or reduce their amplitude. When the generalist can adaptively adjust its relative foraging on the two resources, coexistence conditions are broadened considerably, and coexistence commonly occurs readily with exogenous variation in resource growth and with resources located in distinct habitats. Adaptive behavior increases the generalist's ability to both synchronize and dampen resource cycles.

Animals↗
PubMed2006

Maximal yields from multispecies fisheries systems: rules for systems with multiple trophic levels.

Increasing centralization of the control of fisheries combined with increased knowledge of food-web relationships is likely to lead to attempts to maximize economic yield from entire food webs. With the exception of predator-prey systems, we lack any analysis of the nature of such yield-maximizing strategies. We use simple food-web models to investigate the nature of yield- or profit-maximizing exploitation of communities including two types of three-species food webs and a variety of six-species systems with as many as five trophic levels. These models show that, for most webs, relatively few species are harvested at equilibrium and that a significant fraction of the species is lost from the web. These extinctions occur for two reasons: (1) indirect effects due to harvesting of species that had positive effects on the extinct species, and (2) intentional eradication of species that are not themselves valuable, but have negative effects on more valuable species. In most cases, the yield-maximizing harvest involves taking only species from one trophic level. In no case was an unharvested top predator part of the yield-maximizing strategy. Analyses reveal that the existence of direct density dependence in consumers has a large effect on the nature of the optimal harvest policy, typically resulting in harvest of a larger number of species. A constraint that all species must be retained in the system (a "constraint of biodiversity conservation") usually increases the number of species and trophic levels harvested at the yield-maximizing policy. The reduction in total yield caused by such a constraint is modest for most food webs but can be over 90% in some cases. Independent harvesting of species within the web can also cause extinctions but is less likely to do so.

Animals↗
PubMed2006

Adaptive change in the resource-exploitation traits of a generalist consumer: the evolution and coexistence of generalists and specialists.

Mathematical models of consumer-resource systems are used to explore the evolution of traits related to resource acquisition in a generalist consumer species that is capable of exploiting two resources. The analysis focuses on whether evolution of traits determining the capture rates of two resources by a consumer species produce one generalist, two specialists, or all three types, when all types are characterized by a common fitness function. In systems with a stable equilibrium, evolution produces one generalist or two specialists, depending on the second derivative of the trade-off relationship. When there are sustained population fluctuations, the nature of the trade-off between the consumer's capture rates of the two resources still plays a key role in determining the evolutionary outcome. If the trade-off is described by a choice variable between zero and one that is raised to a power n, polymorphic states are possible when n > 1, which implies a positive second derivative of the curve. These states are either dimorphism, with two relatively specialized consumer types, or trimorphism, with a single generalist type and two specialists. Both endogenously driven consumer-resource cycles, and fluctuations driven by an environmental variable affecting resource growth are considered. Trimorphic evolutionary outcomes are relatively common in the case of endogenous cycles. In contrast to a previous study, these trimorphisms can often evolve even when new lineages are constrained to have phenotypes very similar to existing lineages. Exogenous cycles driven by environmental variation in resource growth rates appear to be much less likely to produce a mixture of generalists and specialists than are endogenous consumer-resource cycles.

Animals↗
PubMed2005

The impact of mortality on predator population size and stability in systems with stage-structured prey.

The relationships between a predator population's mortality rate and its population size and stability are investigated for several simple predator-prey models with stage-structured prey populations. Several alternative models are considered; these differ in their assumptions about the nature of density dependence in the prey's population growth; the nature of stage-transitions; and the stage-selectivity of the predator. Instability occurs at high, rather than low predator mortality rates in most models with highly stage-selective predation; this is the opposite of the effect of mortality on stability in models with homogeneous prey populations. Stage-selective predation also increases the range of parameters that lead to a stable equilibrium. The results suggest that it may be common for a stable predator population to increase in abundance as its own mortality rate increases in stable systems, provided that the predator has a saturating functional response. Sufficiently strong density dependence in the prey generally reverses this outcome, and results in a decrease in predator population size with increasing predator mortality rate. Stability is decreased when the juvenile stage has a fixed duration, but population increases with increasing mortality are still observed in large areas of stable parameter space. This raises two coupled questions which are as yet unanswered; (1) do such increases in population size with higher mortality actually occur in nature; and (2) if not, what prevents them from occurring? Stage-structured prey and stage-related predation can also reverse the 'paradox of enrichment', leading to stability rather than instability when prey growth is increased.

Animals↗
PubMed2005

Transient dynamics limit the effectiveness of keystone predation in bringing about coexistence.

We analyze the transient dynamics of simple models of keystone predation, in which a predator preferentially consumes the dominant of two (or more) competing prey species. We show that coexistence is unlikely in many systems characterized both by successful invasion of either prey species into the food web that lacks it and by a stable equilibrium with high densities of all species. Invasion of the predator-resistant consumer species often causes the resident, more vulnerable prey to crash to such low densities that extinction would occur for many realistic population sizes. Subsequent transient cycles may entail very low densities of the predator or of the initially successful invader, which may also preclude coexistence of finite populations. Factors causing particularly low minimum densities during the transient cycles include biotic limiting resources for the prey, limited resource partitioning between the prey, a highly efficient predator with relatively slow dynamics, and a vulnerable prey whose population dynamics are rapid relative to the less vulnerable prey. Under these conditions, coexistence of competing prey via keystone predation often requires that the prey's competitive or antipredator characteristics fall within very narrow ranges. Similar transient crashes are likely to occur in other food webs and food web models.

Animals↗
PubMed2004

Coexistence of cycling and dispersing consumer species: Armstrong and McGehee in space.

Two competing consumer species may coexist using a single homogeneous resource when the more efficient consumer--the one having the lowest equilibrium resource density--has a more nonlinear functional response that generates consumer-resource cycles. We extend this model of nonequilibrium coexistence, as proposed by Armstrong and McGehee, by putting the interaction into a spatial context using two frameworks: a spatially explicit individual-based model and a spatially implicit metapopulation model. We find that Armstrong and McGehee's mechanism of coexistence can operate in a spatial context. However, individual-based simulations suggest that decreased dispersal restricts coexistence in most cases, whereas differential equation models of metapopulations suggest that a low rate of dispersal between subpopulations often increases the coexistence region. This difference arises in part because of two potentially opposing effects on coexistence due to the asynchrony in the temporal dynamics at different locations. Asynchrony implies that the less efficient species is more likely to be favored in some spatial locations at any given time, which broadens the conditions for coexistence. On the other hand, asynchrony and dispersal can also reduce the amplitude of local population cycles, which restricts coexistence. The relative influence of these two effects depends on details of the population dynamics and the representation of space. Our results also demonstrate that coexistence via the Armstrong-McGehee mechanism can occur even when there is little variation in the global densities of either the consumers or the resource, suggesting that empirical studies of the mechanisms should measure densities on several spatial scales.

Animal Migration↗
PubMed2004

The prevalence of asymmetrical indirect effects in two-host-one-parasitoid systems.

Empirical studies of indirect effects mediated by shared enemies have been characterized by several puzzling features: (a) there exist far fewer documented cases than for interactions via shared resources; (b) the majority of empirical studies have measured indirect effects where one of the two reciprocal effects could not be distinguished from zero; (c) there is a lack of documented positive effects mediated by a shared enemy, in spite of several mechanisms that could produce such effects. One potential explanation is that these are statistical expectations over the range of potential species characteristics. We systematically examine the indirect interactions between two hosts with a shared parasitoid across all potential parameter values, using a family of simple models. By including a detection limit for nonzero interspecific effects, we demonstrate that (-,0) indirect interactions between hosts are the most common type for many variants of the model. However, the absence of positive indirect effects in empirical studies constitutes a puzzling inconsistency between the empirical and theoretical literatures.

Algorithms↗
PubMed2003

Dynamic versus instantaneous models of diet choice.

We investigate the dynamics of a series of two-prey-one-predator models in which the predator exhibits adaptive diet choice based on the different energy contents and/or handling times of the two prey species. The predator is efficient at exploiting its prey and has a saturating functional response; these two features combine to produce sustained population cycles over a wide range of parameter values. Two types of models of behavioral change are compared. In one class of models ("instantaneous choice"), the probability of acceptance of the poorer prey by the predator instantaneously approximates the optimal choice, given current prey densities. In the second class of models ("dynamic choice"), the probability of acceptance of the poorer prey is a dynamic variable, which begins to change in an adaptive direction when prey densities change but which requires a finite amount of time to approach the new optimal behavior. The two types of models frequently predict qualitatively different population dynamics of the three-species system, with chaotic dynamics and complex cycles being a common outcome only in the dynamic choice models. In dynamic choice models, factors that reduce the rate of behavioral change when the probability of accepting the poorer prey approaches extreme values often produce complex population dynamics. Instantaneous and dynamic models often predict different average population densities and different indirect interactions between prey species. Alternative dynamic models of behavior are analyzed and suggest, first, that instantaneous choice models may be good approximations in some circumstances and, second, that different types of dynamic choice models often lead to significantly different population dynamics. The results suggest possible behavioral mechanisms leading to complex population dynamics and highlight the need for more empirical study of the dynamics of behavioral change.

Adaptation, Physiological↗
PubMed2003

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.

Animals↗
PubMed2002

The impact of consumer-resource cycles on the coexistence of competing consumers.

This article seeks to determine the extent to which endogenous consumer-resource cycles can contribute to the coexistence of competing consumer species. It begins with a numerical analysis of a simple model proposed by Armstrong and McGehee. This model has a single resource and two consumers, one with a linear functional response and one with a saturating response. Coexistence of the two consumer species can occur when the species with a saturating response generates population cycles of the resource, and also has a lower resource requirement for zero population growth. Coexistence can be achieved over a wide range of relative efficiencies of the two consumers provided that the functional response of the saturating consumer reaches its half-saturation value when the resource population is a small fraction of its carrying capacity. In this case, the range of efficiencies allowing coexistence is comparable to that when two competitors have stable dynamics and a high degree of resource partitioning. A variety of modifications of this basic model are analyzed to investigate the consequences for coexistence of different resource growth equations, different functional and numerical response shapes, and other factors. Large differences in functional response shape appear to be the most important factor in producing robust coexistence via resource cycles. If the unstable species has a concave numerical response, this greatly expands the conditions allowing coexistence. If the stable consumer species has a convex (accelerating) functional and/or numerical response, the range of conditions allowing coexistence is also expanded. We argue that large between-species differences in functional response form can often be produced by between-consumer differences in the adaptive adjustments of foraging effort to food density. Consumer-resource cycles can also expand the conditions allowing coexistence when there is resource partitioning, but do so primarily when resource partitioning is relatively slight; this makes the ease of coexistence relatively independent of consumer similarity.

Ecosystem↗
PubMed2002

The role of size-specific predation in the evolution and diversification of prey life histories.

Some of the best empirical examples of life-history evolution involve responses to predation. Nevertheless, most life-history theory dealing with responses to predation has not been formulated within an explicit dynamic food-web context. In particular, most previous theory does not explicitly consider the coupled population dynamics of the focal species and its predators and resources. Here we present a model of life-history evolution that explores the evolutionary consequences of size-specific predation on small individuals when there is a trade-off between growth and reproduction. The model explicitly describes the population dynamics of a predator, the prey of interest, and its resource. The selective forces that cause life-history evolution in the prey species emerge from the ecological interactions embodied by this model and can involve important elements of frequency dependence. Our results demonstrate that the strength of the coupling between predator and prey in the community determines many aspects of life-history evolution. If the coupling is weak (as is implicitly assumed in many previous models), differences in resource productivity have no effect on the nature of life-history evolution. A single life-history strategy is favored that minimizes the equilibrium resource density (if possible). If the coupling is strong, then higher resource productivities select for faster growth into the predation size refuge. Moreover, under strong coupling it is also possible for natural selection to favor an evolutionary diversification of life histories, possibly resulting in two coexisting species with divergent life-history strategies.

Animals↗