Effect of resource subsidies on predator–prey population dynamics: a mathematical model

The influence of a resource subsidy on predator–prey interactions is examined using a mathematical model. The model arises from the study of a biological system involving arctic foxes (predator), lemmings (prey), and seal carcasses (subsidy). In one version of the model, the predator, prey and subsidy all occur in the same location; in a second version, the predator moves between two patches, one containing only the prey and the other containing only the subsidy. Criteria for feasibility and stability of the different equilibrium states are studied both analytically and numerically. At small subsidy input rates, there is a minimum prey carrying capacity needed to support both predator and prey. At intermediate subsidy input rates, the predator and prey can always coexist. At high subsidy input rates, the prey cannot persist even at high carrying capacities. As predator movement increases, the dynamic stability of the predator–prey-subsidy interactions also increases.     

The Lotka-Volterra predator-prey model with foraging-predation risk trade-offs

This article studies the effects of adaptive changes in predator and/or prey activities on the Lotka-Volterra predator-prey population dynamics. The model assumes the classical foraging-predation risk trade-offs: increased activity increases population growth rate, but it also increases mortality rate. The model considers three scenarios: prey only are adaptive, predators only are adaptive, and both species are adaptive. Under all these scenarios, the neutral stability of the classical Lotka-Volterra model is partially lost because the amplitude of maximum oscillation in species numbers is bounded, and the bound is independent of the initial population numbers. Moreover, if both prey and predators behave adaptively, the neutral stability can be completely lost, and a globally stable equilibrium would appear. This is because prey and/or predator switching leads to a piecewise constant prey (predator) isocline with a vertical (horizontal) part that limits the amplitude of oscillations in prey and predator numbers, exactly as suggested by Rosenzweig and MacArthur in their seminal work on graphical stability analysis of predator-prey systems. Prey and predator activities in a long-term run are calculated explicitly. This article shows that predictions based on short-term behavioral experiments may not correspond to long-term predictions when population dynamics are considered.     

Induced defenses within food webs: The role of community trade-offs,delayed responses,and defense specificity

In nature, prey and predator species are embedded in complex networks of ecological interactions. As a consequence, organism level reactions such as predator-induced prey defenses will not only influence the dynamics of both the prey exhibiting the response and its inducer predator, but also that of a wider set of populations that interact directly or indirectly with them.In this work our aim is to determine the consequences of community-level side effects, defense specificity, and timing of inducible defenses for the stability of model ecological communities. We shall consider small webs of two and three trophic levels, containing one to three species per level. The model food webs include well-known community motifs that will be studied by means of qualitative analyses of the community matrix. Our results show that side effects that suppress non-focal interactions were able to decrease community stability, particularly when defensive responses were delayed. Conversely, side effects that increase the strength of non-focal interactions stabilized communities. This work also shows that as the defensive response became more specific, it is more likely to obtain a stable community. In general terms, our results revealed that delayed responses decrease the likelihood of system stability. Our results highlight the importance of the underlying biology of species interactions for the definition of the proper topology, and consequently dynamics, of complex ecological networks.     

High reproductive rates result in high predation risks: a mechanism promoting the coexistence of competing prey in spatially structured populations

I tested the hypothesis that spatial structure provides a trade-off between reproduction and predation risk and thereby facilitates predator-mediated coexistence of competing prey species. I compared a cellular automata model to a mean-field model of two prey species and their common predator. In the mean-field model, the prey species with the higher reproductive rate (the superior competitor) always outcompeted the other species (the inferior competitor), both in the presence of and the absence of the predator. In the cellular automata model, both prey species, which differed only in their reproductive rates, coexisted for a long time in the presence of their common predator at intermediate levels of predation. At low predation rates, the superior competitor dominated, while high predation rates favored the inferior competitor. This discrepancy in the results of the different models was due to a trade-off that spontaneously emerged in spatially structured populations; that is, the more clustered distribution of the superior competitor made it more susceptible to predation. In addition, coexistence of competing prey species declined with increasing dispersal ranges of either prey or predator, which suggests that the trade-off that results from spatial structure becomes less important as either prey or predator disperse over a broader range.     

Warming up the system: higher predator feeding rates but lower energetic efficiencies

Predictions on the consequences of the rapidly increasing atmospheric CO₂ levels and associated climate warming for population dynamics, ecological community structure and ecosystem functioning depend on mechanistic energetic models of temperature effects on populations and their interactions. However, such mechanistic approaches combining warming effects on metabolic (energy loss of organisms) and feeding rates (energy gain by organisms) remain a key, yet elusive, goal. Aiming to fill this void, we studied the metabolic rates and functional responses of three differently sized, predatory ground beetles on one mobile and one more resident prey species across a temperature gradient (5, 10, 15, 20, 25 and 30 °C). Synthesizing metabolic and functional‐response theory, we develop novel mechanistic predictions how predator–prey interaction strengths (i.e., functional responses) should respond to warming. Corroborating prior theory, warming caused strong increases in metabolism and decreases in handling time. Consistent with our novel model, we found increases in predator attack rates on a mobile prey, whereas attack rates on a mostly resident prey remained constant across the temperature gradient. Together, these results provide critically important information that environmental warming generally increases the direct short‐term per capita interaction strengths between predators and their prey as described by functional‐response models. Nevertheless, the several fold stronger increase in metabolism with warming caused decreases in energetic efficiencies (ratio of per capita feeding rate to metabolic rate) for all predator–prey interactions. This implies that warming of natural ecosystems may dampen predator–prey oscillations thus stabilizing their dynamics. The severe long‐term implications; however, include predator starvation due to energetic inefficiency despite abundant resources.     

Complexity in a prey-predator model with prey refuge and diffusion

Prey-predator interaction is one of the most commonly observed relationships in ecosystem. In the study of prey-predator models, it is frequently assumed that the changes in population densities are only time-dependent and the dynamics is generally represented by coupled nonlinear ordinary differential equations. In natural system, however, either prey or predator or both move from one place to another for various reasons. In such a case, their dynamic interaction depends both on time and space and requires coupled nonlinear partial differential equations for its dynamic representation. It is also well documented that prey refuges affect the interaction between prey and predator significantly. In this paper, we studied the dynamics of a diffusive prey-predator interaction with prey refuge and type III response function. We have considered both one and two dimensional diffusivity in the model system and presented different stability results under the assumptions that one or both species may be mobile or sedentary. Our results showed that the system may exhibit different spatiotemporal (non-Turing) patterns, like spiral waves, patchy structures, spot pattern, or even spatiotemporal chaos depending on the refuge availability and diffusion rate of species. Another interesting finding was that the dynamic complexity in a prey-predator model increases in case of mobile predator and sedentary prey compare to mobile prey and sedentary predator while refuge availability is varied.     

Modeling the Fear Effect in Predator–Prey Interactions with Adaptive Avoidance of Predators

Recent field experiments on vertebrates showed that the mere presence of a predator would cause a dramatic change of prey demography. Fear of predators increases the survival probability of prey, but leads to a cost of prey reproduction. Based on the experimental findings, we propose a predator–prey model with the cost of fear and adaptive avoidance of predators. Mathematical analyses show that the fear effect can interplay with maturation delay between juvenile prey and adult prey in determining the long-term population dynamics. A positive equilibrium may lose stability with an intermediate value of delay and regain stability if the delay is large. Numerical simulations show that both strong adaptation of adult prey and the large cost of fear have destabilizing effect while large population of predators has a stabilizing effect on the predator–prey interactions. Numerical simulations also imply that adult prey demonstrates stronger anti-predator behaviors if the population of predators is larger and shows weaker anti-predator behaviors if the cost of fear is larger.     

Omnivorous food web,prey preference and allochthonous nutrient input

This work purports to analyze the influence of allochthonous nutrient input into consumer level in the ultimate dynamics of an omnivory food web, where consumption is dictated by non-switching and switching predators. Within this behavioral context, prey consumption structure is shown to have a markedly effect on food web dynamics under a gradient of allochthonous input and primary productivity. A striking feature is that in the non-switching model invasion of consumer and predator occurs sequentially in this order as density of carrying capacity increases, while in the switching model both predators and consumers are able to invade and persist irrespective of the considered carrying capacity levels.     

Bifurcation structure of a chemostat model for an age-structured predator and its prey

We model a chemostat containing an age-structured predator and its prey using a linear function for the uptake of substrate by the prey and two different functional responses (linear and Monod) for the consumption of prey by the predator. Limit cycles (LCs) caused by the predator's age structure arise at Hopf bifurcations at low values of the chemostat dilution rate for both model cases. In addition, LCs caused by the predator–prey interaction arise for the case with the Monod functional response. At low dilution rates in the Monod case, the age structure causes cycling at lower values of the inflowing resource concentration and conversely prevents cycling at higher values of the inflowing resource concentration. The results shed light on a similar model by Fussmann et al. [G. Fussmann, S. Ellner, K. Shertzer, and N. Hairston, Crossing the Hopf bifurcation in a live predator–prey system, Science 290 (2000), pp. 1358–1360.], which correctly predicted conditions for the onset of cycling in a chemostat containing an age-structured rotifer population feeding on algal prey.     

Toward the Quantification of Predation with Predator Gut Immunoassays: A New Approach Integrating Functional Response Behavior

Immunological methods have been widely used to identify key predator species and qualitatively evaluate predation of target prey. However, despite the quantitative nature of many immunoassays, the translation to number of prey attacked has been problematic because of the many factors that confound interpretation of the strength of the immunoassay response. We developed a new predation model that couples the proportion of predators positive for prey remains determined by enzyme-linked immunosorbent assay (ELISA), predator density, and predator functional response to prey density for estimating total prey attacked. We used single cotton plant arenas in the greenhouse to develop functional response models for two generalist predators, Geocoris punctipes (Say) and Orius insidiosus (Say), preying on Pectinophora gossypiella (Saunders) eggs. The model was validated and compared with other immunologically based predation models in multiple plant/multiple predator arenas. Our predation model was relatively accurate in predicting the total number of prey attacked by both predator species and was a significant improvement over previous models that rely on simple assumptions regarding predator attack rates. The model also improves the predictive capacity of the functional response model alone by correcting for the number of predators actually consuming prey. Sensitivity analyses indicated that model performance was most sensitive to accurate measurement of input variables such as temperature and the proportion of individuals positive for prey antigens by ELISA and less sensitive to changes in estimates of prey density. Accurate estimation of the functional response parameters is also important, especially for the behavioral parameter defining the decline in plant leaf area searched with increases in prey density. Limitations of the model and application to the field are discussed.     

Testing for predator dependence in predator-prey dynamics: a non-parametric approach

The functional response is a key element in all predator-prey interactions. Although functional responses are traditionally modelled as being a function of prey density only, evidence is accumulating that predator density also has an important effect. However, much of the evidence comes from artificial experimental arenas under conditions not necessarily representative of the natural system, and neglecting the temporal dynamics of the organism (in particular the effects of prey depletion on the estimated functional response). Here we present a method that removes these limitations by reconstructing the functional response non-parametrically from predator-prey time-series data. This method is applied to data on a protozoan predator-prey interaction, and we obtain significant evidence of predator dependence in the functional response. A crucial element in this analysis is to include time-lags in the prey and predator reproduction rates, and we show that these delays improve the fit of the model significantly. Finally, we compare the non-parametrically reconstructed functional response to parametric forms, and suggest that a modified version of the Hassell-Varley predator interference model provides a simple and flexible function for theoretical investigation and applied modelling.     

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.     

Long-term demographic balance in the Broadstone stream insect community

1. Population models based on Lotka–Volterra-type differential equations with logistic prey were made for a simple stream community including two stonefly prey Leuctra nigra Olivier and Nemurella pictetii Klàpalek, and two predators, the caddisfly Plectrocnemia conspersa (Curtis) and the alderfly Sialis fuliginosa Pictet. In order to assess the importance of predation in this system, we constructed both an explicit four-species model and a simplified model with two functional groups which was more amenable to analytical treatment.
2. The models were parameterized using new data on adult emergence and recruitment combined with previously published data on larval densities and prey uptake. The models were falsified if parameterizations led either to negative prey carrying capacities or to unstable dynamics.
3. Both the functional group and four-species models predict asymptotically stable interactions, with feasible carrying capacities. The models are consistent in predicting that the observed prey are in excess of 70% of their carrying capacities. The four-species model indicates that predation impact is not evenly shared between the two prey, with L. nigra being depressed further from its carrying capacity than N. pictetii .
4. Sensitivity analysis shows that the results of the full four-species model remain very robust to realistic levels of stochastic variation in the input data.
5. The four-species model is used to predict the outcome of an ongoing large-scale field experiment involving the transfer of all S. fuliginosa eggs from one stretch of the stream to another. Although the equilibrial prey populations are barely affected by the manipulation, the model predicts marked transient prey-release and prey-depression of L. nigra in the predator addition and removal areas, respectively.     

Effects of a disease affecting a predator on the dynamics of a predator-prey system

We study the effects of a disease affecting a predator on the dynamics of a predator-prey system. We couple an SIRS model applied to the predator population, to a Lotka-Volterra model. The SIRS model describes the spread of the disease in a predator population subdivided into susceptible, infected and removed individuals. The Lotka-Volterra model describes the predator-prey interactions. We consider two time scales, a fast one for the disease and a comparatively slow one for predator-prey interactions and for predator mortality. We use the classical “aggregation method” in order to obtain a reduced equivalent model. We show that there are two possible asymptotic behaviors: either the predator population dies out and the prey tends to its carrying capacity, or the predator and prey coexist. In this latter case, the predator population tends either to a “disease-free” or to a “disease-endemic” state. Moreover, the total predator density in the disease-endemic state is greater than the predator density in the “disease-free” equilibrium (DFE).     

Predator–prey interactions and metabolic rates are altered in stable and unstable groups in a social fish

Understanding the determinants and consequences of predation effort, success and prey responses is important since these factors affect the fitness of predators and prey. When predators are also invasive species, the impacts on prey can be particularly far-reaching with ultimate ecosystem-level consequences. However, predators are typically viewed as behaviourally fixed within this interaction and it is unclear how variation in predator social dynamics affects predator–prey interactions. Using the invasive eastern mosquitofish Gambusia holbrooki and a native glass shrimp Paratya australiensis in Australia, we investigated how varying levels of social conflict within predator groups influences predator–prey interactions. By experimentally manipulating group stability of G. holbrooki, we show that rates of social conflict were lower in groups with large size differences, but that routine metabolic rates were higher in groups with large size differences. Predation effort and success did not vary depending on group stability, but in stable groups predation effort by aggressive dominants was greater than subordinates. The anti-predator responses of prey to the stability of predator groups were mixed. While more prey utilized shelters when exposed to stable compared to unstable groups of predators, a greater proportion were sedentary when predator groups were unstable. Overall, this study demonstrates predator group stability is modulated by differences in body size and can influence prey responses. Further, it reveals a hidden metabolic cost of living in stable groups despite reduced overt social conflict. For invasive species management, it is therefore important to consider the behavioural and physiological plasticity of the invasive predators, whose complex social interactions and metabolic demands can modulate patterns of predator–prey interactions.     

Community structure and stability analysis for intraguild interactions among host, parasitoid, and predator

Intraguild predation (IGP) occurs when one species preys on a competitor species that shares a common resource. Modifying a prey–predator model with prey infection, we propose a model of IG interactions among host, parasitoid, and predator, in which the predator eats parasitized and unparasitized hosts, and the adult parasitoid density is explicitly expressed. Parameter dependences of community structure, including stability of the system, were analytically obtained. Depending on interaction strength (parasitization and predation on unparasitized and parasitized hosts), the model provides six types of community structure: (1) only the host exists, (2) the host and predator coexist stably, (3) the host and parasitoid coexist stably, (4) the host–parasitoid population dynamics are unstable, (5) the three species coexist stably, and (6) the population dynamics of the three species are unstable. In contrast to a traditional prey–predator model with prey infection, which predicts that population dynamics are always locally stable, our model predicts that they are unstable when the parasitization rate is high.     

Predator interference alters foraging behavior of a generalist predatory arthropod

Interactions between predators foraging in the same patch may strongly influence patch use and functional response. In particular, there is continued interest in how the magnitude of mutual interference shapes predator–prey interactions. Studies commonly focus on either patch use or the functional response without attempting to link these important components of the foraging puzzle. Predictions from both theoretical frameworks suggest that predators should modify foraging efforts in response to changes in feeding rate, but this prediction has received little empirical attention. We study the linkage between patch departure rates and food consumption by the hunting spider, Pardosa milvina, using field enclosures in which prey and predator densities were manipulated. Additionally, the most appropriate functional response model was identified by fitting alternative functional response models to laboratory foraging data. Our results show that although prey availability was the most important determinant of patch departure rates, a greater proportion of predators left enclosures containing elevated predator abundance. Functional response parameter estimation revealed significant levels of interference among predators leading to lower feeding rates even when the area allocated for each predator was kept constant. These results suggest that feeding rates determine patch movement dynamics, where interference induces predators to search for foraging sites that balance the frequency of agonistic interactions with prey encounter rates.     

Predator density and the functional responses of coral reef fish

Predation is a key process driving coral reef fish population dynamics, with higher per capita prey mortality rates on reefs with more predators. Reef predators often forage together, and at high densities, they may either cooperate or antagonize one another, thereby causing prey mortality rates to be substantially higher or lower than one would expect if predators did not interact. However, we have a limited mechanistic understanding of how prey mortality rates change with predator densities. We re-analyzed a previously published observational dataset to investigate how the foraging response of the coney grouper (Cephalopholis fulva) feeding on the bluehead wrasse (Thalassoma bifasciatum) changed with shifts in predator and prey densities. Using a model-selection approach, we found that per-predator feeding rates were most consistent with a functional response that declines as predator density increases, suggesting either antagonistic interactions among predators or a shared antipredator behavioral response by the prey. Our findings suggest that variation in predator density (natural or anthropogenic) may have substantial consequences for coral reef fish population dynamics.     

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.     

拟环纹狼蛛对褐飞虱的捕食作用及其模拟模型的研究 Ⅳ.单种捕食者-两种猎物系统的模拟模型及其稳定性分析

本文提出了描述单种捕食者-两种猎物系统的模拟模型。在功能反应和选择捕食实验的基础上,应用数值模拟方法分析了模型中各参数对稳定性的影响,以及拟环纹狼蛛-褐飞虱、稻纵卷叶螟三物种系统的稳定性。