Spatial Patterns of a Predator-Prey System of Leslie Type with Time Delay.
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ABSTRACT:
SUBMITTER: Wang C
PROVIDER: S-EPMC4773104 | biostudies-literature | 2016
REPOSITORIES: biostudies-literature
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Project description:We consider a Leslie predator-prey system with mutual interference and feedback controls. For general nonautonomous case, by using differential inequality theory and constructing a suitable Lyapunov functional, we obtain some sufficient conditions which guarantee the permanence and the global attractivity of the system. For the periodic case, we obtain some sufficient conditions which guarantee the existence, uniqueness, and stability of a positive periodic solution.
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Project description:The outcome of species interactions may manifest differently at different spatial scales; therefore, our interpretation of observed interactions will depend on the scale at which observations are made. For example, in ladybeetle-aphid systems, the results from small-scale cage experiments usually cannot be extrapolated to landscape-scale field observations. To understand how ladybeetle-aphid interactions change across spatial scales, we evaluated predator-prey interactions in an experimental system. The experimental habitat consisted of 81 potted plants and was manipulated to facilitate analysis across four spatial scales. We also simulated a spatially explicit metacommunity model parallel to the experiment. In the experiment, we found that the negative effect of ladybeetles on aphids decreased with increasing spatial scales. This pattern can be explained by ladybeetles strongly suppressing aphids at small scales, but not colonizing distant patches fast enough to suppress aphids at larger scales. In the experiment, the positive effects of aphids on ladybeetles were strongest at three-plant scale. In a model scenario where predators did not have demographic dynamics, we found, consistent with the experiment, that both the effects of ladybeetles on aphids and the effects of aphids on ladybeetles decreased with increasing spatial scales. These patterns suggest that dispersal was the primary cause of ladybeetle population dynamics in our experiment: aphids increased ladybeetle numbers at smaller scales because ladybeetles stayed in a patch longer and performed area-restricted searches after encountering aphids; these behaviors did not affect ladybeetle numbers at larger spatial scales. The parallel experimental and model results illustrate how predator-prey interactions can change across spatial scales, suggesting that our interpretation of observed predator-prey dynamics would differ if observations were made at different scales. This study demonstrates how studying ecological interactions at a range of scales can help link the results of small-scale ecological experiments to landscape-scale ecological problems.
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Project description:In this paper, we present and analyze a spatio-temporal eco-epidemiological model of a prey predator system where prey population is infected with a disease. The prey population is divided into two categories, susceptible and infected. The susceptible prey is assumed to grow logistically in the absence of disease and predation. The predator population follows the modified Leslie-Gower dynamics and predates both the susceptible and infected prey population with Beddington-DeAngelis and Holling type II functional responses, respectively. The boundedness of solutions, existence and stability conditions of the biologically feasible equilibrium points of the system both in the absence and presence of diffusion are discussed. It is found that the disease can be eradicated if the rate of transmission of the disease is less than the death rate of the infected prey. The system undergoes a transcritical and pitchfork bifurcation at the Disease Free Equilibrium Point when the prey infection rate crosses a certain threshold value. Hopf bifurcation analysis is also carried out in the absence of diffusion, which shows the existence of periodic solution of the system around the Disease Free Equilibrium Point and the Endemic Equilibrium Point when the ratio of the rate of intrinsic growth rate of predator to prey crosses a certain threshold value. The system remains locally asymptotically stable in the presence of diffusion around the disease free equilibrium point once it is locally asymptotically stable in the absence of diffusion. The Analytical results show that the effect of diffusion can be managed by appropriately choosing conditions on the parameters of the local interaction of the system. Numerical simulations are carried out to validate our analytical findings.
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Project description:The geographic mosaic theory of coevolution predicts 1) spatial variation in predatory structures as well as prey defensive traits, and 2) trait matching in some areas and trait mismatching in others mediated by gene flow. We examined gene flow and documented spatial variation in crushing resistance in the freshwater snails Mexipyrgus churinceanus, Mexithauma quadripaludium, Nymphophilus minckleyi, and its relationship to the relative frequency of the crushing morphotype in the trophically polymorphic fish Herichthys minckleyi. Crushing resistance and the frequency of the crushing morphotype did show spatial variation among 11 naturally replicated communities in the Cuatro Ciénegas valley in Mexico where these species are all endemic. The variation in crushing resistance among populations was not explained by geographic proximity or by genetic similarity in any species. We detected clear phylogeographic patterns and limited gene flow for the snails but not for the fish. Gene flow among snail populations in Cuatro Ciénegas could explain the mosaic of local divergence in shell strength and be preventing the fixation of the crushing morphotype in Herichthys minckleyi. Finally, consistent with trait matching across the mosaic, the frequency of the fish morphotype was negatively correlated with shell crushing resistance likely reflecting the relative disadvantage of the crushing morphotype in communities where the snails exhibit relatively high crushing resistance.
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Project description:Our understanding of coevolution in a predator-prey system is based mostly on pair-wise interactions.Here I analyze a one-predator-two-prey system in which the predator's attack ability and the defense abilities of the prey all evolve. The coevolutionary consequences can differ dramatically depending on the initial trait value and the timing of the alternative prey's invasion into the original system. If the invading prey species has relatively low defense ability when it invades, its defense is likely to evolve to a lower level, stabilizing the population dynamics. In contrast, if when it invades its defense ability is close to that of the resident prey, its defense can evolve to a higher level and that of the resident prey may suddenly cease to evolve, destabilizing the population dynamics. Destabilization due to invasion is likely when the invading prey is adaptively superior (evolution of its defense is less constrained and fast), and it can also occur in a broad condition even when the invading prey is adaptively inferior. In addition, invasion into a resident system far from equilibrium characterized by population oscillations is likely to cause further destabilization.An invading prey species is thus likely to destabilize a resident community.
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Project description:Specialist predators with oscillating dynamics are often strongly affected by the population dynamics of their prey, yet they are not always the cause of prey cycling. Only those that exert strong (delayed) regulation of their prey can be. Inferring predator-prey coupling from time series therefore requires contrasting models with top-down versus bottom-up predator-prey dynamics. We study here the joint dynamics of population densities of the Icelandic gyrfalcon Falco rusticolus, and its prey, the rock ptarmigan Lagopus muta. The dynamics of both species are likely not only linked to each other but also to stochastic weather variables acting as confounding factors. We infer the degree of coupling between populations, as well as forcing by abiotic variables, using multivariate autoregressive models MAR(p), with p = 1 and 2 time lags. MAR(2) models, allowing for species to cycle independently from each other, further suggest alternative scenarios where a cyclic prey influences its predator but not the other way around (i.e., bottom-up scenarios). The classical MAR(1) model predicts that the time series exhibit predator-prey feedback (i.e., reciprocal dynamic influence between prey and predator), and that weather effects are weak and only affecting the gyrfalcon population. Bottom-up MAR(2) models produced a better fit but less realistic cross-correlation patterns. Simulations of MAR(1) and MAR(2) models further demonstrate that the top-down MAR(1) models are more likely to be misidentified as bottom-up dynamics than vice versa. We therefore conclude that predator-prey feedback in the gyrfalcon-ptarmigan system is likely the main cause of observed oscillations, though bottom-up dynamics cannot yet be excluded with certainty. Overall, we showed how to make more out of ecological time series by using simulations to gauge the quality of model identification, and paved the way for more mechanistic modeling of this system by narrowing the set of important biotic and abiotic drivers.
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Project description:Many organisms display oscillations in population size. Theory predicts that these fluctuations can be generated by predator-prey interactions, and empirical studies using life model systems, such as a rotifer-algae community consisting of Brachionus calyciflorus as predator and Chlorella vulgaris as prey, have been successfully used for studying such dynamics. B. calyciflorus is a cyclical parthenogen (CP) and clones often differ in their sexual propensity, that is, the degree to which they engage into sexual or asexual (clonal) reproduction. Since sexual propensities can affect growth rates and population sizes, we hypothesized that this might also affect population oscillations. Here, we studied the dynamical behaviour of B. calyciflorus clones representing either CPs (regularly inducing sex) or obligate parthenogens (OPs). We found that the amplitudes of population cycles to be increased in OPs at low nutrient levels. Several other population dynamic parameters seemed unaffected. This suggests that reproductive mode might be an important additional variable to be considered in future studies of population oscillations.
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Project description:Eco-evolutionary frameworks can explain certain features of communities in which ecological and evolutionary processes occur over comparable timescales. Here, we investigate whether an evolutionary dynamics may interact with the spatial structure of a prey-predator community in which both species show limited mobility and predator perceptual ranges are subject to natural selection. In these conditions, our results unveil an eco-evolutionary feedback between species spatial mixing and predators perceptual range: different levels of mixing select for different perceptual ranges, which in turn reshape the spatial distribution of prey and its interaction with predators. This emergent pattern of interspecific interactions feeds back to the efficiency of the various perceptual ranges, thus selecting for new ones. Finally, since prey-predator mixing is the key factor that regulates the intensity of predation, we explore the community-level implications of such feedback and show that it controls both coexistence times and species extinction probabilities.
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