Model Of Predator-prey System Research Articles

Mathematical modelling and bifurcation analysis of an eco-epidemiological system with multiple functional responses subjected to Allee effect and competition

This article deals with an eco-epidemiological predator–prey model system with Allee effect on prey species and different functional responses. The growth function of the prey species is considered to follow Allee effect as this effect has an important and fundamental aspect on population growth. In this study we explore stability behaviour of the system along with bifurcation properties. It is also shown that the system experiences chaotic behaviour via period-doubling bifurcation as the parameters pass through some threshold values. The study’s validity is authenticated through numerical simulations using appropriate tools. The numerical simulations reveal that the system exhibits diverse dynamic behaviours with slight variations in system parameters.

White-tailed deer detection rates increase when coyotes are present.

Predator species can indirectly affect prey species through the cost of anti-predator behavior responses, which may involve shifts in occupancy, space use, or movement. Quantifying the various strategies implemented by prey species to avoid adverse interactions with predators can lead to a better understanding of potential population-level repercussions. Therefore, the purpose of this study was to examine predator-prey interactions by quantifying the effect of predator species presence on detection rates of prey species, using coyotes (Canis latrans) and white-tailed deer (Odocoileus virginianus) in Central Appalachian forests of the eastern United States as a model predator-prey system. To test two competing hypotheses related to interspecific interactions, we modeled species detections from 319 camera traps with a two-species occupancy model that incorporated a continuous-time detection process. We found that white-tailed deer occupancy was independent of coyote occupancy, but white-tailed deer were more frequently detectable and had greater detection intensity at sites where coyotes were present, regardless of vegetation-related covariates. In addition, white-tailed deer detection rates at sites with coyotes were highest when presumed forage availability was relatively low. These findings suggest that white-tailed deer may be exhibiting an active avoidance behavioral response to predators by increasing movement rates when coyotes are present in an area, perhaps due to reactive evasive maneuvers and/or proactive attempts to reduce adverse encounters with them. Concurrently, coyotes could be occupying sites with higher white-tailed deer densities. Because white-tailed deer did not exhibit significant shifts in daily activity patterns based on coyote occupancy, we further suggest that white-tailed deer in our study system generally do not use temporal partitioning as their primary strategy for avoiding encounters with coyotes. Overall, our study implements a recently developed analytical approach for modeling multi-species occupancy from camera traps and provides novel ecological insight into the complex relationships between predator and prey species.

Grazer-induced changes in molecular signatures of cyanobacteria

Algal biomass production is an emerging renewable source of fuels, nutrients, manufacturing materials, and pharmaceuticals. Industrial-scale production is predominantly performed in open raceway ponds that are inexpensive to build, operate, and maintain compared to closed bioreactors. However, these open pond systems suffer from increased opportunities for biological contamination from predators, pathogens, and competitors, which result in reduced biomass quality and yields and often the complete destruction of the crop over a short period of time. Early detection of contaminants is a necessary step of integrated pest management for triggering and informing interventions to prevent crop losses. To develop a sensitive method of detection utilizing mass spectrometry (MS), we used three methods – imaging mass spectrometry (imaging MS), liquid chromatography MS/MS (LC-MS/MS) combined with molecular networking, and gas chromatography MS/MS (GC–MS/MS) – to observe and identify molecular signatures from a model predator-prey system of the heterolobosean amoeba HGG1 preying on the filamentous cyanobacterium Anabaena sp. PCC 7120. Imaging MS enabled the association of molecules with the crop, the predator, or the activity of protozoan grazing, while LC-MS/MS-based molecular networking identified a subset of the grazing-specific signals as the chlorophyll breakdown products pyropheophytin, pheophorbide A, and pyropheophorbide. Application of MS techniques to other amoeba-cyanobacterial predator-prey pairs allowed categorization of grazing signatures as universal or specific to the species of prey, predator, or the prey-predator pairing, indicating that MS-based techniques can distinguish crops from competitors and potentially identify predators. Finally, GCMS/MS was shown to be capable of monitoring novel volatile organic compounds (VOCs), including those predicted to be released through chlorophyll breakdown, in the headspace over algal cultures under predation. These results demonstrate that the combination of multiple MS technologies creates a predictive framework to identify and catalog relevant molecular signatures for informing crop protection strategies.

Chemosensory Exploitation and Predator-Prey Arms Races

Thousands of armed predatory species, distributed widely across the metazoan tree-of-life, consume only hard-shell or exoskeleton-bearing organisms (called “durophagy”). Prey armor clearly has evolved in response to selection by predators, but there is little evidence of the contrary, counter-adaptation by predators. Evolved consumer responses to prey, in general, might be more readily expressed in ways other than morphological traits, including via sensory cues. Here, we explored the chemosensory basis for durophagy in a model predator-prey system, and identified intimate associations between durophagous predators and their shelled prey. Barnacles (Balanus glandula and Semibalanus cariosus) bear hard shells and secrete, respectively, a 199 or 201 kDa glycoprotein ortholog (named “MULTIFUNCin”), with expression limited to the body armor (epidermis, cuticle, and live shell). To test for effects of MULTIFUNCin on predators, we constructed faux prey to mimic meaningful physical and chemical characteristics of live barnacles. In separate experiments, each consumer species was presented MULTIFUNCin, purified from either B. glandula or S. cariosus, at a typical armor concentration. All six predatory species (sea star, Pisaster ochraceus; whelks, Acanthinucella spirata, Nucella emarginata, N. ostrina, N. canaliculata, and N. lamellosa) attacked and ate MULTIFUNCin-infused faux prey significantly more than controls. Akin to barnacles, secretion of glycoprotein-rich extracellular matrices is common among armored prey species—from marine sponges to terrestrial vertebrates. Our results, therefore, suggest that chemosensory exploitation of glycoproteins could be widespread, with notable consequences for life on land and in the sea.

An alternating active-dormitive strategy enables disadvantaged prey to outcompete the perennially active prey through Parrondo\u2019s paradox

BackgroundDormancy is widespread in nature, but while it can be an effective adaptive strategy in fluctuating environments, the dormant forms are costly due to the inability to breed and the relatively high energy consumption. We explore mathematical models of predator-prey systems, in order to assess whether dormancy can be an effective adaptive strategy to outcompete perennially active (PA) prey, even when both forms of the dormitive prey (active and dormant) are individually disadvantaged.ResultsWe develop a dynamic population model by introducing an additional dormitive prey population to the existing predator-prey model which can be active (active form) and enter dormancy (dormant form). In this model, both forms of the dormitive prey are individually at a disadvantage compared to the PA prey and thus would go extinct due to their low growth rate, energy waste on the production of dormant prey, and the inability of the latter to grow autonomously. However, the dormitive prey can paradoxically outcompete the PA prey with superior traits and even cause its extinction by alternating between the two losing strategies. We observed higher fitness of the dormitive prey in rich environments because a large predator population in a rich environment cannot be supported by the prey without adopting an evasive strategy, that is, dormancy. In such environments, populations experience large-scale fluctuations, which can be survived by dormitive but not by PA prey.ConclusionWe show that dormancy can be an effective adaptive strategy to outcompete superior prey, recapitulating the game-theoretic Parrondo’s paradox, where two losing strategies combine to achieve a winning outcome. We suggest that the species with the ability to switch between the active and dormant forms can dominate communities via competitive exclusion.

A predator–prey model with Crowley–Martin functional response: A nonautonomous study

AbstractWe investigate a nonautonomous predator–prey model system with a Crowley–Martin functional response. We perform rigorous mathematical analysis and obtain conditions for (a) global attractivity and permanence in the form of integrals which improve the traditional conditions obtained by using bounds of involved parameters; and (b) the existence of periodic solutions applying continuation theorem from coincidence degree theory which has stronger results than using Brouwer fixed point theorem. Our result also indicates that the global attractivity of periodic solution is positively affected by the predator's density dependent death rate. We employ partial rank correlation coefficient method to focus on how the output of the model system analysis is influenced by variations in a particular parameter disregarding the uncertainty over the remaining parameters. We discuss the relations between results (permanence and global attractivity) for autonomous and nonautonomous systems to get insights on the effects of time‐dependent parameters.Recommendations for Resource Managers: The natural environment fluctuates because of several factors, for example, mating habits, food supplies, seasonal effects of weathers, harvesting, death rates, birth rates, and other important population rates. The temporal fluctuations in physical environment (periodicity) plays a major role in community and population dynamics along with the impacts of population densities. Periodic system may suppress the permanence of its corresponding autonomous system with parameters being the averages of periodic parameters. As the human needs crosses a threshold level, then we require to observe the sustainability of resources of the associated exploited system. Therefore, the concept of stability and permanence become our main concern in an exploited model system (system with harvesting). The mutual interference at high prey density may leave negative effect on the permanence of the system. In harvested system, permanence becomes an important issue because if we harvest too many individuals then species may be driven to extinction. Interestingly, in many biological/agricultural systems, harvesting (due to fishing in marine system, hunting or disease) of a particular species/crop can only be more beneficial at certain times (e.g., the time and stage of harvest of a particular crop play greater role in its production and hence the particular crop is many times harvested at its physiological maturity or at harvest maturity).

Temperature Affects Chemical Defense in a Mite-Beetle Predator-Prey System

Temperature influences all biochemical and biophysiological processes within an organism. By extension, it also affects those ecological interactions that are mediated by gland-produced chemical compounds, such as reservoir-based chemical defense. Herein, we investigate how environmental temperature affects the regeneration of defensive secretions and influences the efficacy of chemical defense in a model predator-prey system: the oribatid mite Archegozetes longisetosus and the predaceous rove beetle Stenus juno. Through a combination of chemical analyses, non-linear regression modeling and theoretical simulations we show that the amount of defensive secretion responded to temperature in a unimodal optimum curve: the regeneration rate followed a positive, linear relationship up to 35°C, but rapidly broke down beyond this temperature ("tipping point" effect). Using functional response simulations, there is an initially positive dampening effect on the predation rate when regeneration is optimal, but at higher temperatures chemical defense does not counteract the previously described effects of elevated predatory pressure. In a larger context, our results demonstrate the need to integrate relevant environmental factors in predator-prey modeling approaches.

Mathematical analysis of prey predator system with immigrant prey using a new approach to Homotopy perturbation method

A mathematical model for predator prey system with immigrant prey previously proposed is solved analytically to get an approximate analytical solution for local prey population density, immigrant prey population density and the predator population density. The analytical solution derived is compared with the numerical solution obtained using MATLAB and is found to make a good fit. The derived results have been illustrated with their graphs for certain parametric values.

Predation shapes the impact of cancer on population dynamics and the evolution of cancer resistance.

Cancer is a widespread disease that affects most of the metazoans. However, cancer development is a slow process and, long before causing the death of the individual, may weaken organisms’ capacities and impair their interactions with other species. Yet, the impact of cancer development on biotic interactions, and over the dynamics of the whole ecosystem, is still largely unexplored. As well, the feedback of altered biotic interactions on the evolution of resistance against cancer in the context of community ecology has not been investigated. From this new perspective, we theoretically investigate how cancer can challenge expected interaction outcomes in a predator–prey model system, and how, in return, these altered interaction outcomes could affect evolution of resistance mechanism against cancer. First, we demonstrate a clear difference between prey and predator vulnerability to cancer, with cancer having a limited impact on prey populations. Second, we show that biotic interactions can surprisingly lead to a null or positive effect of cancer on population densities. Finally, our evolutionary analysis sheds light on how biotic interactions can lead to diverse resistance levels in predator populations. While its role in ecosystems is mostly unknown, we demonstrate that cancer in wildlife is an important ecological and evolutionary force to consider.

Examining intraspecific multiple predator effects across shifting predator sex ratios

Predator-predator interactions, or “multiple predator effects” (MPEs), are pervasive in the structuring of communities and complicate predictive quantifications of ecosystem dynamics. The nature of MPEs is also context-dependent, manifesting differently among species, prey densities and habitat structures. However, there has hitherto been a lack of consideration for the implications of intraspecific demographic variation within populations for the strength of MPEs. The present study extends MPE concepts to examine intraspecific interactions among male and female predators across differences in prey densities using a functional response approach. Focusing on a copepod-mosquito model predator-prey system, interaction strengths of different sex ratio pairs of Lovenula raynerae were quantified towards larval Culex pipiens complex prey, with observations compared to both additive and substitutive model predictions. Copepods exhibited destabilising Type II functional responses in all treatments, with female copepods significantly more voracious than males under multiple predator groups. Lovenula raynerae exhibited significantly negative MPEs overall which resulted in prey risk reductions. However, whilst not statistically clear, the magnitude of antagonistic interactions subtly differed among predator-predator compositions and prey densities, with female-female antagonisms generally prevalent at low prey densities, and male-male negative interactions greater under high prey densities. Mixed-sex copepod group predation was predicted by both additive and substitutive models, and additive models generated significantly higher consumption estimates than substitutive equivalents given that their predictions were based on the absence of antagonistic non-trophic interactions. We propose the importance of internal population sex demographics as a further context-dependency which influences the nature of MPEs, with demographic implications requiring investigation across other taxonomic and trophic groups.

Dynamics and pattern formation of a diffusive predator–prey model with predator-taxis

We propose a new reaction–diffusion predator–prey model system with predator-taxis in which the preys could move in the opposite direction of predator gradient. A similar situation also occurs when susceptible population avoids the infected ones in epidemic spreading. The global existence and boundedness of solutions of the system in bounded domains of arbitrary spatial dimension and any predator-taxis sensitivity coefficient are proved. It is also shown that such predator-taxis does not qualitatively affect the existence and stability of coexistence steady state solutions in many cases. For diffusive predator–prey system with diffusion-induced instability, it is shown that the presence of predator-taxis may annihilate the spatial patterns.

Time-delayed conjugate coupling in dynamical systems

We study the effect of time-delay when the coupling between nonlinear systems is “conjugate”, namely through dissimilar variables. This form of coupling can induce anomalous transitions such as the emergence of oscillatory dynamics between regimes of amplitude death and oscillation death. The specific cases of coupled Landau-Stuart oscillators as well as a predator-prey model system with cross-predation are discussed. The dynamical behaviour is analyzed numerically and the regions corresponding to different asymptotic states are identified in parameter space.

Dynamic behaviour of a reaction–diffusion predator–prey model with both refuge and harvesting

An appropriate mathematical structure to describe the population dynamics is given by the partial differential equations of reaction–diffusion type. The spatiotemporal dynamics and bifurcations of a ratio-dependent Holling type II predator–prey model system with both the effect of linear prey harvesting and constant proportion of prey refuge are investigated. The existence of all ecologically feasible equilibria for the non-spatial model is determined, and the dynamical classifications of these equilibria are developed. The model system representing initial boundary value problem under study is subjected to zero flux boundary conditions. The conditions of diffusion-driven instability and the Turing bifurcation region in two parameter space are explored. The consequences of spatial pattern analysis in two-dimensional domain by means of numerical simulations reveal that the typical dynamics of population density variation is the formation of isolated groups, i.e. spotted or stripe-like patterns or coexistence of both the patterns or labyrinthine patterns and so on. The results around the unique interior feasible equilibrium solution indicate that the effect of refuge and harvesting plays a significant role on the control of spatial pattern formation of the species. Finally, the paper ends with a comprehensive discussion of biological implications of our findings.

The “Destabilizing” Effect of Cannibalism in a Spatially Explicit Three-Species Age Structured Predator-Prey Model

Cannibalism, the act of killing and consumption of conspecifics, is generally considered to be a stabilising process in ODE models of predator-prey systems. On the other hand, Sun et al. were the first to show that cannibalism can cause Turing instability, in the classical Rosenzweig-McArthur two-species PDE model, which is an impossibility without cannibalism. Magnússon’s classic work is the first to show that cannibalism in a structured three-species predator-prey ODE model can actually be destabilising. In the current manuscript we consider the PDE form of the three-species model proposed in Magnússon’s classic work. We prove that, in the absence of cannibalism, Turing instability is an impossibility in this model, forany range of parameters. However, theinclusionof cannibalism can cause Turing instability. Thus, to the best of our knowledge, we report thefirstcannibalism induced Turing instability result, in spatially explicit three-species age structured predator-prey systems. We also show that, in the classical ODE model proposed by Magnússon, cannibalism can act as a life boat mechanism,for the prey.

Stationary patterns induced by self- and cross-diffusion in a Beddington–DeAngelis predator–prey model

The study of spatial pattern formation through diffusion-driven instability of reaction–diffusion models of interacting species has long been one of the fundamental problems in mathematical ecology. The present article is concerned with interacting predator–prey reaction–diffusion model with Beddington–DeAngelis type functional response. The essential conditions for Hopf and Turing bifurcations are derived on the spatial domain. The parameter space for Turing spatial structure is established. Based on the bifurcation analysis, the spatial pattern formation in Turing space through numerical simulations is carried out in order to study the evolution procedure of the proposed model system in the vicinity of coexistence equilibrium point. The consequences of the results obtained reveal that the effects of self- and cross-diffusion play significant role on the steady state spatiotemporal pattern formation of the reaction–diffusion predator–prey model system which concerns the influence of intra-species competition among predators. Finally, ecological implications of the present results obtained are discussed at length towards the end in order to validate the applicability of the model under consideration.

Assessment of agglomeration, co-sedimentation and trophic transfer of titanium dioxide nanoparticles in a laboratory-scale predator-prey model system

Nano titanium dioxide (nTiO2) is the most abundantly released engineered nanomaterial (ENM) in aquatic environments. Therefore, it is prudent to assess its fate and its effects on lower trophic-level organisms in the aquatic food chain. A predator-and-prey-based laboratory microcosm was established using Paramecium caudatum and Escherichia coli to evaluate the effects of nTiO2. The surface interaction of nTiO2 with E. coli significantly increased after the addition of Paramecium into the microcosm. This interaction favoured the hetero-agglomeration and co-sedimentation of nTiO2. The extent of nTiO2 agglomeration under experimental conditions was as follows: combined E. coli and Paramecium > Paramecium only > E. coli only > without E. coli or Paramecium. An increase in nTiO2 internalisation in Paramecium cells was also observed in the presence or absence of E. coli cells. These interactions and nTiO2 internalisation in Paramecium cells induced statistically significant (p < 0.05) effects on growth and the bacterial ingestion rate at 24 h. These findings provide new insights into the fate of nTiO2 in the presence of bacterial-ciliate interactions in the aquatic environment.

Mutations in Novel Lipopolysaccharide Biogenesis Genes Confer Resistance to Amoebal Grazing in Synechococcus elongatus.

In natural and artificial aquatic environments, population structures and dynamics of photosynthetic microbes are heavily influenced by the grazing activity of protistan predators. Understanding the molecular factors that affect predation is critical for controlling toxic cyanobacterial blooms and maintaining cyanobacterial biomass production ponds for generating biofuels and other bioproducts. We previously demonstrated that impairment of the synthesis or transport of the O-antigen component of lipopolysaccharide (LPS) enables resistance to amoebal grazing in the model predator-prey system consisting of the heterolobosean amoeba HGG1 and the cyanobacterium Synechococcus elongates PCC 7942 (R. S. Simkovsky et al., Proc Natl Acad Sci U S A 109:16678-16683, 2012,http://dx.doi.org/10.1073/pnas.1214904109). In this study, we used this model system to identify additional gene products involved in the synthesis of O antigen, the ligation of O antigen to the lipid A-core conjugated molecule (including a novel ligase gene), the generation of GDP-fucose, and the incorporation of sugars into the lipid A core oligosaccharide ofS. elongatus Knockout of any of these genes enables resistance to HGG1, and of these, only disruption of the genes involved in synthesis or incorporation of GDP-fucose into the lipid A-core molecule impairs growth. Because these LPS synthesis genes are well conserved across the diverse range of cyanobacteria, they enable a broader understanding of the structure and synthesis of cyanobacterial LPS and represent mutational targets for generating resistance to amoebal grazers in novel biomass production strains.

Remarks on the number of persistent states to a fragmented predator–prey model system

We consider a predator–prey model system for spatially distributed species over patches. Each predator species has a unique preferred patch (shelter and reproduction site) and travel for chasing prey. Its individuals are split into resident from the preferred patch and travelers. Further there is at most one resident predator species per patch. Depending on the availability of local anthropized resources not related to local prey on the preferred patch, one distinguishes between well-fed and starving predators. We assume prey species do not disperse at the predator scale.In this study we are interested in the number of persistent stationary states for the resulting ordinary differential equations model system. There exists at most one persistent predator–prey stationary state when there is exactly one starving resident predators per patch provided all functional responses to predation are Lotka–Volterra like or when a single starving resident predators is available. Else multiple persistent predator–prey stationary state are likely to exist. A specific emphasis is put on toy-model systems with 2 or 3 patches. Slow–fast dynamical methodology is also used for locally asymptotically stable purposes.Numerical experiments suggest that several scalings may govern the dynamics at stabilization.

Feedback between size balance and consumption strongly affects the consequences of hatching phenology in size‐dependent predator–prey interactions

In many size‐dependent predator–prey systems, hatching phenology strongly affects predator–prey interaction outcomes. Early‐hatched predators can easily consume prey when they first interact because they encounter smaller prey. However, this process by itself may be insufficient to explain all predator–prey interaction outcomes over the whole interaction period because the predator–prey size balance changes dynamically throughout their ontogeny. We hypothesized that hatching phenology influences predator–prey interactions via a feedback mechanism between the predator–prey size balance and prey consumption by predators. We experimentally tested this hypothesis in an amphibian predator–prey model system. Frog tadpoles Rana pirica were exposed to a predatory salamander larva Hynobius retardatus that had hatched 5, 12, 19 or 26 days after the frog tadpoles hatched. We investigated how the salamander hatch timing affected the dynamics of prey mortality, size changes of both predator and prey, and their subsequent life history (larval period and size at metamorphosis). The predator–prey size balance favoured earlier hatched salamanders, which just after hatching could successfully consume more frog tadpoles than later hatched salamanders. The early‐hatched salamanders grew rapidly and their accelerated growth enabled them to maintain the predator‐superior size balance; thus, they continued to exert strong predation pressure on the frog tadpoles in the subsequent period. Furthermore, frog tadpoles exposed to the early‐hatched salamanders were larger at metamorphosis and had a longer larval period than other frog tadpoles. These results suggest that feedback between the predator‐superior size balance and prey consumption is a critical mechanism that strongly affects the impacts of early hatching of predators in the short‐term population dynamics and life history of the prey. Because consumption of large nutrient‐rich prey items supports the growth of predators, a similar feedback mechanism may be common and have strong impacts on phenological shifts in size‐dependent trophic relationships.

Complex dynamics in a ratio-dependent two-predator one-prey model

A three-species ratio-dependent predator prey model system is considered. The global dynamic behavior of the model is investigated through (local) stability results for its equilibriums and large time computer simulations. Irregular patterns and existence of complex dynamics are noticed for different sets of parameter values. The model is shown to have chaotic attractors for suitable choice of values of parameters.