Disease-induced modification of prey competition in eco-epidemiological models

Stability and Hopf bifurcation in an eco-epidemiological system with the cost of anti-predator behaviors

The fear effect is a powerful force in prey-predator interaction, eliciting a variety of anti-predator responses which lead to a reduction of prey growth rate. To study the impact of the fear effect on population dynamics of the eco-epidemiological system, we develop a predator-prey interaction model that incorporates infectious disease in predator population as well as the cost of anti-predator behaviors. Detailed mathematical results, including well-posedness of solutions, stability of equilibria and the occurrence of Hopf bifurcation are provided. It turns out that population density diminishes with increasing fear, and the fear effect can either destabilize the stability or induce the occurrence of periodic behavior. The theoretical results here provide a sound foundation for understanding the effect of the anti-predator behaviors on the eco-epidemiological interaction.

Dynamics of an Eco-Epidemic Predator–Prey Model Involving Fractional Derivatives with Power-Law and Mittag–Leffler Kernel

In this paper, we consider a fractional-order eco-epidemic model based on the Rosenzweig–MacArthur predator–prey model. The model is derived by assuming that the prey may be infected by a disease. In order to take the memory effect into account, we apply two fractional differential operators, namely the Caputo fractional derivative (operator with power-law kernel) and the Atangana–Baleanu fractional derivative in the Caputo (ABC) sense (operator with Mittag–Leffler kernel). We take the same order of the fractional derivative in all equations for both senses to maintain the symmetry aspect. The existence and uniqueness of solutions of both eco-epidemic models (i.e., in the Caputo sense and in ABC sense) are established. Both models have the same equilibrium points, namely the trivial (origin) equilibrium point, the extinction of infected prey and predator point, the infected prey free point, the predator-free point and the co-existence point. For a model in the Caputo sense, we also show the non-negativity and boundedness of solution, perform the local and global stability analysis and establish the conditions for the existence of Hopf bifurcation. It is found that the trivial equilibrium point is a saddle point while other equilibrium points are conditionally asymptotically stable. The numerical simulations show that the solutions of the model in the Caputo sense strongly agree with analytical results. Furthermore, it is indicated numerically that the model in the ABC sense has quite similar dynamics as the model in the Caputo sense. The essential difference between the two models is the convergence rate to reach the stable equilibrium point. When a Hopf bifurcation occurs, the bifurcation points and the diameter of the limit cycles of both models are different. Moreover, we also observe a bistability phenomenon which disappears via Hopf bifurcation.

Persistence and extinction of species in a disease-induced ecological system under environmental stochasticity

Population extinction is a serious issue both from the theoretical and practical points of view. We explore here how environmental noise influences persistence and extinction of interacting species in presence of a pathogen even when the populations remain stable in its deterministic counterpart. Multiplicative white noise is introduced in a deterministic predator-prey-parasite system by randomly perturbing three biologically important parameters. It is revealed that the extinction criterion of species may be satisfied in multiple ways, indicating various routes to extinction, and disease eradication may be possible with the right environmental noise. Predator population cannot survive, even when its focal prey strongly persists if its growth rate is lower than some critical value, measured by half of the corresponding noise intensity. It is shown that the average extinction time of population decreases with increasing noise intensity and the probability distribution of the extinction time follows the log-normal density curve. A case study on red grouse (prey) and fox (predator) interaction in presence of the parasites trichostrongylus tenuis of grouse is presented to demonstrate that the model well fits the field data.

DETERMINISTIC PREDATOR–PREY MODELS WITH DISEASE IN THE PREY POPULATION

A class of deterministic predator–prey systems, where the prey population is subject to an infectious disease, is studied. The disease can be transmitted both horizontally and vertically within the host population but cannot be spread between the two trophic levels. Using the mathematical tools of uniform persistence, we derive sufficient conditions for which the interacting populations can coexist. Criteria based on model parameters for which either only the infected prey or healthy prey persists are also provided. It is found through numerical investigations that predation can change competition outcomes between healthy and infected prey populations. Depending on the parameter regimes and initial conditions, predation can either eradicate or promote the disease. As infected prey provides a resource for the predators, disease may promote persistence of the predators. However, infected prey may dominate the predator–prey community if disease is very infectious. In addition, disease in the prey population can mediate a hydra effect in predators and may induce chaotic interactions.

Parasites shape community structure and dynamics in freshwater crustaceans

Parasites directly and indirectly influence the important interactions among hosts such as competition and predation through modifications of behaviour, reproduction and survival. Such impacts can affect local biodiversity, relative abundance of host species and structuring of communities and ecosystems. Despite having a firm theoretical basis for the potential effects of parasites on ecosystems, there is a scarcity of experimental data to validate these hypotheses, making our inferences about this topic more circumstantial. To quantitatively test parasites' role in structuring host communities, we set up a controlled, multigenerational mesocosm experiment involving four sympatric freshwater crustacean species that share up to four parasite species. Mesocosms were assigned to either of two different treatments, low or high parasite exposure. We found that the trematode Maritrema poulini differentially influenced the population dynamics of these hosts. For example, survival and recruitment of the amphipod Paracalliope fluviatilis were dramatically reduced compared to other host species, suggesting that parasites may affect their long-term persistence in the community. Relative abundances of crustacean species were influenced by parasites, demonstrating their role in host community structure. As parasites are ubiquitous across all communities and ecosystems, we suggest that the asymmetrical effects we observed are likely widespread structuring forces.

Host traits and competitive ability jointly structure disease dynamics and community assembly

Parasitism and competition are both ubiquitous interactions in ecological communities. The ability of host species to interact directly via competition and indirectly through shared parasites suggests that host traits related to competition and parasitism are likely important in structuring communities and disease dynamics. Specifically, those host traits affecting competition and those mediating parasitism are often correlated either because of trade-offs (in resource acquisition or resource allocation) or condition dependence, yet the consequences of these trait relationships for community and epidemiological dynamics are poorly understood. We conducted a literature review of parasite-related host traits-competitive ability relationships. We found that transmission-competitive ability relationships were most often reported, and that superior competitors exhibited elevated transmission relative to their less-competitive counterparts in nearly 80% of the cases. We also found a significant number of virulence-competitive ability and parasite shedding-competitive ability relationships. We investigated these links by altering the relationship between host competitive ability and three parasite-related traits (transmission, virulence and parasite shedding rates) in a simple model, incorporating competitive asymmetries in a multi-host community. We show that these relationships can lead to a range of different communities. For example, depending on the strength and direction of these distinct trait relationships, we observed communities with anywhere from high parasite prevalence to complete parasite extinction, and either one, two or the maximum of three host species coexisting. Our results suggest that parasite-competitive ability relationships may be common in nature, that further integration of these relationships can produce novel and unexpected community and disease dynamics, and that generalizations may allow for the prediction of how parasitism and competition jointly structure disease and diversity in natural communities.

The Impact of Selective Predation on Host-Parasite SIS Dynamics

While models of host-parasite interactions are widespread in the theoretical literature, we still have limited understanding of the impact of community dynamics on infectious disease dynamics. When the wider host ecology is taken into account, the underlying inter-species feedbacks can lead to counter-intuitive results. For example, the 'healthy herd' hypothesis posits that the removal of a predator species may not be beneficial for a prey population infected by an endemic disease. In this work, we focus on the effects of including a predator species in a susceptible-infected-susceptible model. Specifically, a key role is played by predator selectivity for either healthy or infected prey. We explored both cases and found important differences in the asymptotic behaviours of the system. Independently from selectivity, large portions of parameter space allow for the coexistence of the three species. However, when predators feed mainly on susceptible prey we find that a fold bifurcation can occur, leading to a region of bi-stability between coexistence and parasite extinction. Conversely, when predator selection is strongly towards infected prey, total prey population density can be maximal when the three species coexist, consistent with the 'healthy herd' hypothesis. Our work further highlights the importance of community interactions to infectious disease dynamics.

Interaction rates, vital rates, background fitness and replicator dynamics: how to embed evolutionary game structure into realistic population dynamics

In this paper we are concerned with how aggregated outcomes of individual behaviours, during interactions with other individuals (games) or with environmental factors, determine the vital rates constituting the growth rate of the population. This approach needs additional elements, namely the rates of event occurrence (interaction rates). Interaction rates describe the distribution of the interaction events in time, which seriously affects the population dynamics, as is shown in this paper. This leads to the model of a population of individuals playing different games, where focal game affected by the considered trait can be extracted from the general model, and the impact on the dynamics of other events (which is not neutral) can be described by an average background fertility and mortality. This leads to a distinction between two types of background fitness, strategically neutral elements of the focal games (correlated with the focal game events) and the aggregated outcomes of other interactions (independent of the focal game). The new approach is useful for clarification of the biological meaning of concepts such as weak selection. Results are illustrated by a Hawk-Dove example.

Hydra effects in stable communities and their implications for system dynamics

A hydra effect occurs when the mean density of a species increases in response to greater mortality. We show that, in a stable multispecies system, a species exhibits a hydra effect only if maintaining that species at its equilibrium density destabilizes the system. The stability of the original system is due to the responses of the hydra-effect species to changes in the other species' densities. If that dynamical feedback is removed by fixing the density of the hydra-effect species, large changes in the community make-up (including the possibility of species extinction) can occur. This general result has several implications: (1) Hydra effects occur in a much wider variety of species and interaction webs than has previously been described, and may occur for multiple species, even in small webs; (2) conditions for hydra effects caused by predators (or diseases) often differ from those caused by other mortality factors; (3) introducing a specialist or a switching predator of a hydra-effect species often causes large changes in the community, which frequently involve extinction of other species; (4) harvest policies that attempt to maintain a constant density of a hydra-effect species may be difficult to implement, and, if successful, are likely to cause large changes in the densities of other species; and (5) trophic cascades and other indirect effects caused by predators of hydra-effect species can exhibit amplification of effects or unexpected directions of change. Although we concentrate on systems that are originally stable and models with no stage-structure or trait variation, the generality of our result suggests that similar responses to mortality will occur in many systems without these simplifying assumptions. In addition, while hydra effects are defined as responses to altered mortality, they also imply counterintuitive responses to changes in immigration and other parameters affecting population growth.

Alternative prey use affects helminth parasite infections in grey wolves

Predators affect prey populations not only through direct predation, but also by acting as definitive hosts for their parasites and completing parasite life cycles. Understanding the affects of parasitism on prey population dynamics requires knowing how their predators' parasite community is affected by diet and prey availability. Ungulates, such as moose (Alces americanus) and white-tailed deer (Odocoileus virginianus), are often important prey for wolves (Canis lupus), but wolves also consume a variety of alternative prey, including beaver (Castor canadensis) and snowshoe hare (Lepus americanus). The use of alternative prey, which may host different or fewer parasites than ungulates, could potentially reduce overall abundance of ungulate parasites within the ecosystem, benefiting both wolves and ungulate hosts. We examined parasites in wolf carcasses from eastern Manitoba and estimated wolf diet using stable isotope analysis. Taeniidae cestodes were present in most wolves (75%), reflecting a diet primarily comprised of ungulates, but nematodes were unexpectedly rare. Cestode abundance was negatively related to the wolf's δ(13) C value, indicating diet affects parasite abundance. Wolves that consumed a higher proportion of beaver and caribou (Rangifer tarandus), estimated using Bayesian mixing models, had lower cestode abundance, suggesting the use of these alternative prey can reduce parasite loads. Long-term consumption of beavers may lower the abundance of adult parasites in wolves, eventually lowering parasite density in the region and ultimately benefiting ungulates that serve as intermediate hosts. Thus, alternative prey can affect both predator-prey and host-parasite interactions and potentially affect food web dynamics.