Constructive effects of environmental noise in an excitable prey–predator plankton system with infected prey

An excitable model of fast phytoplankton and slow zooplankton dynamics is considered for the case of lysogenic viral infection of the phytoplankton population. The phytoplankton population is split into a susceptible (S) and an infected (I) part. Both parts grow logistically, limited by a common carrying capacity. Zooplankton (Z) is grazing on susceptibles and infected, following a Holling-type III functional response. The local analysis of the S–I–Z differential equations yields a number of stationary and/or oscillatory regimes and their combinations. Correspondingly interesting is the behaviour under multiplicative noise, modelled by stochastic differential equations. The external noise can enhance the survival of susceptibles and infected, respectively, that would go extinct in a deterministic environment. In the parameter range of excitability, noise can induce prey–predator oscillations and coherence resonance (CR). In the spatially extended case, synchronized global oscillations can be observed for medium noise intensities. Higher values of noise give rise to the formation of stationary spatial patterns.     

An eco-epidemiological system with infected prey and predator subject to the weak Allee effect

In this article, we propose a general prey–predator model with disease in prey and predator subject to the weak Allee effects. We make the following assumptions: (i) infected prey competes for resources but does not contribute to reproduction; and (ii) in comparison to the consumption of the susceptible prey, consumption of infected prey would contribute less or negatively to the growth of predator. Based on these assumptions, we provide basic dynamic properties for the full model and corresponding submodels with and without the Allee effects. By comparing the disease free submodels (susceptible prey–predator model) with and without the Allee effects, we conclude that the Allee effects can create or destroy the interior attractors. This enables us to obtain the complete dynamics of the full model and conclude that the model has only one attractor (only susceptible prey survives or susceptible-infected coexist), or two attractors (bi-stability with only susceptible prey and susceptible prey–predator coexist or susceptible prey-infected prey coexists and susceptible prey–predator coexist). This model does not support the coexistence of susceptible-infected-predator, which is caused by the assumption that infected population contributes less or are harmful to the growth of predator in comparison to the consumption of susceptible prey.     

Predation may defeat spatial spread of infection

A model of a phytoplankton–zooplankton prey-predator system with viral infection of phytoplankton is investigated. Virus particles (V) are taken into account by an explicit equation. Phytoplankton is split into a susceptible (S) and an infected (I) class. A lytic infection is considered, thus, infected phytoplankton cells stop reproducing as soon as the infection starts and die at an increased mortality rate. Zooplankton (Z) is grazing on both susceptible and infected phytoplankton following a Holling-type II functional response. After the local dynamics of the V?S?I?Z system is analysed, numerical solutions of a stochastic reaction–diffusion model of the four species are presented. These show a spatial competition between zooplankton and viruses, although these two species are not explicitly coupled by the model equations.     

Parasite modification of predator functional response

Parasite alteration of the host (predator) functional response provides a mechanism by which parasites can alter predator–prey population dynamics and stability. We tested the hypothesis that parasitic infection of a crab (Eurypanopeus depressus) by a rhizocephalan barnacle (Loxothylacus panopei) can modify the crab’s functional response to mussel (Brachidontes exustus) prey and investigated behavioral mechanisms behind a potential change in the response. Infection dramatically reduced mussel consumption by crabs across mussel densities, resulting in a decreased attack rate parameter and a nearly eightfold reduction in maximum consumption (i.e. the asymptote, or inverse of the handling time parameter) in a type II functional response model. To test whether increased handling time of infected crabs drove the decrease in maximum consumption rate, we independently measured handling time through observation. Infection had no effect on handling time and thus could not explain the reduction in consumption. Infection did, however, increase the time that it took crabs to begin handling prey after the start of the handling time experiment. Furthermore, crabs harboring relatively larger parasites remained inactive longer before making contact with prey. This behavioral modification likely contributed to the reduced mussel consumption of infected crabs. A field survey revealed that 20 % of crabs inhabiting oyster reefs at the study site (North Inlet estuary, Georgetown, South Carolina, USA) are infected by the barnacle parasite, indicating that parasite infection could have a substantial effect on the population level crab-mussel interaction.     

Evolution of virulence driven by predator-prey interaction: Possible consequences for population dynamics

The evolution of pathogen virulence in natural populations has conventionally been considered as a result of selection caused by the interactions of the host with its pathogen(s). The host population, however, is generally embedded in complex trophic interactions with other populations in the community, in particular, intensive predation on the infected host can increase its mortality, and this can affect the course of virulence evolution. Reciprocally, in the long run, the evolution of virulence within an infected host can affect the patterns of population dynamics of a predator consuming the host (e.g. resulting in large amplitude oscillations, causing a severe drop in the population size, etc.). Surprisingly, neither the effect of predation on the evolution of virulence within a host, nor the influence of the evolution of virulence upon the consumer's dynamics has been addressed in the literature yet. In this paper, we consider a classical S-I ecoepidemiological model in which the infected host is consumed by a predator. We are particularly interested in the evolutionarily stable virulence of the pathogen in the model and its dependence upon ecologically relevant parameters. We show that predation can prominently shift the evolutionarily stable virulence towards more severe strains as compared to the same system without predation. We demonstrate that the evolution of virulence can result in a succession of dynamical regimes and can even lead to the extinction of the predator in the long run. The presence of a predator can indirectly affect the evolution within its prey since the evolutionarily stable virulence becomes a function of the prey growth rate, which would not be the case in a predator-free system. We find that the evolutionarily stable virulence largely depends on the carrying capacity K of the prey in a non-monotonous way. The model also predicts that in an eutrophic environment the shift of virulence towards evolutionarily stable benign strains can cause demographically stochastic evolutionary suicide, resulting in the extinction of both species, thus artificially maintaining severe strains of pathogen can enhance the persistence of both species.     

Comparing functional responses in predator-infected eco-epidemics models

The current paper deals with the mathematical models of predator–prey system where a transmissible disease spreads among the predator species only. Four mathematical models are proposed and analysed with several popular predator functional responses in order to show the influence of functional response on eco-epidemic models. The existence, boundedness, uniqueness of solutions of all the models are established. Mathematical analysis including stability and bifurcation are observed. Comparison among the results of these models allows the general conclusion that relevant behaviour of the eco-epidemic predator–prey system, including switching of stability, extinction, persistence and oscillations for any species depends on four important parameters viz. the rate of infection, predator interspecies competition and the attack rate on susceptible predator. The paper ends with a discussion of the biological implications of the analytical and numerical results.     

Complex dynamics of a predator–prey–parasite system: An interplay among infection rate,predator's reproductive gain and preference

Parasites are considered as an important factor in regulating their host populations through trait-mediated effects. On the other hand, predation becomes particularly interesting in host–parasite systems because predation can significantly alter the abundance of parasites and their host population. The combined effects of parasites and predator on host population and community structure therefore may have larger effect. Different field experiments confirm that predators consume disproportionately large number of infected prey in comparison to their susceptible counterpart. There are also substantial evidences that predator has the ability to distinguish prey that have been infected by a parasite and avoid such prey to reduce fitness cost. In this paper we study the predator–prey dynamics, where the prey species is infected by some parasites and predators consume both the susceptible and infected prey with some preference. We demonstrate that complexity in such systems largely depends on the predator's selectivity, force of infection and predator's reproductive gain. If the force of infection and predator's reproductive gain are low, parasites and predators both go to extinction whatever be the predator's preference. The story may be totally different in the opposite case. Survival of species in stable, oscillatory or chaotic states, and their extinction largely depend on the predator's preference. The system may also show two coexistence equilibrium points for some parameter values. The equilibrium with lower susceptible prey density is always stable and the equilibrium with higher susceptible prey density is always unstable. These results suggest that understanding the consequences of predator's selectivity or preference may be crucial for community structure involving parasites.     

On competition of predators and prey infection

A class of prey–predator models with infected prey is investigated. Predation terms are either of Holling type II or III, infection is either modelled by mass action or standard incidence. It is shown that the key for understanding the model behaviour is the competition of predators versus infection. In the presented models the predator is not susceptible to the infection and the infection of the prey has no influence on the ability of the predator of catching the prey. However, the prey population can be seen as a resource which both the predators and the infection depend on. The competition for this resource is strong—the principle of competitive exclusion holds for biologically meaningful choices of parameters as long as there is no destabilisation by a Hopf bifurcation. The representation of models in competition diagrams which are introduced in this article can be used for a wide range of competition models which seems to be a promising method with many potential applications.     

The role of virus infection in a simple phytoplankton zooplankton system

Many planktonic species show spectacular bursts ("blooms") in population density. Though viral infections are known to cause behavioural and other changes in phytoplankton and other aquatic species, yet their role in regulating the phytoplankton population is still far from being understood. To study the role of viral diseases in the planktonic species, we model the phytoplankton-zooplankton system as a prey-predator system. Here the prey (phytoplankton) species is infected with a viral disease that divides the prey population into susceptible and infected classes, with the infected prey being more vulnerable to predation by the predator (zooplankton). The dynamical behaviour of the system is investigated from the point of view of stability and persistence both analytically and numerically. The model shows that infection can be sustained only above a threshold of force of infection, and, there exists a range in the infection rate where this system shows "bloom"-like stable limit cycle oscillations. The time series of natural "blooms" with different types of irregular oscillations can arise in this model simply from a biologically realistic feature, i.e., by the random variation of the epidemiological parameter (rate of infection) in the infected prey population. The difference in mean strength of infection alone can lead to the different types of patterns observed in natural planktonic blooms.     

Modeling the impacts of global warming on predation and biotic resistance: mosquitoes, damselflies and avian malaria in Hawaii

Biotic resistance from native predators can play an important role in regulating or limiting exotic prey. We investigate how global warming potentially alters the strength and spatial extent of these predator–prey interactions in aquatic insect ecosystems. As a simple model system, we use rock pools in streams of rainforests of Hawaii, which contain the beautiful Hawaiian damselfly Megalagrion calliphya as predator and the invasive southern house mosquito Culex quinquefasciatus as prey. This abundant mosquito is the major vector of avian malaria transmission to native forest birds. We use mathematical modeling to evaluate the potential impacts of damselfly predation and temperature on mosquito population dynamics. We model this predator–prey system along an elevational gradient (749-1952 m elevation) and assess the effect of 1°C and 2°C climate warming scenarios as well as the effects of El Niño and La Niña oscillations, on predator–prey dynamics. Our results indicate that the strength of biotic resistance of native predators on invasive prey may decrease with increasing temperature because demographic rates of predator and prey are differentially affected by temperature. Future warming could therefore increase the abundance of invasive species by releasing them from predation pressure. If the invasive species is a disease vector, these shifts could increase the impact of disease on both humans and wildlife.     

An incubating diseased-predator ecoepidemic model

We present a model for transmissible diseases spreading among predators in a predator–prey system. Upon successful contact, a susceptible individual becomes infected but is not yet able to spread the disease further. After an incubation period, the diseased individual becomes infectious. We investigate the system’s equilibria by analytical and numerical means. For a suitable set of parameter values, the system shows persistent oscillations. The model also exhibits bistability of the coexistence equilibrium with the prey-only equilibrium.     

Reversed predator–prey cycles are driven by the amplitude of prey oscillations

Ecoevolutionary feedbacks in predator–prey systems have been shown to qualitatively alter predator–prey dynamics. As a striking example, defense–offense coevolution can reverse predator–prey cycles, so predator peaks precede prey peaks rather than vice versa. However, this has only rarely been shown in either model studies or empirical systems. Here, we investigate whether this rarity is a fundamental feature of reversed cycles by exploring under which conditions they should be found. For this, we first identify potential conditions and parameter ranges most likely to result in reversed cycles by developing a new measure, the effective prey biomass, which combines prey biomass with prey and predator traits, and represents the prey biomass as perceived by the predator. We show that predator dynamics always follow the dynamics of the effective prey biomass with a classic ¼‐phase lag. From this key insight, it follows that in reversed cycles (i.e., ¾‐lag), the dynamics of the actual and the effective prey biomass must be in antiphase with each other, that is, the effective prey biomass must be highest when actual prey biomass is lowest, and vice versa. Based on this, we predict that reversed cycles should be found mainly when oscillations in actual prey biomass are small and thus have limited impact on the dynamics of the effective prey biomass, which are mainly driven by trait changes. We then confirm this prediction using numerical simulations of a coevolutionary predator–prey system, varying the amplitude of the oscillations in prey biomass: Reversed cycles are consistently associated with regions of parameter space leading to small‐amplitude prey oscillations, offering a specific and highly testable prediction for conditions under which reversed cycles should occur in natural systems.     

Threat of Infection and Threat-Avoidance Behavior in the Predator <Emphasis Type="Italic">Dicyphus hesperus</Emphasis> Feeding on Whitefly Nymphs Infected with an Entomopathogen

The nature and severity of intraguild interactions between predators and entomopathogens will be determined, in part, by a combination of threat of infection, and avoidance of that threat by the predator. We determined the threat of infection posed by the entomopathogen, Paecilomyces fumosoroseus (as PFR-97™) to the generalist predator, Dicyphus hesperus. We then asked if D. hesperus displays behavioral avoidance of infection while foraging for whitefly nymphs at different stages of infection by the pathogen. When exposed to leaf surfaces treated with the pathogen, 28% of adult female predators died due to infection. Consumption of Ephestia kuehniella eggs by surviving predators over 6 d was significantly reduced, suggesting effects of a sublethal infection. Whitefly nymphs that had been treated with P. fumosoroseus 3 d prior were acceptable as prey to D. hesperus but whitefly nymphs that had been treated with P. fumosoroseus 5 days prior were not. When foraging for whitefly nymphs, adult D. hesperus females rejected infected nymphs 96% of the time, compared to 39% of non-infected nymphs. Paecilomyces fumosoroseus therefore presents a measurable threat to D. hesperus through mortality and reduced prey consumption. Dicyphus hesperus does not avoid initial contact with infected prey but does not feed on such prey. The mechanism underlying these rejections could be due to either avoidance of infection or rejection of prey already consumed by the infectious agent. These results suggest that predation by D. hesperus foraging among infected whitefly nymphs under greenhouse or natural conditions could be reduced through a combination of pathogenicity and reduced efficiency of foraging.     

The effectiveness of post-contact defenses in a prey with no pre-contact detection

Most empirical and theoretical papers on prey–predator interactions are for animals with long-range detection, animals that can detect and react to predators long before these touch the prey. Heavy-bodied and chemically defended harvestmen (Arachnida, Opiliones) are an exception to this general pattern and rely on contact to detect arthropod predators. We examined the interactions between the Brazilian wandering spider Ctenus ornatus with harvestmen (Mischonyx cuspidatus) or control prey (Gryllus sp. and M. cuspidatus immature, both with soft integuments). Considering a prey–predator system in which fleeing from or reacting to a predator at a distance is not possible, we predicted both a high survival value of near-range defense mechanisms and that mortality would be higher in the absence of such defense mechanisms. We also expected the predator to behave differently when interacting with harvestmen or with a control prey without such defense mechanisms. Our results from laboratory experiments partially matched our predictions: First of all, histological sections showed that the integument of adult harvestmen is thicker than that of immature harvestmen and that of crickets. Adult harvestmen were less preyed upon than the control prey; the heavy armature increases the survival rate but the secretions from the scent glands do not. The predator did behave differently when attacking harvestmen compared to crickets. Despite the large size difference between predator and harvestmen, the protection provided by the armature allowed some of the harvestmen to survive encounters without pre-contact detection, thus greatly reducing the reliance on long-range detection to survive encounters with predators. Harvestmen call for theoretical and empirical work on prey–predator interactions that take into account the possibility that prey may not detect the predator before contact is established.     

Introduced species provide a novel temporal resource that facilitates native predator population growth

Non-native species are recognized as important components of change to food web structure. Non-native prey may increase native predator populations by providing an additional food source and simultaneously decrease native prey populations by outcompeting them for a limited resource. This pattern of apparent competition may be important for plants and sessile marine invertebrate suspension feeders as they often compete for space and their immobile state make them readily accessible to predators. Reported studies on apparent competition have rarely been examined in biological invasions and no study has linked seasonal patterns of native and non-native prey abundance to increasing native predator populations. Here, we evaluate the effects of non-native colonial ascidians (Diplosoma listerianum and Didemnum vexillum) on population growth of a native predator (bloodstar, Henricia sanguinolenta) and native sponges through long-term surveys of abundance, prey choice and growth experiments. We show non-native species facilitate native predator population growth by providing a novel temporal resource that prevents loss of predator biomass when its native prey species are rare. We expect that by incorporating native and non-native prey seasonal abundance patterns, ecologists will gain a more comprehensive understanding of the mechanisms underlying the effects of non-native prey species on native predator and prey population dynamics.     

Role of infection on the stability of a predator-prey system with several response functions--a comparative study

In this paper, we have proposed and analyzed a mathematical model of an infected predator-prey system with different predators' functional response. The existence and uniqueness of solutions are established and solutions are shown to be uniformly bounded for all nonnegative initial values. Our overall mathematical and biological studies reveal that if the prey population is infected by a lethal disease, coexistence of all three species (i.e. host, parasite and predator) for any of three functional responses is never possible but different interesting dynamical behaviors are possible by varying two key parameters viz. the rate of infection and the attack rate on susceptible prey. Interplay between these two factors yields a diverse array of biologically relevant behavior, including switching of stability, extinction and oscillations.     

The dynamics of two diffusively coupled predator-prey populations

I analyze the dynamics of predator and prey populations living in two patches. Within a patch the prey grow logistically and the predators have a Holling type II functional response. The two patches are coupled through predator migration. The system can be interpreted as a simple predator-prey metapopulation or as a spatially explicit predator-prey system. Asynchronous local dynamics are presumed by metapopulation theory. The main question I address is when synchronous and when asynchronous dynamics arise. Contrary to biological intuition, for very small migration rates the oscillations always synchronize. For intermediate migration rates the synchronous oscillations are unstable and I found periodic, quasi-periodic, and intermittently chaotic attractors with asynchronous dynamics. For large predator migration rates, attractors in the form of equilibria or limit cycles exist in which one of the patches contains no prey. The dynamical behavior of the system is described using bifurcation diagrams. The model shows that spatial predator-prey populations can be regulated through the interplay of local dynamics and migration.     

Restricting Prey Dispersal Can Overestimate the Importance of Predation in Trophic Cascades

Predators can affect prey populations and, via trophic cascades, predators can indirectly impact resource populations (2 trophic levels below the predator) through consumption of prey (density-mediated indirect effects; DMIEs) and by inducing predator-avoidance behavior in prey (trait-mediated indirect effects; TMIEs). Prey often employ multiple predator-avoidance behaviors, such as dispersal or reduced foraging activity, but estimates of TMIEs are usually on individual behaviors. We assessed direct and indirect predator effects in a mesocosm experiment using a marine food chain consisting of a predator (toadfish – Opsanus tau), prey (mud crab - Panopeus herbstii) and resource (ribbed mussel – Geukensia demissa). We measured dispersal and foraging activity of prey separately by manipulating both the presence and absence of the predator, and whether prey could or could not disperse into a predator-free area. Consumption of prey was 9 times greater when prey could not disperse, probably because mesocosm boundaries increased predator capture success. Although predator presence did not significantly affect the number of crabs that emigrated, the presence of a predator decreased resource consumption by prey, which resulted in fewer resources consumed for each prey that emigrated in the presence of a predator, and reduced the overall TMIE. When prey were unable to disperse, TMIEs on mussel survival were 3 times higher than the DMIEs. When prey were allowed to disperse, the TMIEs on resource survival increased to 11-times the DMIEs. We found that restricting the ability of prey to disperse, or focusing on only one predator-avoidance behavior, may be underestimating TMIEs. Our results indicate that the relative contribution of behavior and consumption in food chain dynamics will depend on which predator-avoidance behaviors are allowed to occur and measured.     

The negative effects of pathogen‐infected prey on predators: a meta‐analysis

Intra‐guild predation (IGP) – where a top predator (IG_Pred) consumes both a basal resource and a competitor for that resource (IG_Prey) – has become a fundamental part of understanding species interactions and community dynamics. IGP communities composed of intraguild predators and prey have been well studied; however, we know less about IGP communities composed of predators, pathogens, and resources. Resource quality plays an important role in community dynamics and may influence IGP dynamics as well. We conducted a meta‐analysis on predator–pathogen–resource communities to determine whether resource quality mediated by the pathogen affected predator life‐history traits and if these effects met the theoretical constraints of IGP communities. To do this, we summarized results from studies that investigated the use of predators and pathogens to control insect pests. In these systems, the predators are the IG_Pred and pathogens are the IG_Prey. We found that consumer longevity, fecundity, and survival decreased by 26%, 31% and 13% respectively, when predators consumed pathogen‐infected prey, making the infected prey a low quality resource. Predators also significantly preferred healthy prey over infected prey. When we divided consumers by enemy type, strict predators (e.g. wolf spiders) had no preference while parasitoids preferred healthy prey. Our results suggest that communities containing parasitoids and pathogens may rarely exhibit intraguild predation; whereas, communities composed of strict predators and pathogens are more likely dominated by IGP dynamics. In these latter communities, the consumption of low and high quality resources suggests that IGP communities composed of strict predators, pathogens and prey should naturally persist, supporting IGP theory. Synthesis We investigated how consuming pathogen‐infected prey influence important life‐history parameters of insect predators. Pathogens are used in a variety of biocontrol programs, especially to control crop pests. We found that true predators (i.e. wolf spiders) have no preference for healthy or infected prey and have reduced fecundity, survival and longevity consuming infected prey. However, parasitoids avoided infected prey when possible. In biocontrol programs with multiple control agents, parasitoids and pathogens would do a better job controlling pests as predators would reduce the amount of pathogen available and have reduced fitness from consuming infected prey. However, theory suggests that true predators, prey and pathogens may coexist long term.