Predator–prey system with strong Allee effect in prey

Global bifurcation analysis of a class of general predator–prey models with a strong Allee effect in prey population is given in details. We show the existence of a point-to-point heteroclinic orbit loop, consider the Hopf bifurcation, and prove the existence/uniqueness and the nonexistence of limit cycle for appropriate range of parameters. For a unique parameter value, a threshold curve separates the overexploitation and coexistence (successful invasion of predator) regions of initial conditions. Our rigorous results justify some recent ecological observations, and practical ecological examples are used to demonstrate our theoretical work.     

Effects of rapid prey evolution on predator–prey cycles

We study the qualitative properties of population cycles in a predator-prey system where genetic variability allows contemporary rapid evolution of the prey. Previous numerical studies have found that prey evolution in response to changing predation risk can have major quantitative and qualitative effects on predator-prey cycles, including: (1) large increases in cycle period, (2) changes in phase relations (so that predator and prey are cycling exactly out of phase, rather than the classical quarter-period phase lag), and (3) "cryptic" cycles in which total prey density remains nearly constant while predator density and prey traits cycle. Here we focus on a chemostat model motivated by our experimental system (Fussmann et al. in Science 290:1358-1360, 2000; Yoshida et al. in Proc roy Soc Lond B 424:303-306, 2003) with algae (prey) and rotifers (predators), in which the prey exhibit rapid evolution in their level of defense against predation. We show that the effects of rapid prey evolution are robust and general, and furthermore that they occur in a specific but biologically relevant region of parameter space: when traits that greatly reduce predation risk are relatively cheap (in terms of reductions in other fitness components), when there is coexistence between the two prey types and the predator, and when the interaction between predators and undefended prey alone would produce cycles. Because defense has been shown to be inexpensive, even cost-free, in a number of systems (Andersson et al. in Curr Opin Microbiol 2:489-493, 1999: Gagneux et al. in Science 312:1944-1946, 2006; Yoshida et al. in Proc Roy Soc Lond B 271:1947-1953, 2004), our discoveries may well be reproduced in other model systems, and in nature. Finally, some of our key results are extended to a general model in which functional forms for the predation rate and prey birth rate are not specified.     

Salmonid predator–prey dynamics in Lake Pend Oreille,Idaho, USA

Our objective was to evaluate the long-term sustainability of lake trout Salvelinus namaycush and rainbow trout Oncorhynchus mykiss populations subjected to a range of fishing mortality (F) in Lake Pend Oreille, Idaho, USA, while providing for bull trout Salvelinus confluentus and kokanee Oncorhynchus nerka recovery. In order to achieve our objective, we developed a density-dependent stochastic predator–prey simulation model for the three major predators (lake trout, rainbow trout, and bull trout) on kokanee in Lake Pend Oreille. As F increased from 0.0 to 1.0, lake trout numbers in 2015 declined 90% for gillnetting, 76% for angling, and 48% for trap netting. At fishing mortality rates observed in Lake Pend Oreille during 2006, all methods combined and angling alone suppressed the lake trout population, but not gillnetting or trap netting alone. As F increased from 0.0 to 0.3, rainbow trout numbers in 2015 declined by 38%. Abundance of adult bull trout increased by 5.8% per year during 1996–2006, after implementation of no-kill regulations, which met the Federal Recovery Plan criterion of a stable or increasing trend in abundance. By 2010, total consumption of kokanee by lake trout, rainbow trout, and bull trout would increase by 20% if fishing mortality on lake trout and rainbow trout declined by 30% from 1996 levels, and would decrease by 14% if fishing mortality on lake trout and rainbow trout increased by 30% from 1996 levels. At rates of fishing mortality exerted on lake trout and rainbow trout in 2006, the likelihood of kokanee collapse was 65% within the next decade. Therefore, fishing mortality would need to be at least 6% higher on both lake trout and rainbow trout to reduce the likelihood of kokanee collapse to 50%. We conclude that kokanee biomass is presently out of balance with predation in Lake Pend Oreille, because kokanee production cannot compensate for all predation loss. Our findings suggest that a combination of unusually high kokanee production and unusually low predation are likely needed for kokanee to survive the next decade in Lake Pend Oreille.     

Analysis of a competitive prey–predator system with a prey refuge

Gauss's competitive exclusive principle states that two competing species having analogous environment cannot usually occupy the same space at a time but in order to exploit their common environment in a different manner, they can co-exist only when they are active in different times. On the other hand, several studies on predators in various natural and laboratory situations have shown that competitive coexistence can result from predation in a way by resisting any one prey species from becoming sufficiently abundant to outcompete other species such that the predator makes the coexistence possible. It has also been shown that the use of refuges by a fraction of the prey population exerts a stabilizing effect in the interacting population dynamics. Further, the field surveys in the Sundarban mangrove ecosystem reveal that two detritivorous fishes, viz. Liza parsia and Liza tade (prey population) coexist in nature with the presence of the predator fish population, viz. Lates calcarifer by using refuges.     

Minor pollinator–prey conflict in the carnivorous plant, Drosera anglica

We studied the physical and temporal isolation of two arthropod guilds interacting with Drosera anglica Huds., a terrestrial carnivorous plant. Flowers are separated from basal trap leaves by a leafless stalk. Since arthropods are potentially employed both as prey and pollinators, we asked whether separation of traps from flowers reduces the frequency with which flower visitors are captured by the leaves. Plants captured prey throughout the season, with peak trapping activity occurring before flowering began. The diverse prey spectrum included at least 109 species in 94 genera in 26 of 37 identified families representing 11 arthropod orders. The most common prey were adult flies of Nematocera, particularly Ceratopogonidae (50%) and Chironomidae (42%). The following taxa were periodically abundant: Acarina, Diptera–Cecidomyiidae, Chloropidae, Sciaridae, Hemiptera nymphs and Thysanoptera–Thripidae. Flies (Diptera) were chief flower visitors (95%), dominated by Syrphidae (66%), Bombyliidae and Muscidae (10% each), Calliphoridae (7%), Tachinidae and Dolichopodidae (3% each). Additionally, visitors were a bee (Hymenoptera–Halictidae) and thrips (Thysanoptera–Thripidae). Four families were common to both guilds: Diptera–Dolichopodidae, Muscidae, Tachinidae; and Thysanoptera–Thripidae. However, direct comparisons of identified taxa within these families showed that overlap between flower visitors and prey occurred for Thrips sp. larvae alone, which comprised only 3% of all flower visitors and 0.5% of prey. Drosera anglica exploits distinct guilds of insects for pollinators and prey.     

Do unprofitable prey evolve traits that profitable prey find difficult to exploit?

Prey that are unprofitable to attack (for example, those containing noxious chemicals) are often conspicuously patterned and move in a slower and more predictable manner than species lacking these defences. Contemporary theories suggest these traits have evolved as warning signals because they can facilitate both associative and discriminative avoidance learning in predators. However, it is unclear why these particular traits and not others have tended to evolve in unprofitable prey. Here we show using a signal detection model that unprofitable prey will evolve conspicuous colours and patterns partly because these characteristics cannot readily evolve in profitable prey without close mimicry. The stability of this signal is maintained through the costs of dishonesty in profitable prey. Indeed, unprofitable prey will sometimes evolve a conspicuous form to reduce mimetic parasitism, even in the unlikely event that this form can be more closely mimicked. This is one of the first mathematical models of the evolution of warning signals to allow for the possibility of mimicry, yet our analyses suggest it may offer a general explanation as to why warning signals take the form that they do. Warning signals and mimicry may therefore be more closely related than is currently supposed.     

Host plant quality,spatial heterogeneity,and the stability of mite predator–prey dynamics

Population dynamics models suggest that both the over-all level of resource productivity and spatial variability in productivity can play important roles in community dynamics. Higher productivity environments are predicted to destabilize consumer–resource dynamics. Conversely, greater heterogeneity in resource productivity is expected to contribute to stability. Yet the importance of these two factors for the dynamics of arthropod communities has been largely overlooked. I manipulated nutrient availability for strawberry plants in a multi-patch experiment, and measured effects of overall plant quality and heterogeneity in plant quality on the stability of interactions between the phytophagous mite Tetranychus urticae and its predator Phytoseiulus persimilis. Plant size, leaf N content and T. urticae population growth increased monotonically with increasing soil nitrogen availability. This gradient in plant quality affected two correlates of mite population stability, population variability over time (i.e., coefficient of variation) and population persistence (i.e., proportion of plant patches colonized). However, the highest level of plant quality did not produce the least stable dynamics, which is inconsistent with the “paradox of enrichment”. Heterogeneity in plant productivity had modest effects on stability, with the only significant difference being less variable T. urticae densities in the heterogeneous compared to the corresponding homogeneous treatment. These results are generally congruent with metapopulation theory and other models for spatially segregated populations, which predict that stability should be governed largely by relative movement rates of predators and prey—rather than patch quality.     

How to analyse prey preference when prey density varies? A new method to discriminate between effects of gut fullness and prey type composition

Summary State-dependent changes in prey preference are among the phenomena to be expected in studies of predator behaviour. For example, the rate of attack on each prey type is well known to be affected by the state of satiation, the dynamics of which is often assumed to parallel that of gut fullness. An interesting question is whether satiation alone is the determinant of the attack rate or whether the particular mixture of prey types in the predator's direct environment has an additional influence by itself. To detect examples of the latter type the predictive method proposed by Cock (1978) may be useful. In the present paper the predictive tool is a model built on the assumption that gut fullness is the sole internal state variable determining the attack rate. It is provided with parameter estimates from observations in monocultures of each type and then used to predict predation in mixtures of prey types. When measured predation on these prey types differs from what is predicted, the model may be too simple in various respects, one of which is that predators change prey preference in response to their own sample estimates of the densities of each prey type and their (innate or sample) estimate of the profitability of each prey type in terms of reproductive success. Thus, the lack of fit of the model poses a challenging problem, for to explain it one must identify underlying causes, such as differences in prey quality with respect to scarce nutrients or noxious chemicals that need to be detoxified or rendered harmless in other ways. The predictive approach is illustrated by analysis of preference of predatory mites (Phytoseiulus persimilis Athias-Henriot and Typhlodromus occidentalis Nesbitt) with respect to various stages of development of their prey, the two-spotted spider mite (Tetranychus urticae Koch). The results show that the relation between attack rate and gut fullness might well explain prey stage preference of predatory mites when the prey stages are presented together rather than each alone. In another paper by Dicke et al. (1989) marked deviations between predicted and measured diet are reported when the predatory mite, Typhlodromus pyri Scheuten, was offered a choice between two prey species, i.e. apple rust mites and (larvae of) European red spider mites. The underlying causes are to be revealed by further research, the impetus of which is born out by use of the method proposed by Cock (1978) and extended in this paper.     

The nature of predation: prey dependent, ratio dependent or neither?

To describe a predator-prey relationship, it is necessary to specify the rate of prey consumption by an average predator. This functional response largely determines dynamic stability, responses to environmental influences and the nature of indirect effects in the food web containing the predator-prey pair. Nevertheless, measurements of functional responses in nature are quite rare. Recently, much work has been devoted to comparing two idealized forms of the functional response: prey dependent and ratio dependent. Although we agree that predator abundance often affects the consumption rate of individual predators, this phenomenon requires more attention. Disagreement remains over which of the two idealized responses serves as a better starting point in building models when data on predator dependence are absent.     

Effects of the probability of a predator catching prey on predator–prey system stability

To understand the effect of the probability of a predator catching prey, P_catch, on the stability of the predator–prey system, a spatially explicit lattice model consisting of predators, prey, and grass was constructed. The predators and prey randomly move on the lattice space, and the grass grows according to its growth probability. When a predator encounters prey, the predator eats the prey in accordance with the probability P_catch. When a prey encounters grass, the prey eats the grass. The predator and prey give birth to offspring according to a birth probability after eating prey or grass, respectively. When a predator or prey is initially introduced or newly born, its health state is set at a high given value. This health state decreases by one with every time step. When the state of an animal decreases to less than zero, the individual dies and is removed from the system. Population densities for predator and prey fluctuated significantly according to P_catch. System stability was characterized by the standard deviation ? of the fluctuation. The simulation results showed that ? for predators increased with an increase of P_catch; ? for prey reached a maximum at P_catch = 0.4; and ? for grass fluctuated little regardless of P_catch. These results were due to the tradeoff between P_catch and the predator–prey encounter rate, which represents the degree of interaction between predator and prey and the average population density, respectively.     

Can species‐specific prey responses to chemical cues explain prey susceptibility to predation?

The perception of danger represents an essential ability of prey for gaining an informational advantage over their natural enemies. Especially in complex environments or at night, animals strongly rely on chemoreception to avoid predators. The ability to recognize danger by chemical cues and subsequent adaptive responses to predation threats should generally increase prey survival. Recent findings suggest that European catfish (Silurus glanis) introduction induce changes in fish community and we tested whether the direction of change can be attributed to differences in chemical cue perception. We tested behavioral response to chemical cues using three species of freshwater fish common in European water: rudd (Scardinius erythrophthalmus), roach (Rutilus rutilus), and perch (Perca fluviatilis). Further, we conducted a prey selectivity experiment to evaluate the prey preferences of the European catfish. Roach exhibited the strongest reaction to chemical cues, rudd decreased use of refuge and perch did not alter any behavior in the experiment. These findings suggest that chemical cue perception might be behind community data change and we encourage collecting more community data of tested prey species before and after European catfish introduction to test the hypothesis. We conclude that used prey species can be used as a model species to verify whether chemical cue perception enhances prey survival.     

Fish–prey interactions in,and associated data from,a temperate stream of the Yura River,Kyoto, Japan

Although quantitative data on interspecific interactions within complex food webs are essential for evaluation of assumptions, hypotheses, and predictions of ecological theories; empirical studies yielding quantitative data on complex food webs are very limited. Ecological information on body size, habitat use, and seasonality of the component species of food webs aids in determining the mechanisms of food web structures. Ideally, ecological information on component species should be obtained contemporaneously when used to describe quantitative food webs, but such observations and sampling strategies are labor intensive and thus have been rarely described. We conducted year-round samplings of, and performed observations on, a temperate stream: the upper reaches of the Yura River, Kyoto, Japan. We derived quantitative data on the abundance, biomass, body mass, microhabitat use, and those seasonality of 7 fish species and 167 invertebrate taxa of the temperate stream food web. In addition, we estimated the per mass consumption rates of 7 predatory fish species, consuming 183 prey invertebrates, and the ratios between the per mass consumption rates of the 7 predatory fish species and the production rates of 78 prey invertebrates in each trophic link. All fishes and aquatic invertebrates were identified to species or lowest possible taxon. Our data may contribute to the construction of mathematical models explaining the behavior of stream communities/ecosystems.     

What best explains vigilance in elk: characteristics of prey, predators, or the environment?

We quantified the vigilance levels of elk (Cervus elaphus) preyedon by wolves (Canis lupus) in Yellowstone National Park, betweenJanuary and May in 2005 and 2006, and used Akaike's informationcriterion to compare a set of 38 regression models for vigilancelevels. These models combined up to 9 predictor variables of3 types: characteristics of the prey group (herd size and composition),characteristics of the predator (wolf pack size, distance away,and the presence/absence of a kill), and characteristics ofthe local environment (distance to woodland edges, snow depth,and snow cover). The set of models spanned a range of complexityfrom simple univariate models to complex combinations with upto 3 variables of each type. Complex models incorporating thecharacteristics of the wolf pack, the structure of the elk herd,and the environmental conditions had higher information contentthan simple models. Although univariate models of vigilancedetect significant relationships, they have low informationcontent relative to multivariate models. These results showthat elk assesses factors of several types when assessing riskand deciding how much time to allocate to vigilance. In particular,we found that all well-supported models of vigilance includedseveral "prey" variables and several "predator" variables. Thisresult highlights the need to consider information about predatorswhen trying to explain variation in vigilance levels in prey.     

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.     

The complex dynamics of a diffusive prey–predator model with an Allee effect in prey

This paper investigates complex dynamics of a predator–prey interaction model that incorporates: (a) an Allee effect in prey; (b) the Michaelis–Menten type functional response between prey and predator; and (c) diffusion in both prey and predator. We provide rigorous mathematical results of the proposed model including: (1) the stability of non-negative constant steady states; (2) sufficient conditions that lead to Hopf/Turing bifurcations; (3) a prior estimates of positive steady states; (4) the non-existence and existence of non-constant positive steady states when the model is under zero-flux boundary condition. We also perform completed analysis of the corresponding ODE model to obtain a better understanding on effects of diffusion on the stability. Our analytical results show that the small values of the ratio of the prey's diffusion rate to the predator's diffusion rate are more likely to destabilize the system, thus generate Hopf-bifurcation and Turing instability that can lead to different spatial patterns. Through numerical simulations, we observe that our model, with or without Allee effect, can exhibit extremely rich pattern formations that include but not limit to strips, spotted patterns, symmetric patterns. In addition, the strength of Allee effects also plays an important role in generating distinct spatial patterns.     

Predator–prey encounter rates in freshwater piscivores: effects of prey density and water transparency

One of the most fundamental components of predator–prey models is encounter rate, modelled as the product of prey density and search efficiency. Encounter rates have, however, rarely been measured in empirical studies. In this study, we used a video system approach to estimate how encounter rates between piscivorous fish that use a sit-and-wait foraging strategy and their prey depend on prey density and environmental factors such as turbidity. We first manipulated prey density in a controlled pool and field enclosure experiments where environmental factors were held constant. In a correlative study of 15 freshwater lakes we then estimated encounter rates in natural habitats and related the results to both prey fish density and environmental factors. We found the expected positive dependence of individual encounter rates on prey density in our pool and enclosure experiments, whereas the relation between school encounter rate and prey density was less clear. In the field survey, encounter rates did not correlate with prey density but instead correlated positively with water transparency. Water transparency decreases with increasing prey density along the productivity gradient and will reduce prey detection distance and thus predator search efficiency. Therefore, visual predator–prey encounter rates do not increase, and may even decrease, with increasing productivity despite increasing prey densities.     

Seabird abundance, biomass and prey consumption within Prydz Bay, Antarctica, 1980/1981–1992/1993

Annual observations of seabirds within Prydz Bay, East Antarctica, between the 1980/1981 and 1992/1993 seasons revealed siginificant changes in abundance of the 9 resident and 15 non-resident species. An estimated 4.85 million individual residents and 2.35 million individual non-residents were present each season. For resident and non-resident species, mean abundance was 3.75 and 1.81 birds/km², and mean biomass was 6.67 and 1.70 kg/km², respectively. Based on estimated abundances, the total consumption of marine resources by the seabird community within Prydz Bay ranged from 471,000 to 1.1 million tonnes (mean 752,000±176,000 tonnes) per 6-month summer, or between 2.02 and 4.53 kg/km² per day (mean 3.23±0.76 kg/km² per day). The mean energy flux to the seabird community within Prydz Bay each summer was 3.13*10¹² kJ, (range: 2.0*10¹² kJ–4.4*10¹² kJ), of which 66% went to the resident species. Regional abundance and biomass estimates for resident and non-resident species were both negatively correlated; when the estimated abundance and biomass of resident species were high, those of non-resident species were low. Received: 4 January 1996/Accepted: 3 July 1996     

No silver bullet? Snow leopard prey selection in Mt. Kangchenjunga,Nepal

In this study, we investigated the impact of domestic and wild prey availability on snow leopard prey preference in the Kangchenjunga Conservation Area of eastern Nepal—a region where small domestic livestock are absent and small wild ungulate prey are present. We took a comprehensive approach that combined fecal genetic sampling, macro‐ and microscopic analyses of snow leopard diets, and direct observation of blue sheep and livestock in the KCA. Out of the collected 88 putative snow leopard scat samples from 140 transects (290 km) in 27 (4 × 4 km²) sampling grid cells, 73 (83%) were confirmed to be from snow leopard. The genetic analysis accounted for 19 individual snow leopards (10 males and 9 females), with a mean population size estimate of 24 (95% CI: 19–29) and an average density of 3.9 snow leopards/100 km² within 609 km². The total available prey biomass of blue sheep and yak was estimated at 355,236 kg (505 kg yak/km² and 78 kg blue sheep/km²). From the available prey biomass, we estimated snow leopards consumed 7% annually, which comprised wild prey (49%), domestic livestock (45%), and 6% unidentified items. The estimated 47,736 kg blue sheep biomass gives a snow leopard‐to‐blue sheep ratio of 1:59 on a weight basis. The high preference of snow leopard to domestic livestock appears to be influenced by a much smaller available biomass of wild prey than in other regions of Nepal (e.g., 78 kg/km² in the KCA compared with a range of 200–300 kg/km² in other regions of Nepal). Along with livestock insurance scheme improvement, there needs to be a focus on improved livestock guarding, predator‐proof corrals as well as engaging and educating local people to be citizen scientists on the importance of snow leopard conservation, involving them in long‐term monitoring programs and promotion of ecotourism.     

Geometric optimization for prey–predator strategies

This paper investigates several strategies for prey and predator in both bounded and unbounded domains, assuming they have the same speed. The work describes how the prey should move to escape from the predator and how predator should move to catch the prey. The approach is agent-based and explicitly tracks movement of individuals as prey and predator. We show that the prey escapes one or two competing predators, while might be caught in the case of three predators. The paper also describes a strategy for finding a well camouflaged static prey which emits signals.