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.     

Parametric Analysis of a Predator–prey System Stabilized by a Top Predator

We present a complete parametric analysis of a predator–prey system influenced by a top predator. We study ecosystems with abundant nutrient supply for the prey where the prey multiplication can be considered as proportional to its density. The main questions we examine are the following: (1) Can the top predator stabilize such a system at low densities of prey? (2) What possible dynamic behaviors can occur? (3) Under which conditions can the top predation result in the system stabilization? We use a system of two nonlinear ordinary differential equations with the density of the top predator as a parameter. The model is investigated with methods of qualitative theory of ODEs and the theory of bifurcations. The existence of 12 qualitatively different types of dynamics and complex structure of the parametric space are demonstrated. Our studies of phase portraits and parametric diagrams show that a top predator can be an important factor leading to stabilization of the predator-prey system with abundant nutrient supply. Although the model here is applied to the plankton communities with fish (or carnivorous zooplankton) as the top trophic level, the general form of the equations allows applications of our results to other ecological systems.     

Predator group size distributions in predator–prey systems

The grouping behavior is common in nature, e.g., fish school, bird flocks and insects swarms. Indeed, numerous theoretical and empirical predator-prey models have demonstrated the impact of group-living animals on ecosystems. To examine the interactions between individuals in the same group or competition between groups, we introduced different models based on Monte Carlo simulation and mean-field theory and found that the predator group sizes follow the geometric distribution and logarithmic distribution, as in previous empirical and theoretical cases. Our models also provide an intuitive explanation for these distributions. A new distribution based on the Holling-III functional response is presented; this distribution is heavy tailed in some specific cases.     

Predator–prey interactions and metabolic rates are altered in stable and unstable groups in a social fish

Understanding the determinants and consequences of predation effort, success and prey responses is important since these factors affect the fitness of predators and prey. When predators are also invasive species, the impacts on prey can be particularly far-reaching with ultimate ecosystem-level consequences. However, predators are typically viewed as behaviourally fixed within this interaction and it is unclear how variation in predator social dynamics affects predator–prey interactions. Using the invasive eastern mosquitofish Gambusia holbrooki and a native glass shrimp Paratya australiensis in Australia, we investigated how varying levels of social conflict within predator groups influences predator–prey interactions. By experimentally manipulating group stability of G. holbrooki, we show that rates of social conflict were lower in groups with large size differences, but that routine metabolic rates were higher in groups with large size differences. Predation effort and success did not vary depending on group stability, but in stable groups predation effort by aggressive dominants was greater than subordinates. The anti-predator responses of prey to the stability of predator groups were mixed. While more prey utilized shelters when exposed to stable compared to unstable groups of predators, a greater proportion were sedentary when predator groups were unstable. Overall, this study demonstrates predator group stability is modulated by differences in body size and can influence prey responses. Further, it reveals a hidden metabolic cost of living in stable groups despite reduced overt social conflict. For invasive species management, it is therefore important to consider the behavioural and physiological plasticity of the invasive predators, whose complex social interactions and metabolic demands can modulate patterns of predator–prey interactions.     

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.     

Predator hunting modes and predator–prey space games

Predators and prey are often engaged in a game where their expected fitnesses are affected by their relative spatial distributions. Game models generally predict that when predators and prey move at similar temporal and spatial scales that predators should distribute themselves to match the distribution of the prey's resources and that prey should be relatively uniformly distributed. These predictions should better apply to sit-and-pursue and sit-and-wait predators, who must anticipate the spatial distributions of their prey, than active predators that search for their prey. We test this with an experiment observing the spatial distributions and estimating the causes of movements between patches for Pacific tree frog tadpoles (Pseudacris regilla), a sit-and-pursue dragonfly larvae predator (Rhionaeschna multicolor), and an active salamander larval predator (Ambystoma tigrinum mavortium) when a single species was in the arena and when the prey was with one of the predators. We find that the sit-and-pursue predator favors patches with more of the prey's algae resources when the prey is not in the experimental arena and that the prey, when in the arena with this predator, do not favor patches with more resources. We also find that the active predator does not favor patches with more algae and that prey, when with an active predator, continue to favor these higher resource patches. These results suggest that the hunting modes of predators impact their spatial distributions and the spatial distributions of their prey, which has potential to have cascading effects on lower trophic levels.     

Undamped oscillations in prey–predator models on a finite size lattice

Sustained oscillation is frequently observed in population dynamics of biospecies. The oscillation comes not only from deterministic but also from stochastic characteristics. In the present article, we deal with a finite size lattice which contains prey and predator. The interaction between a pair of lattice points is carried out by two different methods; local and global interactions. In the former, interaction occurs between adjacent sites, while in the latter interaction takes place between any pair of lattice sites. It is found that both systems exhibit undamped oscillations. The amplitude of oscillation decreases with the increase of the total lattice sites. In the case of global interaction, we can present a stochastic differential equation which is composed of two factors, i.e., the Lotka–Volterra equation with density dependence and noise term. The quantitative agreement between theory and simulation results of global interaction is almost perfect. The stochastic theory qualitatively expresses characteristics of sustainable oscillation for local interaction.     

Evidence for the Predator Attraction Hypothesis in an amphibian predator–prey system

Many species possess damage-released chemical alarm cues that function in alerting nearby individuals to a predator attack. One hypothesis for the evolution and/or maintenance of such cues is the Predator Attraction Hypothesis, where predators, rather than prey, are the “intended” recipients of these cues. If a predator attack attracts additional predators, these secondary predators might interfere with the predation event, providing the prey with a better chance to escape. In this study, we conducted two experiments to explore this hypothesis in an amphibian predator/prey system. In Experiment 1, we found that tiger salamanders (Ambystoma mavortium) showed a foraging attraction to chemical cues from wood frog (Lithobates sylvaticus) tadpoles. Salamanders that were experienced with tadpole prey, in particular, were strongly attracted to tadpole alarm cues. In Experiment 2, we observed experimental encounters between a tadpole and either one or two salamanders. The presence of the second predator caused salamanders to increase attack speed at the cost of decreased attack accuracy (i.e., increasing the probability that the tadpole would escape attacks). We also found that the mere presence of visual and chemical cues from a second predator did not affect this speed/accuracy trade-off but did cause enough of a distraction to increase tadpole survival. Thus, our findings are consistent with the Predator Attraction Hypothesis for the evolution and/or maintenance of alarm cues.     

Predator–prey relationships in a Mediterranean vertebrate system: Bonelli’s eagles,rabbits and partridges

How predators impact on prey population dynamics is still an unsolved issue for most wild predator–prey communities. When considering vertebrates, important concerns constrain a comprehensive understanding of the functioning of predator–prey relationships worldwide; e.g. studies simultaneously quantifying ‘functional’ and ‘numerical responses’ (i.e., the ‘total response’) are rare. The functional, the numerical, and the resulting total response (i.e., how the predator per capita intake, the population of predators and the total of prey eaten by the total predators vary with prey densities) are fundamental as they reveal the predator’s ability to regulate prey population dynamics. Here, we used a multi-spatio-temporal scale approach to simultaneously explore the functional and numerical responses of a territorial predator (Bonelli’s eagle Hieraaetus fasciatus) to its two main prey species (the rabbit Oryctolagus cuniculus and the red-legged partridge Alectoris rufa) during the breeding period in a Mediterranean system of south Spain. Bonelli’s eagle responded functionally, but not numerically, to rabbit/partridge density changes. Type II, non-regulatory, functional responses (typical of specialist predators) offered the best fitting models for both prey. In the absence of a numerical response, Bonelli’s eagle role as a regulating factor of rabbit and partridge populations seems to be weak in our study area. Simple (prey density-dependent) functional response models may well describe the short-term variation in a territorial predator’s consumption rate in complex ecosystems.     

Viable populations in a prey–predator system

 Lotka–Volterra equations are considered a dynamical game, where the phenotypes of the predator and of the prey can vary. This differs from the usual procedure of specifying as a priori laws according to which strategies are supposed to change. The question at stake is the survival of each of the species, instead of the maximization of a given pay-off by each player, as it is commonly discussed in games. The predator needs the prey, while the prey can survive without the predator. These obvious and simplistic constraints are enough to shape the regulation of the system: notably, the largest closed set of initial conditions can be delineated, from which there exists at least one evolutionary path where the population can avoid extinction forever. To these so-called viable trajectories, viable strategies are associated, respectively for the prey or for the predator. A coexistence set can then be defined. Within this set and outside the boundary, strategies can vary arbitrarily within given bounds while remaining viable, whereas on the boundary, only specific strategies can guarantee the viability of the system. Thus, the largest set can be determined, outside of which strategies will never be flexible enough to avoid extinction. Received 2 May 1995; received in revised form 15 August 1995     

Effects of perturbation on the predator–prey system in a heterogeneous landscape

Environmental perturbations occur in ecosystems as the result of disturbance, which is closely related to ecosystem stability and resilience. To understand how perturbations can affect ecosystems, we constructed a spatially explicit lattice model to simulate the integrative predator–prey–grass relationships. In this model, a predator (or prey) gives birth to offspring, according to a specific birth probability, when it is able to feed on prey (or grass). When a predator or prey animal was initially introduced or newly born, its health state was set at a given high value. This state decreased by 1 with each time step. When the state of an animal decreased to zero, the animal was considered dead and was removed from the system. In this model, the perturbation was defined as the sudden death of some portion of the population. The heterogeneous landscape was characterized by a parameter, H, which controlled the degree of heterogeneity. When H ≥ 0.6, the predator population size was positively influenced by the perturbation. However, the perturbation had little effect upon the population sizes of prey or grass, regardless of the value of H.     

Have bird distributions shifted along an elevational gradient on a tropical mountain?

An upward shift in elevation is one of the most conspicuous species responses to climate change. Nevertheless, downward shifts and, apparently, the absences of response have also been recently reported. Given the growing evidence of multiple responses of species distributions due to climate change and the paucity of studies in the tropics, we evaluated the response of a montane bird community to climate change, without the confounding effects of land‐use change. To test for elevational shifts, we compared the distribution of 21 avian species in 1998 and 2015 using occupancy models. The historical data set was based on point counts, whereas the contemporary data set was based on acoustic monitoring. We detected a similar number of species in historical (36) and contemporary data sets (33). We show an overall pattern of no significant change in range limits for most species, although there was a significant shift in the range limit of eight species (38%). Elevation limits shifted mostly upward, and this pattern was more common for upper than lower limits. Our results highlight the variability of species responses to climate change and illustrate how acoustic monitoring provides an easy and powerful way to monitor animal populations along elevational gradients.     

Ecological speciation along an elevational gradient in a tropical passerine bird?

Local adaptation of populations along elevational gradients is well known, but conclusive evidence that such divergence has resulted in the origin of distinct species in parapatry remains lacking. We integrated morphological, vocal, genetic and behavioural data to test predictions pertaining to the hypothesis of parapatric ecological speciation associated with elevation in populations of a tropical montane songbird, the Grey‐breasted Wood‐wren (Henicorhina leucophrys: Troglodytidae), from the Sierra Nevada de Santa Marta, Colombia. We confirmed that two distinct populations exist along the elevational gradient. Phylogenetic analyses tentatively indicate that the two populations are not sister taxa, suggesting they did not differentiate from a single ancestor along the gradient, but rather resulted from separate colonization events. The populations showed marked divergence in morphometrics, vocalizations and genetic variation in mitochondrial and nuclear loci, and little to no evidence of hybridization. Individuals of both populations responded more strongly to their own local songs than to songs from another elevation. Although the two forms do not appear to have differentiated locally in parapatry, morphological and vocal divergence along the elevational gradient is consistent with adaptation, suggesting a possible link between adaptive evolution in morphology and songs and the origin of reproductive isolation via a behavioural barrier to gene flow. The adaptive value of phenotypic differences between populations requires additional study.     

Variation in woody plant δ13C along a topoedaphic gradient in a subtropical savanna parkland

δ¹³C values of C₃ plants are indicators of plant carbon–water relations that integrate plant responses to environmental conditions. However, few studies have quantified spatial variation in plant δ¹³C at the landscape scale. We determined variation in leaf δ¹³C, leaf nitrogen per leaf area (N_area), and specific leaf area (SLA) in April and August 2005 for all individuals of three common woody species within a 308 × 12-m belt transect spanning an upland–lowland topoedaphic gradient in a subtropical savanna in southern Texas. Clay content, available soil moisture, and soil total N were all negatively correlated with elevation. The δ¹³C values of Prosopis glandulosa (deciduous N₂-fixing tree legume), Condalia hookeri (evergreen shrub), and Zanthoxylum fagara (evergreen shrub) leaves increased 1–4‰ with decreasing elevation, with the δ¹³C value of P. glandulosa leaves being 1–3‰ higher than those of the two shrub species. Contrary to theory and results from previous studies, δ¹³C values were highest where soil water was most available, suggesting that some other variable was overriding or interacting with water availability. Leaf N_area was positively correlated with leaf δ¹³C of all species (p < 0.01) and appeared to exert the strongest control over δ¹³C along this topoedaphic gradient. Since leaf N_area is positively related to photosynthetic capacity, plants with high leaf N_area are likely to have low p _I/p _a ratios and therefore higher δ¹³C values, assuming stomatal conductance is constant. Specific leaf area was not correlated significantly with leaf δ¹³C. Following a progressive growing season drought in July/August, leaf δ¹³C decreased. The lower δ¹³C in August may reflect the accumulation of ¹³C-depleted epicuticular leaf wax. We suggest control of leaf δ¹³C along this topoedaphic gradient is mediated by leaf N_area rather than by stomatal conductance limitations associated with water availability.     

Predator–prey relationships in a middle Asian Montane steppe: Persian leopard versus urial wild sheep in Northeastern Iran

Management controversies arise when both of the prey and predator in an ecosystem are species of conservation concern. We investigated trophic interactions between the endangered Persian leopard (Panthera pardus saxicolor) and a declining mountain ungulate, urial wild sheep (Ovis vignei), on a high-altitude steppe of Iran. During two consecutive photo-trapping seasons of 1,300 nights in total, a minimum population of four adult leopards (one female and three males) was documented. Scat analysis indicated that urial wild sheep was the staple of the leopard diet with 48.44 % of total biomass consumed. Remains of domestic livestock in leopard scats were negligible yet alarming (14.53 % biomass consumed), followed by wild pigs (8.13 %) and wild goat (1.26 %). Financial costs of leopard depredation to livestock breeders during our study period were comparatively lower than livestock–leopard conflict hotspots across Iran. Using distance sampling, urial density was 15.8 individuals km^?2 (±SE 6.2), and a total biomass of 47,621.5 kg for wild ungulates in the study area was estimated. We estimated that the annual removal rate of urial by leopards during our study period was 9.4 % of the total urial population. We suggest that continuous monitoring of the leopard and prey populations to assess predation impact should be considered, particularly in areas where a single species comprises a remarkable proportion of the leopard diet. In the meantime, assessing probable conflicts with local communities is recommended as a parallel management action to ensure long-term human–leopard coexistence. Our findings will aid wildlife managers in prey-depleted arid environments of western Asia to identify susceptible wild prey populations to predation by large carnivores; hence, significantly contribute in development and implementation of effective conservation measures to mitigate management conflicts.     

Predator interference emerging from trophotaxis in predator–prey systems: An individual-based approach

An individual-based model describing predator–prey interactions within a closed rectangular habitat was developed to study how different assumptions about the individual movements lead to the emergence at the population level of various kinds of prey- and predator-dependence in the spatially aggregated trophic function.In addition to random walk, both species are capable of directional movement, i.e., the model accounts for the predator prey-taxis and evasion of predators by prey individuals. The taxis stimulus of each species is the odour of the other species, which is distributed continuously in space. Spatial behaviour of individuals is determined by the specific response to the odour gradient and the tendency to maintain the taxis velocity.In order to facilitate the assessment of the trophic function, the model allows removing the effect of demographic density variations on the predator ration, keeping population sizes constant.Analyzing the dependence of the trophic function with the average predator density, we found that, depending on the intensity of taxis, the predator population exhibits various degrees of interference, from very low to very high values. In particular, a moderate taxis generates distinct levels of interference including the ratio-dependent case. The letter maximizes the average consumption rate.A new generalized function containing ratio-dependence and prey-dependence as special cases, at high and low population abundances, is suggested. This trophic function fits the simulated data better than the Hassell–Varley–Holling expression does.     

Optimal Culling and Biocontrol in a Predator–Prey Model

Invasive species cause enormous problems in ecosystems around the world. Motivated by introduced feral cats that prey on bird populations and threaten to drive them extinct on remote oceanic islands, we formulate and analyze optimal control problems. Their novelty is that they involve both scalar and time-dependent controls. They represent different forms of control, namely the initial release of infected predators on the one hand and culling as well as trapping, infecting, and returning predators on the other hand. Combinations of different control methods have been proposed to complement their respective strengths in reducing predator numbers and thus protecting endangered prey. Here, we formulate and analyze an eco-epidemiological model, provide analytical results on the optimal control problem, and use a forward–backward sweep method for numerical simulations. By taking into account different ecological scenarios, initial conditions, and control durations, our model allows to gain insight how the different methods interact and in which cases they could be effective.     

Impacts of Biotic Resource Enrichment on a Predator–Prey Population

The environmental carrying capacity is usually assumed to be fixed quantity in the classical predator–prey population growth models. However, this assumption is not realistic as the environment generally varies with time. In a bid for greater realism, functional forms of carrying capacities have been widely applied to describe varying environments. Modelling carrying capacity as a state variable serves as another approach to capture the dynamical behavior between population and its environment. The proposed modified predator–prey model is based on the ratio-dependent models that have been utilized in the study of food chains. Using a simple non-linear system, the proposed model can be linked to an intra-guild predation model in which predator and prey share the same resource. Distinct from other models, we formulate the carrying capacity proportional to a biotic resource and both predator and prey species can directly alter the amount of resource available by interacting with it. Bifurcation and numerical analyses are presented to illustrate the system’s dynamical behavior. Taking the enrichment parameter of the resource as the bifurcation parameter, a Hopf bifurcation is found for some parameter ranges, which generate solutions that posses limit cycle behavior.