Predator Model Research Articles

Dynamics for a diffusive prey–predator model with advection and free boundaries

This article deals with a free boundary problem of the Lotka–Volterra type prey–predator model with advection in one space dimension. The model considered here may be applied to describe the expanding of an invasive or new predator species adopting a combination of random movement and advection upward or downward along the resource gradient, with the free boundaries representing expanding fronts of predator species. The main purpose of this article is to understand the influence of the advection environment on the dynamics of the model. We provide sufficient conditions for spreading and vanishing of the predator species, and we find a sharp threshold between the spreading and vanishing concerning this model. Moreover, for the case of successful spreading for the predator, we give estimates of asymptotic spreading speeds and nonlocal long‐time behavior of the prey and the predator.

Behavioral responses of Vinaceous-breasted Amazon parrots to anti-predator training

Conservation translocations have a low success rate mainly due the lack of skills of introduced animals to survive in the new environment, such as naivety facing a potential predator. Pre-release training based on classical conditioning may allow those animals to identify threats. Here we evaluated the behavioral responses to anti-predator training by an endangered tropical species, the Vinaceous-breasted Amazon parrot (Amazona vinacea). We investigated the hypothesis that anti-predator training of captive parrots can stimulate aversive behavior towards predators, also investigating whether animals habituated to the training. Eleven parrots were submitted to anti-predator training using four different predator models (jaguar, bird of prey, dog, and human) and a chair as control. During training, the predator models were associated with an aversive stimulus, represented by a disguised person chasing the animals. All training sessions were video recorded and parrots’ behaviors were collected through footage analysis. Generalized Linear Mixed Models (GLMMs) were adjusted to evaluate the animals’ behaviors during training and to evaluate changes in behavior according to the predator model. We also carried out a Time Series Analysis (TSA) through a Temporal Autocorrelation to identify signs of habituation. Parrots escaped more in training with all predators than in training with the chair. Parrots also walked in the presence of the dog, the human, and the bird of prey, which is a mild response than escaping but also suggests a risk perception. The behaviors eating and preening were most observed in training with the chair. The parrots showed behavioral changes throughout the training sessions, with a decrease in the frequency of the behavior walking and an increase in the behavior alert, which is an indication that parrots did not habituate to stimuli used during training. The results obtained by TSA also corroborated this finding. Overall, our results demonstrated that anti-predator training can elicit proper behaviors in captive animals, which, after release, may contribute to the animals survival in the wild. Thus, anti-predator training should be applied as a pre-release technique in parrot conservation programs.

Factors related to sound production by the Chinese grasshopper Acrida cinerea during escape

Many grasshopper species produce conspicuous sounds while escaping from approaching predators; however, they occasionally escape without producing sounds. The Chinese grasshopper, Acrida cinerea, often exhibits noisy escape behavior. Therefore, a field experiment was conducted using A. cinerea to identify factors related to the production of sound during escape. This study utilized a predator model with an investigator approaching A. cinerea three times. We examined the relationship between the production of sound during escape and the following factors: ambient temperature and relative humidity as environmental factors; sex, body length, body weight, and limb autotomy as prey traits; and the repeated approach as a predator trait. The relationships between noisy escape and flight initiation distance (i.e., predator-prey distance when the prey initiates the escape), distance fled (i.e., distance the prey covered during the escape), and the mode of locomotion during escape (i.e., flying or jumping) were also examined. Noisy escape was observed only in males that escaped by flying, whereas the females and males that escaped by jumping invariably escaped silently. Among males that flew, noisy escape was related to ambient temperature, limb autotomy, and distance fled. The proportion that produced sound increased in parallel with the ambient temperature and distance fled. This proportion was lower among individuals that had autotomized one of their hind legs. These results indicate that noisy escape behavior is most frequent in healthy male A. cinerea under warm conditions.

Distinctive chemotactic responses of three marine herbivore protists to DMSP and related compounds.

Marine planktonic predator-prey interactions occur in microscale seascapes, where diffusing chemicals may act either as chemotactic cues that enhance or arrest predation, or as elemental resources that are complementary to prey ingestion. The phytoplankton osmolyte dimethylsulfoniopropionate (DMSP) and its degradation products dimethylsulfide (DMS) and acrylate are pervasive compounds with high chemotactic potential, but there is a longstanding controversy over whether they act as grazing enhancers or deterrents. Here, we investigated the chemotactic responses of three herbivorous dinoflagellates to point-sourced, microscale gradients of dissolved DMSP, DMS, and acrylate. We found no evidence for acrylate being a chemotactic repellent and observed a weak attractor role of DMS. DMSP behaved as a strong chemoattractor whose potential for grazing facilitation through effects on swimming patterns and aggregation depends on the grazer's feeding mode and ability to incorporate DMSP. Our study reveals that predation models will fail to predict grazing impacts unless they incorporate chemotaxis-driven searching and finding of prey.

Stability analysis of fuzzy differential equation for prey–predator system underZ-number fuzzy and granular differentiability concept

The stability analysis is one of the basic problems in the field of system, prey–predator, production inventory control, signal processing etc. The goal of stability analysis for prey–predator and production inventory control model is to determine the region of the different variables and parameters at which the system is stable or unstable. This paper explores an uncertain prey–predator model where both prey and predator populations are fuzzy variables. Also we have considered all the prey–predator parameters of the system are imprecise. This fuzzy prey–predator model is converted to an equivalent crisp model using granular differentiability approach. The condition of local stability is obtained mathematically by analysis the eigenvalues of characteristic equation. And also we introduced a production inventory model as a case study of fuzzy dynamical system to illustrate the efficiency of the result and practical aspects.

Schoener-Polis-Holt's model of the intraguild predation with predator taxis and repulsive chemotaxis

Schoener-Polis-Holt's model of the intraguild predation with predator taxis and repulsive chemotaxis

A Dynamic Model of Predation

A Dynamic Model of Predation

Dynamics of an ecological prey–predator model based on the generalized Hattaf fractional derivative

In this paper, we propose and analyze a fractional prey–predator model with generalized Hattaf fractional (GHF) derivative. We prove that our proposed model is ecologically and mathematically well-posed. Furthermore, we show that our model has three equilibrium points. Finally, we establish the stability of these equilibria.

The role of the fear, hunting cooperation, and anti-predator behavior in the prey predator model having disease in predator

The role of the fear, hunting cooperation, and anti-predator behavior in the prey predator model having disease in predator

A double time-delay Holling Ⅱ predation model with weak Allee effect and age-structure

<abstract><p>A double-time-delay Holling Ⅱ predator model with weak Allee effect and age structure was studied in this paper. First, the model was converted into an abstract Cauchy problem. We also discussed the well-posedness of the model and the existence of the equilibrium solution. We analyzed the global stability of boundary equilibrium points, the local stability of positive equilibrium points, and the conditions of the Hopf bifurcation for the system. The conclusion was verified by numerical simulation.</p></abstract>

Optimal control problem of a discrete spatiotemporal prey–predator three-species fishery model

In this work, we discuss a spatiotemporal discrete prey–predator model. It consists of three compartments: prey, predator, and super-predator. The proposed model describes the interaction between prey, predator, and super-predator in a region with a discrete displacement. We also provide research on appropriate regional control strategies. The controls are applied to the predator and the super-predator, respectively; they represent catching these in measured quantities in a space and a time chosen. The aim is to increase the number of prey and reduce the number of predators, restore the food chain system, and ensure its sustainability. Finally, we provide graphical visuals and numerical simulations to support our analytical findings.

Laplace transform method for logistic growth in a population and predator models with fractional order

In this paper, we develop a new application of the Laplace transform method (LTM) using the series expansion of the dependent variable for solving fractional logistic growth models in a population as well as fractional prey-predator models. The fractional derivatives are described in the Caputo sense. To illustrate the reliability of the method some examples are provided. The results reveal that the technique introduced here is very effective and convenient for solving fractional-order nonlinear differential equations.

How antibiotic exposure affect predator-prey interactions by population dynamics in ciliates?

Biodiversity loss resulting from environmental pollution is a global concern. While interspecific interactions are central to ecology, the impact of environmental pollution on predator-prey interactions and its ecological consequences, such as extinction and biodiversity loss, remain unclear. To investigate the effects of antibiotic exposure on predation strength and the resulting ecological consequence, the Didinium-Paramecium was utilized as a predator-prey model and exposed to nitrofurazone or erythromycin, two common pollutants, respectively. Initially, we determined prey population growth dynamics, body size, and predator numerical-functional responses. Subsequently, these above parameters were integrated into a mathematical model of predator-prey predation. Then both the long time-series data and phase portraits obtained through model simulation were used to estimate interaction strength and to predict the outcome of predator-prey coexistence. Our results revealed that exposure to either antibiotic significantly reduced prey population growth parameters (e.g., μmax and K) while increasing individual body size. The combined effects of antibiotic exposure and predation pressure on population growth inhibition or body size promotion were variable, mostly additive, with a few cases of synergy and extremely rare antagonism, depending on antibiotic exposure concentration. As antibiotic exposure concentration increased, the predator rmax generally declined, while functional responses varied depending on specific parameters, implying a decrease in predator-prey interaction strength. Analyses of phase portrait features showed that the population oscillation amplitude decreased with increasing antibiotic exposure concentrations, the cycle length of adjacent peaks increased, and prey extinction occurred earlier. In conclusion, antibiotic exposure reduced both predator and prey fitness, underlying the reason antibiotics reduces the strength of predator-prey interaction. Despite the indirect benefits of prey gain from this, the presence of predators can expedite the process of prey extinction caused by antibiotic exposure.

Stability analysis of Filippov prey–predator model with fear effect and prey refuge

Mathematical ecosystems play a crucial role in our comprehension and conservation of ecology. Within these ecosystems, prey exhibits protective instincts that compel refuging behaviors to avoid predation risk. When the ratio of prey to predators falls below a threshold, prey seeks refuge. However, when prey is abundant relative to predators, these protective instincts are overridden as prey ventures out to forage. Therefore, this study develops a Filippov prey–predator model with fear effect on prey and switching of prey refuge behavior based on the ratio of prey to predators. Analytical and numerical approaches are used to address the dynamic behaviors, bifurcation sets, existence, and stability of various equilibria in this model. Additionally, the regions of sliding and crossing segments are analyzed. The bifurcation sets of pseudo-equilibrium and local and global sliding bifurcations are investigated. The numerical simulations are conducted to investigate the interplay between fear factor and other relevant parameters within the Filippov model, such as the threshold ratio and prey refuge. These investigations shed light on the influence of them in the model. The results indicate that increasing the fear factor results in a decrease in both prey and predator densities, thereby changing the behavior of the dynamics from a limit cycle oscillation to a stable state and vice versa. Notably, despite these population changes, neither species faces complete extinction.

Dynamic Behaviors in a Discrete Model for Predator–Prey Interactions Involving Hibernating Vertebrates

This paper presents a discrete predator–prey interaction model involving hibernating vertebrates, with detailed analysis and simulation. Hibernation contributes to the survival and reproduction of organisms and species in the ecosystem as a whole. In addition, it also constitutes a wise sharing of time, space, and resources with others. We have created a new predator–prey model by integrating the two species, Holling-III and Holling-I, which have a bifurcation within a specified parameter range. We discovered that this system possesses the stability of fixed points as well as several bifurcation behaviors. To accomplish this, the center manifold theorem and bifurcation theory are applied to create existence conditions for period-doubling bifurcations and Neimark–Sacker bifurcations, which are depicted in the graph as distinct structures. Examples of numerical simulations include bifurcation diagrams, maximum Lyapunov exponents, and phase portraits, which demonstrate not just the validity of theoretical analysis but also complex dynamical behaviors and biological processes. Finally, the Ott–Grebogi–Yorke (OGY) method and phases of chaos control bifurcation were used to control the chaos of predator–prey model in hibernating vertebrates.

Study of dynamical behaviors of harvested stage-structured predator–prey fishery model with fear effect on prey under interval uncertainty

The lack of clarity in many parameters used in ecological models is due to the constant changes in nature. The fundamental predator–prey model discussed in this article takes into account several ecological parameters as parametric-functional interval numbers. It discusses the dynamic characteristics of the model within the context of an uncertain environment. To account for this uncertainty, the model incorporates the concepts of bionomic equilibria and maximum sustainable yield (MSY). The article explores the optimal harvesting policy by applying Pontryagin’s maximum principle in an imprecise and uncertain environment. The proposed imprecise model formulation includes two additional variables: the influence of fear on prey population growth rate and the harvesting of prey and juvenile predator populations. The system of interval differential equations governs the interactions between these imprecise species, allowing for mathematical analysis of the proposed system. The aim of this study is to evaluate the robustness of an imprecise prey–predator model within an unpredictable environment. The article concludes by presenting rigorous numerical simulations that support all the analytical findings.

Model of mesopelagic fish predation on eggs and larvae shows benefits of tuna spawning under full moon

AbstractMost mesopelagic fish are small planktivores that migrate up at nightfall to feed in the safety of darkness and descend to depth at dawn to escape visual predators. However, the trophic roles can reverse since mesopelagic fishes also predate eggs and larvae of their predators. We use the Atlantic bluefin tuna as a model species to test the hypothesis that fishes in the open ocean synchronize spawning to moon‐lit nights (when mesopelagic fishes avoid near‐surface waters) to increase offspring fitness. Our analysis over two decades of field observations shows that tuna spawn most intensively the week before full moon. This fits predictions from a mechanistic model where spawning around full moon increases offspring fitness by two orders of magnitude due to low predation from mesopelagic fishes. Circalunar patterns of food availability can also favor fitness of offspring spawned the days before full moon. Our findings suggest that mesopelagic fishes may have an important impact on pelagic fish through predation of early life stages and cause an evolutionary drive to synchronize spawning to the lunar cycle.

Predator–prey power laws: trophic interactions give rise to scale-invariant ecosystems

Scaling laws and power-law distributions are ubiquitous in ecological systems. However, it is not clear what factors give rise to such universal regularities. Here, I show scaling laws are a simple consequence of scale-invariant distributions, and both result from simple commonalities of diverse ecosystems. I introduce a simple model of predator–prey interactions in which predators and prey move on a two-dimensional space in search of resources that they use to survive and reproduce. As primary resources increase, the food web exhibits a series of transitions to phases with equilibrium dynamics and top-down control of the food web, non-equilibrium dynamics with bottom-up control, and unstable dynamics exhibiting the paradox of enrichment. The model shows resource heterogeneity can solve the paradox of enrichment and ensure the stability of ecosystems. Scale-invariant spatial distribution of prey and predators and a surprisingly rich set of scaling laws, including predator–prey and Taylor’s power laws, appear in the non-equilibrium phase. The model predicts both Taylor’s power law and predator–prey power law can be extended to a rich set of fluctuation scaling laws governing the fluctuation of predator’s and prey’s densities and growth. A mathematical theory suggests scaling laws result from the scale-invariance of the spatial distribution of prey and predators.

Dynamics of a Leslie-Gower type predation model with non-monotonic functional response and weak Allee effect on prey

This research concerns with analysis of a class of modified predator- prey type Leslie-Gower models. The model is described by an autonomous nonlinear ordinary differential equation system. The functional response of predators is Holling IV type or non-monotone, and the growth of prey is affected by the Allee effect. An important aspect is the study of the point (0, 0) since it has a strong influence on the behavior of the system being essential for the existence and extinction of both species, although the proposed system is not define there.

Color morphs of the fire salamander are discriminated at night by conspecifics and predators

AbstractThe coexistence of multiple discrete color phenotypes (i.e. color polymorphism) has been studied in many diurnal species where environmental light allows most visual systems to chromatically discriminate color morphs. However, there is a large gap in our understanding of the discrimination thresholds and the function color polymorphisms play at night. We collected spectral data from the throats of red‐ and yellow‐morph males in a polymorphic population of the nocturnal amphibian Salamandra salamandra gallaica. We estimated the discriminability between morphs and their conspicuousness at night by fitting visual models of conspecifics and predators. We also collected morphological, behavioral and physiological data and assessed the abundance and activity patterns of each morph to explore their potential function. Visual models indicated that both conspecifics and predators can visually discriminate salamander color morphs under night‐light conditions. Assuming the potential role of yellow and red color patches as visual signals, putatively related to social signaling, we could suspect that these colors represent different adaptive optima. Red‐morph individuals had shorter bodies and lower body condition, but both morphs showed similar space use. In addition, both color morphs exhibited similar metabolic physiology, suggesting that the observed similarity in these traits may be better explained by the shared environmental conditions, rather than color. Finally, differences in the conspicuousness of red and yellow morphs could result in differential predation pressure.