Predator-prey Research Articles

A Nonlocal Reaction‐Diffusion‐Advection System Modeling the Phytoplankton and Zooplankton

ABSTRACTWe present a nonlocal reaction‐diffusion‐advection system that models the predator–prey relationship between zooplankton and phytoplankton species in a eutrophic vertical water column. The invasion dynamics of zooplankton are analyzed in terms of the spontaneous death rates and buoyant/sinking velocities of both phytoplankton and zooplankton. Our analysis reveals that the zooplankton species can successfully invade and coexist with the phytoplankton only under conditions of low spontaneous death rates and matching buoyant/sinking velocities with phytoplankton. Additionally, we derived asymptotic profiles for the unique positive steady state of this system when one of the sinking or buoyant velocities of either phytoplankton or zooplankton approaches infinity, while the other velocity remains fixed. These findings highlight the significant role of advection due to buoyancy in shaping the dynamics of plankton ecosystems.

A study for analysing predator–prey ecological system using Legendre polynomial

This paper presents a mathematical model to examine the effects of the coexistence of predators on single prey. Based on Caputo operators, we present a newly developed system of differential equations for the predator–prey system using wavelet method. It is well known that a system of nonlinear singular models cannot operate smoothly since they are singular and nonlinear. Therefore, with the help of this numerical approach, we have converted the system into a nonlinear system of algebraic equations by extending it through operational matrix of Legendre wavelets. Using the wavelet collocation scheme, we have calculated these unknown coefficients. It has been demonstrated in tables and graphs that the developed approach is consistent and proficient. Further bifurcation diagrams, as well as phase portraits, have been used to study the proposed system numerically and to analyse its behaviour. In addition, a nonlinear functional analysis have used to establish uniformly boundedness for the proposed model. Also we have discussed residual error analysis and Lyapunov exponent. The applicability and efficacy of this methodology have been demonstrated through this nonlinear system. Additionally, a comparison with existing results highlights the advantages of our numerical approach. All calculations have been done using MATLAB.

The Stability of a Predator–Prey Model with Cross-Dispersal in a Multi-Patch Environment

This paper investigates the stability of predator–prey models within multi-patch environments, with a particular focus on the influence of cross-dispersion across patches. We apply Kirchhoff’s matrix tree theorem and Liapunov’s method to derive criteria related to the cross-dispersion topology, thus solving the challenge of determining global asymptotic stability conditions. The method incorporates realistic ecological interactions and spatial heterogeneity, offering a framework for stability analysis. Our findings demonstrate that an appropriate level of cross-dispersion can effectively mitigate oscillations and foster convergence toward equilibrium. Two numerical examples validate these theoretical results and demonstrate the feasibility and effectiveness of the model across multiple patches.

Analysis of an Imprecise Fractional-Order Eco-epidemiological Model with Various Forms of Prey Refuges and Predator Harvesting

Analysis of an Imprecise Fractional-Order Eco-epidemiological Model with Various Forms of Prey Refuges and Predator Harvesting

Widespread resilience of animal species, functional diversity, and predator–prey networks to an unprecedented gigafire

Abstract Climate change is altering fire regimes globally, leading to an increased incidence of large and severe wildfires, including gigafires (>100,000 ha), that homogenise landscapes. Despite this, our understanding of how large, severe wildfires affect biodiversity at the landscape scale remains limited. We investigated the impact of a gigafire that occurred during the unprecedented 2019–20 Australian ‘Black Summer’ on terrestrial fauna. We selected 24 study landscapes, each 0.785 km2 in size, that represented a gradient in the extent of high severity fire, unburnt vegetation, and the diversity of fire severity classes (‘pyrodiversity’). We used wildlife cameras to survey biodiversity across each landscape and quantified species activity, community and functional diversity, and predator–prey network metrics. We used Bayesian mixed‐effects models to assess the influence of fire‐induced landscape properties on these measures. Most native species showed resilience to the 2019–20 wildfires, displaying few relationships with fire‐induced properties of landscapes, including the extent of high severity fire, unburnt vegetation, or pyrodiversity. Community and functional diversity and measures of predator–prey networks were also largely unaffected by fire‐induced landscape properties, although landscapes with a greater proportion of high severity fire had higher abundance and richness of introduced animal species. Synthesis and applications: Despite prevailing narratives of widespread ecological destruction following the 2019–20 wildfires, our findings suggest widespread resilience, potentially facilitated by evolutionary adaptations of animals to fire. Interventions aimed at helping such species recover may not be necessary and could instead focus on the subset of species that are vulnerable to severe fire. While mixed‐severity fires are often advocated to promote biodiversity through pyrodiversity, our results suggest that such management efforts might not be necessary in our study region. Given that severe fire favours introduced animal species, invasive species management could focus on large, severely burnt areas.

Impact of Honest Signal, Cues, Prey’s Experience Rate and Environmental Toxicity in a Predator–Prey Interaction Model

Biological signaling plays a crucial role in predator–prey interaction systems, serving both intraspecific and interspecific communication purposes. Prey populations utilize signaling internally, employing honest signals among themselves to enhance their defense capabilities. Conversely, they also use signaling for interspecific communication, emitting cues to predators to increase their own chances of survival. Recently, Al-Salman et al. [Appl. Math. Modell. 89, 1405 (2021)] proposed a two-species interaction model incorporating Holling Type II predation along with honest signals and cues. In this paper, we extend and modify their study by incorporating factors such as prey’s experience rate and environmental toxicity in prey populations. We conduct a comprehensive mathematical and numerical analysis of the model. We investigate the positive invariance and dissipativeness of the model, discuss the existence of equilibrium points and analyze the behavior of the system around all equilibrium points. Particularly, we determine conditions for local stability and Hopf bifurcation of the system. Furthermore, we perform a detailed numerical analysis to study periodic solutions through Hopf bifurcations in the proposed system. We plot two-parameter bifurcation diagrams to examine changes in the system with combined effects, identifying critical values for stability switching. There is no chaotic dynamics seen in our investigation. Numerical results indicate that the system tends to stabilize when the experience rate is high, and the rate of error-prone honest signals regulates system stability. Additionally, we analyze how environmental toxicity affects the stability of the system.

Dynamics of a discrete Rosenzweig–MacArthur predator–prey model with piecewise-constant arguments

This paper investigates the dynamics of a new discrete form of the classical continuous Rosenzweig–MacArthur predator–prey model and the biological implications of the dynamics. The discretization method used here is to modify the continuous model to another with piecewise-constant arguments and then to integrate the modified model, which is quite different from the traditional Euler discretization method. First, the existence and local stability of fixed points have been thoroughly discussed. Then, all codimension-1 bifurcations have been studied, including the transcritical bifurcations at the trivial fixed point and the boundary fixed point, and the Neimark–Sacker bifurcation at the unique positive fixed point. Furthermore, it is proved that there are no codimension-2 bifurcations. Finally, the control of the bifurcations is studied. Regarding the biological significance, we have considered the following four aspects: When no harvesting effort is applied to both predators and prey, it is observed that providing more resources to the prey species leads to predator extinction, causing the ecosystem to lose stability. This implies that the paradox of enrichment occurs. When predators are harvested, the system exhibits the hydra effect, i.e. increasing the harvesting effort on predators will lead to an increase in the mean population density of predators. When the prey is harvested, numerical examples indicate that increasing the harvesting effort initially reduces prey density. Upon reaching the bifurcation point, prey density stabilizes while the predator density continues to decline. When both prey and predators are harvested, the biological significance is similar to the previous case. The outcomes of this paper have significant theoretical meaning in the study of population ecology. By MATLAB, the bifurcation diagrams, maximal Lyapunov exponent diagrams, phase portraits and mean population density curves are plotted. Numerical simulations not only show the correctness of the theoretical findings but also reveal many new and interesting dynamics.

The modified predator–prey model response to the effects of global warming, wind flow, fear, and hunting cooperation

The modified predator–prey model response to the effects of global warming, wind flow, fear, and hunting cooperation

Bifurcation analysis in a modified Leslie-type predator–prey system with Holling-type III functional response and special Allee effect induced by fear factors

In this paper, a modified Leslie-type predator–prey system with Holling-type III functional response is formulated to investigate the dynamics in the presence of special Allee effect induced by fear factors. First, we calculate the first three focal values by the method of successor function to ensure that the system has an unstable weak focus of multiplicity 3. A focus- or center-type degenerate Bogdanov–Takens singularity of codimension 3 and a weak focus of multiplicity 1 or 2 together with a cusp of codimension 2 are derived for the system. Then multiple bifurcations are explored. It is shown that the system undergoes Hopf bifurcation of codimension 3 and hence three limit cycles are generated. There exists another large stable limit cycle enclosing these three limit cycles by Poincaré–Bendixson theorem. We demonstrate that a degenerate focus-type Bogdanov–Takens bifurcation of codimension 3 can occur by calculating the universal unfolding. It is also shown that a subcritical, supercritical or degenerate Hopf bifurcation occurs together with a Bogdanov–Takens bifurcation. Finally, numerical simulations are used to support the theoretical results. The analysis results reveal that the special Allee effect is beneficial for the persistence and diversity of ecosystem.

Impact of the Prey Refuge Parameter in the Presence of Fear Effect on the Fuzzy Two-Prey–One Predator Model with Switching Effect

It has been thought of as a class of models where a generalist predator feeds on two distinct prey species. We wish to examine how prey refuge factors affect prey–predator models when fear effects are present. In order to achieve this, a two-prey–one predator model with prey refuge has been taken into consideration in the presence of the predator’s fear effect on two prey species. Both prey species engage in intra-specific competition. We enhance our model by including a switching mechanism in predation. In order to account for the inherent imperfection of environmental conditions, some parameters have been taken as fuzzy numbers. Analytical and numerical results on the system have been examined in fuzzy sense. The system’s positivity, boundedness, and permanence are examined. The system’s local and global stability analyses have been investigated. Hopf bifurcation analysis around the positive interior equilibrium point has been explored. The stability of the limit cycle of our suggested fuzzy system has been discussed. The system’s numerical simulations have been investigated with pertinent tables and graphical illustrations. When the prey refuge parameter and fear parameter exceed the critical value, the system experiences Hopf bifurcation at the positive interior equilibrium point.

Enhancing maximum sustainable yield in a patchy prey–predator environment

In this paper, we investigate a prey–predator community of fish coexisting in a multi-patches model, where different fishing patches are interconnected through migration terms. Only the predator is caught, while the prey grows logistically on each patch. The main objective of our research is to compare the maximum sustainable yield achieved in two contrasting scenarios: unconnected patches and connected patches with rapid stock movements. We show that the total maximum sustainable yield for the connected patches can be greater than the sum of the maximum sustainable yield on each isolated patch. The analysis of the model allows us to establish the conditions under which one of the two cases is more favorable from the viewpoint of yield. As a result, we provide a complete classification for all possible cases. This valuable information can be used to assist decision-makers in selecting the best management strategy for a particular fishery.

A spatially explicit drift foraging model quantifies salmon rearing habitat enhancement

Salmonid rearing habitat restoration is often intended to increase juvenile prey abundance, predator refugia, and physical conditions that enhance growth, development, and survival. A common restoration evaluation approach is to quantify habitat quality via physical metrics such as depth and velocity. However, such an approach does not account for the bioenergetic implications of habitat occupancy. We developed a spatially explicit predictive framework to assess net rate of energy intake (NREI) for juvenile Chinook salmon (Oncorhynchus tshawytscha) experiencing pre-existing and post-project conditions in a restored side channel complex. Energetic submodels from existing juvenile salmonid drift foraging literature are used in combination with site-specific macroinvertebrate drift data and a 2D hydraulic model. We address the following question: does our model predict increased net available energy for foraging juveniles in a restored channel condition compared to pre-existing conditions under varying discharges, thermal conditions, and seasonality? Observed macroinvertebrate drift data was extrapolated to the model domain via random forest models. Modeled post-project conditions showed statistically significant improvements in foraging opportunity compared to existing conditions, with depth ranked as the most important NREI predictor. The novel framework presented here improves upon previous applications that model drift from a single fish perspective and generalize prey density.

Life History Traits of Ambassidae Fish, Chanda nama (Hamilton, 1822) From the Old Brahmaputra River of Northeastern Bangladesh

ABSTRACTThe present study provides a comprehensive analysis of the population structure (length–frequency distributions), growth pattern (length–weight relationships [LWRs] and length–length relationships), physiological condition factors (allometric [KA], Fulton's [KF] and relative [KR]), relative weight (WR) and form factor (a3.0) of Chanda nama. A total of 1200 specimens were collected from the Old Brahmaputra River, northeastern Bangladesh, for 12 months by traditional fishing gear, including seine net and cast net. The total length (TL) of several individuals varied from 2.3 to 7.2 cm. The highest percentage contributed to the population's 4.0–4.5‐cm‐sized group. The LWRs indicated a positive allometric growth pattern (b > 3.0). Fulton's condition factor significantly correlated with TL and body weight (p < 0.0001). The calculated WR ranged from 67.38 to 137.64. No significant variations from 100 were found using the Wilcoxon rank test (p = 0.034), suggesting that C. nama might live there in a balanced predator–prey environment. Furthermore, the measured value for the form factor (a3.0) was 0.0105. In addition, fish with a TL of 7–8 cm should be caught since they are in good condition and have enough meat. The study's findings will greatly contribute to the efficient and enduring management of C. nama in the Old Brahmaputra River and its adjacent ecosystems.

Landscape use by prey: Bottom‐up regulation prevails under reduced predation risk

AbstractResource specialist herbivores may suppress antipredator strategies to access scarcely available key resources, while proactive antipredator behaviors should be favored by generalists or when resources are abundant. We quantified the relative effects of predation‐ (top‐down) and resource‐driven (bottom‐up) constraints on spatiotemporal patterns of landscape use by a prey community in a dynamic system under low predator abundance, and investigated how prey manage the risk posed by predators with different hunting strategies. We fitted Royle–Nichols co‐abundance models to camera‐trapping data collected between 2017 and 2019 in Bicuar National Park (Angola), to assess spatial association/segregation across predator–prey dyads, while accounting for the effects of water and food availability during dry and wet seasons. We further estimated pairwise seasonal differences in diel activity overlap between predator and prey. We failed to detect spatiotemporal proactive antipredator responses either toward the cursorial or ambush predator. The community‐wide predator–prey association patterns we found support that predation pressure is insufficient to displace prey from their preferred habitats or to adjust their endogenous clock, and support predominantly bottom‐up regulated behaviors. We suggest that, in landscapes where predator density is low, limited perception of risk may prevent the employment of proactive antipredator behavior.

Camouflage or Coincidence? Investigating the Effects of Spatial and Temporal Environmental Features on Feral Cat Morphology in Tasmania.

Variations in coat morphology are well documented among felids and are theorised to aid in camouflage during stalk and ambush hunting. A diverse array of coat types has arisen in Felis catus (feral cats) through domestication and subsequent selective breeding. This species has successfully spread across Australia over the past 200 years, raising the question of whether any specific coat types offer an adaptive advantage. We used 24,657 camera-trap images of feral cats in Tasmania, Australia, and assigned each cat observation a coat colour and pattern. We analysed these data to examine how different spatial features affect the modal coat type present at a site. We also tested if cats with differing coat types were active on different days in response to temporal features, including moon luminosity (full or new). Elevation was positively associated with the presence of orange (odds ratio = 2.5, 97.5% confidence interval = 1.5, 4.4) and tortoiseshell (odds ratio = 4.1, CI = 1.6, 10.5) cats, while blotched brown cats were negatively associated with elevation (odds ratio = 0.64, CI = 0.5, 0.9), relative to black cats. Brown mackerel cats were more common in eucalypt and rainforests (odds ratio = 1.9, CI = 1.1, 3.3), as well as sites with a higher FPAR (odds ratio = 1.3, CI = 1.1, 1.6). All coat types were 1.2-2 times more likely to be active on nights with a new moon, except for orange cats who were equally active regardless of moon luminosity (odds ratio = 0.94, CI = 0.62, 1.42). Our results indicate that coat types are equally successful across Tasmania, perhaps owing to naïve prey or limited predator competition. The high activity of orange cats irrespective of moon phase may be reflective of the male cat's tendency to patrol territory, as opposed to favouring dark nights for hunting. Future studies should consider comparing the coat types found in feral cats to adjacent domestic populations, and against a wider array of habitat types to further investigate the potential for selective pressure on feral cat coat types in Australia.

Climate, predation, and the controls of island lizard abundance and community structure

AbstractAlternative ecological theories make divergent predictions about the relationship between predators and their prey. If predators exert top‐down ecosystem control, increases in predation should diminish prey abundance and could either diminish or enhance community diversity of prey species. However, if bottom‐up ecosystem controls predominate, predator populations should track underlying variation in prey diversity and abundance, which ultimately should reflect available energy. Past research, both across islands and comparing islands with the mainland, has frequently invoked the importance of predation in regulating lizard abundance and diversity, suggesting an important role of top‐down control when predators are present. However, others have posited a stronger role of food limitation, via competition or bottom‐up forces. If top‐down control predominates, then negative correlations between prey abundance and predator occurrence should emerge within and among islands. Using data from eBird, we inferred landscape‐level presence data for bird species on the islands of Jamaica and Hispaniola. By summing occurrence probabilities of all known anole‐predator birds, we estimated total avian predation pressure and combined these estimates with anole community data from a mark‐recapture study that spanned spatial and climatic gradients on both islands. Avian predators and anole lizards were both affected by climate, with total predator occurrence, anole abundance and anole species richness increasing with mean annual temperature. Anole abundance and predator occurrence showed a curvilinear relationship, where abundance and predator occurrence increased together until predator occurrence became sufficiently high that anole abundance was negatively impacted. This indicates that bottom‐up ecosystem controls drive richness of both anoles and their predators, mitigating the negative effects predators might have on their prey, at least until predator occurrence reaches a threshold. We did not detect consistent evidence of predator occurrence reducing anole community richness. These findings support past research showing that islands with more predators tend to have lower prey abundances, but it does not seem that these top‐down forces are strongly limiting species coexistence. Instead, bottom‐up forces linked with climate may be more important drivers of diversity in both lizards and their avian predators on these islands.

Turing patterns in exploited predator–prey systems with habitat loss

Turing patterns in exploited predator–prey systems with habitat loss

Dynamics of a delayed discrete-time predator prey model proposed from a nonstandard finite difference scheme

Existing literature established stability in a delayed logistic Lotka–Volterra predator- prey model in terms of equilibrium analysis. However, several researchers did not construct the time-series analysis in such models. It has also been observed that both the RK4 methods and the inbuilt ‘dde23’ MATLAB solver were unable to generate stable solutions. This motivated us to develop a nonstandard scheme to capture the numerical solutions which are well consistent with the analytical equilibrium analysis of continuous delayed predator–prey model. In this paper, we will propose a nonstandard finite difference (NSFD) scheme for a delayed predator–prey model. We shall prove that the developed scheme preserves the qualitative behavior of the system, including the local stability of the equilibrium, and stability switching for any step size h=1m,m∈Z+. It is observed that the discretized system shows the occurrence of a Neimark-Sacker bifurcation. Moreover, the convergence analysis of the numerical scheme establishes first-order convergence. The bifurcation diagram and comparison of delay τ−sequence generated by NSFD with the ones obtained by analytical means have been discussed graphically.

Harvesting strategies in ecological systems: Evaluating their efficiency in infection dominance

In population biology, the interplay between prey and predators in the presence of infection can give rise to complex dynamics. On the flip side, implementing harvesting is an infection control measure. In the present work, we use the dynamical system theory to discuss the dynamics of the harvested prey–predator system in the presence of infection in prey species. Detailed mathematical and numerical evaluations have been presented to discuss the susceptible‐free state, infection‐free state, predator‐free state, species coexistence, stability, and occurrence of various bifurcations (saddle‐node, transcritical, and Hopf bifurcation). The study reveals the impact of harvesting parameters on the dynamics. Interestingly, we observe that an infection‐free state could be achieved by varying the harvesting parameter under all three harvesting schemes (linear, quadratic, and nonlinear). Moreover, with the help of reproduction number, we claim that linear harvesting is more effective in controlling the infection than quadratic and nonlinear harvesting provided the half‐saturation constant for nonlinear harvesting is greater than a threshold value ; otherwise, nonlinear harvesting is more effective. Also, the system can support more susceptible prey in the presence of harvesting. The present theoretical study suggests different threshold values of implemented harvesting to control the disease.

Habitat dimensionality and feeding strategies but not temperature as determinants of body size-trophic structure relationship in a marine food web.

Disentangling the determinants of trophic structure is central to ecology. The capacity to capture subjugate and consume a prey (i.e. gape limitation) is a relevant limitation to acquire energy for most organisms, especially those in smaller size ranges. This generates a size hierarchy of trophic positions in which large organisms consume small ones. Body size is tightly correlated to gape limitation and explains a large fraction of variance in the body size-trophic position relationship. However, a considerable fraction of variance still remains to be explained. Consumer search space dimensionality (2D or 3D) and feeding strategies, temperature and the size structure of primary producers can alter the trophic structure, but tests based on information from natural food webs are scarce. We generated specific predictions about the body size trophic position relationship and evaluated them using information from a subtropical South Atlantic coastal marine ecosystem: benthic realm (2D, rocky shore and sandy beach) and the pelagic realm (3D). We characterized this marine coastal food web based on stable isotopes of carbon and nitrogen from 256 samples from primary producers (macroalgae and phytoplankton) to large predators (sand shark) in summer and winter. Consumer body size encompassed six orders of magnitude in weight from 10-2 to 6 × 104 g. Isotopic signal corresponded to an integration of carbon sources from basal consumers to top predators. The body size-trophic position relationship showed a linear positive association with different slopes for the benthic and pelagic environments. This implies a smaller predator prey size ratio for pelagic (3D) with respect to benthic consumers (2D) as theoretically expected. No seasonal differences were found in slopes and most of the overall variance in benthic environments was largely explained by feeding strategies of the different taxonomic groups. We provide an integrated evaluation on the role of body size, consumer search space and feeding strategy to understand the determinants of trophic position. Results demonstrate that integrating gape limitation hypothesis, the dimensionality of consumer search space and feeding strategies into a formal robust framework to understand trophic structure is feasible even in complex natural ecosystems.