Prey Growth Research Articles

Enchanting dynamics: Juvenile and adult predators with prey model in an intuitionistic fuzzy environment

This study represents an interaction model including juvenile and adult predators along with prey, involving key characteristics like the inability of juvenile predators to reproduce, the impact of adult predators on juvenile growth rates and the transformation of some juveniles to adulthood. Furthermore, it is supposed that adult predators intake prey for sustenance, and the logistic growth of prey is assumed in the non-appearance of adult predators. Intra-species competition among adult predators, together with predation of juveniles and chasing, is conveyed. To tackle the imprecise biological parameters, most parametric values are considered as triangular intuitionistic fuzzy numbers. The model is further processed into an intuitionistic fuzzy model using the Hukuhara derivative and Yager’s ranking method is implemented to make the model crispified. Non-negativity and boundedness of the model are explored, after that, an investigation of possible equilibrium points is discussed. Local and global stability analyses close to these points are supervised. The study accentuates the significant influence of uncertain model parameters on the solution. Especially, uncertain estimates of intra-species competition among adult predators remarkably regulate the model’s stability. Extended uncertainty in intra-species competition for prey, although, is discovered to stabilize the system. In addition, increased consumption of juvenile predators by adult predators is observed to provide the system’s instability.

Docosahexaenoic acid (DHA) is a driving force regulating gene expression in bluefin tuna (Thunnus thynnus) larvae development

This study elucidated the role of DHA-modulated genes in the development and growth of Atlantic bluefin tuna (Thunnus thynnus) larvae ingesting increasing levels of DHA in their rotifer prey. The effect of feeding low, medium, and high rotifer (Brachionus rotundiformis) DHA levels (2.0, 3.6 and 10.9 mg DHA g−1 DW, respectively) was tested on 2–15 days post hatching (dph) bluefin tuna larvae. Larval DHA content markedly (P < 0.05) increased in a DHA dose-dependent manner (1.5, 3.9, 6.1 mg DHA g−1 DW larva, respectively), that was positively correlated with larval prey consumption and growth (P < 0.05). Gene ontology enrichment analyses of differentially expressed genes (DEGs) demonstrated dietary DHA significantly (P < 0.05) affected different genes and biological processes at different developmental ages. The number of DHA up-regulated DEGs was highest in 10 dph larvae (491), compared to 5 (12) and 15 dph fish (34), and were mainly involved in neural and synaptic development in the brain and spinal cord. In contrast, DHA in older 15 dph larvae elicited fewer DEGs but played critical roles over a wider range of developing organs. The emerging picture underscores the importance of DHA-modulated gene expression as a driving force in bluefin tuna larval development and growth.

Dynamical Behavior of a Juvenile Predator, Adult Predator and Prey Model Through Uncertain and Parametric Technique

In this study, an interaction model involving a juvenile predator, an adult predator, and the prey has been developed. It is considered that juvenile predators are unable to reproduce. The adult predator is considered to have an impact on the growth rate of the juvenile predators. It is also assumed that a portion of juvenile predators may become adults. Also, it is considered that adult predators consume prey for food. The logistic growth of prey has been taken into consideration in the absence of an adult predator. The intra-species competition among adult predators is discussed here. It is also assumed that adult predators could chase and eat juvenile predators. Then most of the parametric values are considered interval-valued uncertain numbers. Since it is very hard for us to solve the model when the parametric values are interval-valued. Thus, all of the interval-valued parameters have been simplified into linear parametric form. After that, the nonnegativity and boundedness of the model were discussed. Various possible equilibrium points in the model are analyzed. The model’s local stability and global stability are investigated near these points. It has been noted that the proposed model’s solution is significantly impacted by the uncertain values of the model parameters. Uncertain estimates of intra-species competition among adult predators have been found to have a considerable impact on the stability of the model. It is observed that the increased uncertainty of intra-species competition for prey may stabilize the system. It is reported that the increasing rate of conversion of prey into adult predators can destabilize the ecosystem. It is found that the increasing rate of predation on juvenile predators by adults reduces the number of juveniles that can mature into adults which may create instability in the system.

Turing–Hopf bifurcation in a diffusive predator–prey model with schooling behavior and Smith growth

This paper explores the dynamics of a diffusive predator–prey model, considering schooling behavior and Smith growth in prey. Initially, we have formulated the pertinent characteristic equations. Subsequently, We proceed to examine the existence of the Turing bifurcation and Hopf bifurcation, phenomena that describe the emergence of spatial and temporal patterns due to diffusion and oscillations, respectively, and focusing on the parameters of the intrinsic growth rate γ and the diffusion coefficient d2 of the prey. Finally, we conduct numerical simulations to validate our theoretical findings and further illustrate the dynamics of the predator–prey system, considering schooling behavior and Smith growth in prey.

Visual and chemical stimuli from live prey affect feed intake, weight gain, and growth of juvenile Florida pompano (Trachinotus carolinus)

Visual and chemical stimuli from live prey affect feed intake, weight gain, and growth of juvenile Florida pompano (Trachinotus carolinus)

How can we avoid the extinction of any species naturally? A mathematical model

A large number of herbivorous mammals and reptiles in many terrestrial ecosystems across the globe are presently in the receiving end of extinction. Over-exploitation by its immediate predator and anthropogenic actions is one of the main reasons. Reintroduction of apex predator or top predator at some instances has proven to be a successful strategy in restoring ecological balance. In this paper, we conceptualize the role of top predator in enriching the density of vulnerable species of lower trophic level, with the help of mathematical modeling. First, the dynamical behavior of two species system (prey and mesopredator) is studied, where growth of prey is subject to strong Allee effect. Also, the cost of predation induced fear is incorporated in the growth term. Parametric regions, for which the species perceive extinction risk are analyzed and depicted numerically. We consider that whenever density of the vulnerable species reach a certain threshold, minimum viable population, top predator is introduced in the habitat. Our obtained results show that a species population can be restored from the verge of extinction to a stable state with much higher population density with the introduction of top predator and even it stabilizes an oscillatory system.

Dynamical behavior of a discrete-time predator–prey system incorporating prey refuge and fear effect

This paper explores the effects of fear and refuge in a discrete-time two species predator–prey model. The fraction of prey that seeks refuge is assumed to be proportional to the amount of predators. The local stability of the corresponding fixed points is analyzed. The conditions of flip bifurcation and Neimark–Sacker bifurcation at the positive fixed point are described. The sufficient conditions for the positive fixed point to be globally asymptotically stable are derived in this article. Utilization of hybrid control strategy stabilizes the system’s chaotic nature. Finally, the paper supports the theoretical analysis with a numerical simulation that demonstrates the intricate nature of the system. It is observed that both fear effect and prey refuge can destabilize or stabilize the system depending on the value of handling time. Also, fear effect can restore stability in the system that exhibits chaos due to a high prey growth rate.

Chaos and extinction risks of sexually reproductive generalist top predator in a seasonally forced food chain system with Allee effect.

This paper investigates the dynamics of a tritrophic food chain model incorporating an Allee effect, sexually reproductive generalist top predators, and Holling type IV and Beddington-DeAngelis functional responses for interactions across different trophic levels. Analytically, we explore the feasible equilibria, their local stability, and various bifurcations, including Hopf, saddle-node, transcritical, and Bogdanov-Takens bifurcations. Numerical findings suggest that higher Allee intensity in prey growth leads to the inability of species coexistence, resulting in a decline in species density. Likewise, a lower reproduction rate and a higher strength of intraspecific competition among top predators also prevent the coexistence of species. Conversely, a rapid increase in the reproduction rate and a decrease in the strength of intraspecific competition among top predators enhance the densities of prey and top predators while decreasing intermediate predator density. We also reveal the presence of bistability and tristability phenomena within the system. Furthermore, we extend our autonomous model to its nonautonomous counterpart by introducing seasonally perturbed parameters. Numerical analysis of the nonautonomous model reveals that higher seasonal strength in the reproduction rate and intraspecific competition of top predators induce chaotic behavior, which is also confirmed by the maximum Lyapunov exponent. Additionally, we observe that seasonality may lead to the extinction of species from the ecosystem. Factors such as the Allee effect and growth rate of prey can cause periodicity in population densities. Understanding these trends is critical for controlling changes in population density within the ecosystem. Ecologists, environmentalists, and policymakers stand to benefit significantly from the invaluable insights garnered from this study. Specifically, our findings offer pivotal guidance for shaping future strategies aimed at safeguarding biodiversity and maintaining ecological stability amidst changing environmental conditions. By contributing to the existing body of knowledge, our study advances the field of ecological science, enhancing the comprehension of predator-prey dynamics across diverse ecological conditions.

A discrete-time dynamical model of prey and stage-structured predator with juvenile hunting incorporating negative effects of prey refuge

This paper examines a discrete predator–prey model that incorporates prey refuge and its detrimental impact on the growth of the prey population. Age structure is taken into account for predator species. Furthermore, juvenile hunting along with its negative effects in the form of prey counterattack is considered. This paper provides a comprehensive analysis of the existence and stability conditions pertaining to all possible fixed points of this system. The impact of the parameters reflecting prey growth and prey refuge is thoroughly discussed. This paper delves into the occurrence of the Neimark–Sacker bifurcation and period-doubling bifurcation, specifically in relation to the parameters associated with prey growth rate and prey refuge. Numerous numerical simulations are presented in order to validate the theoretical findings.

Pattern formation and delay-induced instability in a Leslie–Gower type prey–predator system with Smith growth function

In this article, we have investigated the spatiotemporal dynamics and delay-induced instability of a Leslie–Gower type prey–predator model under the influence of environmental toxicants with Smith growth function. This growth function is more realistic than logistic growth as it better describes the growth of the biological population. It has been used where the growth limitations are based on the proportion of available resources not utilized. A few works of Smith’s growth models are reported in the literature. Therefore, spatiotemporal dynamics and pattern formation with delay effect remain an exciting area of research, which motivates the present work. This work has studied two types of dynamical systems: (i) an ordinary differential temporal system with time delay and (ii) a reaction–diffusion system with time delay. The existence of equilibrium points and their stability conditions are discussed. Hopf bifurcation emerges in both proposed systems with respect to delay parameter. The stability and direction of Hopf bifurcation and delay–diffusion-driven instability have been investigated for the reaction–diffusion system. Numerical simulation is performed to support the analytical results and theorems. Moreover, the existence of Hopf and delay-induced instability are proved numerically. Interesting one-dimensional regular and irregular stripe patterns are obtained for increased values of the time delay parameter. Also, the presence of natural toxicants has a negative impact on the growth of prey–predator species.

Examining the influence of prey dynamics on predator–prey interactions

ABSTRACT We develop variations of a discrete-time predator–prey model to examine how intrinsic properties of the prey population may impact overall system dynamics. We focus on two properties of the prey species, namely developmental stage structure and undercompensatory (contest competition) versus overcompensatory (scramble competition) density dependence. Through analysis of these models, we examine how these different prey features affect system stability. Our results show that when prey growth is overcompensatory, the predator may have a stabilizing effect on the system dynamics with increasing predator density reversing the period doubling route to chaos observed with Ricker-type nonlinearities. Moreover, we find that stage structure in the prey does not have a destabilizing effect on the system dynamics unless the prey projection matrix is imprimitive or close to imprimitive, as may occur for semelparous species. In this case, a sufficiently large predator density may stabilize cycles that are otherwise unstable.

An analysis of the stability and bifurcation of a discrete-time predator-prey model with the slow-fast effect on the predator.

In many environments, predators have significantly longer lives and meet several generations of prey, or the prey population reproduces rapidly. The slow-fast effect can best describe such predator-prey interactions. The slow-fast effect ε can be considered as the ratio between the predator's linear death rate and the prey's linear growth rate. This paper examines a slow-fast, discrete predator-prey interaction with prey refuge and herd behavior to reveal its complex dynamics. Our methodology employs the eigenvalues of the Jacobian matrix to examine the existence and local stability of fixed points in the model. Through the utilization of bifurcation theory and center manifold theory, it is demonstrated that the system undergoes period-doubling bifurcation and Neimark-Sacker bifurcation at the positive fixed point. The hybrid control method is utilized as a means of controlling the chaotic behavior that arises from these bifurcations. Moreover, numerical simulations are performed to demonstrate that they are consistent with analytical conclusions and to display the complexity of the model. At the interior fixed point, it is shown that the model undergoes a Neimark-Sacker bifurcation for larger values of the slow-fast effect parameter by using the slow-fast effect parameter ε as the bifurcation parameter. This is reasonable since a large ε implies an approximate equality in the predator's death rate and the prey's growth rate, automatically leading to the instability of the positive fixed point due to the slow-fast impact on the predator and the presence of prey refuge.

Trophic cascades within and across ecosystems: The role of anti-predatory defences, predator type and detritus quality.

Species in one ecosystem can indirectly affect multiple biodiversity components and ecosystem functions of adjacent ecosystems. The magnitude of these cross-ecosystem effects depends on the attributes of the organisms involved in the interactions, including traits of the predator, prey and basal resource. However, it is unclear how predators with cross-ecosystem habitat interact with predators with single-ecosystem habitat to affect their shared ecosystem. Also, unknown is how such complex top-down effects may be mediated by the anti-predatory traits of prey and quality of the basal resource. We used the aquatic invertebrate food webs in tank bromeliads as a model system to investigate these questions. We manipulated the presence of a strictly aquatic predator (damselfly larvae) and a predator with both terrestrial and aquatic habitats (spider), and examined effects on survival of prey (detritivores grouped by anti-predator defence), detrital decomposition (of two plant species differing in litter quality), nitrogen flux and host plant growth. To evaluate the direct and indirect effects each predator type on multiple detritivore groups and ultimately on multiple ecosystem processes, we used piecewise structural equation models. For each response variable, we isolated the contribution of different detritivore groups to overall effects by comparing alternate model formulations. Alone, damselfly larvae and spiders each directly decreased survival of detritivores and caused multiple indirect negative effects on detritus decomposition, nutrient cycling and host plant growth. However, when predators co-occurred, the spider caused a negative non-consumptive effect on the damselfly larva, diminishing the net direct and indirect top-down effects on the aquatic detritivore community and ecosystem functioning. Both detritivore traits and detritus quality modulated the strength and mechanism of these trophic cascades. Predator interference was mediated by undefended or partially defended detritivores as detritivores with anti-predatory defences evaded consumption by damselfly larvae but not spiders. Predators and detritivores affected ecosystem decomposition and nutrient cycling only in the presence of high-quality detritus, as the low-quality detritus was consumed more by microbes than invertebrates. The complex responses of this system to predators from both recipient and adjacent ecosystems highlight the critical role of maintaining biodiversity components across multiple ecosystems.

Ecological determinants of spotted hyena Crocuta crocuta occupancy in Comoé National Park, Côte d’Ivoire

Knowledge of the large carnivore guild is important in view of a possible lion reintroduction into the Comoé National Park (CNP), northern Côte d’Ivoire. We used camera trapping to assess activity patterns, habitat selection, and ecological factors influencing the occupancy of the spotted hyena Crocuta crocuta. Our results showed that the presence of leopard Panthera pardus, the only current other large carnivore and thus potential competitor, did not influence hyena occupancy. Hyena occupancy was only significantly related to Euclidian distance to nearest water point. Manly’s alpha habitat selection index values show a preference of spotted hyena for shrub savannah (αSa = 0.71), and Pianka’s overlap index showed low spatial competition with leopard (OIJ(PNC) = 0.12). Our findings showed that spotted hyena were mostly nocturnal, and generally active at the same time slots with leopard, leading to a high index of temporal overlap (OIJ(time) = 0.78). The kernel density estimation confirmed that spotted hyenas and leopard shared almost half of their activity patterns (Δ1 = 0.49 and 95% CI = 0.26–0.71). Prey diversity is high in CNP but anthropogenic threats appear to suppress population growth of prey and predators. Conservation efforts should continue to reduce pressures before contemplating a potential lion Panthera leo reintroduction.

A nonautonomous model for the effect of rarity value on the dynamics of a predator–prey system with variable harvesting

The human inclination to value rarity contributes to the exploitation of many wildlife species by driving up their market value when their numbers are scarce. This research investigates a model to explore how the value attached to rarity impacts the harvesting of predator species and subsequently influences the dynamics of predator–prey interactions in an ecological system. To broaden the model's scope, it's extended to its nonautonomous form by allowing the harvesting rate of predator species and the degree of neutrality in consumers to respond for the rarity of predator species to change over time. Both the autonomous and nonautonomous systems are explored through analytical and numerical investigation. Numerical findings reveal that as the prey population's growth rate gradually increases, the unforced system shifts from stable boundary equilibrium (harvesting absent) to stable interior equilibrium, then to oscillatory interior equilibrium, followed by period doubling oscillations leading to chaotic behavior. The autonomous system exhibits limit cycle oscillations around the boundary equilibrium when predator species are minimally harvested. Moderate harvesting stabilizes the system, while excessive harvesting induces instability. However, the chaotic oscillations can be eliminated through period‐halving route upon decreasing the consumers' response to predator rarity. Furthermore, the seasonally forced model demonstrates periodic solutions, higher order periodic solutions, and chaotic dynamics contingent upon different settings of prey growth rate, the strength of seasonality in predator harvesting, and the consumers' response to predator rarity.

Stability and bifurcation analysis of a discrete Leslie predator-prey system via piecewise constant argument method

&lt;abstract&gt;&lt;p&gt;The objective of this study was to analyze the complex dynamics of a discrete-time predator-prey system by using the piecewise constant argument technique. The existence and stability of fixed points were examined. It was shown that the system experienced period-doubling (PD) and Neimark-Sacker (NS) bifurcations at the positive fixed point by using the center manifold and bifurcation theory. The management of the system's bifurcating and fluctuating behavior may be controlled via the use of feedback and hybrid control approaches. Both methods were effective in controlling bifurcation and chaos. Furthermore, we used numerical simulations to empirically validate our theoretical findings. The chaotic behaviors of the system were recognized through bifurcation diagrams and maximum Lyapunov exponent graphs. The stability of the positive fixed point within the optimal prey growth rate range $ A_1 &amp;lt; a &amp;lt; A_2 $ was highlighted by our observations. When the value of $ a $ falls below a certain threshold $ A_1 $, it becomes challenging to effectively sustain prey populations in the face of predation, thereby affecting the survival of predators. When the growth rate surpasses a specific threshold denoted as $ A_2 $, it initiates a phase of rapid expansion. Predators initially benefit from this phase because it supplies them with sufficient food. Subsequently, resource depletion could occur, potentially resulting in long-term consequences for populations of both the predator and prey. Therefore, a moderate amount of prey's growth rate was beneficial for both predator and prey populations.&lt;/p&gt;&lt;/abstract&gt;

Dynamics of a nonlinear state-dependent feedback control ecological model with fear effect

&lt;p&gt;Integrated pest management is a pest control strategy that combines biological and chemical methods to reduce environmental pollution and protect biodiversity. Recent research indicated that the fear caused by predators had a significant effect on the growth, development, and reproductive processes of prey. Therefore, we have proposed a pest-natrual enemy system, which is a nonlinear state-dependent feedback control model that incorporated the fear effect in the predator-prey relationship. We discussed impulsive sets and phase sets of the model and derived an expression for the Poincaré map. Furthermore, we analyzed the existence and stability of order-$ 1 $ periodic solutions and explored the existence of order-$ k $ $ (k\ge2) $ periodic solutions. Finally, numerical simulations were conducted to validate our theoretical results and reveal their biological implications.&lt;/p&gt;

The dynamics of nonlocal diffusion problems with a free boundary in heterogeneous environment

This paper studies two nonlocal diffusion problems with a free boundary and a fixed boundary in heterogeneous environment. The main goal is to understand how the evolution of the two species is affected by the heterogeneous environment. We first prove the existence and uniqueness of a global solution for such systems. Then, for models with Lotka–Volterra type competition or predator–prey growth terms, we establish the spreading‐vanishing dichotomy. Sharp criteria of spreading and vanishing are also obtained. Furthermore, we show that accelerated spreading occurs if and only if the kernel function violates the threshold condition.

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.

Perturbation of a piecewise regular-singular Liénard system

In this paper we discuss the perturbation of a generalized Liénard system, defined in two regions. For x≤0 the system is regular, while for x > 0 the system is singularly perturbed. An essential difference with other papers is that a degenerate canard point appears which requires a blow-up analysis.We prove that under generic conditions the perturbed system has at most one small-amplitude limit cycle and at most N canard limit cycles, where N is the number of local extrema of the function F(x) in the singular part of the Liénard system. For critical values of the control parameters the mechanism of a canard explosion is discussed.As an application we prove that the upper bound for the number of limit cycles in a Gause predator-prey system with a general monotonic functional response function with cut-off is two times the number of maxima of the natural prey growth function after the cut-off.