Immature Predators Research Articles

Stability and bifurcation analysis of a delayed stage-structured predator–prey model with fear, additional food, and cooperative behavior in both species

The stability of predator–prey interactions in ecosystems is influenced by both inherent species interactions and external factors. For instance, the presence of additional food, as an external factor, may affect the system. To further explore this, a stage-structured predator–prey model is constructed, incorporating the influences of fear and delay on prey-population growth, which provides additional food for immature predators and facilitates cooperative behavior between mature and immature predators. The analysis evaluates the positivity, boundedness, equilibrium points, local stability around each equilibrium point, and certain bifurcations of the system. Additionally, numerical simulations are provided to correspond with the results of the theoretical analysis. It is observed that an appropriate level of fear contributes positively to system stability. While cooperation among predators can benefit immature predators, it also has the potential to harm the overall system. The introduction of additional food complicates the system dynamics, although it benefits predators, it places prey at a disadvantage. Furthermore, we observe a correlation between the level of fear and the effects of additional food, as well as the capacity of additional food to mitigate the influence of delay.

Role reversal in a stage-structured prey-predator model with fear, delay, and carry-over effects.

The present work highlights the reverse side of the same ecological coin by considering the counter-attack of prey on immature predators. We assume that the birth rate of prey is affected by the fear of adult predators and its carry-over effects (COEs). Next, we introduce two discrete delays to show time lag due to COEs and fear-response. We observe that the existence of a positive equilibrium point and the stability of the prey-only state is independent of fear and COEs. Furthermore, the necessary condition for the co-existence of all three species is determined. Our system experiences several local and global bifurcations, like, Hopf, saddle-node, transcritical, and homoclinic bifurcation. The simultaneous variation in the attack rate of prey and predator results in the Bogdanov-Takens bifurcation. Our numerical results explain the paradox of enrichment, chaos, and bi-stability of node-focus and node-cycle types. The system, with and without delay, is analyzed theoretically and numerically. Using the normal form method and center manifold theorem, the conditions for stability and direction of Hopf-bifurcation are also derived. The cascade of predator attacks, prey counter-attacks, and predator defense exhibit intricate dynamics, which sheds light on ecological harmony.

Hydra effects predator-prey bazykin's model with stage-structure and intraspecific for predator

Bazykin's predator-prey population model is considered to represent the exchange stability condition of population growth. The existence of the hydra effect and, at the same time, analyzing its influence on population growth. The condition of the model divides the species into a stage structure, namely, prey, immature predators, and mature predators. The population growth of the three species has its own characteristics. This research revealed that the Holling type II and intraspecific predatory function responses together induce the Hydra effect. In the model formed, there are 12 equilibrium points, with details for every seven points of negative imaginary equilibrium and five points of non-negative equilibrium. The findings of research studies center on five points of non-negative equilibrium. All real roots that interpret the species population's growth conditions are taken and tested for long-term stability. The test results show one point of equilibrium that meets the Routh-Hurwitz criteria and their characteristic equations. In numerical simulations, the maximum sustained yield is in the local asymptotic stable state. The growth of prey trajectories increased significantly, although at the beginning of the interaction there was a slowdown in population growth. Meanwhile, the population of immature predators and mature predators was not significantly different. Both populations grow steadily toward the point of population stability. It turns out that the two populations grow inversely, the faster the rate of predation by predators, the faster the growth rate of the prey population.

Stage and sex-dependent responses of immature predatory mites (Blattisocius dentriticus) to predation risk from cannibalistic conspecifics

Blattisocius dendriticus (Acari: Blattisociidae) is a predatory gamasid mite with the potential for the biological control of mites attacking stored products. However, its interactions with its cannibalistic conspecifics are poorly understood. In this study, we determined the effects of predation risk from cannibalistic conspecifics on the survival, development, prey consumption, and behaviour of the predator by comparing the performance of predators exposed to cues from their conspecifics with their counterparts exposed to cues of their prey and the prey food source. The results show that the survivorship of immature predators was similar across treatments. However, predators under cannibalistic risks extended the duration of their immature stages due to a prolonged protonymphal stage. Moreover, the effects of predation risk were also sex-specific, with the males responding to the risk of cannibalism, but not the females. By highlighting the non-consumptive effects of cannibalistic conspecifics on predators associated with sex and maternal age, the present study improves our understanding of the indirect effects of cannibalism and its interactions with other factors, which may affect the performance of B. dentriticus as a biological agent.

Hopf Bifurcation and Control of a Fractional-Order Delay Stage Structure Prey-Predator Model with Two Fear Effects and Prey Refuge

A generalized delay stage structure prey-predator model with fear effect and prey refuge is considered in this paper via introducing fractional-order and fear effect induced by immature predators. Hopf bifurcation and control of this system are investigated though regarding the delay as the parameter. Firstly, by using the method of linearization and Laplace transform, the roots of the characteristic equation of the linearized system of the original system are discussed, and the sufficient conditions for the system exhibits an unstable state of symmetrical periodic oscillation (Hopf bifurcation) are explored. Secondly, a linear delay feedback controller is added to the system to increase the stability domain successfully. Thirdly, numerical simulations are performed to validate the theoretical analysis, and the various impacts on the dynamical behavior of the system occurring by fear effects, prey refuge, and each fractional-order are illustrated, respectively. Furthermore, the influence of feedback gain on the bifurcation critical point is analyzed. Finally, an analysis based on the results and in-depth research about this system under the biological background is stated in the conclusion.

Complex Dynamic Behaviour of Food Web Model with Generalized Fractional Operator

We apply a new generalized Caputo operator to investigate the dynamical behaviour of the non-integer food web model (FWM). This dynamical model has three population species and is nonlinear. Three types of species are considered in this population: prey species, intermediate predators, and top predators, and the top predators are also divided into mature and immature predators. We calculated the uniqueness and existence of the solutions applying the fixed-point hypothesis. Our study examines the possibility of obtaining new dynamical phase portraits with the new generalized Caputo operator and demonstrates the portraits for several values of fractional order. A generalized predictor–corrector (P-C) approach is utilized in numerically solving this food web model. In the case of the nonlinear equations system, the effectiveness of the used scheme is highly evident and easy to implement. In addition, stability analysis was conducted for this numerical scheme.

Analysis of food chain mathematical model under fractal fractional Caputo derivative.

In this article, the dynamical behavior of a complex food chain model under a fractal fractional Caputo (FFC) derivative is investigated. The dynamical population of the proposed model is categorized as prey populations, intermediate predators, and top predators. The top predators are subdivided into mature predators and immature predators. Using fixed point theory, we calculate the existence, uniqueness, and stability of the solution. We examined the possibility of obtaining new dynamical results with fractal-fractional derivatives in the Caputo sense and present the results for several non-integer orders. The fractional Adams-Bashforth iterative technique is used for an approximate solution of the proposed model. It is observed that the effects of the applied scheme are more valuable and can be implemented to study the dynamical behavior of many nonlinear mathematical models with a variety of fractional orders and fractal dimensions.

Immature development and survival of Neoseiulus cucumeris (Oudemans) (Acari: Phytoseiidae) on eggs of Tyrophagus curvipenis (Fain & Fauvel) (Acari: Acaridae)

Establishment and maintenance of the natural enemy are critical for successful biological control of pests on plants without alternative food for predators. Great efforts have been devoted to exploring suitable supplementary food for predators. In this study, we evaluated the feasibility of using Tyrophagus curvipenis (Fain and Fauvel) (Acari: Acaridae) as a supplementary food source for Neoseiulus cucumeris (Oudemans) (Acari: Phytoseiidae) by investigating the survival and development of N. cucumeris at different prey densities with the influence of conspecifics. Furthermore, we investigated predation rates and their body size at adult emergence. The results showed that N. cucumeris developed from egg to adult in approximately six days. Survival rates of immature predators increased significantly with the given prey density. No significant difference in body size was found between the survived adults fed at different prey density, but the females were always larger than males. To conclude, T. curvipenis can be an excellent alternative food source for the biological control agent N. cucumeris.

<p class="Body"><strong>Indirect effects in predator-prey interaction: development and predation rates by immature <em>Neoseiulus cucumeris</em> increased by odour from its prey (<em>Tyrophagus putrescentiae</em>) </strong></p>

Predator-prey interactions have long been of great interest to ecologists. Although the direct consumptive effects have received extensive research, indirect influences of odour derived from their conspecifics and prey on predators have largely been underestimated and overlooked. In this study, the indirect effects of predator-prey interactions were determined with predatory mites Neoseiulus cucumeris and its factitious prey Tyrophagus putrescentiae. The responses of immature N. cucumeris to mixed odour with their conspecifics and prey were determined in a laboratory experiment. Our results showed that the mixed odour with their conspecifics did not demonstrate any obvious influences on the survival rates, developmental periods, predation rates and activities of the predatory mites. Intriguingly, the predators prolonged their protonymphal stage and consumed more prey eggs when exposed to mixed odour with their prey. Our results indicated that the mixed odour with their conspecifics was weak and its influence was insignificant for this species, but the prey odour showed a signifcant influence on the growth and consumption rates of immature predators, which highlighted that the indirect influences of predator-prey interactions on the predator were substantial and cannot be neglected.

Periodic solution of a stage-structured predator-prey model incorporating prey refuge

In this paper, we consider a delayed stage-structured predator-prey model incorporating prey refuge with Holling type II functional response. It is assumed that prey can live in two different regions. One is the prey refuge and the other is the predatory region. Moreover, in real world application, we should consider the stage-structured model. It is assumed that the prey in the predatory region can divided by two stages: Mature predators and immature predators, and the immature predators have no ability to attack prey. Based on Mawhin's coincidence degree and novel estimation techniques for a priori bounds of unknown solutions to Lu = λNu, some sufficient conditions for the existence of periodic solution is obtained. Finally, an example demonstrate the validity of our main results.

Dynamics of stage-structure predator-prey systems under density-dependent effect and mortality

We develop a four dimensional predator-prey system in continuous time with stage-structure for both the communities. The reproduction rate of the prey and the transition rate for the predator, in our model, are assumed to be density-dependent. The stability results for the coexisting equilibrium are obtained by making use of Routh–Hurwitz criteria. Because of the density-dependent effects, numerical simulations are applied in complex situations. We observe that increasing values of the coefficients linked with density-dependent term promote the stability of the coexisting steady state. Our main focus is to understand the variation of stocks when mortality rates on different stage classes are increased. We verified that stable stock on mature predator increases with its increasing mortality rate in three different modeling frameworks. However, no such positive effect on the biomass of the immature predator occurs when immature predators are removed, culled or harvested. Therefore, we could conclude that the appearance of hydra effect on many unstructured predator-prey models is due to the mortality of the mature predator only. No hydra effect is also detected when mature prey is removed in several situations we discussed. Overall, the obtained results are new and could be interesting contribution in theoretical ecology.

Associative learning in immature lacewings (Ceraeochrysa cubana)

AbstractIt is known that many social insects and arthropod predators and parasitoids can learn the association between a resource and volatile cues. Although there are various studies on the effect of experience in immature arthropods on behavior later in adult life, not much is known about the effects of such experiences on immature behavior. This was investigated here in the lacewing Ceraeochrysa cubana (Hagen) (Neuroptera: Chrysopidae). Whereas adults of this lacewing feed on plant‐provided food and honeydew, larvae are voracious polyphagous predators of several insect pests, and therefore important for biological control. Hence, studying the foraging behavior and the effects of learning in immatures of this species is important. We exposed immatures to the volatile methyl salicylate (MeSA), which was either associated with food or with the absence of food. Subsequently, their response to this volatile was tested in an olfactometer. Immatures that had experienced the association of MeSA with food were attracted to it and immatures that were exposed to MeSA during food deprivation were repelled. Subsequently, predator immatures that had experienced the association between MeSA and food were released on a plant without food and were found to use this volatile in locating patches with food. In contrast, larvae without such experience were found equally on food patches with and without the volatile. We conclude that these immature predators are capable of learning the association between volatiles and food, or the absence of food, and use this during foraging.

Locking out predators by silk, a new counterattack behaviour in a social spider mite

1. A type of arms race that includes predation, counterattacks and cross‐counterattacks occurs between the phytophagous mite Stigmaeopsis nanjingensis (Ma et Yuan), which lives in self‐woven nests and exhibits cooperative sociality, and its specialised phytoseiid mite predator, Typhlodromus bambusae Ehara.2. First, the efficiency of the S. nanjingensis (prey) counterattacking T. bambusae (predator) was observed. The prey females frequently locked the immature predators out of their nests using silk web, and the predators subsequently died of starvation. Furthermore, the prey males often killed immature T. bambusae mites after they invaded the nests.3. This reversal of roles in the predator–prey system was then re‐reversed (returned to a normal state) by the behaviour of T. bambusae females. Immature predators could maintain their predacious natures due to the presence of attending adult females, which are able to cope with the prey counterattack behaviours.

Dynamics of delayed prey-predator model with parental care for predators

In this paper, a stage structured prey-predator model (stage structure on predators) with two discrete time delays has been discussed. It is assumed that immature predators are raised by their parents in the sense that they cannot catch the prey and their foods are provided by parents. We suppose that the growth of the prey is of exponential type. The two discrete time delays occur due to maturation delay and gestation delay. Linear stability analysis for both non delay as well as with delays reveals that certain thresholds have to be maintained for coexistence. Numerical simulation shows that the system exhibits Hopf bifurcation, resulting in a stable limit cycle.

Multiple periodic solutions of a delayed predator–prey model with non-monotonic functional response and stage structure

The paper studies a periodic and delayed predator–prey system with non-monotonic functional responses and stage structure. In the system, both the predator and prey are divided into immature individuals and mature individuals by two fixed ages. It is assumed that the immature predators cannot attack preys, and the case of the mature predators attacking the immature preys is also ignored. Based on Mawhin's coincidence degree, sufficient conditions are obtained for the existence of two positive periodic solutions of the system. An example is presented to illustrate the feasibility of the main results.

Mathematical analysis of a delayed stage-structured predator–prey model with impulsive diffusion between two predators territories

In most models of population dynamics, diffusion between two patches is assumed to be either continuous or discrete, but in reality, many species diffuse only during a single period, and diffusion often occurs in regular pulses. Further, in forest habitats, the highest-level predator species are restricted to a specific territory, but prey can impulsively move between territories. Therefore, in this paper, we consider a delayed stage-structured predator–prey model with impulsively diffusive prey between two patches; in the model, patches represent the territories of two different predator populations. Here, we analytically obtain the global attractivity condition of predator-extinction periodic solutions for the system by using the concepts of Hui and Chen (2005); a numerical simulation is also included to illustrate this result. Further, we establish permanence conditions for the coexistence of the species using the theory of impulsive delayed differential equations. Finally, we explore the possibilities of the permanence of the system by using the growth rates of immature predators and the impulse period as critical parameters, and we also obtain the parameters’ threshold limits using numerical experimentation.

Habitat functionality for the ecosystem service of pest control: reproduction and feeding sites of pests and natural enemies

Landscape management for enhanced natural pest control requires knowledge of the ecological function of the habitats present in the landscape mosaic. However, little is known about which habitat types in agricultural landscapes function as reproduction habitats for arthropod pests and predators during different times of the year. We studied the arthropod assemblage on six crops and on the seven most abundant native plant species in two landscapes over 1 year in Australia. Densities of immature and adult stages of pests and their predators were assessed using beat sheet sampling. The native plants supported a significantly different arthropod assemblage than crops. Native plants had higher predator densities than crops over the course of the year, whereas crops supported higher pest densities than the native plants in two out of four seasonal sampling periods. Crops had higher densities of immature stages of pests than native plants in three of four seasonal sampling periods, implying that crops are more strongly associated with pest reproduction than native plants. Densities of immature predators, excluding spiders, were not different between native plants and crops. Spiders were, however, generally abundant and densities were higher on native plants than on crops but, because some species disperse when immature, there is less certainty in identifying their reproduction habitat. Because the predator to pest ratio on native plant species showed little variation, and spatial variation in arthropod assemblages was limited, the predator support function of native vegetation may be a general phenomenon. Incentives that maintain and restore native remnant vegetation can increase the predator to pest ratio at the landscape scale, which could enhance pest suppression in crops.

Sex-specific developmental plasticity of generalist and specialist predatory mites (Acari: Phytoseiidae) in response to food stress

We studied developmental plasticity under food stress in three female-biased size dimorphic predatory mite species, Phytoseiulus persimilis, Neoseiulus californicus, and Amblyseius andersoni. All three species prey on two-spotted spider mites but differ in the degree of adaptation to this prey. Phytoseiulus persimilis is a specialized spider mite predator, N. californicus is a generalist with a preference for spider mites, and A. andersoni is a broad generalist. Immature predators were offered prey patches of varying density and their survival chances, dispersal tendencies, age and size at maturity measured. Amblyseius andersoni dispersed earlier from and had lower survival chances in low density prey patches than N. californicus and P. persimilis. Age at maturity was not affected by prey density in the generalist A. andersoni, whereas both the specialist P. persimilis and the generalist N. californicus accelerated development at low prey densities. Species-specific plasticity in age at maturity reflects opposite survival strategies when confronted with limited prey: to prematurely leave and search for other food (A. andersoni) or to stay and accelerate development (P. persimilis, N. californicus). In all species, size at maturity was more plastic in females than males, indicating that males incur higher fitness costs from deviations from optimal body size. © 2011 The Linnean Society of London, Biological Journal of the Linnean Society, 2011, 102, 650–660.

Prey Predator Fishery Model with Stage Structure in Two Patchy Marine Aquatic Environment

In this paper, we propose and analyze a mathematical model to study the dynamics of a fishery resource system with stage structure in an aquatic environment that consists of two zones namely unreserved zone (fishing permitted) and reserved zone (fishing is strictly prohibited). In this model we introduce a stage structure in which predators are split into two kinds as immature predators and mature predators. It is assumed that immature predators cannot catch the prey and their foods are given by their parents (mature predators). It is also assumed that the fishing of immature predators prohibited in the unreserved zone and predator species are not allowed to enter inside the reserved zone. The local and global stability analysis has been specified. Biological and Bionomical equilibriums of the system are derived. Mathematical formulation of the optimal harvesting policy is given and its solution is derived in the equilibrium case by using Pontryagin’s maximum principle.

Analysis of a Nonautonomous Delayed Predator‐Prey System with a Stage Structure for the Predator in a Polluted Environment

A two‐species nonautonomous Lotka‐Volterra type model with diffusional migration among the immature predator population, constant delay among the matured predators, and toxicant effect on the immature predators in a nonprotective patch is proposed. The scale of the protective zone among the immature predator population can be regulated through diffusive coefficients Di(t), i = 1, 2. It is proved that this system is uniformly persistent (permanence) under appropriate conditions. Sufficient conditions are derived to confirm that if this system admits a positive periodic solution, then it is globally asymptotically stable.