Prey Growth Research Articles

Relaxation oscillations of a slow–fast predator–prey model with a piecewise smooth functional response

The paper investigates the relaxation oscillations of a classical predator–prey model, based on the natural ecological assumption that the maximum per capita birth rate of the predator is small in comparison with the intrinsic prey growth rate. Predator’s feeding rate is assumed to be modeled by a piecewise smooth Holling type I functional response including a predator interference, which yields a piecewise smooth slow–fast system. Using geometry singular perturbation theory, we prove that the model has exactly two nested relaxation oscillations surrounding the unique stable node. Additional numerical simulations are provided to verify the analytical results.

A review of mesocosm experiments on heavy metals in marine environment and related issues of emerging concerns.

Mesocosms are real-world environmental science tools for bridging the gap between laboratory-scale experiments and actual habitat studies on ecosystem complexities. These experiments are increasingly being applied in understanding the complex impacts of heavy metals, ocean acidification, global warming, and oil spills. The insights of the present review indicate how metals and metal-bound activities impact on various aspects of ecological complexities like prey predator cues, growth, embryonic development, and reproduction. Plankton and benthos are used more often over fish and microbes owing to their smaller size, faster reproduction, amenability, and repeatability during mesocosm experiments. The results of ocean acidification reveal calcification of plankton, corals, alteration of pelagic structures, and plankton blooms. The subtle effect of oil spills is amplified on sediment microorganisms, primary producers, and crustaceans. An overview of the mesocosm designs over the years indicates that gradual changes have evolved in the type, size, design, composition, parameters, methodology employed, and the outputs obtained. Most of the pelagic and benthic mesocosm designs involve consideration of interactions within the water columns, between water and sediments, trophic levels, and nutrient rivalry. Mesocosm structures are built considering physical processes (tidal currents, turbulence, inner cycling of nutrients, thermal stratification, and mixing), biological complexities (population, community, and ecosystem) using appropriate filling containers, and sampling facilities that employ inert materials. The principle of design is easy transportation, mooring, deployment, and free floating structures besides addressing the unique ecosystem-based science problems. The evolution of the mesocosm tools helps in understanding further advancement of techniques and their applications in marine ecosystems.

Predation potential of hunting and web-building spiders on rice pests of Indian subcontinent

The present study investigated the predation attributes of hunting and web-building spiders of Indian subcontinent against rice-pests, under in-vitro conditions. Field observations revealed that the lynx spider, Oxyopes javanus and the ground-dwelling wolf-spider, Pardosa sumatrana were the most abundant arboreal hunting spiders, while Neoscona theisi and Tetragnatha javana, were the most abundant arboreal web-making spiders, throughout the crop growing season. Laboratory results showed that the prey consumption rates and growth rates of spiders were highest on abundant prey, but the conversion efficiencies were highest on scarce prey. Results identified the highest consumption and growth rates for O. javanus, while conversion efficiencies were highest for N. theisi. The four spider species under study consumed higher number of leafhoppers and lepidopteron adult stage pests in comparison to Leptocorisa bugs and grasshopper nymphs. We, therefore, suggest that the predatory impacts of spiders may be strongly influenced by their species-specific feeding and behavioural attributes, and the anti-predation features of the potential prey.

A widespread interaction between generalist and specialist enemies: The role of intraguild predation and Allee effect

A natural food web system involves a diverse community of natural enemies and one of the widespread and common phenomena of such systems is intraguild predation (IGP) (i.e., presence of eating and killing among potential competitors). Here, we investigate the dynamics of a food web system with Allee effect and intraguild predation. In the present study, generalist and specialist natural enemies competing for a shared resource (prey) (intraguild predation) have been introduced. The Allee effect has also been incorporated in the shared prey growth rate. We investigate how parameters defining Allee effect and intraguild predation affect the long-term persistence, extinction and co-existence regions of such species. We outline the conditions under which different types of interior and non-interior equilibria exist and are locally stable. Bi-stable dynamics has also been investigated for the proposed model system for a suitable range of parametric values. A threshold condition on the strength of Allee effect has been obtained assuring the absence of IG predator population along with extinction region of shared prey. To understand the dynamics of the system, a comprehensive study of bifurcation analysis has also been provided taking Allee effect and fertility rate of intraguild predator as bifurcation parameters. These two parameters generate various interesting bifurcations like saddle-node bifurcation and Hopf-bifurcation. We have obtained different parametric regions of Allee parameter for the existence of different boundary and interior equilibria. All the analytical results related with local stability of equilibrium points and all possible successive bifurcations have been supported by different numerical examples, one and two parameter bifurcation diagrams, bi-stability diagram and stability regions of all possible equilibrium points. The impacts of Allee effect on co-existence, stability, extinction of species, their persistence, bistability and bifurcations have been explicitly discussed and the whole dynamics has also been successfully compared with the dynamics of food web without Allee effect. It is observed that the introduction of Allee effect and IG predator induce more rich dynamics and compel the system to be more sensitive to initial population densities.

Spatiotemporal pattern formation in 2D prey-predator system with nonlocal intraspecific competition

There is growing evidence that ecological interactions are often nonlocal. Correspondingly, increasing attention is paid to mathematical models with nonlocal terms as such models may provide a more realistic description of ecological dynamics. Here we consider a nonlocal prey-predator model where the movement of both species is described by the standard Fickian diffusion, and hence is local, but the intra-specific competition of prey is nonlocal and is described by a convolution-type term with the ‘top-hat’ (piecewise-constant) kernel. The prey growth rate also includes the strong Allee effect. The system is studied using a combination of analytical tools and extensive numerical simulations. We obtain that nonlocality makes possible the pattern formation due to the Turing instability, which is not possible in the corresponding local model. We also obtain that the nonlocality creates bistability: it depends on the initial conditions which of the two spatially heterogeneous distributions emerges. Finally, we show that the bifurcation structure of the system is less sensitive to the choice of parametrization than it is in the corresponding nonspatial case, suggesting that nonlocality may decrease the structural sensitivity of the system.

Effect of parasitized prey on prey consumption, survival, growth, and development of Coccinella septempunctata L. (Coleoptera: Coccinellidae) under laboratory conditions

A study of interactions among natural enemies is important to develop a better biological control program. Among these interactions, one that is crucial is the consumption of parasitized prey by a predator. Feeding on aphid mummies could affect the predator as well as the parasitoid species. In this study, the effect of parasitized prey on prey consumption, survival, growth, and development of 4th instar larvae of the predatory species, Coccinella septempunctata L. (Coleoptera: Coccinellidae), as an active predator of aphids, was studied. Moreover, the effect of parasitized and mummified aphids on female fecundity was also evaluated. The green peach aphid, Myzus persicae Sulzer (Hemiptera: Aphididae) was used. Obtained results showed that the parasitized aphids, as a predatory food, significantly affected the predator. The prey consumption was highest on parasitized (24.10 ± 0.53) and lowest on mummified (9.75 ± 0.40) aphids. The survival rate was in the order of non-parasitized > parasitized > mummified. The mass gained by the 4th instar larvae of C. septempunctata was in the order of parasitized (26.25 mg ± 0.89) > non-parasitized (19.25 mg ± 0.86) > mummified aphids (10.20 mg ± 0.52), when fed on different prey. Developmental time of the predator was recorded highest, when it consumed mummified aphids (13.6 ± 0.39). As well, female fecundity was affected positively. The female was observed to lay the most eggs (323.55 ± 1.57) to have the highest number of hatched eggs (38.70 ± 0.92), and to have the highest egg mass (196.10 μg ± 1.22), when it consumed the parasitized aphids in contrast to non-parasitized and mummified aphids. It was also found that the type of prey did not affect the incubation period of the eggs.

Rich Bifurcation Structure of Prey–Predator Model Induced by the Allee Effect in the Growth of Generalist Predator

Prey–predator models are building blocks for many food-chain and food-web models in theoretical population biology. These models can be divided into two groups depending on the nature of predators, namely, specialist predator and generalist predator. Generalist predators can survive in the absence of prey but specialist predators go to extinction. Prey–predator models with specialist predator and Allee effect in prey growth have been investigated by several researchers and various types of interesting dynamics have been reported. In this paper, we consider a prey–predator model with generalist predator subject to Allee effect in predator’s growth rate. In general, a prey–predator system with saturating functional response can be destabilized due to the increase of the carrying capacity of prey which is known as paradox of enrichment. In our model with Allee effect in predator growth, we have shown that increase in carrying capacity of prey helps the populations to survive in a coexistence steady state. The considered model is capable of producing bistable dynamics for a reasonable range of parameter values. The complete dynamics of the system are quite rich and all possible local and global bifurcations are studied to understand the dynamics of the model. Analytical results are verified with numerical examples and successive bifurcations are identified with the help of bifurcation diagrams.

Analytical and numerical detection of traveling wave and wave-train solutions in a prey–predator model with weak Allee effect

The traveling wave and wave-train fronts correspond to the transition zones from a trivial steady state to a coexistence steady state and a limit cycle around the coexistence steady state, respectively. In this study, we establish the existence of both types of fronts for a reaction–diffusion system of prey–predator interactions with weak additive Allee effect in prey growth, Holling type II functional response and density-dependent death rate for predators. For analytical simplicity, we consider immobile prey population. Under this consideration, the existence of both the traveling fronts is mathematically equivalent to the existence of point-to-point and point-to-cycle heteroclinic connections in $$\mathbb {R}^{3}$$. The proof for the existence of traveling fronts relies on the construction of an unbounded wedged region, a shooting argument and an appropriate Lyapunov function. Also, by employing the Hopf bifurcation theorem we show the existence of traveling wave-train solution. In both the cases, we find successful invasion by the predator species. Further, we provide adequate numerical illustrations in order to corroborate our theoretical predictions. Our numerical simulations also suggest that the theoretically obtained minimum wave speed serves as an asymptotic speed of traveling wave propagation.

Sex‐specific differences in the response of prey to predation risk

Abstract The non‐consumptive effects of predation risk can strongly affect prey behaviour and fitness with emergent effects on community structure and ecosystem functioning. Prey may respond differently to predation risk based on key traits such as sex, but the influence of sex‐specific variation is typically explored in species with strong sexual dimorphism. However, sex‐specific responses to predation risk may arise even in prey species lacking sexual dimorphisms based on differences in the relative cost of reproduction. Using a rocky intertidal food chain, we conducted a laboratory mesocosm experiment to explore sex‐specific responses of morphologically similar, reproductively mature prey (the snail Nucella lapillus) to predation risk and whether risk affected female fecundity. We found that predation risk suppressed prey growth only in males via effects on growth efficiency, suggesting that sex‐specific disparities may arise due to differences in the energy required for reproduction and/or the costs of mounting a physiological stress response. Moreover, while risk did not affect overall female fecundity, it eliminated the positive relationship between female size and fecundity observed in the absence of risk. We hypothesize that these sex‐specific disparities arise due to differences in the energy required for reproduction and/or the costs of mounting a physiological stress response. Reproduction is likely more energetically costly for females than males, so females may display weaker antipredator responses in order to maintain energetic reserves needed for reproduction. Our results suggest that sex‐specific responses may be an important component of inter‐individual differences in prey responses to risk and influence prey population growth and demography even in species lacking sexual dimorphism. A free Plain Language Summary can be found within the Supporting Information of this article.

Coexistence in seasonally varying predator–prey systems with Allee effect

A general seasonally-varying predator–prey model with Allee effect in the prey growth is investigated. The analysis is performed only on the basis of some properties determining the shape of the prey growth rate and the functional responses. General conditions for coexistence are determined, both in the case of weak and strong Allee effect. Finally, a modified Leslie–Gower predator–prey model with Allee effect is investigated. Numerical results illustrate the qualitative behaviors of the system, in particular the presence of periodic orbits.

The effects of predation risk on prey stoichiometry: a meta-analysis.

A decade ago, the general stress paradigm (GSP) aimed to develop a predictive framework linking predator effects to ecosystem function. The GSP was based on the notion that animals, across taxa, exhibit similar physiological responses to predation risk that divert resources from growth and reproduction (which require N-rich biomolecules [i.e., protein]) to emergency functions (which require C-rich biomolecules [e.g., carbohydrates]). The GSP predicts that stressed prey should have a greater dietary demand for C-rich resources, a higher body C:N ratio, and elevated N excretion. Now, 10 yr later, we aim to revisit the GSP-using quantitative meta-analysis to test the original predictions of the GSP and how (1) predator hunting mode, (2) multiple stressors, and (3) prey dietary shifts affect prey stoichiometric responses to predation risk. Our data set was consistent with previous work showing that predation risk increases prey glucocorticoid levels and metabolic rates and decreases prey growth rates. We found that predation risk tended to decrease the fat, carbohydrate, and protein content of prey bodies; increased the C:P and N:P of prey bodies; but had no effect on the C, N, P, or C:N content of prey bodies. Additionally, we found no effect of predation risk on the N content of prey excretions. Prey responses to predation risk were unaffected by multiple stressors or the prey's ability to shift their diet, but predator hunting mode did affect the nature of prey stoichiometric responses. Specifically, ambush predators decreased prey macronutrient content and suppressed prey growth, and active predators had no effect on prey macronutrient content and a smaller effect on prey growth than ambush predators. The significant effects of predation risk were supported by robust fail-safe numbers, despite the high between-comparison heterogeneity that was found in all analyses. Our findings highlight the need (1) to test the underlying mechanisms and emerging patterns of the GSP in diverse taxa, (2) to explore the mismatch between prey macronutrient content and elemental stoichiometry, and (3) to expand the conceptual framework to include more inducible defenses (e.g., behavioral and morphological) and predator traits.

Allee effect can simplify the dynamics of a prey-predator model

In this work, we investigate a prey-predator model which includes the Allee effect phenomena in prey growth function, density dependent death rate for predators and ratio dependent functional response. we fulfill a comprehensive bifurcation analysis, constructing the two-parametric bifurcation diagrams which describes the effect of density dependent death rate parameter, and also show possible phase portraits. We have also investigated the model in the absence of Allee effect and corresponding bifurcation diagram has been presented to show the dynamical changes in the system. Then we compare the properties of the ratio dependent prey-predator model with and without the Allee effect and show that Allee effect has a significant role in the dynamics. Allee effect can preserve local extinction of populations and suppress the stability of interior equilibrium point. Finally, all the analytical results are validated with the help of numerical simulations.

Impact of fear effect on the growth of prey in a predator-prey interaction model

Several field data and experiments on a terrestrial vertebrates exhibited that the fear of predators would cause a substantial variability of prey demography. Fear for predator population enhances the survival probability of prey population, and it can greatly reduce the reproduction of prey population. Based on the experimental evidence, we proposed and analyzed a prey-predator system introducing the cost of fear into prey reproduction with Holling type-II functional response. We investigate all the biologically feasible equilibrium points, and their stability is analyzed in terms of the model parameters. Our mathematical analysis exhibits that for strong anti-predator responses can stabilize the prey-predator interactions by ignoring the existence of periodic behaviors. Our model system undergoes Hopf bifurcation by considering the birth rate r0 as a bifurcation parameter. For larger prey birth rate, we investigate the transition to a stable coexisting equilibrium state, with oscillatory approach to this equilibrium state, indicating that the greatest characteristic eigenvalues are actually a pair of imaginary eigenvalues with real part negative, which is increasing for r0. We obtained the conditions for the occurrence of Hopf bifurcation and conditions governing the direction of Hopf bifurcation, which imply that the prey birth rate will not only influence the occurrence of Hopf bifurcation but also alter the direction of Hopf bifurcation. We identify the parameter regions associated with the extinct equilibria, predator-free equilibria and coexisting equilibria with respect to prey birth rate, predator mortality rates. Fear can stabilize the predator-prey system at an interior steady state, where all the species can exists together, or it can create the oscillatory coexistence of all the populations. We performed some numerical simulations to investigate the relationship between the effects of fear and other biologically related parameters (including growth/decay rate of prey/predator), which exhibit the impact that fear can have in prey-predator system. Our numerical illustrations also demonstrate that the prey become less sensitive to perceive the risk of predation with increasing prey growth rate or increasing predators decay rate.

Spatio-temporal Bazykin's model with space-time nonlocality.

This work deals with a reaction-diffusion model for prey-predator interaction with Bazykin's reaction kinetics and a nonlocal interaction term in prey growth. The kernel of the integral characterizes nonlocal consumption of resources and depends on space and time. Linear stability analysis determines the conditions of the emergence of Turing patterns without and with nonlocal term, while weakly nonlinear analysis allows the derivation of amplitude equations. The bifurcation analysis and numerical simulation carried out in this work reveal the existence of stationary and dynamic patterns appearing due to the loss of stability of the coexistence homogeneous steady-state.

Bifurcation analysis and dynamic behavior to a predator-prey model with Beddington-DeAngelis functional response and protection zone

<p style='text-indent:20px;'>In this paper we study the protection zone problem to a predator-prey model subject to Beddington-DeAngelis functional responses and small prey growth rate. This is a successive work to a previous paper of the authors [X. He, S. N. Zheng, Protection zone in a diffusive predator-prey model with Beddington-DeAngelis functional response, J. Math. Biol. 75 (2017) 239-257], where the model with large prey growth rate was considered. At first we establish the existence and multiplicity of positive steady state solutions, and then give the dynamic behavior of the evolution problem. It is proved that there may be no positive steady state, or may have at leat one, two, or even three positive steady states, depending on the parameters involved such as the growth rate, the predation rate, and the food handling time of the predators, the growth rate and the refuge ability of the preys, and the sizes of the habitat with protection zone. In addition, it is shown that the dynamics of the solutions rely on the initial state as well, e.g., though there could be multiple positive steady states, the prey will go to extinction as time tends to infinity if its initial value is small.

A class of discrete predator–prey interaction with bifurcation analysis and chaos control

The interaction between prey and predator is well-known within natural ecosystems. Due to their multifariousness and strong link population dynamics, predators contain distinct features of ecological communities. Keeping in view the Nicholson-Bailey framework for host-parasitoid interaction, a discrete-time predator–prey system is formulated and studied with implementation of type-II functional response and logistic prey growth in form of the Beverton-Holt map. Persistence of solutions and existence of equilibria are discussed. Moreover, stability analysis of equilibria is carried out for predator–prey model. With implementation of bifurcation theory of normal forms and center manifold theorem, it is proved that system undergoes transcritical bifurcation around its boundary equilibrium. On the other hand, if growth rate of consumers is taken as bifurcation parameter, then system undergoes Neimark-Sacker bifurcation around its positive equilibrium point. Methods of chaos control are introduced to avoid the populations from unpredictable behavior. Numerical simulation is provided to strengthen our theoretical discussion.

Global dynamics of a tritrophic food chain model subject to the Allee effects in the prey population with sexually reproductive generalized‐type top predator

In this article, we have considered a continuous tritrophic food chain model subject to the Allee effect on the prey growth function with prey-dependent Holling type II functional response between the prey and intermediate predator; Crowley-Martin senses functional response between intermediate predator and top predator, and the top predator is of sexually reproductive type. We have established the positivity and boundedness of the system and the condition of existence of different equilibrium points. The local and global stability of the solutions about the various equilibrium points has been investigated. The center manifold theorem has been used to find the nature of the solution in the neighborhood of the nonhyperbolic equilibrium points and the direction of Hopf bifurcations. Numerical simulation has been carried out to establish the theoretical findings and finally some concluding remarks are given.

Synchronization and Bursting Activity in the Model for Two Predator-Prey Systems Coupled By Predator Migration

The papers is devoted to a model for two non-identical predator-prey communities coupled by migration and characterized by logistic growth of prey and Holling type II functional response. The coupling is a predator migration at constant weak rate. The non-identity is the difference in the prey growth rates or predator mortalities in each patch. We studied the equilibrium states of model and scenarios of loss of their stability and emerge of complex periodic solutions. It was shown that in some domains of the parameter space there is a bursting activity which are that the dynamics of two communities contain segments of slowly resting dynamic (as part of a fast-slow cycle or canard) and regular bursts of spikes. In the resting part, the dynamics of the second community, as a rule, follow the slow changes in the first community, i.e. the dynamics in different patches are synchronous. But in the fast part there is only phase synchronization between the fast-slow cycle in first patch and bursts in second. We classified the scenarios of transition between different types of bursting activity by location spiking manifold and canard. These types differ not so much in size, shape or numbers of spikes as in the order of bursts emerge relative a slow-fast cycle. In a typical case the start of burst (divergent fast oscillations) coincides with the minimum numbers or quasi-extinction of prey in the first patch. After a rapid increase in the prey number in the first patch, diverging fluctuations give way to damped in the second patch. Such dynamics correspond to the rhombus-wave shape of spikes cluster. Another case is interesting, when the burst of spikes is formed after the full recovery of prey and with a certain predator number in the first patch. In this case, the spikes cluster takes the shape of a triangle-wave or a truncated rhombus-wave. It was shown that transitions between these types of bursts are accompanied by a change in the oscillation period and the degree of synchronization. Triangular-wave bursters correspond to complete synchronization of the predator dynamics in the resting part and rhomboid-wave correspond to antiphase synchronization. In the fast part with many spikes, communities are completely asynchronous to each other.

Growth, developmental, and size structure responses in tadpole prey under increasing threat from gape-limited newts

Size variability within a cohort can have profound effects on community ecology and evolution. Although competition for resources generally increases size variability, the effect of (non-consumptive) predation on this demographic trait remains relatively poorly understood. Existing models suggest a positive correlation between growth rate (mediated by resource level) and expression of size variability (as measured by the coefficient of variation) in prey cohorts. We tested this prediction by exposing the tadpoles of the Japanese Forest Green Treefrog (Rhacophorus arboreus (Okada and Kawano, 1924) = Zhangixalus arboreus (Okada and Kawano, 1924)) to the non-lethal presence of gape-limited Japanese Fire-bellied Newts (Cynops pyrrhogaster (Boie, 1826)) at low and high predator densities in an outdoor mesocosm experiment. Tadpole growth rates and periphyton biomass increased with newt density. But in contrast to prediction, elevated growth rates did not increase but, reversely, decreased cohort size variability in the tadpoles. We discuss two potential mechanisms behind this outcome. First, increased resource availability mediated by predator feeding may have reduced the strength of competition, ultimately leading to more evenly distributed resource gains among individuals; second, if smaller individuals grew relatively faster than larger individuals, as to quicken entry to a size refuge against the gape-limited predator, then inter-individual size differences could diminish over time.

The non‐consumptive effects of predators and personality on prey growth and mortality

AbstractIndividual organisms vary in personality, and the ecological consequences of that variation can affect the strength of predator–prey interactions. Prey with bolder tendencies can mitigate the strength of species interactions by altering growth and initiating ontogenetic niche shifts (ONS). While the link between personality and growth has been established, recent research has highlighted the important interplay between ONS and predator cues in community ecology. The objective of this study was to evaluate the effects of prey personality and predator cues on prey growth and ONS. We predicted growth–mortality trade‐offs among personalities with higher survival, larger size, and accelerated ONS for bold individuals in comparison with shy individuals. To evaluate this objective, we conducted behavioral assays and a mesocosm experiment to test how southern leopard frog (Rana sphenocephala) tadpole personality and predatory fish (bluegill, Lepomis macrochirus) cues affects tadpole growth and metamorphosis. On average, bold tadpoles had higher mortality across all treatments in comparison with shy tadpoles. The effects of fish cues were dependent on tadpole personality with shy tadpoles metamorphosing significantly later than bold tadpoles. Bold tadpoles were larger than shy tadpoles at metamorphosis; however, that pattern reversed with fish cues as shy individuals metamorphosed larger than bold individuals. Our results suggest personality may be useful for predicting growth and life history for some prey species with predators. Specifically, the threat of predation can interact with personality to incur a benefit (earlier ONS) while also incurring a cost (size at metamorphosis). Hence by incorporating predator cues with personality, ecologists will be able to elucidate growth–mortality trade‐offs mediated by personality.