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FUNCTIONAL RESPONSES WITH PREDATOR INTERFERENCE: VIABLE ALTERNATIVES TO THE HOLLING TYPE II MODEL
Ecology
... response [9,12,13], which intricately models mutual interference among predators [14][15][16][17] and closely aligns with empirical observations in predator-prey communities [18]. Recent studies further elaborate on the dynamical complexity and transient behavior of these systems, showing significant ecological and mathematical implications [19,20]. ...
... Our research primarily investigates the existence of heteroclinic orbits that asymptotically connect the equilibriaẼ * = (u * , v * , 0) andẼ 1 = (1, 0, 0) (see Lemma 4) in systems (17) and (18). Furthermore, these equilibriaẼ * andẼ 1 correspond to equilibria E * = (u * , v * ) and E 1 = (1, 0) in Theorem 1. ...
... Lemma 5 shows that the normal to the M =0, =0 is hyperbolic and repelling for < c , that is, the direction of the trajectory of the layer system is determinable. Therefore, the dynamics of the three-dimensional system (18) can be obtained by analyzing the dynamical behavior of system (23) on critical manifold M =0, =0 . Then, utilizing the Fisher-KPP dynamics and GSPT with small parameter , we get the existence of heteroclinic orbits for system (17) with 1 + < < c (see Lemma 9 and Figure 5). ...
In this paper, we consider a singular diffusive predator–prey model with Beddington–DeAngelis functional response, employing geometric singular perturbation theory and Bendixson's criteria. Our investigation revolves around transforming the reaction–diffusion equation into a multi‐scale four‐dimensional slow–fast system with two different orders of small parameters. Through once singular perturbation analysis, our focus shifts towards exploring the existence of heteroclinic orbits in a three‐dimensional system. We analyze these dynamics through the perspective of the Fisher–KPP equation in two limit cases. In the first case, only the normal to the two‐dimensional slow manifold is unstable. This allows for the deduction of existence of heteroclinic orbits in the three‐dimensional system through investigating the dynamics on the two‐dimensional slow manifold. Consequently, we obtain both monotonic traveling fronts and non‐monotonic fronts with oscillatory tails. In the second case, the normal to the one‐dimensional slow manifold exhibits both stable and unstable directions, then it is impossible to restrict the dynamics of the three‐dimensional system entirely to the slow manifold. Instead, we integrate the slow orbits of the reduced system with the fast orbits of the layer system to construct a singular heteroclinic orbit. According to Fenichel's theorem, we discover the existence of exact heteroclinic orbits of three‐dimensional system and derive the monotonic traveling fronts under weaker parameter conditions. Additionally, we also discuss the nonexistence of traveling fronts. Finally, we demonstrate our theoretical results with numerical simulations.
... Here, k is the magnitude of mutual interference among the predators. The boundedness of the response is a consequence of physiological constraints on the feeding rate as suggested in [2]. The formulation of the response indicates that it is also a function of the predator species (here, v). ...
... The formulation of the response indicates that it is also a function of the predator species (here, v). If we assume that k = 0 then the response would turn into the classical Holling type II response [2]. Compared to another predator-dependent functional response, the Michaelis-Menten response [3], it qualitatively exhibits many similar properties while eliminating some of the singularities observed in the Menten response. ...
... Compared to another predator-dependent functional response, the Michaelis-Menten response [3], it qualitatively exhibits many similar properties while eliminating some of the singularities observed in the Menten response. From a mathematical perspective, both the Holling type and the Michaelis-Menten response can be regarded as limiting cases of the DeAngelis response [2]. The rationale for incorporating this response is explained in [2]. ...
The study involves examining the global bifurcation structure associated with the nonconstant steady states of a reaction-diffusion predator-prey system where both the species interact in accordance with the Beddington DeAngelis response and the movement flux of the predator incorporates attractive transition. We consider the magnitude of population flux by attractive transition as the bifurcation parameter and employ the Crandall-Rabinowitz bifurcation theorem to study the global bifurcation structure associated with the problem. We have also derived some a priori estimates associated with the problem and carried out numerical simulations to support our theoretical results. This work can be regarded as the first step towards inclusion of population flux by attractive transition in scenarios where interactions are governed by complex functional responses.
... where u represents the density of prey population, p and c 1 reflects the effect of attack rate and the time needed for handling per prey. A large number of research about predator-prey theory was based on Holling type II functional response, see [6,34]. Taking account of the time spent in encounters with other predators, Beddington [1] and DeAngelis et al. [11] in 1975 proposed a predator-dependent functional response: ...
... where c 2 measures the level of interference between predators. In 2001, Skalski and Gilliam [34] carried out statistical tests by using data sets from 19 predator-prey systems, and found that Beddington-DeAngelis functional response can better fit 18 data sets than Holling type II functional response. The predator-prey species corresponding to 18 data sets include parasitoid-house fly, fish-cladoceran, coyotehare and so on. ...
... Moreover, the functional response is different from the predator-taxis about considering the avoidance of predation risk. In fact, the term −puv/(1+c 1 u+c 2 v) in the model describes the rate at which prey can be consumed by predators [6,13,34], where the effect of avoiding predation risk is related to the predator density v [13]. The predator-taxis term α∇ · (u∇v) in the model shows the effect of the tendency of prey moving away from the high gradient of predator density on the change rate of prey density [2,45,51], where the gradient of predator density ∇v affects the change rate of prey density. ...
... They discussed that the growth of predator is characterized by density of prey, also the ratio of density of the predator to prey. Michaelis-Menten functional response [4,5] is another functional response and it is read in the following way: ...
... Then Eqs. (5) and (6) have formal solution, respectively, as ...
... (16) and (17) and corresponding derivatives in Eqs. (5) and (6), respectively, and equating the coefficients of the same power of q(ρ) equal to zero, we obtained the system of equations and solved the system of Eq. (5) and with the help of M aple, we get the following results: ...
Ecological system is the interaction of biological community with other organisms and to their physical environments. One of the important model is spatiotemporal prey-predator model of Michaelis Menten–type functional response and reaction diffusion with constant harvest rate. This paper investigates the spatiotemporal structures of ratio-dependent prey and predator densities under different constraint conditions and suitable parameters. The φ6 model expansion technique is followed to extract these densities. The prey and predator densities behave differently depending on the diffusion coefficients and other parametric ratios. The 3-D and 2D behavior of these densities are also plotted and observed. These results may help for better understanding to study the biological community in a real marine environments or ecological system.
... where C in is the carrion supply rate, and C is the rate at which carrion is lost to invertebrate scavengers. Consistent with Assumption 1 above, the functional responses of vertebrate scavengers are prescribed to be Holling Type II, a commonly used resource-dependent functional response (Skalski & Gilliam, 2001). This means that the rate of carrion consumption by the four scavengers is governed by discovery rates e J , e H , e L and e V and handling times h J , h H , h L and h V . ...
... The scavenging model that we have used focuses on exploitation competition. Such models represent a minimal-resolution description of energy flow from resource to consumer (Skalski & Gilliam, 2001). ...
Vultures play a crucial role in scavenging communities as apex scavengers. Scavenging communities in turn are a key component of terrestrial ecosystems, ensuring that dead biomass is removed quickly and efficiently. Anthropogenic disturbances, particularly mass poisonings, have caused crashes in vulture populations in Africa and Asia.
We ask if vultures can re‐establish themselves in a scavenging community from a point of near extirpation. To allow for maximum knowledge transfer across ecosystems, we focus on an ecosystem that is otherwise considered pristine.
We chose Kruger National Park (KNP), a well‐documented African scavenging community, as our focal ecosystem and parameterised a mathematical model of scavenging‐community dynamics using field data from the park. We predicted the upper limit of vulture population size in an ecosystem like KNP. We then analysed vultures' path to recovery, using this empirically parameterised scavenging‐community model. We used perturbation methods to determine how parameter values that may be specific to KNP influence our predictions.
Comparisons of predicted vulture carrying capacity with recent population estimates suggest that the cumulative effect of human activities on vulture abundance is larger than previously believed. Our analysis shows that vulture populations can reach their carrying capacity approximately five decades after a poisoning event that would almost extirpate the population. Over shorter time scales, we predict a decade of enhanced mammal abundance (i.e. mesoscavenger release) before the mammals are excluded from the scavenging community. In our study system, jackals and hyenas are the mammalian groups predicted to benefit from the absence of vultures. However, neither group removes biomass as efficiently as vultures and animal carcasses are predicted to accumulate in the ecosystem while the vulture population recovers.
In our framework, the carrying capacity for vulture populations is determined by carcass availability. As evidence for an alternative regulating factor is lacking, we conclude that present‐day vulture population densities are orders of magnitude below their upper limits. Our results therefore suggest that with a recovery plan in place, the long‐term prospects for vulture species and the associated ecosystems are positive.
... Different functional responses, such as the Holling type-I, Holling type-II, and ratio-dependent functional responses, are utilized in mathematical analyses of eco-epidemiological systems. Among the ratio-dependent functional response is oft regarded as very emphatic in modeling prey-predator interactions [23][24][25][26]. Other studies [27,28] have considered scenarios in which healthy prey exhibit greater activity than infected ones, making them less susceptible to predation by predators. ...
... where, Then evaluation of the determinant of the characteristic equation |A − λI| = 0 gives a fourth-order algebraic equation of the form λ 4 + C 1 λ 3 + C 2 λ 2 + C 3 λ + C 4 = 0. Using the Hurwitz criterion the coexistence will be stable if the following conditions are satisfied. According to the Routh-Hurwitz criterion, the characteristic equation (24) will possess eigenvalues with negative real parts under the conditions: ...
In this paper, the system including communicable infection from prey to predator , represented by the growing rate of the prey as a healing of a predator’s, has been utilized to develop and analyze a four-dimensional, non-linear eco-epidemic model. In the context of the analysis, the exploration of all potential equilibrium points, along with an examination of their local stability conditions, has been conducted both with and without considering time delays. Additionally, the confirmation of the model’s positivity and boundedness has been carried out. The positive and negative impact of the proposed model on the prey-predator population has been investigated aided by sensitivity analysis where the presence and validence of Bifurcation were elucidated by the numerical studies. The parameters were identified which explained the influence of disease and recovery delay over the model population. A right base for the perception of the behavioural effects of the prey-predator on eco-epidemiology has been prepared through the theoretical result. Based on the analytical result furthermore, numerical simulations were done so that the authenticity of the author’s numerical analytical approach using parameter values may be verified.
... In fact, Crowley-Martin functional response and Beddington-DeAngelis functional response are more or less similar, except the term αβ uv. But in some scenarios to explain the exact dynamics of natural density of possible preys and predators, Crowley-Martin type functional response is superior to Beddington-DeAngelis functional response, see [106]. Subsequent peer group of mathematicians and biologists tried to extend the prey-predator models with several kinds of functional response features to measure the realistic phenomena of our natural ecosystem, see [19,118,124]. ...
... Specifically if v = 1, it falls off to the classic Holling Type II response. These types of interference among predators using Crowley-Martin functional response were analyzed by several authors [106,110,114]. ...
This paper presents a survey of research on the study of the impact
of different functional responses on prey-predator models in ecology.
These functional responses impact the qualitative behaviours of prey-predator models. Further stability and bifurcation analysis of these
models are discussed. Graphical representation through numerical
simulations are presented.
... b. Holling Type -II Hulling Type -II, it is also called the Cyrtid Functional response and it is represented by the function ( ) = 1+ (2) ℎ , , they are positive constants that describe the effects of capture rate and handling time on the feeding rate of the predator (Skalski and Gillian -2001). The Holling Tulu Leta Tirfe 1 , RAJAR Volume 09 Issue 07 July 2023 ...
... An important distinction between the Bedding ton -DeAngelis Model and the Crowly -Martin Model is that the effects of predator interference (Competition/Infighting among predators) on the feeding rate becomes negligible under conditions of high prey density while the latter assumes that the interference remains important even at high prey density (Skalski and Gillian -2001). This can be seen by letting ( ) ⟶ ∞ in both models. ...
In the Modern World, everything will be systematically developed by using best modelling. In our article we will prepare and analyzed in the area of Dynamics of System of Two Prey and One Predator by using Holling Type – II Functional Response, and we designed the model such as First Prey and the Second prey a ratio – dependent response, where harvesting of each prey species is taken into consideration. And also, the model is used to study the Ecological Dynamics of the Fox – Antelope – Rabit (FAR) in a given habitat. We also focus the effect of harvesting on prey species. We discussed Local and Global Stability Analysis of the system were carried out, and also we analyze numerical simulation for particular variables and then, we conclude and show that the Result of Analysis of our model that the Three Species would co – exist if the Antelope and Rabbit were not harvesting beyond their Intrinsic Growth Rate (IGR).
... While the specific aim of our analysis was to test whether the functional response is of type II or type III, our adaptive experimental design approach could be potentially used in future research to test several scientific hypotheses concerning predator feeding behavior; that is, to explore if the nature of predation is predator, prey or ratio dependent, which is a core question regarding predator-prey interactions [38][39][40][41] or to select the most appropriate functional response model that incorporates mutual interference effects and best describe the data (e.g. [19,42,43]). Thus, it is expected that following our experimental framework, the description, understanding and quantitative predictions of predator-prey interactions can be improved, towards a precise understanding and integrated analysis of ecological processes. ...
... This study considered relatively simple stochastic models of predator-prey systems. However, in principle, more complex models can be accommodated in our framework, such as those modelling predator interference [42]. For experiments conducted in different spatial locations, a fixed or random spatial effect can be added to the model. ...
Ecological dynamics are strongly influenced by the relationship between prey density and predator feeding behavior—that is, the predatory functional response. A useful understanding of this relationship requires us to distinguish between competing models of the functional response, and to robustly estimate the model parameters. Recent advances in this topic have revealed bias in model comparison, as well as in model parameter estimation in functional response studies, mainly attributed to the quality of data. Here, we propose that an adaptive experimental design framework can mitigate these challenges. We then present the first practical demonstration of the improvements it offers over standard experimental design. Our results reveal that adaptive design can efficiently identify the preferred functional response model among the competing models, and can produce much more precise posterior distributions for the estimated functional response parameters. By increasing the efficiency of experimentation, adaptive experimental design will lead to reduced logistical burden.
... In [2], based on the bifurcation theory and the slow-fast analysis method, the authors explored the existence and the equilibrium of the autonomous predator-prey model. For predator-prey systems with Holling functional response, see [3][4][5][6]; for predator-prey systems with Beddington-DeAngelis response, see [7][8][9][10][11]; for predator-prey systems with stage-structure, see [12][13][14][15][16]. In recent years, the predator-prey systems on time scales have been concerned by many authors, see [17][18][19][20][21]. ...
In this note, we investigate the existence and asymptotic property of positive periodic solutions to non-autonomous predator-prey system with stage-structured predator on time scales. Via Schauder’s fixed theorem, easily verifiable sufficient existence conditions of positive periodic solutions for the considered system are obtained. We also study asymptotic property of positive periodic solutions on the basis of existence conditions. Due to the symmetry of periodic solutions, the results of this paper have a certain impact on the study of symmetry. It should be pointed out that the system we are studying is built on arbitrary time scale, so our results generalize the results of existing continuous or discrete systems. Furthermore, we develop Schauder’s fixed theorem for studying the delay system on time scales.
... Territorial disputes, an adverse habitat, or insufficient prey biomass can all contribute to this interference. For this reason, models with a predator-dependent functional response can be a good alternative to models with a prey-dependent functional response [27]. Beddington [28] and DeAngelis et al. [29] independently proposed a functional response in 1975 that took into account predators' mutual interference to mediate between theoretical and experimental viewpoints [30]. ...
There are various examples of phenotypic plasticity in ecosystems that serve as the basis for a wide range of inducible defences against predation. These strategies include camouflage, burrowing, mimicry, evasive actions, and even counterattacks that enhance survival under fluctuating predatory threats. Additionally, the ability to exhibit plastic responses often influences ecological balances, shaping predator-prey coexistence over time. This study introduces a predator-prey model where prey species show inducible defences, providing new insights into the role of adaptive strategies in these complex interactions. The stabilizing impact of the defensive mechanism is one of several intriguing outcomes produced by the dynamics. Moreover, the predator population rises when the interference rate increases to a moderate value even in the presence of lower prey defence but decreases monotonically for stronger defence levels. Furthermore, we identify a bistable domain when the handling rate is used as a control parameter, emphasizing the critical role of initial population sizes in determining system outcomes. By considering the species diffusion in a bounded region, the study is expanded into a spatio-temporal model. The numerical simulation reveals that the Turing domain decreases as the level of protection increases. The study is subsequently extended to incorporate taxis, known as the directed movement of species toward or away from another species. Our investigation identifies the conditions under which pattern formation emerges, driven by the interplay of inducible defences, taxis as well as species diffusion. Numerical simulations demonstrate that including taxis within the spatio-temporal model exerts a stabilizing influence, thereby diminishing the potential for pattern formation in the system.
... The feeding terms include saturation at high prey densities, and a predator interference term in the denominator (Beddington functional response 25,26 ). Similar predator interference terms are also used by other modellers 27 . ...
The four-year oscillations of the number of spawning sockeye salmon (Oncorhynchus nerka) that return to their native stream within the Fraser River basin in Canada are a striking example of population oscillations. The period of the oscillation corresponds to the dominant generation time of these fish. Various - not fully convincing - explanations for these oscillations have been proposed, including stochastic influences, depensatory fishing, or genetic effects. Here, we show that the oscillations can be explained as a stable dynamical attractor of the population dynamics, resulting from a strong resonance near a Neimark Sacker bifurcation. This explains not only the long-term persistence of these oscillations, but also reproduces correctly the empirical sequence of salmon abundance within one period of the oscillations. Furthermore, it explains the observation that these oscillations occur only in sockeye stocks originating from large oligotrophic lakes, and that they are usually not observed in salmon species that have a longer generation time.
... For ecosystems consisting of a single pair of predator and prey, or a simple chain reaching from a bottom-level producer through intermediate species to a top predator, the most common forms of functional response are due to Holling [21]. For more complicated, interconnected food webs, a number of functional forms have been proposed in the recent literature [8,9,22,23,31,32,42], but there is as yet no agreement about a standard form. Here we choose the ratio-dependent [8,9,12,31,32,33] Holling Type II form [21], originally introduced by Getz [16], ...
We explore the complex dynamical behavior of two simple predator-prey models of biological coevolution that on the ecological level account for interspecific and intraspecific competition, as well as adaptive foraging behavior. The underlying individual-based population dynamics are based on a ratio-dependent functional response [W.M. Getz, J. Theor. Biol. 108, 623 (1984)]. Analytical results for fixed-point population sizes in some simple communities are derived and discussed. In long kinetic Monte Carlo simulations we find quite robust, approximate 1/f noise in species diversity and population sizes, as well as power-law distributions for the lifetimes of individual species and the durations of periods of relative evolutionary stasis. Adaptive foraging enhances coexistence of species and produces a metastable low-diversity phase and a stable high-diversity phase.
... For such models, we refer to [7,8]. However, some biologists have argued that in many situations, especially when predators have to search for food, the functional response should depend on both prey's and predator's densities; for example, a Holling's type II functional response in a type of xtyt α+βxt [9,10], a ratio-dependent one in a type of xtyt xt+γyt [3]. The model in those papers are deterministic. ...
In this paper, we consider a stochastic ratio-dependent predator-prey model. We firstly prove the existence, uniqueness and positivity of the solutions. Then, the boundedness of moments of population are studied. Finally, we show the upper-growth rates and exponential death rates of population under some conditions.
... Moreover, the absence of predator density in a functional response implies that prey growth rate can be affected by a single predator, that the effects of two or more predators add up, and the competition among predators for food takes place only through prey depletion [77]. Thus, prey-dependent functional responses have been facing challenges from the biological communities, and therefore predator dependence in trophic function is essential [76,78]. In this regard, Beddington [79] and DeAngelis et al. [80] proposed a functional form of prey consumption rate that depends on both prey and predator densities: ...
A patchy ecosystem is a biological community of interacting populations, where the subpopulations of (typically) the same species are distributed in spatially distinct habitat patches. Here, we consider a patchy predator–prey model where the prey population can access two distinct habitats; however, the predator population is confined within one habitat. The key ingredients of our model are the possibility of fragile prey extinction at low densities (Allee effect) and asymmetric dispersal between the patches of the prey. Our study examines two different aspects; first, the effects of asymmetric dispersal between the patches on the dynamics of the patch model and the persistence of the species; second, the impact of dispersal on the predator hydra effect that characterizes an increase in population size in response to greater mortality. Our results show that as the dispersal rate increases, the system experiences transitions from multiple coexistence states to unique coexistence state, to oscillatory coexistence state, to predator-free state. Additionally, for a suitable dispersal rate, the patch model shows multistability between different states, where the final state depends on the initial density of the population. The model exhibits the hydra effect at a stable state in the predator species with or without predator self-interference in the presence of dispersal. However, the predator hydra effect manifests only with predator self-interference in the absence of dispersal. The hydra effect is also observed in our model in a stable oscillatory coexistence state. Additionally, we observe multiple hydra effects in which two alternative stable states exhibit hydra effect. The range of the mortality that causes the hydra effect becomes shorter with increasing dispersal rate until it disappears. Thus, the dispersal rate plays a critical role in the dynamics of the multi-patch model and the appearance of the hydra effect.
... This leads us back to the initial issue of measuring relative yield: estimating population self-regulation could substitute for assessing equilibrium abundances in isolation. Unfortunately, however, few empirical studies actually offer direct assessments of population self-regulation [50,51]. ...
Predicting how ecological communities will respond to disturbances is notoriously challenging, especially given the variability in species’ responses within the same community. Focusing solely on aggregate responses may obscure extinction risks for certain species owing to compensatory effects, emphasizing the need to understand the drivers of the response variability at the species level. Yet, these drivers remain poorly understood. Here, we reveal that despite the typical complexity of biotic interaction networks, species’ responses follow a discernible pattern. Specifically, we demonstrate that the species whose population abundances are most reduced by biotic interactions—which are not always the rarest species—are those that exhibit the strongest responses to disturbances. This insight enables us to pinpoint sensitive species within communities without requiring precise information about biotic interactions. Our novel approach introduces avenues for future research aimed at identifying sensitive species and elucidating their impacts on entire communities.
... Many mathematical models have been developed to understand complex ecological effects. Notable contributions include discussions by researchers who have studied predator-prey patterns in various observation situations in the natural environment [5][6][7][8]. ...
In predator–prey interactions, the effect of fear is an important factor in building ecological communities, affecting biodiversity, and maintaining ecological balance. In this paper, we present a specific predator–prey model that incorporates the effects of fear on prey populations by focusing on non-overlapping generations. Our study aims to explore the existence of biologically feasible equilibrium points and to analyze local asymptotic behavior around these points. Furthermore, using the center manifold theorem and the normal form theory of bifurcations, we study period-doubling bifurcations about prey-free and interior (positive) fixed points. On the other hand, the Neimark-Sacker bifurcation around the positive equilibrium point is investigated by applying the bifurcation theory of normal forms. We study the existence of chaos and present effective strategies to control the fluctuating and chaotic behaviors in the system using various chaos control techniques. Numerical simulations are presented to illustrate the theoretical discussion.
... Gilliam[13]~I Crowley-Martin[14] ...
... The most important functional responses is Lotka-Volterra functional response (Holling type-I functional response) that was pioneered by Holling (1965). After further studies, Holling (1965) along with Murray (1993) and Kot (2001) modified the concept and brought in the Holling type-II functional response that was studied in detail by Skalski and Gilliam (2001), Neverova et al. (2019) and others. Two species prey-predator models have been studied extensively in theoretical ecology for quite a long time. ...
The paper deals with the case of non-selective predation in a partially infected prey-predator system , where both the susceptible prey and predator follow the law of logistic growth and some preys avoid predation by hiding. The disease-free preys get infected in due course of time by a certain rate. However, the carrying capacity of the predator population is considered proportional to the sum-total of the susceptible and infected prey. The positivity and boundedness of the solutions of the system are studied and the existence of the equilibrium points and stability of the system are analyzed at these points. The effect of the infected prey-refuge on each population density is also discussed. It is observed that a Hopf-bifurcation may occur about the interior equilibrium, where the refuge parameter is considered as the bifurcation parameter. The analytical findings are illustrated through computer simulation using Maple that show the reliability of the model from the ecological point of view.
... High attack rates and low handling times indicate effective biocontrol agents. Predator individuals frequently encounter each other, and interference competition, including direct interactions, such as attacking conspecifics or exhibiting threat behavior [26], may decrease the consumption rate [27,28]. ...
The water lily aphid (Rhopalosiphum nymphaeae) is a highly polyphagous herbivore that causes severe damage to many terrestrial and aquatic plants, especially lotus. Due to environmental concerns about water pollution and other issues caused by chemical control methods, there is an urgent need to develop effective and sustainable control methods. The harlequin ladybird (Harmonia axyridis) is a well-known aphid predator and may pose a potential threat to R. nymphaeae. To study the predation ability of H. axyridis at different developmental stages on R. nymphaeae, we assessed the functional response, attack rate, and search effect of H. axyridis larvae and adults preying on R. nymphaeae. The numerical response of this process was also evaluated under a constant ladybird-to-aphid ratio and constant aphid density conditions, respectively. Our results showed that all predator stages exhibited type II functional responses. The predation rate of individual H. axyridis on R. nymphaeae nymphs significantly increased as prey density increased. In contrast, the search effect of H. axyridis gradually decreased with an increase in prey density. Meanwhile, H. axyridis at different developmental stages possess varying predation abilities; fourth instar and adult H. axyridis were found to be highly efficient predators of R. nymphaeae. H. axyridis adults exhibited the highest predation ability and predation rate, while both the adult and fourth-instar larvae exhibited the highest attack rate. Moreover, fourth-instar larvae exhibited the highest search effect value at initially lower prey densities, although adults surpassed them at higher prey densities. Our results also indicated that H. axyridis exhibited varying degrees of intraspecific interference and self-interference influence as predator density increases. These results strongly support H. axyridis as an effective biocontrol agent for R. nymphaeae.
... This system has been studied by many researchers, such as the simplified Holling IV Q(u) = αu u 2 +b [7]. Meanwhile, the generalized Holling IV functional response can describe an ecological phenomenon: When the density of the prey population exceeds a critical value, the group defense capability of the prey population can increase, which not only does not promote the increase of the predator population, but also inhibits its increase [8,9]. Thus, we use the generalized Holling IV functional response function Q(u) = αu u 2 +cu+b to describe the interaction between predators and prey, where α, c, b are biologically meaningful positive numbers. ...
From the perspective of ecological control, harvesting behavior plays a crucial role in the ecosystem natural cycle. This paper proposes a diffusive predator-prey system with predator harvesting to explore the impact of harvesting on predatory ecological relationships. First, the existence and boundedness of system solutions were investigated and the non-existence and existence of non-constant steady states were obtained. Second, the conditions for Turing instability were given to further investigate the Turing patterns. Based on these conditions, the amplitude equations at the threshold of instability were established using weakly nonlinear analysis. Finally, the existence, direction, and stability of Hopf bifurcation were proven. Furthermore, numerical simulations were used to confirm the correctness of the theoretical analysis and show that harvesting has a strong influence on the dynamical behaviors of the predator-prey systems. In summary, the results of this study contribute to promoting the research and development of predatory ecosystems.
... Based on statistical evidence, the study [42] showed that the prey-predator-dependent functional response (BD, CM, and Hassell-Varley) explains predator feeding across an extent of predator-prey abundances more effectively than the Holling type II response. Our model includes predation fear in prey, fear-induced COE, the Allee effect in predators, and a BD functional response. ...
... The functional response of predators, which represents the correlation between the rate of consumption and prey abundance (Holling 1959), is normally used to estimate their predation capability on prey (Houck and Strauss 1985;Skalski and Gilliam 2001;Costa et al. 2014;Song et al. 2016) and the effectiveness of predators in managing prey population (Islam et al. 2020; DeLong and Uiterwaal 2022). The functional response has a significant impact on the assessment of predators' foraging capacity (DeLong and Uiterwaal 2022). ...
The goji berry psyllid, Bactericera gobica Logniova (Homoptera: Psyllidae), is one of the most important pests on goji berry plants (Lycium barbarum L.), whose fruits are widely used in traditional Chinese medicine and food. However, chemical control is still the predominant control strategy of this pest. Recently, two species of predatory mites, Neoseiulus setarius Ma, Meng & Fan and Neoseiulus barkeri Hughes were found to be associated with B. gobica in China. To assess their predation potential against B. gobica, the functional responses of these two phytoseiid species feeding on different densities (2, 4, 8, 12, 16, 24 and 32 individuals) of B. gobica eggs and 1st instar nymphs were compared at a temperature of 25ºC ± 1º C. Logistic regression analysis revealed that both predatory mite species exhibited type Holling-II functional responses on eggs and 1st instar nymphs of B. gobica, with the predation number increased for both predators as the density of prey increased. Overall, N. setarius consumed more prey compared to N. barkeri across all levels of prey densities. Meanwhile, the highest attack rate (α = 0.0283), the lowest handling time (Th = 1.1324 h prey− 1), and the highest estimated maximum predation rate (T/Th = 21.19 prey day− 1) were all observed for N. setarius fed with 1st instar nymphs of B. gobica. These findings suggest that it is worthy considering utilizing N. setarius and N. barkeri as candidate biocontrol agents of B. gobica, with N. setarius appearing to be a more effective predator than N. barkeri.
... In 2001, Skalaski and Gilliam [18] compared the statistical data in some predator-prey systems, and found that the predator-dependent functional response function model has a high degree of fit with the data. The Beddington-DeAngelis functional response function is more practical in reality. ...
In this paper, we considered a delayed predator-prey model with stage structure and Beddington-DeAngelis type functional response. First, we analyzed the stability of the constant equilibrium points of the model by the linear stability method. Furthermore, we considered the existence of traveling wave solutions connecting the zero equilibrium point and the unique positive equilibrium point. Second, we transformed the existence of traveling wave solutions into the existence of fixed points of an operator by constructing suitable upper and lower solutions, and combined with the Schauder fixed point theorem, we gave the existence of fixed points and obtained the existence of traveling wave solutions of the model.
... This leads us back to the initial issue of measuring relative yield: estimating population self-regulation could substitute to assessing equilibrium abundances in isolation. Despite these considerations, however, few empirical studies actually offer direct assessments of population self-regulation (Skalski and Gilliam, 2001;Galiana et al., 2021). ...
... The Crowley-Martin equation (Crowley and Martin 1989;Skalski and Gilliam 2001;Papanikolaou et al. 2021) for functional response is incorporated here to describe the growth rate and compare with (2) later: ...
Several models have been proposed as an extension to the classical Holling’s disc equation to evaluate the predator and prey interactions and their applied aspect in biological control and population regulation of the target organisms. In a one prey and two predator dynamic system with mutual interference (m) as a quadratic parameter of predator density, an evaluation was made to the resultant impact on the prey. A simulation was carried out to see the extinction of prey and the stability of the system at origin, i.e., when all the three species are extinct. We assumed the data obtained for the interactions between the mosquito and the water bug predators that are common in the freshwater wetlands and involved in the population regulation. Despite the benefits to prey population due to interference competition, the expected extinction of prey is still observed. With varying magnitudes of m the declining growth curve of prey population, shifted. The equation proposed was also compared with Crowley–Martin functional response, and considerable differences were observed in selected instances when compared for the growth rate of the predators, in a species-specific manner. The stability of the system was deduced with eigenvalues of Jacobian matrix at origin to prove the extinction is stable. Our assessment supports the possible cooccurrence of the predators and mosquito prey in the wetlands with the mutual interference being one of the major factors.
... These functions can be used to predict interactions between different species in ecosystems, such as how changes in prey abundance affect predator numbers and competition between different species. Functional responses have wide applications in ecology [19,24,31,34], environmental science [5], agriculture [22], and other fields [33,36], helping us better understand the interactions and evolutionary processes among different species in ecosystems. ...
... The predator-prey functional response quantifies the rate at which predators consume prey per unit of time. Mathematical analyses of ecological, epidemiological, and eco-epidemiological systems rely on various functional responses, including the Holling type-I functional response [29], the Holling type-II functional response [33], and the ratio-dependent functional response, Among these, the predator-prey interaction with ratio-dependent functional response is often considered the most effective approach [7]. In this study, we investigate an eco-epidemic model that incorporates the Allee effect in prey and disease in predators. ...
In this work, the dynamics of a food chain model with disease in the predator and the Allee effect in the prey have been investigated. The model also incorporates a Holling type-III functional response, accounting for both disease transmission and predation. The existence of equilibria and their stability in the model have also been investigated. The primary objective of this research is to examine the effects of the
Allee parameter. Hopf bifurcations are explored about the interior and disease-free equilibrium point, where the Allee is taken as a bifurcation point. In numerical simulation, phase portraits have been used to look into the existence of equilibrium points and their stability. The bifurcation diagrams that have been drawn clearly
demonstrate the presence of significant local bifurcations, including Hopf, transcritical, and saddle-node bifurcations. Through the phase portrait, limit cycle, and time series, the stability and oscillatory behaviour of the equilibrium point of the model are investigated. The numerical simulation has been done using MATLAB and Matcont.
... Like the B-D functional response, it was initially used to describe interactions and competitive relationships in predator-prey models [18][19][20]. Skalski et al. [21] analyzed an important distinction between the B-D functional response and the C-M functional response in predator-prey models through mathematical formulas; they suggested using the B-D functional response when the predator's consumption rate is no longer correlated with predator density at high prey densities, whereas they advised employing the C-M functional response when the predator's consumption rate continues to be influenced by higher predator densities at high prey densities. Now, revisiting the immunosuppressive infection model, when the viral quantity is sufficiently high, the B-D functional response can be expressed mathematically as: ...
In this paper, we introduce the Crowley–Martin functional response and nonlocal competition into a reaction–diffusion immunosuppressive infection model. First, we analyze the existence and stability of the positive constant steady states of the systems with nonlocal competition and local competition, respectively. Second, we deduce the conditions for the occurrence of Turing, Hopf, and Turing–Hopf bifurcations of the system with nonlocal competition, as well as the conditions for the occurrence of Hopf bifurcations of the system with local competition. Furthermore, we employ the multiple time scales method to derive the normal forms of the Hopf bifurcations reduced on the center manifold for both systems. Finally, we conduct numerical simulations for both systems under the same parameter settings, compare the impact of nonlocal competition, and find that the nonlocal term can induce spatially inhomogeneous stable periodic solutions. We also provide corresponding biological explanations for the simulation results.
... The Crowley-Martin equation [43][44][45] for functional response is incorporated here to describe the growth rate and compare with Equation (2) later: ...
Several models have been proposed as an extension to the classical Holling’s disc equation to evaluate the predator and prey interactions and their applied aspects in biological control and population regulation of the target organisms. In a one-prey and two-predator dynamic system with mutual interference m as a quadratic parameter of predator density, an evaluation was made of the resultant impact on the prey. A simulation was carried out to see the finite-time extinction of prey and the stability of the system at origin, i.e., when all three species are extinct. We assumed the data obtained was for the interactions between the mosquito and the water bug predators that are common in the freshwater wetlands and involved in population regulation. Despite the benefits to the prey population due to interference and competition, the expected extinction of prey in a finite time is still observed. With varying magnitudes of m, the declining growth curve of the prey population shifted. The equation proposed was also compared with the Crowley-Martin functional response, and considerable differences were observed in selected instances when compared to the growth rate of the predators in a species-specific manner. The stability of the system was deduced from the eigenvalues of the Jacobian matrix at the origin to prove the extinction is stable. Our assessment supports the possible cooccurrence of predators and mosquito prey in the wetlands, with mutual interference being one of the major factors.
... Consequently, researchers have introduced various functional responses to represent the feeding rates of f (u, v) = δu/ (1 + αu) (1 + βv) , which is referred to as the Crowley-Martin functional response. These modifications have proven essential in understanding the dynamics of real-world predator-prey systems, and they offer a more accurate representation of their behavior [38]. ...
In this study, we consider a prey–predator model with prey refuge and intraspecific competition between predators using the Crowley–Martin functional response and investigate the dynamic characteristics of spatial and nonspatial prey–predator systems via both analytical and numerical methods. The local stability of nontrivial interior equilibrium, the existence of a Hopf bifurcation, and the stability of bifurcating periodic solutions are obtained in the absence of diffusion. For the spatial system, the Turing and non-Turing patterns are evaluated for some set of parametric belief functions, and we obtain some interesting results in terms of prey and predator inhabitants. We present the results of numerical simulations that demonstrate that both prey and predator populations do not converge to a stationary equilibrium state at any foreseeable future time when the parametric values are processed in the Turing domain.
In this paper, we present novel seasonal carrying capacity prey–predator models with a general functional response, which is that of Crowley–Martin. Seasonality effects are classified into two categories: sudden and periodic perturbations. Models with sudden perturbations are analytically investigated in terms of good and bad circumstances by addressing the existence, positivity, and boundedness of the solution; obtaining the stability conditions for each equilibrium point and the dynamics involving the existence of a limit cycle; determining the Hopf bifurcation with respect to the carrying capacity; and finding the uniform persistence conditions of the models. Moreover, some numerical simulations are performed to demonstrate and validate our theoretical findings. In contrast, models with periodic perturbations are computationally investigated. In analytical findings, the degree of seasonality and the classification of circumstances play a significant role in the uniqueness of the coexistence equilibrium point, the stability of the system, and the existence of a limit cycle. The model with periodic perturbations shows the presence of different dynamics for prey and predator, such as the doubling of the limit cycle and chaos dynamics, so this influence can have a diverse range of possible solutions, which makes the system more enriched with different dynamics. As a result of these findings, many phenomena and changes can be interpreted in ecosystems from an ecological point of view.
To examine the co-evolution of quantitative traits in hosts and parasites, we present and study a co-evolutionary model of a social parasite-host system that incorporates (1) ecological dynamics that feed back into their co-evolutionary outcomes; (2) variation in whether the parasite is obligate or facultative; and (3) Holling Type II functional responses between host and parasite, which are particularly suitable for social parasites that face time costs for host location and its social manipulation. We perform local and global analyses for the co-evolutionary model and the corresponding ecological model. In the absence of evolution, the facultative parasite system can have one, two, or three interior equilibria, while the obligate parasite system can have either one or three interior equilibria. Multiple interior equilibria result in rich dynamics with multiple attractors. The ecological system, in particular, can exhibit bi-stability between the facultative-parasite-only equilibrium and the interior coexistence equilibrium when it has two interior equilibria. Our findings suggest that: (a) The host and parasite can select different strategies that may result in local extinction of one species. These strategies can have convergence stability (CS), but may not be evolutionary stable strategies (ESS); (b) The host and its facultative (or obligate) parasite can have ESS that drive the host (or the obligate parasite) extinct locally; (c) Trait functions play an important role in the CS of both boundary and interior equilibria, as well as their ESS; and (d) A small variance in the trait difference that measures parasitism efficiency can destabilize the co-evolutionary system, and generate evolutionary arms-race dynamics with different host-parasite fluctuating patterns.
Ungulates serve as the primary carrion source for facultative scavengers in European ecosystems. In the absence of large carnivores, such as wolves (Canis lupus), human hunting leftovers are the main source of carrion for these scavengers. Additionally, wild boars (Sus scrofa) are heavily culled in many ecosystems and are both a significant prey species for wolves as well as a key scavenger. Nowadays, wolves and wild boars are re‐establishing their historical home ranges. However, it remains unclear how their presence influences the population dynamics of facultative scavengers under different scenarios of human hunting strategies. We simulated the biomass densities of all states in the trophic web including European scavengers and wolves using an ordinary differential equations (ODE) model. The presence of wolves led to a positive trend in scavenger biomass in general. However, in general, we found that plant‐based resources were more important for scavenger dynamics than carrion, regardless of whether the carrion originated from human hunting or wolf predation. Only when wolves were absent but boars present, the human hunting strategy became important in determining scavenger dynamics via carrion supply. In conclusion, our model indicates that population dynamics of facultative scavengers are not mainly driven by the availability of carrion, but rather by the presence of and competition for vegetation. Furthermore, our simulations highlight the importance of adapting human hunting strategies in accordance with the re‐establishment of wolf and boar as these can cause fluctuating population patterns over the years.
Authors have detected the importance of the Allee effect and have highlighted significant changes to system dynamics in the ecological environment. In this paper, using the theory of dynamical systems, we explore our investigation of a two-dimensional prey–predator model into two aspects: (i) we modify a competent Allee effect and the self-limitation term for the predator model system by incorporating the Crowley–Martin-type functional response, and (ii) we extend this modified model system by adding a strong Allee effect in prey growth. We report the behavior of the model system under the Crowley–Martin-type functional response and the impact of a strong Allee effect. We examine that an initial condition with high prey and low predator intensity always settles to predator extinction in the absence of a strong Allee effect. In the presence of a strong Allee effect, an initial condition with low prey and predator intensities leads the system to total extinction, while high prey and low predator intensity allows the model system to settle at predator extinction and high prey concentration. The addition of a strong Allee effect in the model system enriches the boundary equilibrium point. In attractor examination, we demonstrated that the model system without the Allee effect has attractors between boundary equilibrium and coexistence equilibrium, and between coexistence equilibria. The addition of a strong Allee effect produces attractors between coexistence equilibrium as well as between boundary equilibrium points. We deduce that both model systems experience enriched coexistence equilibria in a small parametric region. Modifying the model system without the Allee effect produces three attractors (one predator-free equilibrium point and two coexistence equilibrium points). The model system with a strong Allee effect gives four attractors (two predator-free equilibrium points and two coexistence equilibrium points). Our comprehensive bifurcation analysis reports both local and global bifurcations for both types of model systems. We explore bifurcation analysis through codimension-one and codimension-two bifurcations extensively by choosing the Allee effect as one of the key parameters. In this context, our modified model system exhibits saddle-node bifurcation, Hopf bifurcation, Bogdanov–Takens bifurcation and generalized Hopf bifurcation. We derive the sensitivity index of model system parameters for both types of model systems. We validated our analytical findings with the help of numerical simulations.
Ecological systems can generate striking large-scale spatial patterns through local interactions and migration. In the presence of diffusion and advection, this work examines the formation of flow-induced patterns in a predator–prey system with a Crowley–Martin functional response and prey harvesting, where the advection reflects the unidirectional flow of each species migration (or flow). Primarily, the impact of diffusion and advection rates on the stability and the associated Turing and flow-induced patterns are investigated. The theoretical implication of flow-induced instability caused by population migration, mainly the relative migrations between prey and predator, is examined, and it also shows that Turing instability is the particular condition of flow-induced instability. The influence of the relative flow of both species and prey-harvesting effort on the emerging pattern is reported. Advection impacts a wide range of spatiotemporal patterns, including bands, spots, and a mixture of bands and spots in both harvested and unharvested dynamics. We also observe the diagonally bend-type banded patterns and straight-type banded patterns due to positive and negative relative flows, respectively. Here, the increasing relative flow increases the band length. The growing harvesting effort also decreases the band length, producing a thin band and a mixture of spots and bands due to the negative and positive relative flows, respectively. One exciting result observed here is that harvesting effort drives the flow-Turing and flow-Turing–Hopf instability into pure-flow instability.
The patchy distribution of microplastics (MPs) and their size range similar to planktonic organisms, are likely to have major ecological consequences, through MP ingestion, food dilution, and transfer across trophic levels. Our study applied a community module using tritrophic food chain with zooplankton as prey, and a planktivorous seabass fry as predator. We conducted a series of feeding experiments and recorded the direct uptake of MP under six different concentrations ranging from 25 to 800 particles L−1. We also estimated the indirect transfer of MP via trophic link. The ingestion rates for Brachionus plicatilis, Mesocyclops isabellae, and Lates calcarifer, were 3.7 ± 0.3 MP ind−1 min−1, 1.69 ± 0.1 MP ind−1 min−1, and 3.51 ± 0.52 MP ind−1 h−1, respectively. In the presence of a natural diet, rotifers and copepods ingested significantly lower number, whereas, fish fry ingested a higher number of MP, suggesting further vulnerability to the consumers of MP-contaminated fish and potential biomagnification at higher trophic levels. Overall, the MP uptake rate increased with increasing concentration, and finally leveled off, indicating a type II functional response to MP concentration. The presence of natural diet led to a lower Km value. In the indirect transfer experiment, 74 % of B. plicatilis and 78 % of M. isabellae individuals were contaminated with MPs, when offered as prey. Brachionid mastax and MP particles were observed in the gut of copepods. The fish fry gut content also recorded brachionid mastax, MP-contaminated copepods, and MP particles, showing direct evidence of trophic transfer pointing to a cascading effect on higher trophic levels including humans via piscivory.
In this thesis, the dynamical behavior of some Biological models is investigated. First type is prey-scavenger model involving refuge in the prey as well as spread of SIS infectious disease in the prey population, which is divided into two compartments; namely susceptible and infected, is proposed and analyzed. While the second proposed model deals with the ecological model consisting of prey-predator type involving the effect of strong Allee for prey, also Holling type-IV as a functional response, external sources of food for predator specie in the absence of prey, and Michael Mentence for a harvesting function for prey. The last proposed model is epidemiology model deals with infectious diseases type SI which that are transmitted through direct contact between susceptible and infected individuals only using a nonlinear type of incidence rate.
The existing, unique, and bounded solutions of these models are investigated. The stability conditions at each feasible equilibrium point are established. Moreover, the local bifurcation (such as saddle-node, transcritical, and pitchfork) around all the equilibrium points are discussed. Finally, numerical simulation is carried out to investigate the dynamic behavior of these models.
Comprehending the intricacies of predator–prey systems is vital due to their pivotal role in maintaining ecological balance. The present study delves into a predator–prey model, incorporating Smith growth for prey, Beddington–DeAngelis response function, predator growth from additional food sources, and the influence of prey on intraspecies competition among predators. We systematically examine feasibility and stability criteria of system’s equilibria, exploring codimension-1 and 2 bifurcations, revealing two bistability phenomena. Our findings emphasize the critical role of predator growth due to additional foods and intraspecific predator competition in shaping species survival. Different scenarios emerge such as prey extinction and coexistence of species based on the parameter configuration. Higher predator growth due to the supplementary foods leads to prey extinction; lower intraspecific competition among predators has a similar outcome. Conversely, lower predator growth due to the additional foods fosters coexistence of species, which also happens for higher intraspecies predator competition. Additionally, our analysis using the stochastic sensitivity function unveils diverse transition scenarios around deterministic bistabilities. Noise levels’ significance in determining transition thresholds is elucidated through confidence ellipse domains.
In a more realistic scenario, we posit that certain predators engage in cooperative hunting of prey, all the while competing with other predators and occasionally causing fatal harm to one another. It is assumed that prey employ various strategies, including camouflage and concealment, to evade predators. The competition among the predators is considered the bifurcation parameter to analyze the equilibrium states and their characteristics, encompassing phenomena like saddle-node bifurcation, Hopf bifurcation, and the Hydra effect. Our primary focus is to examine how the dynamics of the system are influenced by prey seeking shelter and predator cooperation. Prey shelter effectively conceals a segment of its population from predators, reducing the critical point for outbreak occurrence and heightening vulnerability to outbreaks at lower prey population levels. The addition of cooperation reduces the peak predator population, necessitating increased competition and altering equilibrium thresholds.
We investigated a system of ordinary differential equations that describes the dynamics of prey and predator populations, taking into account the Allee effect affecting the reproduction of the predator population, and mutual interference amongst predators, which is modeled with the Bazykin-Crowley-Martin (BCM) trophic function. Bifurcation analysis revealed a rich spectrum of bifurcations occurring in the system. In particular, analytical conditions for the saddle-node, Hopf, cusp, and Bogdanov-Takens bifurcations were derived for the model parameters, quantifying the strength of the predator interference, the Allee effect, and the predation efficiency. Numerical simulations verify and illustrate the analytical findings. The main purpose of the study was to test whether the mutual interference in the model with BCM trophic function provides a stabilizing or destabilizing effect on the system dynamics. The obtained results suggest that the model demonstrates qualitatively the same pattern concerning varying the interference strength as other predator-dependent models: both low and very high interference levels increase the risk of predator extinction, while moderate interference has a favorable effect on the stability and resilience of the prey-predator system.
The deterministic non‐autonomous multispecies Holling type II model and its stochastic version with a simple type of noise have been proposed to infer multispecies community structure. However, these models fail to account for complex types of noises, which may render the model overly simplistic. In this paper, a non‐autonomous multispecies Holling type II model with a complex type of noise has been proposed. We establish sufficient conditions for various mathematical properties of the solutions, including existence and uniqueness, stochastic permanence and extinction. Additionally, numerical simulation studies are provided to illustrate our theoretical findings.
The aim of this paper is to establish a precise illustration for the structure of the nonconstant steady states for a Beddington–DeAngelis and Tanner predator–prey reaction–diffusion system with prey‐taxis. We treat the nonlinear prey‐taxis as a bifurcation parameter to analyze the bifurcation structure of the system. Furthermore, the exported global bifurcation theorem, under a rather natural condition, offers the existence of nonconstant steady states. In the proof, a priori estimates of steady states will play an important role. The local stability analysis with a numerical simulation and bifurcation analysis are given. Finally, some conclusions including biological meanings are performed to summarize our main analytic results and future investigations.
Trophic interactions underpin the structure of ecological communities by describing the rates at which consumers exploit their resources. The rates at which predators consume their prey are influenced by prey traits, with many species inducing defensive modifications to prey traits following the threat of predation. Here we use different clonal lines of the protist Paramecium being consumed by Stenostomum predators to highlight how differences in prey traits impact rates of predation. Clonal lines differed in their body width traits, and in their ability to induce changes in body width. By using a factorial cross of predator and prey abundances for different clonal lines we demonstrate how evolutionary or induced alterations in prey traits can impact the relative threat of predation. Our experiments show how interference among predators impacts predation rate, and how increased body width increased predator handling times. Given that reductions in the strength of interspecific interactions are associated with increased levels of overall community stability, our results indicate how individual level changes may scale up to impact whole communities.
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