Predator overcomes the Allee effect due to indirect prey–taxis

Tyutyunov, Yu. V.; Sen, Deeptajyoti; Titova, L. I.; Banerjee, Malay

doi:10.1016/j.ecocom.2019.100772

Cited by 24 publications

(17 citation statements)

References 72 publications

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“…Arguing against the spatial heterogeneity justification, they refer to a simple two-patch model (Abrams, 1994) and to spatial models (Barraquand, 2014;Abrams, 2015) that ignore directed movements of predators, and thus cannot demonstrate the emergence of predator-or ratio-dependence at the population level. Predator-prey models with prey-taxis show that the active movements of predators generate spatially heterogeneous dynamics, stabilizing trophic systems at both local and landscape scales (Sapoukhina et al, 2003;Tyutyunov et al, 2019). Emerging population clustering induces predator interference at the population level.…”

Section: Underlying Mechanisms and Minimal Model Of Predator Interferencementioning

confidence: 99%

Ratio-Dependence in Predator-Prey Systems as an Edge and Basic Minimal Model of Predator Interference

Tyutyunov

Titova

2021

Front. Ecol. Evol.

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The functional response (trophic function or individual ration) quantifies the average amount of prey consumed per unit of time by a single predator. Since the seminal Lotka-Volterra model, it is a key element of the predation theory. Holling has enhanced the theory by classifying prey-dependent functional responses into three types that long remained a generally accepted basis of modeling predator-prey interactions. However, contradictions between the observed dynamics of natural ecosystems and the properties of predator-prey models with Holling-type trophic functions, such as the paradox of enrichment, the paradox of biological control, and the paradoxical enrichment response mediated by trophic cascades, required further improvement of the theory. This led to the idea of the inclusion of predator interference into the trophic function. Various functional responses depending on both prey and predator densities have been suggested and compared in their performance to fit observed data. At the end of the 1980s, Arditi and Ginzburg stimulated a lively debate having a strong impact on predation theory. They proposed the concept of a spectrum of predator-dependent trophic functions, with two opposite edges being the prey-dependent and the ratio-dependent cases, and they suggested revising the theory by using the ratio-dependent edge of the spectrum as a null model of predator interference. Ratio-dependence offers the simplest way of accounting for mutual interference in predator-prey models, resolving the abovementioned contradictions between theory and natural observations. Depending on the practical needs and the availability of observations, the more detailed models can be built on this theoretical basis.

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Section: Underlying Mechanisms and Minimal Model Of Predator Interferencementioning

confidence: 99%

Ratio-Dependence in Predator-Prey Systems as an Edge and Basic Minimal Model of Predator Interference

Tyutyunov

Titova

2021

Front. Ecol. Evol.

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“…Thus, this implied mechanism is evolutionary advantageous strategy, which allows prey and predator to coexist safely and avoid the collapse of total overgrazing, and therefore increases the efficiency of the whole system. The effect of increased viability of trophic system due to the active predator's movements was earlier revealed for spatial prey-predator models with the indirect (inertial) prey-taxis [22,23,27,30].…”

Section: Discussionmentioning

confidence: 80%

“…In the model presented here (hereinafter referred to as TZA model), predator's migrations are explicitly formalized as indirect (or equivalently, inertial) prey-taxis stimulated by the degree of starvation, which leads to the Patlak-Keller-Segel flux of the predator population density [8,11]. As shown in [22][23][24][25][26][27][28][29], in the frameworks of the taxis-diffusion-reaction systems this approach enables us to account for the inertial delay in the consumer's response to varying distribution of the prey. Recently, another model of the same biological system has been presented in [7] (hereinafter referred to as SA model).…”

Section: Discussionmentioning

confidence: 99%

Spatiotemporal Pattern Formation in a Prey-Predator System: The Case Study of Short-Term Interactions Between Diatom Microalgae and Microcrustaceans

2020

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A simple mathematical model capable of reproducing formation of small-scale spatial structures in prey–predator system is presented. The migration activity of predators is assumed to be determined by the degree of their satiation. The hungrier individual predators migrate more frequently, randomly changing their spatial position. It has previously been demonstrated that such an individual response to local feeding conditions leads to prey–taxis and emergence of complex spatiotemporal dynamics at population level, including periodic, quasi-periodic and chaotic regimes. The proposed taxis–diffusion–reaction model is applied to describe the trophic interactions in system consisting of benthic diatom microalgae and harpacticoid copepods. The analytical condition for the oscillatory instability of the homogeneous stationary state of species coexistence is given. The model parameters are identified on the basis of field observation data and knowledge on the species ecology in order to explain micro-scale spatial patterns of these organisms, which still remain obscure, and to reproduce in numerical simulations characteristic size and the expected lifetime of density patches.

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“…Note that a particular case of Model ( 1)-( 6) considering a predator-prey system without competing species P, where the predator reproduction subject to the Allee effect, was studied earlier in [22].…”

Section: The Modelmentioning

confidence: 99%

Modeling Study of Factors Determining Efficacy of Biological Control of Adventive Weeds

Tyutyunov,

Govorukhin,

Tsybulin

2024

Mathematics

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We model the spatiotemporal dynamics of a community consisting of competing weed and cultivated plant species and a population of specialized phytophagous insects used as the weed biocontrol agent. The model is formulated as a PDE system of taxis–diffusion–reaction type and computer-implemented for one-dimensional and two-dimensional cases of spatial habitat for the Neumann zero-flux boundary condition. In order to discretize the original continuous system, we applied the method of lines. The obtained system of ODEs is integrated using the Runge–Kutta method with a variable time step and control of the integration accuracy. The numerical simulations provide insights into the mechanism of formation of solitary population waves (SPWs) of the phytophage, revealing the factors that determine the efficacy of combined application of the phytophagous insect (classical biological method) and cultivated plant (phytocenotic method) to suppress weed foci. In particular, the presented results illustrate the stabilizing action of cultivated plants, which fix the SPW effect by occupying the free area behind the wave front so that the weed remains suppressed in the absence of a phytophage.

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Predator overcomes the Allee effect due to indirect prey–taxis

Cited by 24 publications

References 72 publications

Ratio-Dependence in Predator-Prey Systems as an Edge and Basic Minimal Model of Predator Interference

Ratio-Dependence in Predator-Prey Systems as an Edge and Basic Minimal Model of Predator Interference

Spatiotemporal Pattern Formation in a Prey-Predator System: The Case Study of Short-Term Interactions Between Diatom Microalgae and Microcrustaceans

Modeling Study of Factors Determining Efficacy of Biological Control of Adventive Weeds

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