Modeling of the population density flow for periodically migrating organisms

Tyutyunov, Yu. V.; Zagrebneva, A.D.; Surkov, F. A.; Azovsky, Andrey I.

doi:10.1134/s000143701001008x

Cited by 9 publications

(2 citation statements)

References 9 publications

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“…Correspondingly, the indirect prey-taxis movements at the population level do not require the ability of individual predators to sense the gradient of prey-taxis stimulus S, moving along its direction. The prey-taxis is a phenomenon that emerges at the level of the population due to random movements of individuals responding to local concentrations of stimulus; see the detailed explanation and derivation of the prey-taxis flux expression in [60]. Thus, at the level of the individual predator, variation in traits enhancing prey-taxis mobility consists in variation in a predator's sensitivity to the local value of some substance or field S that stimulates the random replacing of the individual.…”

Section: Discussionmentioning

confidence: 99%

Spatial Demo-Genetic Predator–Prey Model for Studying Natural Selection of Traits Enhancing Consumer Motility

Tyutyunov

2023

Mathematics

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Combining explicit modelling of predator movements with the Kostitzin demo-genetic equations, we study conditions promoting natural selection of consumer motility. The model is a system of partial differential equations describing spatial movements of predators pursuing the diffusing prey. Local predator–prey interactions are described by the classical Rosenzweig–MacArthur model, which additionally accounts for the Allee effect affecting reproduction of predators. Spatial activity of predators is determined by the coefficients of diffusion and indirect prey-taxis. The latter characterizes the predator ability to move directionally up the gradient of taxis stimulus (odor, pheromone, exometabolite) continuously emitted by prey. Assuming that the consumer movement ability is governed by a single diallelic locus with recessive ‘mobile’ and dominant ‘settled’ alleles, the predator population in the model consists of three competing genotypes differing by diffusion and taxis coefficients; other parameters characterizing the genotypes are assumed to be equal. Numerical simulations with different spatial patterns imitating habitat deterioration demonstrate that the direction of selection among the consumer genotypes alternates, depending on the degree of habitat deterioration affecting the overall production of the prey population. Theoretical implications of the results are discussed in relation with problems of biological control, predator interference, and evolution of animal motility.

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Section: Discussionmentioning

confidence: 99%

Spatial Demo-Genetic Predator–Prey Model for Studying Natural Selection of Traits Enhancing Consumer Motility

Tyutyunov

2023

Mathematics

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“…Such an assumption leads to multidirectional diurnal velocities, which integrally determine the main direction to the spawning zone. The adoption of such an assumption turns out to be a reflection of the natural fact of skipping spawning of a part of mature fish [15][16][17][18][19][20][21][22][23].…”

Section: Discussionmentioning

confidence: 99%

Prespawning and Spawning Migrations of the Southern Greenling Pleurogrammus azonus (Mathematical Model)

2022

JMSRO

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Prespawning and spawning migrations of the southern one-finned greenling Pleurogrammus azonus in the bay are considered on the basis of the author's and literary numerical material. Peter the Great, in the summer-autumn period. As part of the spatiotemporal model building, the pre-spawning and spawning migrations were formalized. The dynamics of diurnal displacements is made in terms of transport equations. The recording of their representations follows the modified Patlack-Keller-Segel equations, according to which the flow of objects/substance is directed along the gradients of the stimulus zone functions introduced here. It is believed that in the pre-spawning period, morphophysiological and behavioral adaptations to a rather long and energyconsuming spawning occur. It is shown that the intensity of daily movements is proportional to their linear size (the larger the fish, the faster it moves). The equations for the spawning stage take into account the spatial competition of males, which under natural conditions is observed only in the vicinity of spawning areas. For females, clusters of males act as an incentive for movement. The simulation results turn out to be close to the observed migration regime.

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Numerical Study of Bifurcations Occurring at Fast Timescale in a Predator–Prey Model with Inertial Prey-Taxis

Tyutyunov

Zagrebneva

Говорухин

et al. 2019

Advanced Mathematical Methods in Biosciences and Applications

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Modeling of the population density flow for periodically migrating organisms

Cited by 9 publications

References 9 publications

Spatial Demo-Genetic Predator–Prey Model for Studying Natural Selection of Traits Enhancing Consumer Motility

Spatial Demo-Genetic Predator–Prey Model for Studying Natural Selection of Traits Enhancing Consumer Motility

Prespawning and Spawning Migrations of the Southern Greenling Pleurogrammus azonus (Mathematical Model)

Numerical Study of Bifurcations Occurring at Fast Timescale in a Predator–Prey Model with Inertial Prey-Taxis

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