A mathematical model of the invasion of mysid (Mysidacea) into Narochan Lakes

Bobyrev, A. E.; Burmensky, V. A.; Kriksunov, E. A.; Medvinsky, Alexander B.; Nurieva, N. I.; Rusakov, A. V.; Allasia, Giampietro; Venturino, Ezio

doi:10.1134/s0006350910060242

Cited by 2 publications

(2 citation statements)

References 22 publications

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“…Invasions made the behavior of biosystems less predictable [32]. A harmless benthic invader can actually trigger a sequence of changes in the organic matter flow of a water body [33]. The history was previously described in detail for the idea of simulating with regard to both the time lag in biological systems and hereditary properties [34], meaning that the regulatory functional of a process depends on several previous states of the system [35].…”

Section: Simulation Of Delayed Counteraction Scenariosmentioning

confidence: 99%

Simulation of Scenarios of a Deep Population Crisis in a Rapidly Growing Population

Perevaryukha

2021

BIOPHYSICS

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This article focuses on the modeling of crisis and threshold development of the population process during the formation of a new population in a competitive environment. As a population spreads, a deep population crisis may arise as a result an abrupt triggering of biotic countermeasures before resources for a further increase in population size are exhausted. A bottleneck occurred in the history of many populations, including humans at the time of the Neolithic crash in Europe. Invaders with high reproductive potential often exert deleterious effects on biosystems. The emergence of efficient competition can not only cause classical cyclical fluctuations, but also lead to a complete extinction of the population after a series of high peaks in its abundance. Two alternative scenarios provide classical examples of induced population crises. One was observed in Gause's experiments where an introduction of a predatory ciliate drove another ciliate species to extinction. The other scenario was observed in a series of experiments where bacteriophages were introduced into colonies of actively dividing bacteria that had a dynamically adapting antiviral mechanism. In this work, modifications to the model were proposed to describe the actual scenarios of crisis effects in population dynamics. Equations with deviating arguments in the time variable allowed a threshold effect of conditions on reproduction of the invasive species and an aggregated nature of the lagging regulation with two time factors. The computational scenarios described both completion of the process after a repeated outbreak and successful elimination of the population crisis via rapid adaptation. Deep crisis phenomena are characteristic of local population dynamics when organisms interact with viruses that are new to them.

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Section: Simulation Of Delayed Counteraction Scenariosmentioning

confidence: 99%

Simulation of Scenarios of a Deep Population Crisis in a Rapidly Growing Population

Perevaryukha

2021

BIOPHYSICS

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“…As before, it is worth stressing out that this is not only a theoretical aspect. For instance, in an ecological system, the reproduction rate depends on the seasons [28], then an independent-time shape for the nonconservative parameters would not be realistic in that case. Also, when dealing with the immune system interactions, both the proliferation and the destruction of cells are relevant effects in the description that should not be neglected [29,30].…”

Section: Introductionmentioning

confidence: 99%

A kinetic model with time‐dependent proliferative/destructive rates

Menale,

Soares

2023

Math Methods in App Sciences

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This paper presents a new kinetic model with time‐dependent proliferative/destructive parameters, where the activity variable of the system attains its values in a discrete real subset. Therefore, a system of nonautonomous nonlinear ordinary differential equations is gained, with the related Cauchy problem. A first result of local existence and uniqueness of positive and bounded solution is proved. Then, the possibility of extend this result globally in time is discussed, with respect to the shape of nonconservative time‐dependent parameters. Numerical simulations are performed for some scenarios, corresponding to different shapes of time‐dependent parameters themselves. Furthermore, the pattern and long‐time behavior of solutions are numerically analyzed. Finally, these results show that equilibria and oscillations may occur.

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A mathematical model of the invasion of mysid (Mysidacea) into Narochan Lakes

Cited by 2 publications

References 22 publications

Simulation of Scenarios of a Deep Population Crisis in a Rapidly Growing Population

Simulation of Scenarios of a Deep Population Crisis in a Rapidly Growing Population

A kinetic model with time‐dependent proliferative/destructive rates

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