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

Abstract

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.

Hybrid Model of the Collapse of the Commercial Crab Paralithodes camtschaticus (Decapoda, Lithodidae) Population of the Kodiak Archipelago

“…These obvious differences are interesting when considering people from the same ethnic group who live permanently in different regions. Our hypothesis about the immunological cause of such noticeable differences due to the influence of the spread of seasonal coronaviruses in the past, proposed in the spring of 2020 [ 1 ], has been substantiated. Cross-reactive immune T-cells were also detected, and a universal immunodominant peptide was identified [ 3 ].…”

“…The properties of oscillating phenomena in the dynamics of various biological processes were investigated in our previous studies using mathematical methods. It was possible to describe damping fluctuations for a series of decreasing peaks of outbreaks of insect pests in boreal forests [ 1 ]. Transient oscillatory regimes leading to a “bottleneck” population crisis after the active phase of aggressive invasion were considered [ 2 ].…”

Modeling Recovery Effect from the Invasive Population Depression by the Threshold and Delayed Equation

“…Модельный сценарий отличен от ситуации прохождения новой популяцией кризиса в форме «бутылочного горлышка» при стабильной малочисленной группе особей и при временном падении репродуктивного потенциала [29]. Иной вариант итога попадания в стадию депрессии заключается в медленном образовании устойчивого реликтового вида с малым 𝑟, но в рассмотренном модельном сценарии 𝑟 y вида предполагается нами большим.…”