Long-period endogenous oscillations in fish population size: Mathematical modeling

2022

BIOPHYSICS

Degradation of commercial populations remains a frequent phenomenon even with the use of methods of stocktaking and control of production volume. In fish farming, the concept of “overfishing” is used with and the signs of this condition are well known. However, the processes leading to the degradation of reserves develope in various ways. According to the theory of nonlinear dynamical systems, several types of crisis development can be classified. Of particular interest are the phenomena of collapse, that is, variants of a rapid decline in numbers, which are unexpected for the organizations controlling the fishery. Immediately before the collapse, the state of the stock can be assessed as relatively stable and it may experience fluctuations. Contrary to expectations, there was no rapid recovery after a rapid reduction in cod, whitefish Coregonus clupeaformis of the Great Lakes, halibut and other valuable species. This paper considers a hybrid model for the collapse of red king crab Paralithodes camtschaticu s stocks of the Kodiak archipelago of Alaska with unusual distinctive oscillating dynamics. The computational scenario in a hybrid system with survival and growth equations considers the logic of decision-making in operation management. The scenario differs in that after the fall of catches, the crab population goes into the sporadic fluctuations that do not have a regular character and are not characteristic of the population. The collapse itself occurs after a long interval of fishing while the population is in an unstable mode. The analysis shows that a long species life cycle is not a decisive factor for eliminating the risk of a collapse scenario. The presence of reserve generations does not change the situation qualitatively, the efficiency of their reproduction in crab and cod off the coast of Labrador turned out to be unexpectedly low. The status of stocks of large predators that require seasonal moratoriums on fishing must be regularly checked.

Section: The Situation Of the Collapse Of The Commercial Crab Populationmentioning

confidence: 99%

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

2022

BIOPHYSICS

“…Models (10) and (12) were used to consider the variants where rapid growth phase alternate with deep crises, up to risk of sudden extinction in model (14). Using data from Gause's experiments and experiments with bacteriophages, delayed equations were shown to be efficient to use not only for a classical problem of modeling long-term stable endogenous fluctuations in population size [83] or decaying sawtooth-like outbreaks in moths. With the threshold regulatory functional Ψ[N(t -h)] included in the models with N(t -τ), the properties of extreme forms of invasion dynamics and scenarios with rapid adaptation can be described.…”

Section: Simulation Of Passing a Bottleneckmentioning

confidence: 99%

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

2021

BIOPHYSICS

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.

“…Biological justification for application of the numerical solution of a continuous model on time interval in a form of an evolution operator in discrete iterations is based on the Ricker theory of replenishment formation in fish stocks from, which he developed to analyze the management of the pink salmon fishery in British Columbia in [7]. The theory has several modern variants and modifications [8] with different functions [9]. Their difference is in the occurrence of nonlinear effects in the dynamics of iterations.…”

Section: Review Of the Literaturementioning

confidence: 99%

Universal Method for Computational Modeling of Threshold Phenomenon in the Nonsteady Biological Processes

2021

RIC

Context. In modern conditions occur abrupt changes in ecosystems. The species composition of Caspian Sea is changing rapidly. The dynamics of populations acquires an extreme character with the development of rapid invasions. The mathematical description of scale transformations requires new modeling methods. Complicated population regimes of changes have features of the threshold phenomenon in process of its development. Objective. We set the goal of computational modeling of practically important scenarios – groups of situations that relate to extreme and transitional dynamics of ecosystems, like outbreaks at the onset of dangerous invasions. We are developing a method that, on the basis of the survival model of generations, will conduct a description of sudden transitions to rapid but limited outbreak of numbers or, on contrary, a collapse of stocks like Atlantic cod in 1992 or Peruan anchovy Engraulis ringens in 1985. The purpose of our modeling is to improve the accuracy of forecasts of the population size when experts are estimates a rational strategy for the exploitation of biological resources. Method. Situations of abrupt but short-term changes in population processes cannot be calculated by traditional mathematical models and expressed in terms of asymptotic dynamics – closed limit trajectory sets. The basis of the idea of the method proposed by us is the formalization of nonlinear efficiency of reproduction, which changes in a threshold manner only in strictly defined environmental conditions. We use continuous-discrete time in the model for early ontognosis of the cod fish and insect pests. The method with triggers allows us to take into account in simulation experiments logic and motivation of making decisions by experts, people who manage the strategy of exploiting biological resources. Models assess variability for development of situations Results. We have implemented new method of bounded trigger functionals into hybrid system of the equations, that acting in selected specific states of biosystems. Analysis of new model scenarios with modifications of functionals in the basic hybrid system for extreme situations in fish and insect pests is carried out. Conclusions. We consider the method to be universal, since selection of the functional can be adapted to a wide class of models using differential equations on a fixed interval.