О МЕТОДИКЕ МОДЕЛИРОВАНИЯ ОНТОГЕНЕТИЧЕСКИХ ИЗМЕНЕНИЙ В ЖИЗНЕННОМ ЦИКЛЕ РЫБ И НАСЕКОМЫХ

The article discusses the approach to modeling of metamorphoses in the development of a number of species in the context of their influence on the success of long-term trends of population dynamics. Changes in survival during early ontogenesis, controlled by important factor – the rate of individual development in a competing group of individuals, can cause unexpected degradation of population with a small excess fishing impact. The theory of nonlinear efficiency of reproduction leads us to the hypothesis that two different nonlinear effects are controlled by similar mechanisms. For insects such fluctuations in survival during metamorphosis can start another process - the rapid outbreak of pests, where actual formalization of the impact of parasites on the first stage of development, depending on the initial concentration of clutches, but limited resources is taken into account at a finishing. The method has been for submission to decline of generations on the basis of dynamic overriding differential equations with discrete-continuous structure of time. To extend the previously proposed model for the formation of generations is formed computing structure for the account mortality depending on the level of competition, complete with trigger functional and a new scheme describing the changes the growth rate for the example of the Caspian Sea sturgeon in three ecological and physiological stages of development. The new model has a non-trivial possibilities parametrically modification of behavior regimes. The coexistence of alternative cycles is explained by the increase in adaptive interspecies differences.В статье рассматривается подход к моделированию метаморфозов в развитии ряда биологических видов в контексте влияния их успешности на долговременные тренды популяционной динамики. Изменения выживаемости в раннем онтогенезе, контролируемые фактором темпов индивидуального развития в конкурирующей группе особей, могут стать причиной неожиданной деградации популяции при малом избыточном промысловом воздействии. Теория нелинейной эффективности воспроизводства выводит к гипотезе, что два различных нелинейных эффекта контролируются на самом деле схожими механизмами. Для насекомых аналогичные колебания выживаемости при метаморфозах могут запускать другой процесс – стремительной вспышки численности вредителей, где актуальна формализация воздействия паразитов на первой стадии развития, зависящая от начальной концентрации кладок, но ограниченность ресурсов учитывается на завершающей. Рассмотрен метод представления убыли поколений на основе систем динамически переопределяемых дифференциальных уравнений с дискретно-непрерывной структурой времени. В расширении ранее предложенной модели формирования поколений сформирована вычислительная структура для учета зависимости смертности от уровня конкуренции, дополненная триггерным функционалом и новой схемой описания изменений скорости роста для примера осетровых рыб Каспийского моря на трех эколого-физиологических этапах развития. Модель обладает нетривиальными возможностями в параметрическом изменении режимов поведения. Сосуществование альтернативных циклов находит объяснение в адаптивном возрастании внутривидовых различий

МОДЕЛЬ СЦЕНАРИЯ ИНТРОДУКЦИИ МОЛОДИ РЫБ С УЧЕТОМ ДИНАМИКИ БИОГЕННЫХ ЭЛЕМЕНТОВ

The article discusses the expansion of the previously formulated approach to modeling aspects of the reproductive cycle, taking into account the changes in the habitat and metamorphosis in the development of fish. Excessive accumulation of nutrients with prolonged use of a reservoir for artificial growth of juveniles or accelerated decomposition of organic nitrogen and phosphorus may in some cases affect the success of the reproductive process. This creates an indirect effect on long-term trends in population dynamics. In some cases, the increase in the influx of organic phosphorus further leads to a state of eutrophication and may affect the insufficient aeration of breeding sites, leading to hypoxia for hatched larvae. Even worsen the situation with the consumption of oxygen in the water at the mass destruction of eggs. Lack of organic matter leads to insufficient development of planktonic organisms for optimal growth of fishes. The system of survivability equations for calculation competing individuals of the generation is supplemented by a functional extension using an iterative model of biogenic elements dynamics, based on the analysis of processes in the ecosystem of Lake Chao. The block of the model for calculating the inflow and destruction of organic matter is synchronized with a continuous-discrete computational structure that takes into account the interrelated changes in mortality factors and the rate of development of juvenile fish during transitions between generalized ecological and physiological stages of development.Рассматривается расширение ранее сформулированного подхода к моделированию аспектов репродуктивного цикла с учетом происходящих перемен в среде обитания и метаморфозов в развитии рыб. Избыточное накопление биогенных элементов при длительном использовании водоемов для искусственного выращивания молоди или ускоренный распад органики в некоторых случаях могут оказывать влияние на успешность процесса воспроизводства, косвенно влияя на долговременные тренды популяционной динамики. В отдельных случаях усиление притока органического фосфора приводит далее к состоянию эвтрофикации и может сказаться на недостаточной аэрации мест размножения, привести к гипоксии у вылупившихся личинок. При массовой гибели икры еще ухудшится ситуация с расходом кислорода в водоеме. Нехватка органики приводит недостаточному для оптимального роста рыб развитию биомассы кормовых планктонных организмов. Система уравнений выживаемости конкурирующих особей поколения дополнена функциональным расширением, использующим итерационную модель динамики биогенных элементов, построенную на основе анализа процессов в экосистеме озера Чао. Блок модели расчёта притока и деструкции органики синхронизирован с непрерывно-дискретной вычислительной структурой, учитывающей взаимосвязанные изменения факторов смертности и темпов развития молоди рыб при переходах между обобщенными эколого-физиологическими этапами развития

НЕУСТОЙЧИВОЕ КРИТИЧЕСКОЕ РАВНОВЕСИЕ В ДИНАМИКЕ СЛОЖНО-СТРУКТУРИРОВАННОЙ ПОПУЛЯЦИИ ОСЕТРОВЫХ РЫБ

The article deals with the consequences of the existence of special conditions that determine the character of the rapid further development of population processes. The most probable connection of these critical conditions deals with the optimal number of subpopulation groups. These groups are formed by the evolutionary adaptation of the form of restricted access to resources for reproduction. We have proposed a model of population processes, which formalizes the influence of uneven growth rate for two different groups of reproductive sturgeon mortality of migratory fish in the juvenile period of Acipenser gueldenstaedtii development. In the computing environment was investigated the hybrid system, which simulates the effects of the existence of the situation for the population of migrating juvenile disproportionate reduction in the river. Such cases are established by us according to the rapid decline in sturgeon spawning the Volga. For the exploited population threshold effect after the unstable equilibrium with the minimum necessary for the well being of the form number is the count in the implementation of the «collapse». The phenomenon of collapse detached among all scenarios the most valuable long-term degradation of the reproductive group. In addition to the apparent sharp reduction in reproductive performance, threshold effect is reflected in the adverse events previously dominated evolutionary trend for the survival of certain forms of the life cycle of fish in terms of reorganization of the fishery. Informative, that the Volga stellate sturgeon Acipencer stellatus observed some form of non-linearity in the efficiency of spawning and require a different kind of fish-specific mathematical model.В статье рассматриваются последствия существования особых состояний, определяющих стремительный характер дальнейшего развития популяционных процессов. Вероятна связь подобных критических состояний с оптимальной численностью субпопуляционных объединений, образующихся при эволюционной адаптации вида с ограниченным доступом к ресурсам для размножения. Предложена модель популяционного процесса, формализующая влияние неравномерной скорости роста у двух различных репродуктивных групп на смертность мигрирующих рыб в ювенальный период развития. В вычислительной среде исследована гибридная система, описывающая последствия существования для популяции ситуации непропорционального снижения мигрирующей молоди в реке, установленной нами по данным стремительного сокращения нереста волжского осетра. Для эксплуатируемой популяции пороговый эффект после неустойчивого равновесия с минимально необходимой для благополучного размножения вида численностью служит отсчетом реализации «коллапса». Известен ряд примеров подобного особого сценария длительной деградации наиболее ценной для промысла репродуктивной группы. Помимо явного резкого сокращения эффективности воспроизводства, пороговый эффект при коллапсе отражается в неблагоприятном проявлении доминировавшего ранее эволюционного тренда для выживаемости отдельных форм жизненного цикла рыб в условиях реорганизации промысла. Интересно, что для волжской севрюги наблюдается иная форма нелинейности по сведениям об эффективности нереста

ON THE TECHNIQUE OF MODELING ONTOGENETIC CHANGES IN FISH AND INSECTS LIFECYCLE

The article discusses the approach to modeling of metamorphoses in the development of a number of species in the context of their influence on the success of long-term trends of population dynamics. Changes in survival during early ontogenesis, controlled by important factor – the rate of individual development in a competing group of individuals, can cause unexpected degradation of population with a small excess fishing impact. The theory of nonlinear efficiency of reproduction leads us to the hypothesis that two different nonlinear effects are controlled by similar mechanisms. For insects such fluctuations in survival during metamorphosis can start another process - the rapid outbreak of pests, where actual formalization of the impact of parasites on the first stage of development, depending on the initial concentration of clutches, but limited resources is taken into account at a finishing. The method has been for submission to decline of generations on the basis of dynamic overriding differential equations with discrete-continuous structure of time. To extend the previously proposed model for the formation of generations is formed computing structure for the account mortality depending on the level of competition, complete with trigger functional and a new scheme describing the changes the growth rate for the example of the Caspian Sea sturgeon in three ecological and physiological stages of development. The new model has a non-trivial possibilities parametrically modification of behavior regimes. The coexistence of alternative cycles is explained by the increase in adaptive interspecies differences

Methodology of the Construction of Computational Scenarios for Modeling Extreme States in Living Systems

Abstract: We consider a methodology for organizing hybrid computing structures to simulate abrupt changes in controlled natural processes and analyzing phases of extreme environmental phenomena. Systems of differential equations with the dynamically redefinable right-hand side at special moments (events) are used. The truth conditions for transitions are obtained from computing other equations for additional characteristics of the state of a generation. Threshold states in process modeling are the result of the inclusion of trigger functions. Their values on the right-hand side are specifically different from the neutral value only in narrow ranges of the space of changing characteristics of a hybrid system and depend on the initial conditions. The restricted limits of functions and their domain of values rest on the core of the threshold effects for the simulated biosystem, which are observed under special conditions. The method allows us to implement actual qualitative changes in management scenarios as bifurcations of the appearance (reduction) of equilibrium states or the boundary crisis of a complex attractor consisting of intervals scattered in a limited area. Computational scenarios for different population processes are investigated. The collapse of fish stocks is described in the model by the examples of cod in the North Atlantic and sturgeon in the Caspian Sea. The rapid outbreak of their abundance is modeled according to observations on the pulsation of the population size of pests of relict evergreen forests. The threshold scenario of the outbreak of insects in the scenario ends spontaneously due to the local exhaustion of forest resources with a sharp transition to fluctuations of the pest, which are ordinary for the environment. The methodology of organizing the structure for the population model is summarized to predict a wide range of extreme processes related to rapid changes in controlled biological systems and the spread of unwanted biological invasions

SIMULATION SCENARIO OF INTRODUCTION OF FISH WHITEBAIT WITH THE ACCOUNT OF BIOGENIC ELEMENTS DYNAMICS

The article discusses the expansion of the previously formulated approach to modeling aspects of the reproductive cycle, taking into account the changes in the habitat and metamorphosis in the development of fish. Excessive accumulation of nutrients with prolonged use of a reservoir for artificial growth of juveniles or accelerated decomposition of organic nitrogen and phosphorus may in some cases affect the success of the reproductive process. This creates an indirect effect on long-term trends in population dynamics. In some cases, the increase in the influx of organic phosphorus further leads to a state of eutrophication and may affect the insufficient aeration of breeding sites, leading to hypoxia for hatched larvae. Even worsen the situation with the consumption of oxygen in the water at the mass destruction of eggs. Lack of organic matter leads to insufficient development of planktonic organisms for optimal growth of fishes. The system of survivability equations for calculation competing individuals of the generation is supplemented by a functional extension using an iterative model of biogenic elements dynamics, based on the analysis of processes in the ecosystem of Lake Chao. The block of the model for calculating the inflow and destruction of organic matter is synchronized with a continuous-discrete computational structure that takes into account the interrelated changes in mortality factors and the rate of development of juvenile fish during transitions between generalized ecological and physiological stages of development

UNSTABLE CRITICAL EQUILIBRIUM IN THE DYNAMICS OF COMPLEX STRUCTURED POPULATION OF STURGEON

The article deals with the consequences of the existence of special conditions that determine the character of the rapid further development of population processes. The most probable connection of these critical conditions deals with the optimal number of subpopulation groups. These groups are formed by the evolutionary adaptation of the form of restricted access to resources for reproduction. We have proposed a model of population processes, which formalizes the influence of uneven growth rate for two different groups of reproductive sturgeon mortality of migratory fish in the juvenile period of Acipenser gueldenstaedtii development. In the computing environment was investigated the hybrid system, which simulates the effects of the existence of the situation for the population of migrating juvenile disproportionate reduction in the river. Such cases are established by us according to the rapid decline in sturgeon spawning the Volga. For the exploited population threshold effect after the unstable equilibrium with the minimum necessary for the well being of the form number is the count in the implementation of the «collapse». The phenomenon of collapse detached among all scenarios the most valuable long-term degradation of the reproductive group. In addition to the apparent sharp reduction in reproductive performance, threshold effect is reflected in the adverse events previously dominated evolutionary trend for the survival of certain forms of the life cycle of fish in terms of reorganization of the fishery. Informative, that the Volga stellate sturgeon Acipencer stellatus observed some form of non-linearity in the efficiency of spawning and require a different kind of fish-specific mathematical model