Principles of Modeling Invasion Processes with a Pulsing Entropic Diversity Index of the Composition of Biophysical Systems

Physical methods are applicable to assessing the orderliness of the composition of biosystems and to predicting their sharp collapse. Entropy characteristics are used to assess the dynamics of species diversity and the complexity of relations within biosystems during invasions and to systematize the types of nonlinearities in biophysical processes. Evolutionary science uses indices of species diversity of habitats as dominance indices based on the probability of occurrence and it ranks species within a study area but these are not used for modeling. The extent of changes in a system due to invasions can be compared by the equitability value and by an estimate of stable numerical relationships between the components of systems. We propose to track the information index of virus strain diversity adapted from the arsenal of statistical physics to predict new COVID-19 waves. We observe the effect of pulsating evolutionary entropy growth within a clade using the branch relay in SARS-CoV-2 strains as an example. The entropy metric and measure for biodiversity change rapidly and dramatically in case of the crisis of old components and of the aggression of new components into the community structure. Diversity declines after the extinction of old taxa, but slowly increases again and reaches its optimum. Sometimes a group of species descended from a single ancestor rapidly crowds out previously dominant taxa and triggers the process of evolutionary relay. When species with high reproductive potential settle in a new habitat, their invasion processes kick-start a variety of nonlinear processes of mutual adaptation in the trophic chains of biosystems. The entropy indices of community diversity are subject to pulse effects. We have reviewed crisis situations when habitats expanded in the outbreak peak model with dynamically redefined differential equations but the outbreak transfers into the stage of long depression. Invasion processes of forest pests pulsate and last for decades. Outbreaks of invasive or autochthonous species are due to various causes. To model invasion situations and outbreak scenarios of different populations, we advance the method of hybrid computational structures with trigger functions and auxiliary equations. A hybrid model of pulsating invasion is proposed and augmented with an algorithm of synchronized redefinition of a three-equation computational structure. Long-period threshold population effects for locally observed waning pulsed pest outbreaks are described in scenario experiments. The models showed natural developments of invasion or epidemic processes exactly in the form of a series of waves. Adaptation of natural regulators smooths out the peaks of invasion outbreaks, dampens the wave amplitude to a minimum, and reduces the actual reproductive rate compared to its potential value.