Janusz Uchmański | Searcharxiv

arXiv2026

Why I don't like the logistic equation

The logistic equation treats the definition of its variable freely. It is undoubtedly the population density. The logistic equation in the differential version requires continuity of processes occurring in the population. In the differential version, we do not know what happens to the population between time steps. When filling these gaps, models with features different from the logistic equation appear. If we have a micro-scale model describing the fate of individuals and interactions between them, then the macro description for this model is not the equation for population density (e.g. the logistic equation) but the model of matter circulation or energy flow through this system. We lack mathematics to describe purely biological processes.

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arXiv2024

How forest insect outbreaks depend on forest size and tree distribution: an individual-based model results

In this work, an individual-based model of forest insect outbreaks is presented. The results obtained show that the outbreak is an emerging feature of the system. It is a common product of the characteristics of insects, the environment in which the insects live, and the way insects behave in it. The outbreak dynamics is an effect of scale. In a sufficiently large forest regardless of the density of trees and their spatial distribution, provided that the range of insect dispersion is large enough, it develops in the form of an outbreak. In very small forests, the dynamics becomes more chaotic. It loses the outbreak character and, especially in the forest with random tree distribution, there is a possibility that the insect population goes extinct. The local dynamics of the number of insects on one tree in a forest, where the dynamics of all insects has the character of outbreak, is characterized by a rapid increase in number and then a rapid decrease until the extinction of the local population. It is the result of the influx of immigrants from neighboring trees. The type of tree distribution in the forest becomes visible when the density of trees becomes low and/or the range of insect dispersion is small. When trees are uniformly distributed and the range of insect dispersion is small, the system persists as a set of more or less isolated local populations. In the forest with randomly distributed trees, the insect population becomes more susceptible to extinction when the tree density and/or range of insect dispersion are small.

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