Related papers: A statistical interpretation of biologically inspi…
Building upon the eco-evolutionary game dynamics framework established by Tilman et al., we investigate stochastic fluctuations in a two-strategy system incorporating environmental feedback mechanisms, where the payoff matrix exhibits…
Sigmoids (AKA s-curves or logistic curves) are commonly used in a diverse spectrum of disciplines as models for time-varying phenomena showing initial acceleration followed by slowing: technology diffusion, cumulative cases of an epidemic,…
Quantitative predictions about the processes that promote species coexistence are a subject of active research in ecology. In particular, competitive interactions are known to shape and maintain ecological communities, and situations where…
In the work two ways of evolutionary interpretation of entropy model for correspondence matrix calculation are proposed. Both approaches based on the stochastic chemical kinetic evolution under the detailed balance condition. The first…
In this paper we study a model of age-structured ecological populations in continuous interaction with a community of harvesters. We propose an individual-based model for this feedback interactions and prove its convergence to a system of…
In this paper, we show how simple logistic growth that was studied intensively during the last 200 years in many domains of science could be extended in a rather simple way and with these extensions is capable to produce a collection of…
This paper presents a mathematical framework for modeling the dynamics of heterogeneous populations. Models describing local and non-local growth and transport processes, dependent on dynamically changing population structures, appear in a…
Understanding the relationship between a populations probability of extinction and its carrying capacity frames conservation status assessments and guides efforts to understand and mitigate the ongoing biodiversity crisis. Despite this, our…
The gap in statistics between multi-variate and time-series analysis can be bridged by using entropy statistics and recent developments in multi-dimensional scaling. For explaining the evolution of the sciences as non-linear dynamics, the…
The paper reviews the results obtained for spatial population models and the evolution of the genealogies of these populations during the last decade by the author and his coworkers. The focus is on their large scale behaviour and on the…
A number of studies have shown that cumulative mortality followed a Gompertz curve in the initial Covid pandemic period, March-April 2020. We show that the Gompertz curve is incompatible with expected initial logistic growth curves as…
In the last decade, stochastic models have shown to be very useful for quantitative modelling of social processes. Here, a configurational master equation for the description of behavioral changes by pair interactions of individuals is…
We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise…
Infinite population models are important tools for studying population dynamics of evolutionary algorithms. They describe how the distributions of populations change between consecutive generations. In general, infinite population models…
Dynamic models are widely used to mathematically describe biological phenomena that evolve over time. One important area of application is leukaemia research, where leukaemia cells are genetically modified in preclinical studies to explore…
Discrete time, spatially extended models play an important role in ecology, modelling population dynamics of species ranging from micro-organisms to birds. An important question is how 'bottom up', individual-based models can be…
Simple analytic considerations are applied to recently discovered patterns in a generalized Fisher equation for population dynamics. The generalization consists of the inclusion of non-local competition interactions among individuals. We…
Models of population growth and extinction are an increasingly popular subject of study. However, consequences of stochasticity and noise in shaping distributions and outcomes are not sufficiently explored. Here we consider a distributed…
I discuss the so-called stochastic individual based model of adaptive dynamics and in particular how different scaling limits can be obtained by taking limits of large populations, small mutation rate, and small effect of single mutations…
How are granular details of stochastic growth and division of individual cells reflected in smooth deterministic growth of population numbers? We provide an integrated, multiscale perspective of microbial growth dynamics by formulating a…