Related papers: Dynamics of dioecious population with different fi…
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…
Evolution is a dynamic process. The two classical forces of evolution are mutation and selection. Assuming small mutation rates, evolution can be predicted based solely on the fitness differences between phenotypes. Predicting an…
A simple model of species origin resulted from dynamic features of a population, solely, is developed. The model is based on the evolution optimality in space distribution, and the selection is gone over the mobility. Some biological issues…
In population games, a large population of players, modeled as a continuum, is divided into subpopulations, and the fitness or payoff of each subpopulation depends on the overall population composition. Evolutionary dynamics describe how…
We study the evolution of large but finite asexual populations evolving in fitness landscapes in which all mutations are either neutral or strongly deleterious. We demonstrate that despite the absence of higher fitness genotypes, adaptation…
The interaction networks of biological systems are known to take on several non-random structural properties, some of which are believed to positively influence system robustness. Researchers are only starting to understand how these…
We address the problem of predicting the next state of a dynamical system governed by unknown temporal partial differential equations (PDEs) using only a short trajectory. While standard transformers provide a natural black-box solution to…
Population diversity is crucial in evolutionary algorithms as it helps with global exploration and facilitates the use of crossover. Despite many runtime analyses showing advantages of population diversity, we have no clear picture of how…
Complex change is often described as "evolutionary" in economics, policy, and technology, yet most system dynamics models remain constrained to fixed state spaces and equilibrium-seeking behavior. This paper argues that evolutionary…
We study the long-time behaviour of a population structured by age and a phenotypic trait under a selection-mutation dynamics. By analysing spectral properties of a family of positive operators on measure spaces, we show the existence of…
Biological systems are typically highly open, non-equilibrium systems that are very challenging to understand from a statistical mechanics perspective. While statistical treatments of evolutionary biological systems have a long and rich…
We define the harmonic evolution of states of a graph by iterative application of the harmonic operator (Laplacian over $Z_2$). This provides graphs with a new geometric context and leads to a new tool to analyze them. The digraphs of…
The long-term behaviour of dynamic systems can be classified in two different regimes, regular or chaotic, depending on the values of the control parameters, which are kept constant during the time evolution. Starting from slightly…
Crossover and mutation are the two main operators that lead to new solutions in evolutionary approaches. In this article, a new method of performing the crossover phase is presented. The problem of choice is evolutionary decision tree…
We introduce a two-dimensional discrete-time dynamical system which represents the evolution of an angle and angular velocity. While the angle evolves by a fixed amount in every step, the evolution of the angular velocity is governed by a…
Understanding the evolutionary dynamics of reinforcement learning under multi-agent settings has long remained an open problem. While previous works primarily focus on 2-player games, we consider population games, which model the strategic…
A class of models of biological population and communities with a singular equilibrium at the origin is analyzed; it is shown that these models can possess a dynamical regime of deterministic extinction, which is crucially important from…
We study the distribution of the sequence of elements of the discrete dynamical system generated by iterations of the M\"obius map $x \mapsto (ax + b)/(cx+d)$ over a finite field of $p$ elements at the moments of time that correspond to…
We propose a mathematical framework for natural selection in finite populations. Traditionally, many of the selection-based processes used to describe cultural and genetic evolution (such as imitation and birth-death models) have been…
Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We here present a generic stochastic model…