Related papers: On discrete evolutionary dynamics driven by quadra…
In this paper, we show that different types of evolutionary game dynamics are, in principle, special cases of a dynamical system model based on our previously reported framework of generalized growth transforms. The framework shows that…
Formulating quantitative and predictive models for tissue development requires consideration of the complex, stochastic gene expression dynamics, its regulation via cell-to-cell interactions, and cell proliferation. Including all of these…
Discrete ancestral problems arising in population genetics are investigated. In the neutral case, the duality concept has proved of particular interest in the understanding of backward in time ancestral process from the forward in time…
Population games can be regarded as a tool to study the strategic interaction of a population of players. Although several attention has been given to such field, most of the available works have focused only on the unconstrained case. That…
We investigate the evolutionary dynamics of a population structured in phenotype, subjected to trait dependent selection with a linearly moving optimum and an asexual mode of reproduction. Our model consists of a non-local and non-linear…
There are many different models--both continuous and discrete--used to describe gene mutation fixation. In particular, the Moran process, the Kimura equation and the replicator dynamics are all well known models, that might lead to…
We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…
The influence of time-dependent fitnesses on the infinite population dynamics of simple genetic algorithms (without crossover) is analyzed. Based on general arguments, a schematic phase diagram is constructed that allows one to characterize…
State-of-the-art methods for data-driven modelling of non-linear dynamical systems typically involve interactions with an expert user. In order to partially automate the process of modelling physical systems from data, many EA-based…
Conventional population genetics considers the evolution of a limited number of genotypes corresponding to phenotypes with different fitness. As model phenotypes, in particular RNA secondary structure, have become computationally tractable,…
Mathematical modelling of biological population dynamics often involves proposing high fidelity discrete agent-based models that capture stochasticity and individual-level processes. These models are often considered in conjunction with an…
We consider an evolution algebra which corresponds to a bisexual population with a set of females partitioned into finitely many different types and the males having only one type. We study basic properties of the algebra. This algebra is…
Discrete models have a long tradition in engineering, including finite state machines, Boolean networks, Petri nets, and agent-based models. Of particular importance is the question of how the model structure constrains its dynamics. This…
Generative adversarial networks (GANs) are powerful generative models but remain challenging to train due to pathologies suchas mode collapse and instability. Recent research has explored co-evolutionary approaches, in which populations of…
The selection pressures that have shaped the evolution of complex traits in humans remain largely unknown, and in some contexts highly contentious, perhaps above all where they concern mean trait differences among groups. To date, the…
The expansion of a population into new habitat is a transient process that leaves its footprints in the genetic composition of the expanding population. How the structure of the environment shapes the population front and the evolutionary…
The persistence of biodiversity of species is a challenging proposition in ecological communities in the face of Darwinian selection. The present article investigates beyond the pairwise competitive interactions and provides a novel…
We consider a stochastic model for the evolution of a discrete population structured by a trait with values on a finite grid of the torus, and with mutation and selection. Traits are vertically inherited unless a mutation occurs, and…
In ecology and population dynamics, gene-flow refers to the transfer of a trait from one population to another. This phenomenon appears in studying the evolution of social features, such as languages. From the mathematical point of view,…
Solving Quadratic equation is one of the intrinsic interests as it is the simplest nonlinear equations. A novel approach for solving Quadratic Equation based on Genetic Algorithms (GAs) is presented. Genetic Algorithms (GAs) are a technique…