Related papers: Nonlinear deterministic equations in biological ev…
Horizontal gene transfer consists in exchanging genetic materials between microorganisms during their lives. This is a major mechanism of bacterial evolution and is believed to be of main importance in antibiotics resistance. We consider a…
The principle of linearized stability and instability is established for a classical model describing the spatial movement of an age-structured population with nonlinear vital rates. It is shown that the real parts of the eigenvalues of the…
We examine kinetic symmetry breaking phenomena in an evolutionary political game in which voters, inhabiting a multidimensional ideological space, cast ballots via selection mechanisms subject to the competing forces of conformity and…
Using Monte Carlo model of biological evolution we have discovered that populations can switch between two different strategies of their genomes' evolution; Darwinian purifying selection and complementing the haplotypes. The first one is…
Clonal interference, competition between multiple co-occurring beneficial mutations, has a major role in adaptation of asexual populations. We provide a simple individual based stochastic model of clonal interference taking into account a…
This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause…
A model of the dynamics of natural rotifer populations is described as a discrete nonlinear map depending on three parameters, which reflect characteristics of the population and environment. Model dynamics and their change by variation of…
We study a reaction-diffusion equation with an integral term describing nonlocal consumption of resources. We show that a homogeneous equilibrium can lose its stability resulting in appearance of stationary spatial structures. It is a new…
Existing theories for the evolution of aging and death treat senescence as a side-effect of strong selection for fertility. These theories are well-developed mathematically, but fit poorly with emerging experimental data. The data suggest…
Two mathematical models of macroevolution are studied. These models have population dynamics at the species level, and mutations and extinction of species are also included. The population dynamics are updated by difference equations with…
The Lindblad equation describes the dissipative time evolution of a density matrix that characterizes an open quantum system in contact with its environment. The widespread ensemble interpretation of a density matrix requires its time…
A large class of evolutionary processes can be modeled by a rule which involves self-replication of some physical quantity with a non local rescaling. I show that a class of such models are exactly solvable -- in the discrete as well as…
Behavioural differences may arise in the absence of genetic or environmental variation. Chaotic dynamics may influence behavioural development, and so this among-individual variation. We discuss methods and experimental designs to test this…
We study a family of selection-mutation models of a sexual population structured by a phenotypical trait. The main feature of these models is the asymmetric trait heredity or fecundity between the parents : we assume that each individual…
The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales…
The problem of the rate and mechanisms of biological evolution was considered. It was shown that species could not be formed due to undirected mutations in characteristic times of about one million years. A mechanism of deterministic…
We characterize good clocks, which are naturally subject to fluctuations, in statistical terms. We also obtain the master equation that governs the evolution of quantum systems according to these clocks and find its general solution. This…
Regression models are used in a wide range of applications providing a powerful scientific tool for researchers from different fields. Linear, or simple parametric, models are often not sufficient to describe complex relationships between…
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…
We model and study the genetic evolution and conservation of a population of diploid hermaphroditic organisms, evolving continuously in time and subject to resource competition. In the absence of mutations, the population follows a 3-type…