Related papers: Evolution Equation of Phenotype Distribution: Gene…
The evolution of dispersal is a classical question in evolutionary biology, and it has been studied in a wide range of mathematical models. A selection-mutation model, in which the population is structured by space and a phenotypic trait,…
We consider an exponentially growing population of cells undergoing mutations and ask about the effect of reproductive fluctuations (genetic drift) on its long-term evolution. We combine first step analysis with the stochastic dynamics of a…
1) Micro-evolutionary predictions are complicated by ecological feedbacks like density dependence, while ecological predictions can be complicated by evolutionary change. A widely used approach in micro-evolution, quantitative genetics,…
In this paper, we present an abstract framework to obtain convergence rates for the approximation of random evolution equations corresponding to a random family of forms determined by finite-dimensional noise. The full discretization error…
Cryptic genetic sequences have attenuated effects on phenotypes. In the classic view, relaxed selection allows cryptic genetic diversity to build up across individuals in a population, providing alleles that may later contribute to…
In this paper we present a novel tool to evaluate problem solving systems. Instead of using a system to solve a problem, we suggest using the problem to evaluate the system. By finding a numerical representation of a problem's complexity,…
We present an analysis of six deterministic models for epidemic spreading. The evolution of the number of individuals of each class is given by ordinary differential equations of the first order in time, which are set up by using the laws…
The main topic of this thesis is the analysis of evolution equations reflecting issues in ecology and population dynamics. In mathematical modelling, the impact of environmental elements and the interaction between species is read into the…
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…
Large sets of genotypes give rise to the same phenotype because phenotypic expression is highly redundant. Accordingly, a population can accept mutations without altering its phenotype, as long as thegenotype mutates into another one on the…
In a complex community, species continuously adapt to each other. On rare occasions, the adaptation of a species can lead to the extinction of others, and even its own. "Adaptive dynamics" is the standard mathematical framework to describe…
We consider a biological population evolving under the joint action of selection, mutation and random genetic drift. The evolutionary dynamics are described by a one-dimensional Fokker-Planck equation whose eigenfunctions obey a confluent…
Phylogenetic diversity is a measure for describing how much of an evolutionary tree is spanned by a subset of species. If one applies this to the (unknown) subset of current species that will still be present at some future time, then this…
In this paper we study a class of stochastic individual-based models that describe the evolution of haploid populations where each individual is characterised by a phenotype and a genotype. The phenotype of an individual determines its…
We study the evolution of artificial learning systems by means of selection. Genetic programming is used to generate a sequence of populations of algorithms which can be used by neural networks for supervised learning of a rule that…
We outline a phenomenological theory of evolution and origin of life by combining the formalism of classical thermodynamics with a statistical description of learning. The maximum entropy principle constrained by the requirement for…
We describe a method for removing the numerical errors in the modeling of linear evolution equations that are caused by approximating the time derivative by a finite difference operator. The method is based on integral transforms realized…
We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…
In many models of genotypic evolution, the vector of genotype populations satisfies a system of linear ordinary differential equations. This system of equations models a competition between differential replication rates (fitness) and…
Generating function equation has been derived for the probability distribution of the number of nodes with $k \ge 0$ outgoing lines in randomly evolving special trees. The stochastic properties of end-nodes (k=0) have been analyzed, and it…