Related papers: Labelled partitions in action: recombination, sele…

We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number $N$ of particles these simple interaction rules result in a rich variety of extinction scenarios,…

We introduce a population dynamics model, where individual genomes are represented by bit-strings. Selection is described by death probabilities which depend on these genomes, and new individuals continuously replace the ones that die,…

By a re-examination of MacMahon's original proof of his celebrated theorem on the distribution of the major indices over permutations, we give a reformulation of his argument in terms of the structure of labeled partitions. In this…

Population dynamics on a rugged landscape is studied analytically and numerically within a simple discrete model for evolution of N individuals in one-dimensional fitness space. We reduce the set of master equations to a single Fokker-Plank…

The progression of a cell population where each individual is characterized by the value of an internal variable varying with time (e.g. size, weight, and protein concentration) is typically modeled by a Population Balance Equation, a first…

Stochastic dynamics govern many important processes in cellular biology, and an underlying theoretical approach describing these dynamics is desirable to address a wealth of questions in biology and medicine. Mathematical tools exist for…

It is well known that the classical recombination equation for two parent individuals is equivalent to the law of mass action of a strongly reversible chemical reaction network, and can thus be reformulated as a generalised gradient system.…

Speciation is of fundamental importance to understanding the huge diversity of life on Earth. In contrast to current phenomenological models, we develop a biophysically motivated approach to study speciation involving the co-evolution of…

In the infectious disease literature, significant effort has been devoted to studying dynamics at a single scale. For example, compartmental models describing population-level dynamics are often formulated using differential equations. In…

This paper addresses the general problem of modelling and learning rank data with ties. We propose a probabilistic generative model, that models the process as permutations over partitions. This results in super-exponential combinatorial…

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 show that evolutionary computation can be implemented as standard Markov-chain Monte-Carlo (MCMC) sampling. With some care, `genetic algorithms' can be constructed that are reversible Markov chains that satisfy detailed balance; it…

For a given permutation or set partition there is a natural way to assign a genus. Counting all permutations or partitions of a fixed genus according to cycle lengths or block sizes, respectively, is the main content of this article. After…

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…

A new stochastic control problem of population dynamics under partial observation is formulated and analyzed both mathematically and numerically, with an emphasis on environmental and ecological problems. The decision-maker can only…

In this paper a simple procedure to deal with label switching when exploring complex posterior distributions by MCMC algorithms is proposed. Although it cannot be generalized to any situation, it may be handy in many applications because of…

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 explore the connection between evolution and large-deviation theory. To do so, we study evolutionary dynamics in which individuals experience mutations, reproduction, and selection using variants of the Moran model. We show that, in 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…

Finding the most powerful node in a dynamic random network, the largest set in a partition-valued stochastic process, or the largest family in an evolving population at a given time, can be a very difficult problem. This is particularly the…