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A beginner's guide to adaptive dynamics

Odo Diekmann (2003)

Banach Center Publications

The aim of these notes is to illustrate, largely by way of examples, how standard ecological models can be put into an evolutionary perspective in order to gain insight in the role of natural selection in shaping life history characteristics. We limit ourselves to phenotypic evolution under clonal reproduction (that is, we simply ignore the importance of genes and sex). Another basic assumption is that mutation occurs on a time scale which is long relative to the time scale of convergence...

A Computational Framework to Assess the Efficacy of Cytotoxic Molecules and Vascular Disrupting Agents against Solid Tumours

M. Pons-Salort, B. van der Sanden, A. Juhem, A. Popov, A. Stéphanou (2012)

Mathematical Modelling of Natural Phenomena

A computational framework for testing the effects of cytotoxic molecules, specific to a given phase of the cell cycle, and vascular disrupting agents (VDAs) is presented. The model is based on a cellular automaton to describe tumour cell states transitions from proliferation to death. It is coupled with a model describing the tumour vasculature and its adaptation to the blood rheological constraints when alterations are induced by VDAs treatment....

A Mathematical Model of Cancer Stem Cell Lineage Population Dynamics with Mutation Accumulation and Telomere Length Hierarchies

G. Kapitanov (2012)

Mathematical Modelling of Natural Phenomena

There is evidence that cancer develops when cells acquire a sequence of mutations that alter normal cell characteristics. This sequence determines a hierarchy among the cells, based on how many more mutations they need to accumulate in order to become cancerous. When cells divide, they exhibit telomere loss and differentiate, which defines another cell hierarchy, on top of which is the stem cell. We propose a mutation-generation model, which combines...

A Model of Large-Scale Evolution of Complex Food Webs

C. Guill (2010)

Mathematical Modelling of Natural Phenomena

A simple model of biological evolution of community food webs is introduced. This model is based on the niche model, which is known to generate model food webs that are very similar to empirical food webs. The networks evolve by speciation and extinction. Co-extinctions due to the loss of all prey species are found to play a major role in determining the longterm shape of the food webs. The central aim is to design the model such that the characteristic...

Adaptive dynamics in logistic branching populations

Nicolas Champagnat, Amaury Lambert (2008)

Banach Center Publications

The biological theory of adaptive dynamics proposes a description of the long-time evolution of an asexual population, based on the assumptions of large population, rare mutations and small mutation steps. Under these assumptions, the evolution of a quantitative dominant trait in an isolated population is described by a deterministic differential equation called 'canonical equation of adaptive dynamics'. In this work, in order to include the effect of genetic drift in this model, we consider instead...

Analyzing sets of phylogenetic trees using metrics

Damian Bogdanowicz (2011)

Applicationes Mathematicae

The reconstruction of evolutionary trees is one of the primary objectives in phylogenetics. Such a tree represents historical evolutionary relationships between different species or organisms. Tree comparisons are used for multiple purposes, from unveiling the history of species to deciphering evolutionary associations among organisms and geographical areas. In this paper, we describe a general method for comparing phylogenetic trees and give some basic properties of the Matching Split metric, which...

Ancestral processes with selection: Branching and Moran models

Ellen Baake, Robert Bialowons (2008)

Banach Center Publications

We consider two versions of stochastic population models with mutation and selection. The first approach relies on a multitype branching process; here, individuals reproduce and change type (i.e., mutate) independently of each other, without restriction on population size. We analyse the equilibrium behaviour of this model, both in the forward and in the backward direction of time; the backward point of view emerges if the ancestry of individuals chosen randomly from the present population is traced...

Asymptotic behaviour of a discrete dynamical system generated by a simple evolutionary process

Iwona Karcz-Dulęba (2004)

International Journal of Applied Mathematics and Computer Science

A simple model of phenotypic evolution is introduced and analysed in a space of population states. The expected values of the population states generate a discrete dynamical system. The asymptotic behaviour of the system is studied with the use of classical tools of dynamical systems. The number, location and stability of fixed points of the system depend on parameters of a fitness function and the parameters of the evolutionary process itself. The influence of evolutionary process parameters on...

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