As Theodosius Dobzhansky famously noted in 1973, "Nothing in biology makes sense except in the light of evolution," and cancer is no exception to this rule. Our understanding of cancer initiation, progression, treatment, and resistance has advanced considerably by regarding cancer as the product of evolutionary processes. Here we review the literature of mathematical models of cancer evolution ...

The term "evolution" is linked to the idea of development in the sciences of life, and only subsequently did it acquire the present meaning of diversification and origin of new species. The dominant image of the scala naturae, strictly related to the creationist, static and essentialistic positions, was substituted by the image of the tree that characterizes the transformist theories, and that ...

The review by Waxman and Gavrilets illustrates the collision of different mindsets in evolutionary theory. These differences originate from the awe-inspiring complexity of the evolutionary process itself: evolutionary understanding critically depends on processes at many biological levels. Starting out with base pairs and their sequences, scholars of evolution have to consider – in the order of...

Coefficient of relationship (r): the proportion of genes (or alleles) that two individuals share by common descent. Coefficient of relationship is a consequence of meiosis and sexual reproduction. Parents share 50% of their genes with their offspring (r=.50). Grandparents share 25% of their genes with their grand-offspring (r=.25). Half sibling share 25% of their genes, on average (r=.25), whil...

Evolutionary game theory developed as a means to predict the expected distribution of individual behaviors in a biological system with a single species that evolves under natural selection. It has long since expanded beyond its biological roots and its initial emphasis on models based on symmetric games with a finite set of pure strategies where payoffs result from random one-time interactions ...

This report documents the talks and discussions of Dagstuhl Seminar 13271 “Theory of Evolutionary Algorithms”. This seminar, now in its 7th edition, is the main meeting point of the highly active theory of randomized search heuristics subcommunities in Australia, Asia, North America and Europe. Topics intensively discussed include a complexity theory for randomized search heuristics, evolutiona...

The conception of adaptation was not introduced into biology in 1859, Rather what Darwin did was to offer a radically new type of explanation of adaptations and in so doing he altered the conception. As the above quotes indicate we have not in the last century sufficiently delimited this conception and it is important to do so. In this paper we will analyse and, I hope, clarify one aspect of th...

* The figures in Sections VII and IX were created using Dynamo [184] and VirtualLabs [92], respectively. I am grateful to Caltech for its hospitality as I completed this article, and I gratefully acknowledge financial support under NSF Grant SES-0617753.

Ever since Darwin read Malthus, the theory of evolution has benefited from the interaction of ecology with economics. Evolutionary game theory belongs to this tradition: it merges population ecology with game theory. Game theory originally addressed problems confronted by decision makers with diverging interests (for instance, firms competing for a market). The ‘players’ have to choose between ...

A family of replicator-like dynamics, called the escort replicator equation, is constructed using information-geometric concepts and generalized information entropies and diverenges from statistical thermodynamics. Lyapunov functions and escort generalizations of basic concepts and constructions in evolutionary game theory are given, such as an escorted Fisher’s Fundamental theorem and generali...