Evolutionary dynamics is the study of the

mathematical principles Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

according to which biological organisms as well as cultural ideas evolve and

evolved Evolution is change in the heritable characteristics of biological populations over successive generations. These characteristics are the expressions of genes, which are passed on from parent to offspring during reproduction. Variation ...

. This is mostly achieved through the mathematical discipline of

population genetics Population genetics is a subfield of genetics that deals with genetic differences within and between populations, and is a part of evolutionary biology. Studies in this branch of biology examine such phenomena as adaptation, speciation, and pop ...

, along with evolutionary game theory. Most population genetics considers changes in the frequencies of

allele An allele (, ; ; modern formation from Greek ἄλλος ''állos'', "other") is a variation of the same sequence of nucleotides at the same place on a long DNA molecule, as described in leading textbooks on genetics and evolution. ::"The chro ...

s at a small number of

gene In biology, the word gene (from , ; "...Wilhelm Johannsen coined the word gene to describe the Mendelian units of heredity..." meaning ''generation'' or ''birth'' or ''gender'') can have several different meanings. The Mendelian gene is a ba ...

loci. When

infinitesimal In mathematics, an infinitesimal number is a quantity that is closer to zero than any standard real number, but that is not zero. The word ''infinitesimal'' comes from a 17th-century Modern Latin coinage ''infinitesimus'', which originally referr ...

effects at a large number of gene loci are considered, one derives

quantitative genetics Quantitative genetics deals with phenotypes that vary continuously (such as height or mass)—as opposed to discretely identifiable phenotypes and gene-products (such as eye-colour, or the presence of a particular biochemical). Both branches u ...

. Traditional population genetic models deal with alleles and genotypes, and are frequently

stochastic Stochastic (, ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselv ...

. In

evolutionary game theory Evolutionary game theory (EGT) is the application of game theory to evolving populations in biology. It defines a framework of contests, strategies, and analytics into which Darwinian competition can be modelled. It originated in 1973 with John Ma ...

, developed first by

John Maynard Smith John Maynard Smith (6 January 1920 – 19 April 2004) was a British theoretical and mathematical evolutionary biologist and geneticist. Originally an aeronautical engineer during the Second World War, he took a second degree in genetics und ...

, evolutionary biology concepts may take a

deterministic Determinism is a philosophical view, where all events are determined completely by previously existing causes. Deterministic theories throughout the history of philosophy have developed from diverse and sometimes overlapping motives and consi ...

mathematical form, with selection acting directly on inherited phenotypes. These same models can be applied to studying the evolution of human preferences and ideologies. Many variants on these models have been developed, which incorporate weak selection, mutual population structure, stochasticity, etc. These models have relevance also to the generation and maintenance of tissues in mammals, since an understanding of tissue cell kinetics, architecture, and development from adult stem cells has important implications for aging and cancer.

References

External links

Evolutionary Game Dynamics
from

Clay Mathematics Institute The Clay Mathematics Institute (CMI) is a private, non-profit foundation (nonprofit), foundation dedicated to increasing and disseminating mathematics, mathematical knowledge. Formerly based in Peterborough, New Hampshire, the corporate address i ...

Evolutionary biology {{evolution-stub