population genetics - Scope and theoretical considerations, Population geneticists

The study of the genetic constitutions of populations acting in consort with the environment, the processes that affect gene and genotype frequencies, and the mathematical theorems that describe them. The basic theorems were established in the period 1908–30, with the work of British geneticists R A Fisher (1890–1962), J B S Haldane (1892–1964), and US geneticist Sewall Wright (1889–1988). In human population genetics, a great deal is now known about the distribution of gene frequencies for blood groups in different peoples, and rather less for serum proteins and enzymes. DNA technology suggests that there is much variation in DNA sequences, but the frequencies of these variant sequences (restriction fragment length polymorphisms) in different populations are as yet little known.

Population genetics is the study of the allele frequency distribution and change under the influence of the four evolutionary forces: natural selection, genetic drift, mutation, and gene flow. It also takes account of population subdivision and population structure in space. Population genetics was a vital ingredient in the modern evolutionary synthesis, its primary founders were Sewall Wright, J. Fisher, who also laid the foundations for the related discipline of quantitative genetics.

Scope and theoretical considerations

Perhaps the most significant "formal" achievement of the modern evolutionary synthesis has been the framework of mathematical population genetics.

Lewontin (1974) outlined the theoretical task for population genetics. He imagined two spaces: a "genotypic space" and a "phenotypic space". The challenge of a complete theory of population genetics is to provide a set of laws that predictably map a population of genotypes (G1) to a phenotype space (P1), where selection takes place, and another set of laws that map the resulting population (P2) back to genotype space (G2) where Mendelian genetics can predict the next generation of genotypes, thus completing the cycle. Even leaving aside for the moment the non-Mendelian aspects revealed by molecular genetics, this is clearly a gargantuan task. Visualizing this transformation:

(adapted from Lewontin 1974, p.

T is the transformation due to natural selection, T the rules of Mendelian genetics.

In practice, there are two bodies of evolutionary theory that exist in parallel, traditional population genetics operating in the genotype space and the biometric theory used in plant and animal breeding, operating in phenotype space. The missing part is the mapping between the genotype and phenotype space. This leads to a "sleight of hand" (as Lewontin terms it) whereby variables in the equations of one domain, are considered parameters or constants, where, in a full-treatment they would be transformed themselves by the evolutionary process and are in reality functions of the state variables in the other domain.

Population geneticists

The three founders of population genetics were the Britons R.A. Luigi Luca Cavalli-Sforza is a Stanford-based population geneticist particularly interested in human population genetics.