The structure of population genetics

Mathematical population genetics is a key field of evolutionary biology since 1930s, when it reconciled the Mendelian theory of inheritance with the Darwinian theory of natural selection. Perhaps in relation to such a unifying vocation, population genetics is often cited as a unified body of knowledge. But, is it really so? Does population genetics feature internal distinctions, or even a recognizable theoretical structure? This poster follows a poorly known suggestion expressed by Richard Lewontin in the 1980 book “The Evolutionary Synthesis” (eds. Mayr & Provine). I sketch out the division of population genetics in two main “research traditions”, each based on a “theoretical structure”. In the tradition Lewontin calls “biometrical genetics” «everything is dealt with in terms of phenotype», whose variation is continuously distributed, partitioned in genetic (heritable) and nongenetic components. There is no specific reference to populational frequencies of genes: this tradition «talks about rates of changes of means and of variance» (p. 63) and «...the genes get lost in the shuffle. They get absorbed into mysterious parameters like the heritability or the average effect» (p. 59). In the second tradition, “Wrightian” or “Mendelian”, «everything was dealt with in terms of the frequencies of genes». For Lewontin, in Mendelian population genetics «phenotypic transformations get lost in the shuffle because they are assumed constant; a given genotype has a given fitness» (p. 59). The two mathematical traditions share a particulate theory of inheritance (continuous variation is product of a huge array of discrete genetic elements varying discretely); they are related and integrated; moreover, no worker (neither Fisher, nor Wright) belongs purely to one tradition. But the two are distinct theoretical sub-structures of population genetics, substantiable with examples from classical population genetics and from recent textbooks (Hartl & Clark 2007).