Editing Genotype–phenotype distinction (section)

==Importance to evolutionary biology==

According to [[Richard Lewontin|Lewontin]],<ref>{{cite book|last1=Lewontin|first1=Richard C.|title=The genetic basis of evolutionary change|url=https://archive.org/details/geneticbasisofev00lewo|url-access=registration|date=1974|publisher=Columbia University Press|location=New York|isbn=978-0231083188|edition=[4th printing.]}}</ref> the theoretical task for population genetics is a process in 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 [[genotype]]s (''G''<sub>1</sub>) to a [[phenotype]] space (''P''<sub>1</sub>), where [[natural selection|selection]] takes place, and another set of laws that map the resulting population (''P''<sub>2</sub>) back to genotype space (''G''<sub>2</sub>) where [[Mendelism|Mendelian]] genetics can predict the next generation of genotypes, thus completing the cycle. Even if non-Mendelian aspects of [[molecular genetics]] are ignored, this is a gargantuan task. Visualizing the transformation schematically:

:<math>G_1 \; \stackrel{T_1}{\rightarrow} \; P_1 \; \stackrel{T_2}{\rightarrow} \; P_2 \; \stackrel{T_3}{\rightarrow} \; G_2 \;
\stackrel{T_4}{\rightarrow} \; G_1' \; \rightarrow \cdots</math>

(adapted from Lewontin 1974, p.&nbsp;12). ''T''<sub>1</sub> represents the genetic and [[epigenetic]] laws, the aspects of functional biology, or [[developmental biology|development]], that transform a genotype into phenotype. This is the "[[genotype–phenotype map]]". ''T''<sub>2</sub> is the transformation due to natural selection, ''T''<sub>3</sub> are epigenetic relations that predict genotypes based on the selected phenotypes and finally ''T''<sub>4</sub> 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 [[biometry|biometric]] theory used in [[plant breeding|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 ''[[function (mathematics)|function]]s'' of the state variables in the other domain. The "sleight of hand" is assuming that the mapping is known. Proceeding as if it is understood is enough to analyze many cases of interest. For example, if the phenotype is almost one-to-one with genotype ([[sickle-cell disease]]) or the time-scale is sufficiently short, the "constants" can be treated as such; however, there are also many situations where that assumption does not hold.{{cn|date=February 2025}}