Symbol	Definition	Examples
$\Sigma$	Set of alleles	$\{0,1\}$, $\{A,T,G,C\}$
$\mathcal{G}$	Space of genotypes	${\Sigma }^n$ (strings of length $n$ over the alphabet $\Sigma$)
$\mathcal{P}$	Space of phenotypes	Genetic traits
S	Space of all distributions of genotype frequencies
P(t)	A finite collection of genotypes at time t	{(0,0), (0,1), (0,0)}
D(t)	A probability distribution describing the probability of sampling any genotype
$\phi :\mathcal{G}\to \mathcal{P}$	Genotype–phenotype mapping	Transformation from genes to proteins then traits
$\mathrm{V}:{\mathcal{G}}^k\to {\mathcal{G}}^{\ell }$	Variation operator	Mutation $\left(\mathrm{M}\right)$, recombination $\left(\mathrm{R}\right)$
$\mathrm{S}:{\mathcal{G}}^k\to {\mathcal{G}}^{\ell }$	Selection operator	Uniform, proportional selection
$\psi$	Mapping between populations at each time step, composition of variation and selection operators	$\psi =\mathrm{V}○\mathrm{S}$, $P(t+1)=\psi \left(P\right(t\left)\right)$
$\varphi$	Mapping between abstract distributions at each time step, composition of lifted variation and selection operators	$\varphi =\widehat{\mathrm{V}}○\widehat{\mathrm{S}}$, $D(t+1)=\varphi \left(D\right(t\left)\right)$
$\alpha$	Mapping from populations to distributions
${\beta }_k$	Distribution sampling operator	$P(t+1)={\beta }_k\left(D\right(t+1\left)\right)$
$w$	The probability of a genotype to be present in the next generation. Fitness (sensu PG) or reproductive rate (sensu EC)