 Identities among algebraic functions of statistical functions make possible the mathematical manipulation of the Price Equation such that it may feature a variety of different quantities. As with type recursions, quantities in various transformations of the Price Equation are equated with selection at different levels for different systems; Okasha, following Price, treats the covariance of the fitness of collectives with the phenotype of collectives as collective-level selection, while the average of the within-collective covariances between particle character and particular fitness is identified with particle-level selection. The persistence of altruistic variants in natural populations has been explained as the result of the stabilizing conflict between selection at these different levels (Sober &amp; Wilson 1998; and again see entry on  units and levels of selection.  The Price Equation can equally be manipulated to yield distinct notions of inheritance; Bourrat distinguishes temporal, persistence, and generational heritabilities and argues for the temporal notion as appropriate for the purposes of stating conditions for evolution by natural selection (Bourrat 2015). 