The Price Equation since Price: An accessible account and a generalization to categorical variables

The Price equation is usually treated as a description of how the population average value of a trait changes due to selection and other factors. Despite the fact that its generality is often emphasised, the Price equation is typically only applied to numeric traits, like weight and height. After a thorough yet accessible introduction to the numeric form, I derive a version of the Price equation for categorical traits, like colour and shape. The new equation describes how the distribution of types, rather than the population average, changes due to selection and other factors. I argue that this is a useful and conceptually sound extension of the traditional Price equation formalism. Although categorical traits can be represented numerically via dummy coding, I argue that the new version of the equation introduces an important perspective that previous versions lack: selection does not just change averages, it changes distributions.