the genotype. The index indicates the genotype and the number of type genotypes in the child population is: which gives fitness: Since the individual mutability does not change, the average mutabilities will be: with these definitions, the simple Price equation now applies. Lineage fitness In this case we want to look at the idea that fitness is measured by the number of children an organism has, regardless of their genotype. Note that we now have two methods of grouping, by lineage, and by genotype. It is this complication that will introduce the need for the full Price equation. The number of children an -type organism has is: which gives fitness: We now have characters in the child population which are the average character of the -th parent. with global characters: with these definitions, the full Price equation now applies. Criticism The use of the change in average characteristic () per generation as a measure of evolutionary progress is not always appropriate. There may be cases where the average remains unchanged (and the covariance between fitness and characteristic is zero) while evolution is nevertheless in progress. For example, if we have , , and , then for the child population, showing that the peak fitness at is in fact fractionally increasing the population of individuals with . However, the average characteristics are z=2 and z'=2 so that . The covariance is also zero. The simple Price equation is required here, and it yields 0=0. In other words, it yields no information regarding the progress of evolution in this system. A critical discussion of the use of the Price equation can be found in van Veelen (2005), van Veelen et al. (2012), and van Veelen (2020). Frank (2012) discusses the criticism in van Veelen et al. (2012). Cultural references Price's equation features in the plot and title of the 2008 thriller film WΔZ. The Price equation also features in posters in the computer game BioShock 2, in which a consumer of a "Brain Boost" tonic is seen deriving the Price equation while simultaneously reading a book. The game is set in the 1950s, substantially before Price's work. See also Price equation examples References Further reading Equations Evolutionary dynamics Evolutionary biology Population genetics