# WΔZ: Evolutionary Equations on the Big Screen

According to Rotten Tomatoes, the movie WΔZ starts showing today in the UK. The movie is a psychological thriller/horror movie and has been compared to Se7en. What makes this movie interesting is the fact that the screenplay was inspired by Price’s Equation:

Price’s Equation is a broader version of Fisher’s Fundamental Theorem of Natural Selection. It describes how the change in trait $z$ with phenotypes $z_i$ is related to the phenotypes’ fitnesses, $w_i$. Note that the genetics of the trait (mutation, ploidy, etc.) is contained in the second term. See Wikipedia for more details.

Now according to the Rotten Tomatoes exclusive on WΔZ:

The script comes from City of Vice scribe Clive Bradley, who claims to have come up with the movie’s premise after flicking through a book on Darwinism. “It featured a mathematical equation—W Delta Z—formulated by American population geneticist George R. Price,” he explains. “It supposedly shows that there’s no real altruism in nature; no such thing as selflessness. Price was so upset by his findings that he ended up giving away all his possessions to the poor and, eventually homeless himself, committed suicide with a pair of nail scissors in a filthy London squat.”

The study of the evolution of altruism goes beyond the description above, and I hope moviegoers won’t be seduced by this fictional account of evolutionary theory. (I’m waiting to see what demagoguery that AiG, DI, and the Expelled frauds come up with about this movie.) Now, it is true that according to Price’s Equation, altruistic behavior that benefits a species at the cost of individual fitness is selected against. (Note that a deleterious phenotype can still exist in a population through mutation-selection balance or genetic drift.) However, if the altruism only benefits certain members of the species (e.g. relatives), then altruism can be selected for.

This is represented by Hamilton’s rule: $rB > C$. This describes under what conditions an altruistic allele will invade a population. $C$ is the cost of the allele to the “actor”, $r$ is the relatedness of the receiver to the actor, and $B$ is the benefit that the receiver receives by the actor being altruistic. The consequence of Hamilton’s rule is that selfish genes can still be altruistic. There is a lot of interesting literature about the evolution of altruism, including how punishment can reinforce altruism. I recommend Sean Rice’s Evolutionary Theory, Chapter 10, as a good starting point.

So if anyone in the UK goes to see this movie this weekend, please send us an overview/review.