## Fundamental Theorems of Evolution

April 26, 2017 Leave a comment

Queller 2017 Fundamental Theorems of Evolution. The American Naturalist. 189: 345-353.

*Figure 1 from Queller (2017) illustrating the relationship between the Price equation and four other fundamental equations of evolutionary biology. An arrow from one equation to another indicates that the latter can be derived form the former. Variables and subscripts are explained in the main text.*

Conceptual unification of disparate phenomena is a major goal of theory in the natural sciences, and many of the most revolutionary scientific theories are those that have shown how seemingly disparate ideas and observations follow logically from a single unifying framework. The most momentous of these theories include Newton’s unification of gravity and the laws of planetary motion, Darwin’s explanations of adaptation and biodiversity as following from natural selection and descent with modification, respectively, and Einstein’s general relativity unifying gravity, space, and time. In all of these examples, theory has changed how scientists understand the world by revealing a fundamental concept, the consequences of which encompass an entire field of study.

Perhaps to this list of discoveries we should include the unifying equation of George Price, which, in a recent paper in the American Naturalist, David Queller argues to be the most fundamental theorem of evolution. The Price equation as a unifying framework has been a subject of recent interest both within evolutionary biology and across disciplines from mechanics to music. At its core, the Price equation is a unifying framework for understanding any correlated change between any two entities. Queller proposes it to be fundamental because it encompasses all evolutionary forces acting on a population, and because it can be used to derive other less general equations in population and quantitative genetics, all of which require stricter assumptions about the evolutionary forces and environmental conditions affecting entities in the population. The Price equation includes two terms to describe the change in any trait *Δz*.

The first term isolates how a trait (*z*) covaries with fitness (*w*) for entities (*i*), and encompasses the evolutionary processes of natural selection and drift. The second term encompasses everything else that affects trait change (often called the ‘transmission bias’), such as mutation or background changes in environment. Intepreting the Price equation can be a bit daunting at first, perhaps in part because of how abstract the entities (*i*) are — representing anything from alleles, to unmeasured genotypes, to organisms, to even groups of organisms as the situation requires. Likewise, traits (*z*) can be any aspect of phenotype associated with such entities, including fitness (*w*) itself!

It’s here where Queller’s synthesis really shines, as he carefully walks the reader through how Price’s abstract equation can be used to derive multiple other less fundamental equations in which variables represent something concrete and measureable in empirical populations. These equations include Fischer’s average excess equation describing allele frequency change in population genetics, the Robertson and breeder’s equations of trait change in quantitative genetics, and Fischer’s fundamental theorem of evolution. In all cases, Queller notes the additional assumptions that are required to use these equations, particularly that the second term of the Price equation equals zero meaning that no transmission bias exists.

In our discussion, we reviewed the Price equation and its importance in evolutionary biology. We noted the interesting timeline of the discoveries of the equations; although the Price equation is fundamental in the sense that all of the other equations that Queller cites can be derived from it, it is also the most recent equation to be published. All of the other equations, which serve fundamental roles in population or quantitative genetics, were published decades before Price’s equation and have been used regularly by specialists in these sub-fields. This led us to talk a bit about what we value from theorems in evolutionary biology, and whether all of these theorems are better taught as independent solutions to particular problems in evolutionary biology, or as sub-components of a more fundamental framework grounded in the Price equation. Finally, we discussed the second term of the Price equation, noting that all of the equations that can be derived from the Price equation assume that this term equals zero. This effectively isolates natural selection, or some partition of natural selection, but ignores processes that are known to be important for trait change, particularly changing environment.

An extended discussion of Queller’s paper can be found on Brad’s own website.