Our new pick for a “notable” paper is “The formal darwinism project in outline” by Alan Grafen, published in Biology and Philosophy on 25 January 2014. (Unfortunately, the full paper is behind a paywall, but you can request a copy from the author here.)

Here is the abstract:

The formal darwinism project aims to provide a mathematical frame- work within which important fundamental ideas in large parts of biology can be articulated, including Darwin’s central argument in The Origin (that mechanical processes of inheritance and reproduction can give rise to the appearance of design), modern extensions of evolutionary theory including ESS theory and inclusive fitness, and Dawkins’ synthesis of them into a single structure. A new kind of argument is required to link equations of motion on the one hand to optimisation programs on the other, and a major point is that the biologist’s concept of fitness maximisation is not represented by concepts from dynamical systems such as Lyapunov functions and gradient functions. The progress of the project so far is reviewed, though with only a brief glance at the rather complicated mathematics itself, and the centrality of fitness maximisation ideas to many areas of biology is emphasised.

Basically, what Grafen has been trying to do — for years now — is to merge population genetics (the mathematical theory that describes changes in gene frequencies in natural populations) with optimization theory (the mathematical theory that describes adaptation). The same issue of Biology and Philosophy includes a number of commentaries on the main paper.

Here are some choice bits from the paper:

The goal of the formal darwinism project is to construct a mathematical bridge between two of the many ways of studying natural selection. One approach is population genetics, in which models are constructed that trace the change over time of the frequencies of some defined set of genotypes. … The other approach is based on the expectation of finding good design in nature: this stretches back at least to natural theology in the eighteenth century, and was invigorated and reinforced as a scientific approach by Darwin (1859) and later Fisher (1930).

Today, as molecular biologists choose to call some of their discoveries ‘mechanisms’, and ascribe ‘functions’ to enzymes, they use purposive language and so they also adopt the design approach. It is arguably impossible to undertake work in many areas of biology without doing so: purpose in explanations has great power, and attempts to do without it in ethology (for example, Kennedy 1992, reviews his earlier campaign in ethology as well as bringing in further subjects), have long ago been abandoned as unworkable.

A fly in this ointment is that there are serious reasons to doubt that fitness is in fact maximised. The central assumption of the approach has been known to be untrue in general for decades, and it is here that the other of the two approaches to studying natural selection becomes relevant.

In 1984, I coined the term ‘Phenotypic Gambit’ for the research strategy of studying organisms in ignorance of the actual genetic architecture of the trait in question … The Phenotypic Gambit articulates the assumption that is usually made implicitly in this work, and the formal darwinism project aims to understand better why and how the gambit works when it does, and also to identify and understand those cases in which the gambit fails.

Population genetic models (Ewens 2004) are examples of dynamical systems, either differential or difference equations, and are usually highly specific about the genetic architecture. … To represent the design approach, it is natural to take optimisation programs, as used in microeconomics, operations research and game theory, as the formal structure. The project then became about constructing formal links between the mathematics of motion and the mathematics of optimisation.

Because population genetics is fundamental, the first task is to construct the optimisation program from the contents of the population genetic assumptions.

One major purpose of the formal darwinism project is to assist in showing that the exact genetic architecture may reasonably be ignored in many circumstances when the form of a trait is the focus of biological study.

If you exclude simple Mendelian traits like coat colour in Pocket Mice, horn type in Soay Sheep and colour polymorphisms in Gouldian Finches and Snow Geese then we know very little about the molecular genetic basis of most traits. The majority seem to be so polygenic and the effect of each locus so small that identified polymorphisms usually explain a tiny fraction of the genetic variance