Philosophy of Biology

MAXIMISATION PRINCIPLES IN

EVOLUTIONARY BIOLOGY

A. W. F. Edwards

1 INTRODUCTION

Maximisation principles in evolutionary biology (or, more properly, extremum
principles, so as to include minimisation as well) fall into two classes — those
that seek to explain evolutionary change as a process that maximises fitness in
some sense, and those that seek to reconstruct evolutionary history by adopting
the phylogenetic tree that minimises the total amount of evolutionary change.
Both types have their parallels in the physical sciences, from which they originally
drew their inspiration. There are important differences, however, and the naive
introduction of extremum principles into biology has tended to obscure rather
than clarify the underlying processes and estimation procedures, often leading to
controversy. To understand the difficulties it is necessary first to note the use of
extremum principles in physics.

2 EXTREMUM PRINCIPLES IN PHYSICS

Extremum principles exert a peculiar fascination in science. The classic physics
example is from optics, where Fermat in the 17th century established that when
a ray of light passes from a point in one medium through a plane interface to
a point in another medium with a different refractive index its route is the one
which minimises the time it takes for the light to travel. That is, on various
assumptions about the speed of light in the different media, he showed that this
solution corresponded to Snel’s existing Sine Law of refraction. As a matter of
fact modern books on optics find it necessary to frame Fermat’s principle rather
differently, not using the notion of a minimum at all, but the point for us is that
in its original form it solves at least some optical path problems by minimisation.
The mathematics works out just right, but that is not to agree with Fermat that
‘nature is economical’.
In the 18th and 19th centuries mathematical physics unearthed a whole range
of extremum principles of great practical value because they provided a unifying
point of view which gave results that are mathematically identical to the older
approaches. Ideas like potential energy and its minimisation led to the notions

General editors: Dov M. Gabbay,
©c2007 Elsevier B.V. All rights reserved.

Handbook of the Philosophy of Science. Philosophy of Biology

Volume editors:

Paul Thagard and John Woods

Mohan Matthen and Christopher Stephens