342 A. W. F. Edwards
tal Theorem of Natural Selection seems to be about as much as it is possible to
say about the relationship between genetical variation and evolutionary change,
but it does not lead to any grand theory such as is to be found in the physical
sciences.
6 EVOLUTION AS ENTROPY MAXIMISATIONBefore leaving the topic of theories of evolution involving maximisation it should
just be mentioned that occasionally authors become excited at the possibility of
viewing evolution in the language of entropy. Fisher himself was not immune to
this inThe Genetical Theory: he likens the Fundamental Theorem to the second
law of thermodynamics in some important respects, especially that ‘each requires
the constant increase of a measurable quantity, in the one case the entropy of a
physical system and in the other the fitness... of a biological population’.
It seems that he was here carried away by his enthusiasm, for a qualification
quickly follows. Amongst a list of ‘profound differences’: ‘(3) Fitness may be
increased or decreased by changes in the environment...’. Moreover,‘(4) En-
tropy changes are exceptional in the physical world in being irreversible, while
irreversible evolutionary changes form no exception among biological phenomena’.
‘Finally, (5) entropy changes lead to a progressive disorganization of the physi-
cal world... while evolutionary changes are generally recognized as producing
progressively higher organization in the organic world’.
In making the comparison Fisher was here relying on his ‘mathematical ed-
ucation [which] lay in the field of mathematical physics’, as he once wrote (see
[Edwards, 2002c]). He had spent a year in the Cavendish Laboratory, Cambridge,
after his first degree.
Subsequent authors have retraced Fisher’s footsteps with rather less caution and
complete ignorance of the Fundamental Theorem. As an example we may cite the
collection of papers entitledEntropy, Information and Evolution: New perspectives
on physical and biological evolution[Weberet al., 1988] in which some twenty
names have managed to write a whole book aboutentropy,aboutinformation,
and aboutevolution, without once discussing Fisher’s writings on them.
More recentlyFisher informationhas been invoked to develop the mathematics
of population genetics [Friedenet al., 2001]. Fisher information is a statistical
concept distinct from, and earlier than,Shannon informationin communication
theory. Whereas Shannon information measures the capacity of a channel to trans-
mit a message, Fisher information measures the informativeness of a body of data,
or of a statistic derived from data, about the parameter of the underlying probabil-
ity model. Shannon is concerned with the medium, Fisher with the message. All
three concepts are intimately connected with thelikelihood. Shannon information
is minus the expected log-likelihood function at the true value of the parameter
and Fisher information is the second derivative of this with respect to the parame-
ter, and measures the sharpness of the peak of the log-likelihood (see, for example,
[Edwards, 1992]). The basis of the suggestion that Fisher information might be