504 Paul Thompson
of “partially determines” obtain. Ecological dynamics (including the phenotypic
properties of individuals of a population at generationF 0 ) partially determines
selection dynamics on a population atF 0. Selection dynamics onF 0 partially
determines the population genetic structure of the breeding population and hence
the population dynamics resulting in the next generation (F 1 ). Population genetic
dynamics partially determines the molecular genetic structure of the population at
F 1. The molecular genetic dynamics ofF 1 partially determines the developmental
dynamics. The developmental dynamics partially determines the phenotype ofF 1.
The population genetics component of evolutionary theory was the earliest to
be formalised as a result of the work of Ronald A. Fisher, John B.S. Haldane
and Sewall Wright. Fisher published the most comprehensive initial account of
population genetics,The Genetical Theory of Natural Selection[1930]. A superb
contemporary account is found in,Principals of Population Genetics(3rded.)
by Daniel Hartl and Andrew Clark [1997].^34 The richness of Sewall Wright’s
contributions were not fully appreciated until 1960’s.^35
As indicated earlier, Mary Williams’ [1970] axiomatisation of selection theory
fits naturally into this family of mathematical models conception of evolutionary
theory. She has provided an excellent set-theoretical axiomatisation of a crucial
component. Alone, contrary to Rosenberg, it is not a formalisation of evolutionary
theory. In section 3.2, I provide a sketch of her formalisation of selection theory
and indicate why it constitutes a Galilean conception formalisation, namely, that
it formalises selection theory as a set-theoretical model. The third component that
I sketch in section 3 is population ecology.
Returning to the integrative nature of evolutionary theory, one of the marks
of a successful theory is its ability to integrate previously disparate bodies of
knowledge. The power of Darwin’s theory of evolution was its ability to integrate
observations of biogeographic distributions, the geological/paleontological obser-
vations, anatomical observations (homologies and vestiges), observations of the
remarkable adaptedness of most organisms to their environment, etc. This con-
silience of inductions, in Whewell’s terminology, is a manifestation of the power of
the theory. Biological evolution, in all its grandeur, conforms to thisdesideratum
wonderfully. As will be seen below, the variety of mathematical models employed
in evolutionary theory, though integrated and made plausible by the conceptual
framework of evolution, draw on different domains of mathematics. And, recently,
with the increase in computing power available on the desktop and powerful pro-
(^34) Hartl has also produced an excellent primer: A Primer of Population Genetics(3rded.)
[2000].
(^35) For an excellent biography of Sewell Wright and an exposition of his contributions to genetics,
see Provine [1986a]. William Provine has also edited a collection of Wright’s papers [Provine,
1986b]. In the Preface he remarks that “Wright’s papers, especially those published before
about 1950,... were little understood at the time of publication, even if widely read.” Provine’s
explanation for this is: “Evolutionary biologists in general had very little training in mathematics
or specifically in statistics, or in quantitative reasoning generally. Moreover, Wright was rather
insensitive to the inability of his audience to follow his quantitative reasoning. Even those with
some mathematical training had much difficulty following Wright’s idiosyncratic method of path
coefficients.... Now, however, the situation has changed dramatically.”