Philosophy of Biology

Formalisations of Evolutionary Biology 503

relationship between the model and the empirical system within its intended scope.
It is that relationship and not the mathematical model which is the essence of a
scientifictheory.It is also a reason why one mathematical model can participate
in scientific theorising in a number of different domains (e.g., game theory which
has been applied to economic behaviour^29 , ecology^30 and social structure^31 ).
The value and power of mathematical models resides in three characteristics:
abstraction, systematisation and deduction. Constructing a mathematical model
involves abstracting the essential elements of a system’s ontology and dynamics
and constructing a conceptual framework. Once a model has been constructed,
the deductive machinery of the particular domain of mathematics is available to
allow an exploration of the properties of the system. Sunny Auyang has expressed
these features concisely:

More important than calculation is the power of mathematics to ab-

stract and articulate precisely ideas with wide implications, to con-

struct complicated conceptual structures, and to analyse exactly the

interconnection of their elements.^32

2 THE COMPLEX STRUCTURE OF EVOLUTIONARY THEORY

I have argued elsewhere that evolutionary theory is a composite of a number of
interacting sub-theories [Thompson, 1983; 1986; 1989]. Interestingly, this idea was
first suggested by Morton Beckner, ‘A “theory” may be a family of models’ [1959,
53–54]. This insight was lost for the next two decades as philosophers interested in
biology focused on the logical empiricist conception of theories — some attempting
to show that biological theories did not fit the schema and others arguing that it
did. With the advent of the semantic conception of theories and the exploration
of its applicability to biology, a return to Beckner’s insight became possible.
In my earlier works, I suggested that the interacting theories were population
genetics, selection theory, and ecology. It now clear that this was too simplistic.
A complete evolutionary theory also requires a theory of developmental, and of cell
and molecular biology. As is apparent in section III below, of the various domains
comprising evolutionary theory, some have a rich mathematical formalisation (e.g.,
population genetics, ecology), others have a more embryonic formalisation (e.g.,
developmental biology^33 ).
A somewhat crude characterisation of the interrelationship of the component
domains that comprise evolutionary theory can be given by employing the concept,
“partially determines” where “Apartially determinesBif the dynamics ofA
affect the dynamics ofB”. Beginning at the macro-level, the following relations

(^29) See any major economics text.
(^30) See: [Bulmer, 1994, ch. 8; Maynard Smith, 1982; 1983].
(^31) See, [Skyrms, 1996; 2004].
(^32) [Auyang, 1998].
(^33) A measure of the degree of formalisation is the ability to provide a state space representation
of the dynamics and trajectories