Models of Mechanisms: The Case of the Replicator Dynamics - Mechanism and Causality in Biology and Economics - page 86

Fig. 5.2 The biological interpretation of the RD
composition of a population at a certain time and the differential reproduction of the
respective strategies in that population at the next time step.
In particular, the biological interpretation gives causal substance to the formal
five steps of the RD model above. First, individuals are interpreted as organisms and
their strategies as certain inheritable behavioural traits. Second, organisms interact,
for example, by fighting, mating, exchanging or collaborating. In this interaction,
each organism exhibits the behavioural trait it is endowed with. Third, each
organism receives an outcome from that interaction - for example, territory, food
and mating partner - depending on its own behavioural trait and that of the
organism it interacted with. Fourth, this outcome determines the number of off-
spring the organism has in the next period. Fifth, weighing growth of each trait by
overall population growth yields the differential reproduction of each kind of
organism.
The RD model is used to represent this mechanism. But it is not the formal
RD model alone that performs this representational function, but rather a biologi-
cally interpreted RD model. In particular, the causally relevant properties are not
found in the mathematical expressions of RD, but in its biological interpretation.
This interpretation has turned the RD formalism into representations of specific
causal forces and specific arrangement of these forces. Figuratively speaking, it fills
in the black boxes of Fig. 5.1 to yield a causal process from population at t to
population at t + 1, through interaction and differential reproduction, as shown in
Fig. 5.2 .
The biological interpretation of the mathematical expressions specifies the causal
properties that bring about the result and that tell us how the population state changes
from x ( t )to x ( t + 1). Hence, the mathematical RD model in conjunction with the
biological interpretation represents the causal process from initial conditions to
specific outcome, not the formal model alone. 6 The RD model is thus a mere sketch
of the biological mechanisms it represents, as various gaps are filled in by the
biological interpretation. Let me therefore distinguish the - more sketchy - formal
RD model from the - less sketchy - biologically interpreted BRD model.
Even if it is less sketchy than the RD, the BRD does not represent a particular
mechanism. Instead, it is a schema that represents mechanisms differing in many
6 I have elsewhere argued that models consist of a formal structure and a story (Gr¨ne-Yanoff and
Schweinzer 2008 ). In the case I am discussing, the RD equation ( 5.1 ) constitutes the formal
structure. The biological interpretation of its terms, and the account of interaction yielding a
fitness-relevant outcome, leading to differential reproduction, constitutes the story.