A biological view of replication and reproduction

Essentially, the D(x) behavior is the 'female' side of sexual reproduction, in the sense that it is inseminated with information, 'code', to be replicated. The behavior x!(P|D(x)) is the inseminating or 'male' side of sexual reproduction. The behavior P -- whatever form it takes -- is the rest of the agents behavior -- like the 'fruit' around the seed. Here are some of the differences between the mathematical expression and some of the key aspects of sexual reproduction.

• In sexual reproduction the behavior of the progeny is derived by contributions from the male and female of the species. So, P needs to actually be a contribution of the inseminating and inseminated process.
• The behavior P is always deeply entangled with sexual reproduction. For example, if P includes strategies for obtaining food, then the possibility of reproduction must be somehow dependent on successfully obtaining food. Likewise, the sexual reproductive mechanism, when damaged, can actually bring about the death of the entire organism. Thus, the decomposition of sexual reproduction as a wrapper around any behavior is only a crude approximation.

These two observations allow us to derive specifications of behavior, however, that are much closer to the form of reproduction we think of as sexual. Further, once we derive these specifications we can use the calculus to explore reproductive dynamics both in terms of simulation and analysis.