# Could sex alone drive complexity?

Imagine that complexity is measured by a positive number $f_n$.

If one has no prior knowledge about the positive number $f_n$ then from Bayesian theory one can assign $\log f_n$ an "improper" uniform prior over the range $-\infty$ to $\infty$.

A random mutation might increase or decrease the complexity of the offspring $f_{n+1}$. If we assume the offspring's complexity is likely to be close to the parent then we could simply model the random change in complexity by:

$$log f_{n+1} = log f_n + \Delta\ \ \ \ \ \hbox{with probability 0.5}$$

and

$$log f_{n+1} = log f_n - \Delta\ \ \ \ \ \hbox{with probability 0.5}$$

where $\Delta$ is some small number.

Such a random evolution will lead to the log of the complexity performing a random walk.

Assume the complexity of a sexual organism is the average of the complexities of its parents.

$$f_{child} = \frac{f_{male} + f_{female}}{2}.$$

If one evolves the simple model now one finds that the complexity of the population grows exponentially.

Is this idea interesting or not? :)

• What is complexity? I think you need to very explicitly define what this concept is, with regards to your model.
– kmm
Jul 24 '13 at 18:00
• True - I could have modeled simplicity instead but that seemed a bit perverse! Jul 24 '13 at 18:05