Evolutionary Computer Models

Evolutionary phenomena are typically highly complex in a number of ways. They are played out over many generations, involving competition between numerous individuals in a constantly varying (and largely random) context. But also, they crucially depend on tiny probabilistic differences between these individuals, based on inherited traits and random contingencies. All this makes the use of computers inevitable for anyone wishing to model such phenomena with any reliability, and to avoid the risk of creating "Just So" stories by failing to check that their evolutionary speculations genuinely describe a possible scenario.

A range of computer models of evolutionary processes is provided by the BEAGLE: Simulated Evolution project in the Center for Connected Learning (CCL) at Northwestern University. Many others are available elsewhere.

An Illustration: Fisher's Sex Ratio Theorem

A nice illustration of the value of computer modelling is provided by the puzzle over sex ratios associated with the great statistician Ronald Fisher. The problem is to explain why sexually reproducing species typically have a 50%-50% sex ratio, even though it would seem advantageous to most such species to produce more females than males (since, as any farmer knows, a relatively small number of bulls can provide for a much larger number of cows). Fisher famously solved this puzzle with an argument based on consideration of the number of grandchildren that the animal in question would have. If the population contains more females than males, then since each offspring has both a mother and a father, the males on average must be more productive. Hence in that situation, a parent predisposed to give birth to males will have more grandchildren than a parent that gives birth to females, and any gene favouring such a predisposition will therefore spread, pushing the sex balance back towards equality.

Fisher's argument is both clever and successful, but suppose we imagine ourselves back into the situation before it had been proposed, when the empirical observation of the 50%-50% sex ratio was a well-known puzzle (which in 1710 had even been cited by John Arbuthnot as a proof of divine benevolence!). In a similar context today, we might think of writing a computer model of evolution, in which we postulate the existence of a "female offspring probability" (FOP) gene capable of influencing the sex ratio of offspring. We can then frame the following thought experiment: suppose that there were such a gene, what sex ratio would it favour? An appropriate model is then very easy to devise:

  • Generate a population of agents – male and female – who are randomly assigned values of the FOP gene from 0 to 100 (i.e. alleles that confer a probability that each offspring will be female ranging from 0% to 100%).
  • Randomly mate males and females in each "generation", creating new agents whose sex is determined with a probability corresponding to the FOP genes of the parents,* and whose FOP gene value is inherited appropriately,* with some degree of random variation. [* There are various ways of implementing FOP action and inheritance, for example according to maternal, paternal, or average value.]
  • Randomly "kill" a proportion of the agents in each generation, possibly in proportion to their "age".
  • "Seed" the model with a skewed distribution (e.g. an average FOP gene value of over 90%), then run the model through a long sequence of generations, plotting the proportion of females over time to see what happens.

The Simulation of Fisher's Sex-Ratio Theorem pictured on the right provides a simple implementation of exactly this kind. And its outcome (click "Initialise" then "Run Simulation") is exactly in accordance with Fisher's Principle, that the population evolves towards a 50%-50% sex ratio. The simulation – admittedly – does not give us the same level of understanding of the phenomenon as is given by Fisher's clever diagnosis. But what it does demonstrate is that the 50%-50% sex ratio is somehow implicit in the situation of sexual reproduction and evolutionary inheritance, rather than demanding explanation from a quite different quarter (e.g. the mechanics of sperm production or chromosomal behaviour). Note also that producing this sort of computer model is, with modern systems, extremely easy (and almost mechanical) compared with the intellectual imagination required to deliver Fisher's insight. This again illustrates how computer models can be extremely valuable in guiding research and developing understanding, even when they cannot by themselves deliver the satisfying intellectual insights to which we ultimately aspire.

Richard Dawkins

Richard Dawkins

Evolutionary theorist, and strong advocate of computational evolutionary models


Fisher Sex Ratio Simulation

Fisher's Principle

After 2700 generations, the sex ratio hovers around 50%