# Conducting Statistical Analysis on Evolving Populations

I am writing a paper on the evolution of altruism. To do so, I have written a computer program that simulates the environment and allows a population to evolve. Organisms are either altruists or are not altruists. Altruists will try to save organisms that starve on any generation, but their probability of reproduction is decreased by a parameter p.

My test was to conduct the simulation in ten trials with different values of p. For each trial, 5 simulations were run, each lasting 30 generations. Throughout, I tracked the proportion of altruists in the population.

The data tables are massive, but I constructed a summary by averaging the altruist frequency across each of the five exposures, which is shown here:

I've been told that I should conduct an ANOVA to compare each of the series. I want to test the null hypothesis of the altruistic parameter having no effect on the evolution of the population. How do I do that? It was suggested that I take the slopes of each value of p and then do the ANOVA, but I'm entirely unsure how to do so or what the requirements are?

• Well, how did Axelrod and Hamilton do it? It's a replication of their experiment, isn't it? – AdamO Feb 10 at 19:12
• I think you need to run enough simulations that ANOVA isn't compelling or necessary. I understanding the limiting behavior trends to altruism under competing games. So, whatever $p$ is, more of it gets you there faster that much is clear except we expect a much smoother gradient. 5 sims per quadrant simply isn't enough. Also whatever the color and number represent, showing them on the same panel is confusing. – AdamO Feb 10 at 19:15
• His is mathematical, not statistical @AdamO – BooleanDesigns Feb 11 at 0:49
• The assignment requires a statistical test. I simply don't know which one to do. – BooleanDesigns Feb 11 at 0:49
• I'm dubious of this "requirement". Before finding a test you need a) a hypothesis and b) data. Formulating a hypothesis per a) may help you along. It's b) I'm worried about. This simulation study is not giving you data. Each cell is an estimate, and its precision is set arbitrarily by the number of MCMC iterations you choose. You can choose so many iterations there's 0 uncertainty in the estimate, hence no reason for a statistical test. – AdamO Feb 11 at 15:59