# My way Or The Highway

### D. Joyce, J. Kennison, N. Thompson Departments of Mathematics and Psychology Clark University

May, 2002; April, 2005

#### Scenario

Animals live in herds. The herds are arranged in a circle. For the most part, the herds are independent, but at periodic intervals, small bands of animals leave one herd to join the adjacent herds. The bands all have the same number of animals.

Every day a fixed number of animals in each herd dies (selected randomly), and the same number are born (based on vitality, described below), so the population does not change.

Every day the animals pair up for the day's activities. (This pairing is not completely random; see the next paragraph.) Some of the animals are altruists, some are not. An altruist spends some of its vitality called "cost", but its partner receives a greater vitality called "benefit". The births that occur in the herd are random, but weighted accoring to vitality. Each animal gets 10 units of vitality during the day, and if it's so lucky to be paired with an altruist, then it gets 10 + benefit. And cost is subtracted from the vitality of each altruist. It is assumed these animals are haploid, and that a child of an altruist is an altruist while the child of a nonaltruist is a nonaltruist.

What makes this model interesting is that when two altruists are paired one day, then they remain paired. They stick together like two velcro balls. Of course, if one dies or leaves the herd, then the other becomes unpaired. Also, newly born altruists are unpaired.

So there are three kinds of animals: paired altruists, unpaired altruists, and nonaltruists. The question is: is there any chance that the altruists can persist? What if there are only a very few to begin with?

#### The applets

David E. Joyce,
John Kennison,
both of the Department of Mathematics and Computer Science,
and Nicholas Thompson,
of the Frances L. Hiatt School of Psychology.
Clark University
Worcester, MA 01610