CS 5970 Homework 4 — Evolutionary Computation Basics

Due Friday, March 14, 2014

1. Motivation

It is known that in evolutionary systems with only selection and no mechanism for introducing variation, populations will shift composition, monotonically losing diversity (as measured by total distinct genomes), until they converge to a fixed point in which all members of the population are identical. This is even true when selection is neutral, that is, stochastic with no bias toward any particular genome, in which case this shift is known as drift. Convergence is an important feature of selection-only evolutionary systems that should be understood to comprehend more complex evolutionary systems in which variation can take place.

2. Goal

The goal of this assignment is to give you experience with selection-only models of evolutionary computation.

3. Assignment

De Jong (Evolutionary Computation: A Unified Approach, Kenneth A. De Jong, 2006, MIT Press) gives good empirical evidence that the average rate of of genome loss under neutral selection is approximately one genotype every two generations for several population sizes from 200 on down, although there is a wide variance. However, he does not give an estimate for the rate of genome loss on a per generation basis. Your job is to provide that estimate, at least for one population size.

Assume that you begin with a population P(0) of 100 individuals, each with its own unique genotype. Answer the following questions:

  1. How many unique genotypes would you expect there to be in the population after one generation, that is, in population P(1)?
  2. After 10 generations/P(10)?
  3. After 100 generations/P(100)?
  4. After 200 generations/P(200)?
You may use either a mathematical/logical or an empirical approach to answering these questions. In addition to answering the questions, you will need to explain your approach and justify it.

4. What to Turn In

You will turn in both a typed hard copy and a machine readable electronic copy of your homework that answers the questions above, including your explanation and justification. If your approach is empirical, you will also need to submit both hard and electronic copies of your code and an electronic copy of all data generated.