CS 5970 Homework 4 — EC Theory, Part 3, Selection and Variation Models

NOTE: The hardcopies of the parts of this assignment are due at the beginning of the class period. This means that if you are even a minute late, you lose 20%. If you are worried about potentially being late, turn in your assignments ahead of time. Do this by submitting them to me during office hours or by sliding them under my office door. Electronic copies are due by 4:00 pm on the due date. Submit them through D2L before the time they are due. Do not send assignments to me through email or leave them in my departmental mail box.

1. Motivation

It is known that in evolutionary systems with both selection and variation (which De Jong refers to as “reproduction”), the change in some “quality” Q of the population can be studied using Price’s Equation.

2. Goal

The goal of this assignment is to give you experience with Price’s Equation for models of evolutionary computation that involve both selection and variation.

3. Assignment

Consider a generational evolutionary system with a constant population size of 100 that uses truncation selection to select the top half of the population for reproduction and reproduction consists of creating one exact clone of each parent and one clone with mutation. Imagine that at generation g, the quality q_i of each individual i just happens to equal i for all i, and that in creating generation g + 1 each mutation of an offspring of an odd numbered parent i results in an offspring with q = q_i*2 and each mutation of an offspring of an even numbered parent i results in an offspring with q = q_i/2. (Yes, these numbers are completely artificial but the goal here is to give you some numbers to plug into the equation for practice.) The quality that we are interested in is fitness.

Answer the following questions.

1. What is the value of z̅?
2. What is the value of E[z]?
3. What is the value of E[q]?
4. What is the value of Cov(z,q)?
5. What is the contribution to ΔQ from selection?
6. What is the value of ∑_iz_iΔq_i?
7. What is the value of N?
8. What is the contribution to ΔQ from variation with selection (the second major term in Price’s Equation)?
9. What is the value of ΔQ?

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 explanations and justifications. 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.