Figure 8 plots the correlation coefficient of program size
and amount of food eaten by the ant it controls.
(Correlation coefficients are equal to the covariance after it has
been normalised to lie in the range 
.
By considering food eaten we avoid the intermediate stage of
converting program score to expected number of children
required when applying Price's Theorem).
Figure 8 shows that in all cases
there is a positive correlation (typically 
) between
program performance
and length of programs.
Where selection is not used longer programs may be more fit simply
because they are more likely to contain useful primitives (such as
Move) than short programs.
When selection is used the correlation may be because when crossover
reduces the length of a program it is more likely to disrupt the
operation of the program and so reduce its fitness.
Figure 8:
Correlation of program length and fitness,
Normal runs, runs without selection and runs with selection removed
halfway through.
Means of 50 runs.