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2 Does low diversity cause growth?

As the population becomes more similar in shape and content, selection will mate more similar individuals. From the above argument, whether these individuals happen to be the fit or not, a higher rate of growth will generally occur when the individuals are of the same size and shape. When the individuals are similar in both size and shape, they will exchange similar size subtrees to produce their offspring. According to the theories of code growth, the offspring which are slightly larger will be biased to have a higher chance of survival. Also, both offspring will tend to be similar in size to their parents, slightly bigger and slightly smaller, producing more similar size individuals in the next generation and a higher rate of growth. This is in contrast to a population with high shape and content diversity.

In a diverse population (in terms of size, shape and contents), the offspring are more likely to be of varied size, i.e. smaller and larger than parents. Growth will be slower in this case. Although two dissimilar individuals may produce one larger offspring than if they were similar, these two offspring are likely to have a lower chance of survival than two offspring from similar individuals. Thus, a diverse population would not produce code growth as consistently as a low diversity population. A higher selection pressure could reverse the effect of low diversity by over-selecting the best individuals, which are likely to be similar.

Assuming code growth generally occurs with fitness improvement, does the difference in difficulty sufficiently explain the difference in entropy, diversity and rate of growth? The regression problems contain possible conflicts between content and context, noise introduced by the protected division operator and a wide range of intron and neutral code effects that could lead to varied rates of growth. Does the causal hypothesis, described in Figure 6.9, capture the important aspects that lead to an increased rate of code growth and are not influenced by these factors?

Figure 6.9: The symmetrical hypothesis that difficulty effects the rate of code growth by maintaining higher levels of entropy, which causes less diversity by the over-selection of better individuals, and both cause more similar individuals, which are likely to be big and to create bigger offspring.
\begin{figure}\centerline{
\psfig{figure=chapters/ch5figs/hypothesis.eps,height=6.0cm}}\end{figure}


next up previous contents
Next: 2 A Model of Up: 1 Hypothesis Previous: 1 Does high selection   Contents
S Gustafson 2004-05-20