Population-based Measures

In addition to the individual-based measures, a number of collective measures were also used. The population size throughout the run was recorded, as was the population diversity (the number of different types of program--different genotypes--in the population).

Four summary measures based upon the component activity distribution function, described in the previous section, were also used: Cumulative Activity, Mean Cumulative Activity, New Activity and Mean New Activity. These measures were developed by Mark Bedau and colleagues ([Bedau & Packard 91], [Bedau et al. 97], [Bedau et al. 98]) to highlight between them the significant adaptive events occurring during an evolutionary run.

Cumulative Activity, A_cum(t), is a measure of the continual adaptive success of the genotypes in the system at a given time. It is defined at time t as the sum of the activity counters, a_i(t), of all genotypes (i) in the population at that time. The Mean Cumulative Activity ( $\bar{A}_{cum}(t)$, defined as $\frac{A_{cum}(t)}{D(t)}$, where D(t) is the diversity--the number of different genotypes--at time t) is the cumulative activity per genotype.

New Activity, A_new(t), is a measure of the rate at which new adaptively significant genotypes are appearing in the system at time t. It is defined as follows:

``Adaptive innovations correspond to new components flowing into the system and proving their adaptive value through their persistent activity. Let a₀ and a₁ define a strip through the component activity distribution function, C(t,a), such that activity values a in the range $a_{0} \leq a \leq a_{1}$ are among the lowest activity values that can be interpreted as evidence that a component has positive adaptive significance. Then, one reflection of the rate of the evolution of adaptive innovations is the new evolutionary activity, A_new(t), which sums the evolutionary activity per component with values between a₀ and a₁:

$A_{new}(t) = \sum_{i,a_{0}\leq a_{i}(t)\leq a_{1}}a_{i}(t)$'' [Bedau et al. 98]^5.5

Finally, Mean New Activity, $\bar{A}_{new}(t)$, is the new activity per genotype, defined as $\frac{A_{new}(t)}{D(t)}$. For more discussion of these measures, and of the reasons for defining them as they are, see [Bedau et al. 98] and [Bedau & Packard 91].