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, Acum(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, ai(t), of all genotypes (i) in the population at that time. The Mean Cumulative Activity ( , defined as , where D(t) is the diversity--the number of different genotypes--at time t) is the cumulative activity per genotype.
New Activity, Anew(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 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, Anew(t), which sums the evolutionary activity per component with values between a0 and a1:
Finally, Mean New Activity, , is the new activity per genotype, defined as . 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].