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 (
,
defined as
,
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. Leta_{0}anda_{1}define a strip through the component activity distribution function,C(t,a), such that activity valuesain 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,A_{new}(t), which sums the evolutionary activity per component with values betweena_{0}anda_{1}:

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].

1999-05-29