. The symbol 
stands for the ensemble average. In this table
all simulations are done with populations of 100 parents. Two genetic
scenarios are compared, one with a low per locus mutation rate of 
and one with a high mutation rate of 
. 
The intensity of directional selection ranges from
to 
and the strength of stabilizing selection on
the second character equals 
, 10 or 100, where larger
values of 
correspond to weaker stabilizing selection. Clearly there
is a strong relationship between the intensity of stabilizing selection and
the rate of evolution along the corridor. This is in contrast to the
prediction based on phenotypic evolution equations, assuming constant
genetic variance (Wagner, 1988). The effect of stabilizing selection on
the rate of evolution is stronger in the low mutaton rate scenario than in
the high mutation rate scenario. Furthermore, the effect of stabilizing
selection on the rate of evolution interacts with the intensity of
directional selection. The impact of stabilizing selection is stronger
with weak directional selection than with strong directional selection.
However, if one wants to measure the effect of this interaction one has to
scale the results with respect to the expected rate of evolution without
stabilizing selection on pleiotropic effects.
To compare
the results from the corridor simulations with the expected results without
stabilizing selection on pleiotropic effects we use the result by Hill
(1982), which has recently been shown to be robust (Bürger, 1993). The
asymptotic rate of evolution of a single character is predicted to be
. The values in Table 5 are the relative rates of
evolution, 
,
defined as the average rates of evolution measured in the simulations
divided by the expected rate of evolution, based on the effective
population size measured during the simulation and the 
predicted by
the mutation rate and the average mutational effect.
These values give the fraction of the maximally
possible evolution rate attained in the corridor. We call these
values the relative rate of evolution. Only results with the low mutation
rate scenario are shown. Twenty-seven parameter combinations are shown,
varying the parental population size, the strength of stabilizing selection
and the intensity of directional selection. The values range from 4% to
100% of the rate of evolution attainable by a single character without
pleiotropic effects. Clearly the relative rate of evolution is higher
under weak stabilizing selection than under strong stabilizing selection.
Furthermore, the impact of stabilizing selection is stronger with weak than
with strong directional selection. With 
, the relative rate
of evolution with 
is less than 10%, but with 
it is
between 25 to 28%, and about 47% with 
. However, the values
for weak directional and strong stabilizing selection (
,
) are exceptional. All the other values are at or above 50% of the
expected evolution rate without stabilizing selection on pleiotropic
effects. The cases with the very low relative rates are at least one order
of magnitude less than in all the other cases. The reason for these low
rates is seen in the last column in table 5, where the evolvability
criterion for the deterministic model is listed (see above) using the expected allelic effect of the mutation to calculate the criterion. If
is less than 0, then there exist multiple stable fixed points
along the corridor. This means that evolution along the
corridor is only possible by spontaneous peak shifts between successive
stable fixed points along the corridor.
In contrast, with 
,
each mutation can increase by selection independently, since the average
fitness of the heterozygous genotypes is higher than the original
homozygous ones.
Another feature of the data presented in Table 5 is that the relative rate
of evolution is approximately invariant with population size, i.e., the
absolute rate is proportional to 
(except in the case when
).