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3.2
Average Anity Increases with Aggregation Until a Plateau
Is Reached
We were interested in how 'anity' (fitness) levels vary with the level of ag-
gregation, that is, how 'anity' levels vary with the size of the structure where
the GCR occurs. Figure 2 shows the results for different values of the effect of
mutations that increase and decrease anity and for different times of the GCR.
When considering short periods for the GCR,theaveragelevelof'anity'islow,
even lower than the germ-line level of 'anity', which by definition is 1. But as
we consider longer periods, we observe that the level of anity increases as the
size of the structures increase. In particular, given sucient time, above a given
size of the structures, the level of anity reaches a plateau. This qualitative
result is independent of the exact values of the selection parameters
s
d
and
s
b
.
20 generations
40 generations
80 generations
Sd = 0.15; Sb = 0.50
Sd = 0.075; Sb = 0.50
1.7
1.6
1.5
1.5
1.4
1.4
1.3
1.3
1.2
1.2
1.1
1.1
1
1
2
3
4
5
1
2
3
4
5
Sd = 0.15; Sb = 0.25
Sd = 0.075; Sb = 0.25
1.05
1.1
1
1
0.95
0.9
0.9
1
2
3
4
5
1
2
3
4
5
aggregation
aggregation
Fig. 2.
Level of Ab anity for increasing levels of aggregation at different times of the
GC reaction
The reasons for this behaviour are as follows. When the size of the (GC) structure
is small, the number of cells within each structure that are undergoing mutation
and selection is small, so the contribution of the stochastic effects to the process
is large. This means that, in order for a key mutation to overcome the effects of
drift, the increase in anity of that mutation has to be extremely high. Otherwise,
most likely the mutant will be lost by chance. Thus, unless
s
b
is very strong, for low
values of the aggregation the level of anity is low. When the size of the aggregate
is large the stochastic effects are small, and so the probability that the key mutation
spreads is higher. From population genetics theory of simple models of mutation
and selection we know that the effects of selection are more important than the
effects of drift when
s
b
>
1
/N
e
,where
N
e
is the effective population size [9]. In our
