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model, since both beneficial and deleterious mutations can occur, the value of
N
e
depends on the mutation rate and on
s
d
[8][10].
The above result suggests that there is a critical GC size that leads to a maximal
level of anity. GCs of sizes above this value do not lead to further improvements
in anity. We can also see that organisms in which the process of SHM/selection
is spread out in tiny structures may not achieve high levels of anity maturation.
This is compatible with what is observed in lower vertebrates.
3.3
Changes in Average Diversity with Aggregation
Next we have studied how the GC size influences the level of diversity for the
whole set of reactions. The diversity of the surviving cells is measured by counting
the number of pair-wise differences in the Ig V sequences between two random
clones sampled from the GC population.
Figure 3 shows the results for different values of the mutation effects
s
d
and
s
b
and for different times of the GC reaction. Obviously, for short reaction times
the diversity level is low, but as time increases this level approaches equilibrium.
This depends on the values of the parameters governing mutation and selection,
as discussed in the previous section.
20 generations
40 generations
80 generations
Sd = 0.15; Sb = 0.50
Sd = 0.075; Sb = 0.50
11
5
10
9
4.5
8
4
7
6
3.5
5
1
2
3
4
5
1
2
3
4
Sd = 0.15; Sb = 0.25
Sd = 0.075; Sb = 0.25
4.5
9
8
4
7
3.5
6
3
5
1
2
3
4
5
1
2
3
4
5
aggregation
aggregation
Fig. 3.
Level of Ab diversity at different times of the GC reaction for increasing aggre-
gation level
Initially the diversity generated is mainly due to deleterious mutations, but as
time proceeds key mutations start to increase in frequency and they out-compete
lower anity clones. This may lead to an actual reduction in diversity. As larger
aggregates lead to a higher probability of fixing key mutations the decrease
in diversity is more pronounced for the larger aggregates. The wiping out of
diversity in clonal populations is a well-established phenomenon in population
