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0.2
0.2
p(u)
A(u)
p(u)
A(u)
m: 0.12
t: 500
m: 0.12
t: 5000
0.15
0.15
0.1
0.1
0.05
0.05
0
0
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
u
u
Fig. 15.8. Evolution on a two-peaks static tness landscape, after 500 (left) and 5000 (right) time
steps. For a transient period of time the two species co-exist, but in the asymptotic limit only the
ttest one survives.
certainly this is not a generic case. This condition is known in biology under the
name of Gause or competitive exclusion principle [44].
We show in the following that the existence of a degenerate eective tness is a
generic case in the presence of competition, if the two species can co-adapt before
going extinct.
15.3.6. Flat landscapes and neutral evolution
The lineage is the sequence of connections from a son to the father at birth. Going
backward in time, from an existing population, we have a tree, that converges to the
last universal common ancestor (LUCA). In the opposite time direction, we observe
a spanning tree, with lot of branches that go extinct. The lineage of an existing
individual is therefore a path in genetic space. Let us draw this path by using the
vertical axes for time, and the horizontal axes for the genetic space. Such paths
are hardly experimentally observable (with the exception of computer-generated
evolutionary populations), and has to be reconstructed from the dierences in the
existing populations.
The probability of observing such a path, is given by the probability of survival,
for the vertical steps, and the probability of mutation for the horizontal jumps.
While the latter may often be considered not to depend on the population and the
genome itself, g the survival is in general a function of the population. Only in the
case of neutral evolution, one can disregard this factor. Within this assumption,
it is possible to compute the divergence time between two genomes, by computing
their dierences, and reconstruct phylogenetic trees.
15.3.7. A simple example of tness landscape
The main problem in theoretical evolutionary theory is that of forecasting the con-
sequences of mutations, i.e., the tness landscape. If a mutation occurs in a coding
region, the resulting protein changes. The problem of relating the sequence of a
g the inverse of this probability gives the \molecular clock"
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