The Time Scale of Evolutionary Innovation
Figure 3
The search for randomly, uniformly distributed targets in sequence space.
(A) The target set consists of random sequences; each one of them is surrounded by a broad peak of width up to
. The figure shows a pictorial illustration where the
-dimensional sequence space is projected onto two dimensions. From a randomly chosen starting sequence outside the target set, the expected discovery time is at least
, which can be exponential in
. (B) Computer simulations showing the average discovery time of
,
, and
targets, with
. We observe exponential dependency on
. The discovery time is averaged over 200 runs. (C) Success probability estimated as the fraction of the 200 searches that succeed in finding one of the target sequences within
generations. The success probability drops exponentially with
. (D) Success probability as a function of time for
and
. (E) Discovery time for a large number of randomly generated target sequences. Either
or
sequences were generated. For
and
the target set consists of balls of Hamming distance
and
(respectively) around each sequence. The figure shows the average discovery time of 100 runs. As expected we observe that the discovery time grows exponentially with sequence length,
.