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Figure 5 | BMC Evolutionary Biology

Figure 5

From: Collective properties of evolving molecular quasispecies

Figure 5

Search and fixation time (in number of generations) as a function of μ. (a) Curves corresponding to average values of the search time g A when the target structure shows up for the first time in the population (dotted curve) and the total time g F of search plus fixation (solid curve). Most of the transient corresponds to searching time except for values of μ close to the threshold, where the limiting step is fixation. (b) Fixation time for μ = 0.002. After appearance (g A ), it takes few generations to attain stationary values ( ρ ¯ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacuWFbpGCgaqeaaaa@2E8B@ = 0.965 ± 0.008). (c) Fixation time for μ = 0.05 ( ρ ¯ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacuWFbpGCgaqeaaaa@2E8B@ = 0.039 ± 0.020, shown as dashed and dotted horizontal lines). The probability to lose the target structure after its first appearance is high, fixation becomes difficult and, even if the asymptotic regime is reached on average, population fluctuations can lead to the occasional disappearance of the target structure. This is quantified by the very large fluctuations displayed by ρ, here shown as error bars. Simulations have been made for the hairpin structure, N = 602, and averages of 200 (a) and 25 (b, c) realizations have been performed.

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