(m ℓ ) a ℓ + 1 x m − ℓ, we obtain Setting m = 1, the expected coalescence time is Using the density in Equation 1, we can investigate how the initial divergence time and the severity of bottlenecks influence the distribution of coalescence times.
An especially promising approach is approximate Bayesian computation (ABC) which has been used to infer the timing, duration and severity of bottlenecks and to reconstruct prebottleneck ancestral population sizes from present-day data (Hoffman et al. 2011; Fontaine and Snirc 2012).
For the combination of population size and severity of bottleneck we used in our simulations, we found that deleterious mutants were removed from the population most of the time before they could reach appreciable frequencies and lead to compensatory mutations.
For instance, we found limited effect on the posterior distributions for the number of founders (N1 and N2), the severity of bottleneck (K1 and K2) and the split times (T1 and T2), whereas some effects could be noted on the three current effective size parameters (Ne1, Ne2 and Ne3).
In each workshop, after participants had identified the main bottlenecks to each tracer intervention for each health system building block, they came to consensus and graded the severity of the bottlenecks within each health system building block.
For a fixed value of Θ and a fixed severity of the bottlenecks, hardening also becomes more likely the weaker the strength of positive selection and the shorter the recurrence time between bottlenecks, as predicted.
Thus, Figure 2C shows that decreasing the severity of the bottleneck by increasing the bottleneck population size reduces the probability that the lineages coalesce during the most recent bottleneck.
We note, however, that K is inversely related to the severity of the bottleneck and that small values correspond to severe bottlenecks and large values to less severe bottlenecks.
The bottleneck establishment time increases only logarithmically with the severity of the bottleneck and scales inversely with the selection coefficient of the adaptive mutation.
The severity of the bottleneck (k), defined as the ratio of the population size during the bottleneck (Nb) to the duration of the bottleneck (d), was set at 1.2, since in maize it has been estimated by several groups to range from 2.0 [22] to 4.5 [17].
This is because levels of genetic drift are inversely proportional to population size, causing rapid changes in allele frequencies in small populations, and the magnitude of these changes between two time points indicates the severity of the bottleneck [29].
