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In order to compare both bottleneck models, prior knowledge of the bottleneck timing is crucial to distinguish models that do and do not implement ancient gene flow.
We then used the estimated bottleneck timing as a prior estimate in the open population-bottleneck model to infer the degree of historical gene flow that best fits the data.
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The posterior probability distribution for the timing of the bottleneck, fNe after and before the bottleneck and the estimated mutation rate of the closed population-bottleneck model can be seen in Table 2.
The cause and timing of this bottleneck remain unidentified.
Unfortunately, the low variability of T. pennelli cyt b prevented clear timing of the bottleneck, since after fixing the analysis for various values of the time parameter, we obtained very similar likelihood scores.
Noticeably, the timing of the transmission bottleneck is the same, and evidence for a bottleneck is readily apparent under both models.
With a bottleneck size >1, the time of coalescence of the two sampled lineages may occur in previous hosts, and the expected time of coalescence depends on timing of bottlenecks in the bacterial population.
To check whether the observed statistics were compatible with purely demographic events (i.e. bottlenecks in the case of positive tests), all significant mutation-drift equilibrium statistics were re-computed on simulated data sets having the same descriptive statistics as the observed data and having undergone bottlenecks of varying size, duration, and timing.
However, if there is some unexpected bottleneck, unrecognised and hence unaccounted for, the timing might be a few nanoseconds amiss.
Although the reliability of various bottleneck tests to detect the occurrence and timing of genetic bottlenecks has been questioned, particularly the M-ratio test (Peery et al. 2012), we used multiple approaches and found concordant results across these approaches.
We then use a Bayesian approach, informed by available knowledge of the warbler's demographic history, to estimate ancestral population size and determine the timing and severity of the bottleneck.
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