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2016 ; 202
(4
): 1549-61
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The Site Frequency Spectrum for General Coalescents
#MMPMID26883445
Spence JP
; Kamm JA
; Song YS
Genetics
2016[Apr]; 202
(4
): 1549-61
PMID26883445
show ga
General genealogical processes such as ?- and ?-coalescents, which respectively
model multiple and simultaneous mergers, have important applications in studying
marine species, strong positive selection, recurrent selective sweeps, strong
bottlenecks, large sample sizes, and so on. Recently, there has been significant
progress in developing useful inference tools for such general models. In
particular, inference methods based on the site frequency spectrum (SFS) have
received noticeable attention. Here, we derive a new formula for the expected SFS
for general ?- and ?-coalescents, which leads to an efficient algorithm. For
time-homogeneous coalescents, the runtime of our algorithm for computing the
expected SFS is O(n2) where n is the sample size. This is a factor of[Formula:
see text]faster than the state-of-the-art method. Furthermore, in contrast to
existing methods, our method generalizes to time-inhomogeneous ?- and
?-coalescents with measures that factorize as[Formula: see text] and [Formula:
see text]respectively, where ? denotes a strictly positive function of time. The
runtime of our algorithm in this setting is[Formula: see text]We also obtain
general theoretical results for the identifiability of the ? measure when ? is a
constant function, as well as for the identifiability of the function ? under a
fixed ? measure.
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