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SUMMARY:Quantifying convergence of the Kingman coalescent via the ancestra
l process per generation
DTSTART;VALUE=DATE-TIME:20180709T095900Z
DTEND;VALUE=DATE-TIME:20180709T100000Z
DTSTAMP;VALUE=DATE-TIME:20241102T174054Z
UID:indico-contribution-501@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Paul Slade ()\nError threshold being the forefront o
f the issue for computationally-intensive methodologies and statistical mo
dels based on Kingmanâ€™s coalescent\, six main points arise: (i) discrepa
ncy between the exact and linearized non-coalescence probability\; (ii) va
lidity of the linearized coalescence probability\; (iii) conditional proba
bilities of single-pair and multi-coalescences given at least one coalesce
nce\; (iv) parity of reduced ancestral processes that suppress multi-coale
scences\, when compared to the exact ancestral process\; (v) genealogical
topology\; and (vi) subsequent inter-arrival times. Regions of adherence
and detraction from the Wright-Fisher ancestral process were identified\,
in terms of transition probabilities and expected inter-arrival times\, du
e to the linearization of Kingmanâ€™s coalescent that neglects multi-coale
scence events. Empirically\, expected genealogical parity of the single-p
air restricted Wright-Fisher haploid model exceeds 99% where $n\\leq \\fra
c{1}{2} \\sqrt[3] N$\; similarly\, per expected interval where $n\\le {1\\
over 2} \\sqrt{N\\over 6}$. Quantitative parametric analysis on the varie
ties of multi-coalescence events in restricted Wright-Fisher models\, rath
er than stochastic realization\, avoids elaboration of the genealogical sa
mple space under multi-coalescence. Mutational activity\, such as site f
requency spectra\, will not be accurately measured with the Kingman coales
cent when sample sizes exceed these criteria.\n\nhttps://conferences.maths
.unsw.edu.au/event/2/contributions/501/
LOCATION:University of Sydney Holme Building/--The Refectory
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/501/
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