کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8877423 1624130 2018 6 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The coalescent of a sample from a binary branching process
موضوعات مرتبط
علوم زیستی و بیوفناوری علوم کشاورزی و بیولوژیک علوم کشاورزی و بیولوژیک (عمومی)
پیش نمایش صفحه اول مقاله
The coalescent of a sample from a binary branching process
چکیده انگلیسی
At time 0, start a time-continuous binary branching process, where particles give birth to a single particle independently (at a possibly time-dependent rate) and die independently (at a possibly time-dependent and age-dependent rate). A particular case is the classical birth-death process. Stop this process at time T>0. It is known that the tree spanned by the N tips alive at time T of the tree thus obtained (called a reduced tree or coalescent tree) is a coalescent point process (CPP), which basically means that the depths of interior nodes are independent and identically distributed (iid). Now select each of the N tips independently with probability y (Bernoulli sample). It is known that the tree generated by the selected tips, which we will call the Bernoulli sampled CPP, is again a CPP. Now instead, select exactly k tips uniformly at random among the N tips (a k-sample). We show that the tree generated by the selected tips is a mixture of Bernoulli sampled CPPs with the same parent CPP, over some explicit distribution of the sampling probability y. An immediate consequence is that the genealogy of a k-sample can be obtained by the realization of k random variables, first the random sampling probability Y and then the k−1 node depths which are iid conditional on Y=y.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Theoretical Population Biology - Volume 122, July 2018, Pages 30-35
نویسندگان
,