Define
Invite discussion and feedback, especially regarding questions at the end of this document.
Facilitate the discovery of mathematical tools, using this definition, that are useful to downstream empirical research.
The genealogies of a population reflect population events of the past. Lineages, at the organismal level, are lines of descent carrying genetic information through a population's genealogies. These lineages are a link between genetic evidence and population events of the past. In contrast to estimates of purely genetic quantities, estimates of quantities about lineages can have closer correspondence to non-genetic evidence, such as archaeological, geological, and cultural evidence.
We define
a past time horizon when all ancestors are members of separate non-admixed subpopulations, and
an observation time, such as the present.
Given a lineage, the
Stated more compactly, lineal admixture time is time since a lineage's first admixed fertilization. Admixed individuals are all individual whose parents are not from the same non-admixed subpopulations.
The
It is worth noting that non-zero admixture times do not remain constant if the observation time changes. It follows that the non-zero average admixture time of an individual is not fixed. It will increase if the observation time increases with age.
We consider an example of lineal admixture times with Mendel's
famous peas
In this example we will treat the non-admixed ancestral
subpopulations to be true-breeding pea plant varieties in 1860. Plants
Plant
In these lineages the first admixed individuals are
A related definition measures generation number rather than time.
Given a lineage, the
Because peas are annual, the lineal admixture times in years
coincide exactly with the lineal hybrid generation numbers. The first
and second hybrid generations are often referred to as
These definitions are inspired by the use of generation numbers to
infer admixture timing in the study of admixture in Greenland
We give a hypothetical example in Greenland at an observation time
of 1600 CE. We categorize the ancestors at a time horizon of 1000 CE
into separate non-interbreeding Inuit and European subpopulations. We
denote the fertilization and death of an individual with symbols
We imagine Erik as only having European ancestors and Aaju, Natar and Atuat only having Intuit ancestors. As of 1600 CE, the lineages are:
Kiviaq-Tagak-Erik
Kiviaq-Tagak-Aaju
Kiviaq-Mikak-Natar
Kiviaq-Mikak-Atuat
For the Tagak lineages, the first admixed fertilization is in 1530. In contrast, the Mikak lineages have a first admixed fertilization in 1570. Thus the lineal admixture times are equal parts 70 years and 30 years, for an average lineal admixture time of 50 years. The respective lineal hybrid generation numbers are 1 and 2 resulting in an average lineal hybrid generation number of 1.5.
Lineal admixture time has a number of advantages as a quantity for research.
Firstly, it is independent of any particular model of an admixture process. With enough genealogical information one could calculate lineal admixture times of a real group of individuals. There is one true set of lineal admixture times for a real population. But realistically, we can only hope to estimate those numbers based on evidence and models. But the definition exists independent of any particular model used for estimation.
Secondly, the interpretation of lineal admixture time does not require fluency in probability theory. Researchers with interests in empirical evidence and not mathematics can make use of estimates of lineal admixture times.
Thirdly, we conjecture that
The same population events that affect admixture also affect hybridization, introgression, and gene flow. We conjecture that statistical tools for estimating distributions of lineal admixture time will also be useful to these related topics in addition to admixture timing.
The Greenland example illustrates how average lineal admixture time is easily testable against non-genetic lines of evidence. If a genetic model estimates the average lineal admixture time of present day Greenlanders to be 500 years, we can consider historical and archaeological evidence to falsify that estimate.
This document presents a definition of
Is
Does
What are existing terms for this specific definition of admixture time?
Are the following terms:
lineage
genealogy
lineal admixture time
lineal hybrid generation number
potentially confusing in the way they are used in this document?