Figure - PMC

Skip to main content

An official website of the United States government

Here's how you know

Here's how you know

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

View full-text article in PMC

. 2020 Oct 27;216(4):985–994. doi: 10.1534/genetics.120.303680

Search in PMC
Search in PubMed
View in NLM Catalog
Add to search

Copyright © 2020 by the Genetics Society of America

PMC Copyright notice

The variance of genetic relatedness between grandoffspring and grandparent, calculated from the possible segregation patterns of a single parental meiosis. In the figure, the positions of crossovers in a maternal meiosis (and the chromatids involved) are specified, but the segregation pattern in the resulting egg (and therefore offspring) is not. Averaging across the four segregation patterns, we find $E [I B D_{grand}] = (l_{1} + l_{2} + l_{3} + l_{4} + l_{5}) / 4 = 1 / 4$ , and, from Equation 1 in Veller et al. (2019b), ${\bar{r}}^{♀} = (l_{1} + l_{3} + l_{4}) (l_{2} + l_{5}) + (l_{2} + l_{4}) (l_{1} + l_{3} + l_{5})$ . Across the four possible segregation patterns, $E [I B D_{grand}] = 1 / 4$ and $\begin{matrix} Var (I B D_{grand}) = E [I B D_{grand}^{2}] - {(E [I B D_{grand}])}^{2} \\ = \frac{1}{4} [\frac{1}{4} {(l_{1} + l_{3} + l_{5})}^{2} + \frac{1}{4} {(l_{1} + l_{3} + l_{4})}^{2} + \frac{1}{4} {(l_{2} + l_{4})}^{2} + \frac{1}{4} {(l_{2} + l_{5})}^{2}] - \frac{1}{16} \\ = \frac{1}{16} - \frac{1}{8} [(l_{1} + l_{3} + l_{4}) (l_{2} + l_{5}) + (l_{2} + l_{4}) (l_{1} + l_{3} + l_{5})] = \frac{1}{8} (\frac{1}{2} - {\bar{r}}^{♀}), \end{matrix}$ which is Equation 2.