coefficients of relationship – cousin marriage – nuclear family members

so, here are the coefficients of relationship/relatedness (if i’ve done the maths right) for all the nuclear family members in each type of cousin marriage from the point-of-view of a guy — MBD (mother’s brother’s daughter) marriage, MZD (mother’s sister’s daughter) marriage, FBD (father’s brother’s daughter) marriage, and FZD (father’s sister’s daughter) marriage. (here’s a key to the terms so you can keep track of all the players).

notice that the various nuclear family members (probably) share the most dna (i.e. alleles) in MZD marriage, and they share the least in FBD and FZD marriage. (well, they share the least when there’s no inbreeding, but you know what i mean.)

now, here’s what each of the marriage systems looks like. first, MBD:

MZD:

FBD:

FZD:

the calculations are based on the fact that there is differential x- and y-chromosome inheritance from fathers and mothers to sons and daughters. this seems to matter in an inclusive fitness sort-of way between grandmothers and their grandchildren, so why not between all the other members of the family?

throw inbreeding into the mix, and you wind up with the members of some families being more related to one another than members of other families depending on the inbreeding (see chart at top).

here’s a couple of examples of how i did the math. please, tell me if you think my logic is wrong (very possible) and/or my calculations are wrong (very probable!).

first of all, the percentages of autosomal, x- and y-chromosomal dna that men and women have (based on the vega genome browser) are:

Female genome
6068 Mbp
Autosomal DNA: 5758 Mbp (≈94.89%)
X: 155 Mbp (≈2.55%), XX: 310Mb (≈5.11%)

Male genome
5972 Mbp
Autosomal DNA: 5758 Mbp (≈96.42%)
X: 155 Mbp (≈2.60%), Y: 59 Mbp (≈0.99%), XY: 214 Mbp (≈3.58%)

and here, the calculations for the genetic relatedness between father and son (F-s) when there is no inbreeding and in the four different types of cousin marriage:

F-s (no inbreeding)
**parents share no dna
1/2 autosome + y-chromosome = (96.42% x .5) + 0.99% = 0.4920

F-s (MBD marriage)
**a man and his MBD share 1/8 of their autosomal dna + 1/4 x-chromosomal dna
1/2 autosome + 1/16 autosome + 1/8 x-chromosome + y-chromosome = (96.42% x .5) + (96.42% x 0.0625) + (2.60% x 0.125) + 0.99% = 0.5555

F-s (MZD marriage)
**a man and his MZD share 1/8 of their autosomal dna + 1/4 x-chromosomal dna + 1/8 x-chromosomal dna
1/2 autosome + 1/16 autosome + 1/8 x-chromosome + 1/16 x-chromosome + y-chromosome = (96.42% x .5) + (96.42% x 0.0625) + (2.60% x 0.125) + (2.60% x 0.0625) + 0.99% = 0.5571

F-s (FBD marriage)
**a man and his FBD share 1/8 of their autosomal dna
1/2 autosome + 1/16 autosome + y-chromosome = (96.42% x .5) + (96.42% x 0.0625) + 0.99% = 0.5523

F-s (FZD marriage)
**a man and his FZD share 1/8 of their autosomal dna
1/2 autosome + 1/16 autosome + y-chromosome = (96.42% x .5) + (96.42% x 0.0625) + 0.99% = 0.5523

rinse and repeat for all the other characters.

thnx again to the reluctant apostate for his gallant help! (^_^)

p.s. – of course, there are other family members a guy could marry|mate with — niece, aunt, sister, mother(!), second-cousin, double first-cousin (not uncommon in the arab world), etc. i’ll be gettin’ to those at a later date.

previously: fbd marriage – genetic relatedness amongst nuclear family members and new and improved coefficients of inbreeding and new and improved coefficients of relationship

update 06/08: chart updated ’cause i found a couple of errors in my math (see, i TOLD you!) — with the women (e.g. d-F). should be fixed now. (*hbdchick crosses fingers*)

(note: comments do not require an email. but, quite possibly, a pocket protector.)

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s