# the apple of his eye

update 03/26: corrections made thnx to the generous assistance of the reluctant apostate (thnx, r.a.!). corrections in bold.

note that throughout this post, “son” and “daughter” refers only to non-twin, full siblings.
__________

fathers are slightly more similar genetically to their daughters than they are to their sons … if my calculations are (*ahem*) correct.

ken weiss, professor of anthropology and genetics at penn state, has pointed out that:

“[S]ame-sex sibling sets are closer [in terms of genetic proximity] than brother and sister sets….

“Weiss offered a lesson in basic biology: Get a piece of paper and a pen. Draw a circle for the mother and a square for the father. Populate the circle with ‘XX’ for the female sex chromosome and the square with ‘XY’ for the male chromosome. Draw two more circles under the symbols for the parents to represent two sisters.

“‘The two daughters below them are going to inherit an X from their mother, one or the other. Each one gets an independent choice,’ said Weiss. ‘But if they’re daughters, they have to be XX, which means they must both inherit the same X from their father, since he only has one to give them. Everything else is scrambled equally between the two sisters from the two parents. They have one X that they share, and one X that they may or may not share, depending on the luck of the draw from the mother.’

“Now, if you were to draw two squares for brothers under the parents, you would pull one or the other X from the mother and the Y from the father, because to be a son you must be XY and the Y can only come from Dad.

“Humans have 46 chromosomes, inheriting 22 non-sex chromosomes, and one sex chromosome, from each parent. What they inherit from the other chromosomes is similar regardless of sex, which overall makes the child 50 percent related to each other and to each parent. In this sense, Weiss said, ‘Two brothers are as equally close to each other as two sisters. A brother and a sister are not as closely related as two brothers or two sisters. They’re a bit more distantly related.’ This is because one will have an X and the other a Y from their father, whereas two brothers must share the same Y, and two sisters the same X, from him.'”

this is more of the differential x-chromosome inheritance (plus differential y-chromosome inheritance) issue that fox, et. al., discussed in their study of the grandmother effect: different grandmothers (paternal vs. maternal) have different levels of relatedness to their various grandchildren dependent upon how their x-chromosomes are inherited by each type of grandchild.

only weiss is talking about members of the nuclear family: ma, pa, and the kids. he’s saying that brothers are slightly more related to each other, and sisters are slightly more related to each other, than either type of sibling is to the other type — because brothers inherit (virtually) the same y-chromosome from their father (which the sisters do not) AND sisters inherit (virtually) the same unrecombined x-chromosome from their father (which the brothers do not).

fox, et. al., calculated how related each type of grandmother is to each type of grandchild.

here are my calculations for how related the various members of a nuclear family are (assuming there’s no inbreeding). fox, et. al., based their calculations on the number of genes on the x- and y-chromosomes. i’ve decided to work the numbers according to total base-pairs ’cause, hey, junk dna ain’t all junk.

so, here we go…

for males, the autosomes represent 95.5% of their dna material; the x-chromosome, 2.5% of their dna material; and the y-chromosome, 2% of their dna material.

for females, the autosomes represent 95% of their dna material; the two x-chromosomes, 5% of their dna material.

now, sons inherit half their autosomal dna from their father and half from their mother, plus a (virtually) unchanged y-chromosome from their father and a recombined x-chromosome from their mother (triangles=males; circles=females):

so, the genetic relatedness between a father and son (from both the father and son’s points-of-view) is:
(95.5% x 0.5) + 2% = 49.75%

and the genetic relatedness between a mother and son (from the mother’s pov) is:
(95% x 0.5) + (5% x 0.5) = 50%

the genetic relatedness between a mother and son from the son’s pov is:
(95.5% x 0.5) + (5% x 0.5) = 50.25%

daughters inherit half their autosomal dna from their father and half from their mother, plus a (virtually) unchanged x-chromosome from their father and a recombined x-chromosome from their mother:

so, the genetic relatedness between a father and a daughter (from the father’s pov) is:
(95.5% x 0.5) + 2.5% = 50.25%

from the daughter’s pov it is:
(95% x 0.5) + 2.5% = 50%

and the genetic relatedness between a mother and a daughter (from both the mother and daughter’s pov) is:
(95% x 0.5) + (5% x 0.5) = 50%

as weiss pointed out, brothers share (virtually) the same y-chromosome that they inherited from their father, while sisters share (virtually) the same x-chromosome that they inherited from their father. brothers and sisters do not share y-chromosomes or paternal x-chromosomes.

so, the genetic relatedness between full, non-twin brothers can be up to is**:
(95.5% x 0.5) + (2.5% x 0.5) + 2% = 51%

and the genetic relatedness between full, non-twin sisters can be up to is:
(95% x 0.5) + (2.5% x 0.5) + 2.5% = 51.25%

and between brother and sister (from the brother’s pov) can be up to it is:
(95.5% x 0.5) + (2.5% x 0.5) = 49%
(95.5% x 0.5) x 0.5 + (95.5% x 0.5) x 0.5 + (2.5% x 0.5) = 49%

and between brother and sister (from the sister’s pov) it is:
(95% x 0.5) x 0.5 + (95% x 0.5) x 0.5 + (2.5% x 0.5) = 48.75%

so, fathers are genetically closer to their daughters than to their sons, and genetically closer (from the father’s pov) to daughters than mothers are to their daughters. mothers are equally close genetically (from the mother’s pov) to all their children, but are genetically closer to sons than fathers are to their sons.

full (not including twin) sisters can be the most closely related genetically of all nuclear family members (@51.25%), while full (not including twin) sisters and brothers can be the least related (@49% 48.75% [sister’s pov]).

do, please, check my math! (^_^)

**the relationships between siblings are probabilities, not certainties.

(note: comments do not require an email.)

1. Good math on the parent-sibling relationships. However, it is worth noting that there’s an asymmetry between parents and opposite-sexed offspring. Regardless of the sex of the offspring, a mother gives 50% of her genetic material, and as you pointed out a father gives 49.75% of his genetic material to a son and 50.25% to a daughter. However, the percentages aren’t necessarily the same for the offspring.

Like the mother’s unconditional giving of 50% of her genetic material, a daughter receives 50% of her genetic material from each parent. And like the father’s giving ratios, a son receives 50.25% of his genetic material from his mother and 49.75% from his father. While there seems to be symmetry here (and in a way there is), the percentage a parent gives is not necessarily the percentage that is received by the offspring.

Here are some diagrams illustrating this (giving percent on the left, receiving on the right):

Same-sex parent-offspring pairs

50% M → d 50%
49.75% F → s 49.75%

Opposite-sex parent-offspring pairs

50% M → s 50.25%
50.25% F → d 50%

So when you’re talking about the relatedness of these pairs above, you’re really talking about the percent of genetic material given by the parent, not the percentage received by the offspring, which may or may not be the same percentage.

On the sibling relationships, there are two issues. The first is the asymmetry of the brother-sister pairing. Assuming even mixing, the siblings would share half of each of their parents’ autosomal material and half of their mother’s X chromosome material. For sons, this is:
(95.5% × .5) × .5 + (95.5% × .5) × .5 + (2.5% × .5) = 49%

For daughters:
(95% × .5) × .5 + (95% × .5) × .5 + (2.5% × .5) = 48.75%

Like the earlier not with the parent-offspring relationships, this is ultimately rooted in the fact that males have slightly smaller genomes on account of having a Y chromosome where a female has a second X chromosome.

The second is the use of “up to” which suggests a maximum, when it is actually a (soft) minimum. In the case of identical and half-identical twins, the percentages are higher. In identical twins (which are always same-sexed) the percentage of sharing is 100%. For half-identical twins (those that share all the material received from their mother), we have:
sister-sister:
(95% × .5) + (95% × .5) × .5 + 5% = 76.25%

brother-brother:
(95.5% × .5) + (95.5% × .5) × .5 + 2.5% + 2% = 76.125%

sister-brother (sister’s POV):
(95% × .5) + (95% × .5) × .5 + (2.5% × .5) = 72.5%

sister-brother (brother’s POV)
(95.5% × .5) + (95.5% × .5) × .5 + (2.5% × .5) = 72.875%

2. For sh*ts and giggles, I’m going to throw in the half-sibling percentages.
Same mother

sister-sister
25%

brother-brother
(95.5% × .5) × .5 + (2.5 × .5) × .5 = 24.5%

sister-brother (sister’s POV)
25%

sister-brother (brother’s POV)
24.5%

Same father

sister-sister
(95% × .5) × .5 + 2.5% = 26.25%

brother-brother
(95.5% × .5) × .5 + 2% = 25.875%

sister-brother (sister’s POV)
(95% × .5) × .5 = 23.75%

sister-brother (brother’s POV)
(95.5% × .5) × .5 = 23.875%

3. Gah, threw in an extra .5 in the same mother brother-brother relationship. Should be:
(95.5% × .5) × .5 + (2.5 × .5) = 25.125%

sister-brother (brother’s POV) is also 25.125% by the same logic.

4. you ROCK r. apostate! i have to look at these tomorrow, tho, ’cause it’s too late (or is it too early?) now.

THANK YOU! (^_^)

5. @r. apostate – “However, it is worth noting that there’s an asymmetry between parents and opposite-sexed offspring…. However, the percentages aren’t necessarily the same for the offspring.”

yes. that’s what i thought. you mean the calculation is different going in different directions, right? for e.g. mother –> son versus son –> mother. (yes. looking back at your comment i see that you’ve explained that.)

so if one were trying to figure out (heh) which 8 cousins to save (yes, i know it doesn’t really work like that!) — male vs. female and maternal vs. paternal, for instance — you’d wanna to do the calculation from ego –> cousins, not the other way around. amiright?

you’d wanna know how much genetic material you (might probably) share with them, not how much they (might probably) share with you.

6. @r. apostate – “The second is the use of “up to” which suggests a maximum, when it is actually a (soft) minimum. In the case of identical and half-identical twins, the percentages are higher.”

yes, indeedie! but i wasn’t bothering with twins just yet. i shoulda specified that, though.

7. @r. apostate – “Assuming even mixing, the siblings would share half of each of their parents’ autosomal material and half of their mother’s X chromosome material. For sons, this is:
(95.5% × .5) × .5 + (95.5% × .5) × .5 + (2.5% × .5) = 49%

“For daughters:
(95% × .5) × .5 + (95% × .5) × .5 + (2.5% × .5) = 48.75%”

what about the y-chromosome inheritance by the sons and the daughters inheritance of their father’s x-chromosome? two brothers will share a full y-chromsome (almost) with each other, and two sisters will share a full paternal x-chromosome (almost). That needs to be factored in somehow. ¿no?

muchas gracias, señor!

8. “so if one were trying to figure out (heh) which 8 cousins to save (yes, i know it doesn’t really work like that!) — male vs. female and maternal vs. paternal, for instance — you’d wanna to do the calculation from ego –> cousins, not the other way around. amiright?”

Yes, if you’re going to behave in a Haldane-like manner, you should calculate from yourself. On the other hand, if you suspect your cousins of behaving in such a manner, it might be useful to know what the relationship looks like from their point-of-view. Now, you only have to worry about point-of-view for your male cousins, since the percentage of shared material looks the same for cousins of the same sex.

“what about the y-chromosome inheritance by the sons and the daughters inheritance of their father’s x-chromosome? two brothers will share a full y-chromsome (almost) with each other, and two sisters will share a full paternal x-chromosome (almost). That needs to be factored in somehow. ¿no?”

Well, sure, for a pair of brothers or a pair of sisters. Your math in the post was completely correct for those two scenarios. I can see that I worded that part of the comment poorly, but I was referring to the PoV differences between a brother and a sister with regard to their shared material percentage. In the case of siblings of the same sex, the percentages are identical, so there are no PoV effects.

9. @r. apostate – “I was referring to the PoV differences between a brother and a sister with regard to their shared material percentage.”

gotcha! thnx again! (^_^)

10. “eh, no, that’s not right. for example, because of differential x-chromsome inheritance patterns, i (probably) share more dna with my female patrilateral parallel cousins than with my female patrilateral cross cousins.”

Well, you’d certainly need to worry about which cousin it was, but by PoV effects, I was referring to whether you’d have to calculate separately the percentage shared material for the cousin. For a male cousin, you’d have to calculate the percentage separately, as his genome would be a different size than your own and thus the shared material (which is the same total amount for both individuals) is a different percentage of his genome.

But certainly, not all cousins are created equal and you’d have to do separate calculations for different types. However, doing a bit of reflection on the specific case you brought up, I do believe that the percentages are the same for both patrilateral and matrilateral cross cousins. The logic is simple:

You and your patrilateral cross cousin (female) have the same percentage shared genome. You are your patrilateral cross cousin’s matrilateral cross cousin, so given that the relation is symmetrical, you should also expect the same percentage your the matrilateral cross cousin.

There’s also just doing the math to figure that out, but I’m feeling a bit too lazy to do that now, since, as you point out, you’d have to do separate calculations for each of the different types of cousins (and that would change depending upon whether “ego” is male or female). That’s pretty much why I haven’t done those calculations.

11. @r. apostate – “I do believe that the percentages are the same for both patrilateral and matrilateral cross cousins….”

well, i dunno for sure either ’cause i haven’t done the calculations (yet), but i don’t think they can be since my female matrilateral cross cousins inherit an (almost) unrecombined X from their father (my maternal uncle), whereas my matrilateral cross cousins just get a recombined X from their mother (my paternal aunt).

@r. apostate – “There’s also just doing the math to figure that out, but I’m feeling a bit too lazy to do that now….”

please don’t do any calculations on a saturday evening! not on my account anyway!

i’m gonna give these aunt/uncle/cousin calculations a shot during the week and, if it entertains you, perhaps you might point out all my errors after i post them. (^_^)

12. “well, i dunno for sure either ’cause i haven’t done the calculations (yet), but i don’t think they can be since my female matrilateral cross cousins inherit an (almost) unrecombined X from their father (my maternal uncle), whereas my [p]atrilateral cross cousins just get a recombined X from their mother (my paternal aunt)”

Sure, but even there, you can see the symmetry, right? [For simplicity, all cousins mentioned from here on are female.] Your female matrilateral cross cousin inherits an unrecombined X from her father, just as you do from your father, and your patrilateral cross cousin inherits a recombined X from her mother, just as you do from your mother. How this works is that your unrecombined X is related to the recombined X that your patrilateral cross cousin has and your recombined X is related to the unrecombined X that your matrilateral cross cousin.

Obviously, this logic doesn’t work for parallel cousins, since you are your patrilateral parallel cousin’s patrilateral parallel cousin and your matrilateral parallel cousin’s matrilateral parallel cousin, so while you have an excuse not to double your calculations for cross cousins (at least for those of the same sex), you have to do separate calculations for matrilateral and patrilateral parallel cousins.

13. @r.a. – “Sure, but even there, you can see the symmetry, right? [For simplicity, all cousins mentioned from here on are female.]”

heh. i rapidly feel like i’m reaching an “i am my own grandpa” moment here. (~_^)

yes! i am my matrilineal cross cousin’s patrilineal cross cousin, so what you said above is absolutely right.

i have a bad habit of thinking from the pov of a male EGO ’cause that’s who’s on my little charts — and from thinking about father’s brother’s daughter marriage too much. but from hbdchick’s pov, yes, my female cross cousins and i should all share the same amount of dna.

now i need some coffee if i’m going to contemplate this any further….

14. Since it’s now Sunday morning instead of Saturday evening, I’ve done some initial calculations on the cousins. The logic behind my calculations is that in terms of autosomal material, all cousins share 12.5%, so I can set that aside and plug it into the 95% or 95.5% term as it comes up. The variables that differentiate the cousins are the sex chromosomes. The Y’s easy to deal with, the X is quite a bit more messy. Obviously for the sake of definite calculations, I’m assuming that all cross-over events are 50-50 and that the law of large numbers kicks in (two assumptions that I suspect don’t really play out in nature).

Displaying the data in this comment is a bit tricky (I don’t trust that WordPress would handle table HTML well in a comment), but here’s how I’ll lay the data out:

♀♂
X ll
♀♂

That is, the first categorization is matrilateral or patrilateral, the second is cross of parallel and the third is male or female cousin in the order above, so the list will look like:

♀X♀ ♀X♂ ♀ll♀ ♀ll♂ ♂X♀ ♂X♂ ♂ll♀ ♂ll♂

Sorry if this is confusing. In English:

matrilateral cross female, matrilateral cross male,…, patrilateral parallel male

So here’s what I got for the sharing of the chromosomes. X sharing will be in a proportion and Y sharing will be demarcated as a Y, lack of sex chromosome sharing will be a ∅.

Male ego:
.25 ∅ .375 .375 ∅ ∅ ∅ Y

Female ego:
.25 ∅ .375 .375 .25 .25 .5 ∅

Most of these are pretty straightforward. A male gets his Y from his father and that is only shared through the male line, only his patrilateral male parallel cousin, and since his X comes from his mother, there’s no sharing of that at all on his father’s side. A female gets one of her Xs from her father, which he in turn gets from his mother, meaning that there will be 50% overlap with his siblings. His sister’s offspring will then have half that overlap and his brother will only give his X to his daughter.

Obviously, the tricky looking area is the matrilateral cousins. The mother’s brother only shares half an X with his sister, which shares 25% of the material in the Xs of his sister’s offspring and he passes that 25% to a daughter but not to a son. The 37.5% for the parallel cousins stands out, though. That results from the fact that sisters share 100% of their father’s X chromosome. So, 50% of ego’s X comes from the the maternal grandfather’s X as does 50% of ego’s matrilateral parallel cousins, giving 25% overlap, the additional 12.5% comes from the overlap of female line Xs.

Taking those values and plugging them in

Male ego:
.125 .119375 .12875 .12875 .119375 .119375 .119375 .139375

Female ego:
.125 .11875 .128125 .128125 .125 .125 .13125 .11875

Now, obviously, these proportions don’t deserve this number of significant figures, especially considering that the “2.5%” of a male genome that an X chromosome makes up is a larger “2.5%” than that for a female genome, simply because a female genome is larger and the X chromosome doesn’t change size to accommodate its owner.

15. @r.a. – well, ur just a glutton for punishment, eh?! i’m just gonna outsource all my maths to you from now on. (~_^)

ah … nothing like a little math to fry my brain on a sunday morning.

but, i’m happy to say that i got the same results as you did (yay!) — for male ego, anyway — i haven’t done female ego yet.

i did the calcs the long way ’round, though, including the autosomes which, obviously, don’t make a difference since they’re the same for all cousins. anyway, so my calcs looked like this:

e.g. EGO –> MBD (mother’s brother’s daughter | matrilateral cross female)
(95.5% x 0.125) + (2.5% x 0.25) = 12.5625%

etc., etc.

so, for male ego i got:

12.5625%, 11.9375%, 12.875%, 12.875%, 11.9375%, 11.9375%, 11.9375%, 13.9375%

(^_^)

16. @r.a. – “Great…I can always depend on myself to make at least one silly calculation error.”

well i usually make a whole SLEW of ’em! *sigh*

17. @r.a. – “I’m assuming that all cross-over events are 50-50 and that the law of large numbers kicks in (two assumptions that I suspect don’t really play out in nature).”

yeah, that first one there is definitely a big assumption that i’m pretty sure doesn’t happen … but the law of large numbers? no? doesn’t “play out in nature”? say it ain’t so! -??-

18. You know what? I was looking around to try to get better numbers for genome size, and I found them on the Human Genome Wikipedia article (naturally). It turns out that the Y chromosome makes up a smaller portion of the genome. It’s about 2% of the haploid genome, which makes it 1% of the full diploid genome. From the table, here’s what I make to be the sizes and percentages:

Female genome
6044 Mbp
Autosomal DNA: 5734 Mbp (≈94.87%)
X: 155 Mbp (≈2.56%), XX: 310Mb (≈5.13%)

Male genome
5947 Mbp
Autosomal DNA: 5734 Mbp (≈96.42%)
X: 155 Mbp (≈2.61%), Y: 58 Mbp (≈0.96%), XY: 213 Mbp (≈3.58%)

This of course, changes all the calculations. I decided to just draft up a spreadsheet and run them through that way, so here’s the output:

ego ♂ ♀
♀X♀ 12.7% 12.5%
♀X♂ 12.1% 11.9%
♀ll♀ 13.1% 12.8%
♀ll♂ 13.1% 12.8%
♂X♀ 12.1% 12.5%
♂X♂ 12.1% 12.5%
♂ll♀ 12.1% 13.1%
♂ll♂ 13.0% 11.9%
sister 49.6% 51.3%
brother 50.6% 48.7%
♀½s 25.5% 25.0%
♀½b 25.5% 25.0%
♂½s 24.1% 26.3%
♂½b 25.1% 23.7%
½is 75.0% 75.0%
½ib 76.0% 73.7%

All of these are the shared genome percentage from ego’s PoV. Hopefully columns line up after I post this. Obviously, there’s no work shown, so whatever mistakes I may have made will remain mysterious for now.

19. “yeah, that first one there is definitely a big assumption that i’m pretty sure doesn’t happen … but the law of large numbers? no? doesn’t “play out in nature”? say it ain’t so! -??-”

Well, I was thinking of how large the blocks of chromosome were and how much that would affect the multigenerational outlook. So, not only do you have to have the 50-50 split for one generation, but subsequent generations would have to get even mixings to maintain 25%, 12.5% and so on without major stochastic effects and that would only happen if there were a large number of little cross-over blocks. Not sure what the typical X chromosome recombination scenario looks like, but I’m guessing that the number of Chiasmata are too small for the law of large numbers to kick in. Of course, it’s probably also two small to reliably get a 50-50 mix of chromosomes, so…basically everything here should probably be taken as being a theoretical average.

20. @r.a. – “It turns out that the Y chromosome makes up a smaller portion of the genome.”

oh noes! back to the drawing board….

(thnx for finding that. goin’ over there right now to have a look at it! (^_^) )

21. @r.a. – “I’m guessing that the number of Chiasmata are too small for the law of large numbers to kick in….”

i see, i see. and, afaiu (which ain’t much), the amount of recombination varies from person to person, just to make it all the more complicated|interesting.

@r.a. – “so…basically everything here should probably be taken as being a theoretical average.”

i can live with that. (~_^)

22. @a.r. – “I was looking around to try to get better numbers for genome size, and I found them on the Human Genome Wikipedia article (naturally).”

would it make you crazy to know that the numbers don’t add up on that page? (*hbdchick pulls her hair out*)

“total (XX)” is 3Mbp short. i think that’s the number on which you based your “female genome=6044 Mbp.”

the wikipedia page has total(XX)=3,022, but if that’s supposed to be the total of 1 thru 22+X, it’s not. i get 3,019.

-??-

i’m gonna double-check the numbers against the nlm (or, if you can suggest a more reliable source…?).

edit: or maybe i’m not gonna check the nlm — some of those pages haven’t been updated since ’07.

23. ok. going through the vega genome browser (which is where a lot of the numbers on wikipedia seem to have come from), i get the following (numbers rounded to the nearest Mbp):

1-22 = 2,879Mbp
X = 155Mbp
Y = 59Mbp

1=249
2=243
3=198
4=191
5=181
6=171
7=159
8=146
9=141
10=136
11=135
12=134
13=115
14=107
15=103
16=90
17=81
18=78
19=59
20=63
21=48
22=51

24. so, that just made a couple of minor changes:

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%)

25. chick,

mtDNA comes from mom usually. I think I’ve heard of exceptions though.

What I wonder: do mom’s chromosomes have an advantage in the epigenetic battle over which chromosomes get expressed? I suspect so.

26. @randall – “What I wonder: do mom’s chromosomes have an advantage in the epigenetic battle over which chromosomes get expressed? I suspect so.”

i dunno. all i know is that, in my case, it must be only my father’s genes expressing themselves, ’cause i’m – “just like your (my) father!” – or so my mother has always told me. (~_^)

seriously. i don’t know, but that would be real interesting to know! maybe someone else stopping by would be able to answer (intelligently)?

i’ll keep an out eye. if i ever see any info along those lines, i’ll let ya know!