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According to my textbook, when two human gametes fuse, there's $2^{23}$ different combinations of chromosomes, but I don't see how that is. The chromosomes are homologous, so they don't have any choice to make, and if they did have a choice to make, there'd be a different formula. Are there two oocytes perhaps, and each chromosome in the sperm can chose either one of the homologous chromosomes that exists in the respective oocytes, a choice available to each of the 23 chromosomes, thus yielding $2^{23}$ possibilities?

EDIT:

My textbook made the above claim as a sidenote to its explanation of meiosis. See my translated quotation under (bold made by me):

Therefore, four possible gametes can be formed (BR, Br, bR and br). If we take all 23 chromosome pairs into account, it will be almost 8.4 million ($2^{23}$) combination possibilities. And when two gametes are finally to fuse, the number of combination possibilities increase to almost 70 000 billion ($2^{23} \cdot 2^{23}$).

As you can see, my textbook says the fusion of gametes can happen with $2^{23}$ different combinations of chromosomes. Since I think I've read somewhere that the (pre?)fetus is triploid at some point, it makes sense to me that these combinations come from the fact that each chromosome from the sperm can pick a homolog from either of the two homologs available from the two oocytes. That's $2^{23}$ possibilities (assuming the sperm comes with only Xs).

My textbook is Naturfag Påbygging, by Aschehoug.

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  • $\begingroup$ The book says when gametes are formed, not fused, is when there are 2^23 combinations. Where are you getting this triploid idea? $\endgroup$
    – Bryan Krause
    Dec 12, 2023 at 13:46
  • $\begingroup$ @BryanKrause No, the book says there are $2^{23}$ combinations when a gamete are formed and then another $2^{23}$ possibilities when they are later fused. Also, I got the triploid idea from double-fertilization, so nevermind that, I didn't read it properly the first time. $\endgroup$
    – user110391
    Dec 12, 2023 at 20:43
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    $\begingroup$ I think it is difficult to judge the original text on the basis of a translation, but it seems to me to be, at the best ambiguous, and, at the worst, wrong. I think that this ambiguous explanation is widespread and a source of confusion that is not easily remedied by "homework". I think that the question is useful in focussing on this and the downvotes should be reversed. Considering the nonsense we have to put up with from drive-by members of other SE sites, we should consider this question from a genuine student of biology. I have edited the title to fit the situation better. $\endgroup$
    – David
    Dec 12, 2023 at 21:26

2 Answers 2

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The calculation is actually quite simple. Each gamete can contribute one of two sister chromatids for each chromosome, so that in humans (with 23 distinct chromosomes) the number of possible combinations in the progeny cell resulting from fusion of the male and female gametes is:

423 (aka approx. 64 trillion — actually approx 70 trillion)

The number 223 (aka approx. 8 million — hence the erroneous 64 trillion in the source cited below), much loved by various sources including the poster’s text book, is the number of possible combinations of sister chromatids for each individual male or female gamete before fusion.

This is explained with illustration in Biolibre texts in the section entitled “Independent Assortment and Random Fertilization”.

I have no idea why there is an obsession with the number of pre-fusion combinations when the interest of the reader is surely the number of possible outcomes. As a non-biologist the difficulty for me in understanding the explanations I have read is the way that the genetics and cell biology are dealt with together. I admit that the cell biology is important, but if I had to lecture on this topic I would do the genetics first, and then the cell biology.

This explanation is hinted at in the comment from @BryanKrause, but I think that the textbook is at fault, and the poster’s confusion is justified.

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    $\begingroup$ The 2^23 number is useful in describing the meiosis process of gamete formation, which occurs before any interaction with any other gamete is relevant. With crossover it's of course also wrong, but still a useful starting point. $\endgroup$
    – Bryan Krause
    Dec 13, 2023 at 18:08
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Shouldn't it be that there are 2^23 different types of gametes possible from a single individual with 23 chromosomes? The math behind it is as follows:

Case 1: Only one chromosome. Let's say, from the diploid precursor with 2 homologs of chromosome 1. Half of the gametes would be with the 1A homolog, the other half with the 1b homolog. So, 2^1 types of gametes.

Further cases: More chromosomes. Consider two chromosomes, 1 and 2, each with 2 homologs (1A, 1B and 2A, 2B). Because each chromosome assorts independent of every other, 2^2 (= 4) possible combinations are possible. 1A-2A, 1A-2B, 1B-2A, and 1B-2B.

Extending the math, this would amount to 2^23 combinations for 23 chromosomes, leading to these many (~8.3 million) gametes from a single human. Each of these haploid gametes from a male, would combine with a gamete from a female. In each successful fertilization event, the resulting cell would have 46 chromosomes, restoring the diploidy.

I think your textbooks arrives at the 2^23⋅2^23 (= 70,000 billion) by taking into account all the combinations. Since each of the 2^23 male gametes can combine with each of the 2^23 female gametes, the overall combinations come out to be just that. I don't know where you got that fetus is ever triploid (will be happy if you share the source). I still cannot relate this to two oocytes. I'm saying this because your textbook also doesn't mention anything about 2 oocytes (I'm assuming). It just states a combinatorial fact.

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  • $\begingroup$ This is not what I am wondering about, but it is related. See my edit. My textbook claimed what it did as side note to exactly this. $\endgroup$
    – user110391
    Dec 12, 2023 at 9:06
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    $\begingroup$ I think your textbooks arrives at the 2^23⋅2^23 (= 70,000 billion) by taking into account all the combinations. Since each of the 2^23 male gametes can combine with each of the 2^23 female gametes, the overall combinations come out to be just that. I don't know where you got that fetus is ever triploid (will be happy if you share the source). I still cannot relate this to two oocytes. I'm saying this because your textbook also doesn't mention anything about 2 oocytes (I'm assuming). It just states a combinatorial fact. $\endgroup$ Dec 12, 2023 at 13:56
  • $\begingroup$ Ah yes of course, that makes sense. It is the only interpretation that makes sense thus far, so I will accept it if you make that into your answer :) $\endgroup$
    – user110391
    Dec 12, 2023 at 20:44

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