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The cell starts with two copies of every chromosome: one paternal and one maternal. After interphase but before the cell divides every chromosome is duplicated. At this point, the cell has *four* copies of every chromosome: two identical paternal copies and two identical maternal copies (these form the “X”-shaped structures that chromosomes are usually depicted as). After homologous recombination, the cell goes through the first meiotic division (meiosis I) producing two daughter cells. One daughter cell gets the recombined paternal copies and the other daughter cell gets the recombined maternal copies. Both daughter cells then go through the second meiotic division (meiosis II) resulting in four “grand-daughter” cells (gametes). Each grand-daughter cell gets one of the recombined copies from the original “grand-mother” cell: two of the grand-daughter cells each get one of the recombined paternal copies and the other two grand-daughter cells each get one of the recombined maternal copies. Since the DNA mass is split equally (and no more synthesis occurs) the amount of DNA is halved during each meiotic division. Since the mother cell undergoes meiotic division twice after chromosome duplication, each grand-daughter cell contains 1/4 of the DNA that was present in the mother cell right before it entered meiosis (a half of a half = a quarter). N.B.: the cells go from diploid to haploid during meiosis I. The mother cell is diploid. All of the daughter and grand-daughter cells are haploid. The “chromosome number” is not changed by duplication nor by meiosis II. This can be confusing, so ask your teacher to explain the difference between a chromosome and a “chromatid”. Before duplication, each chromosome exists as a single chromatid. After duplication, each chromosome exists as a pair of “sister” chromatids. The number of chromosomes stays the same, but the number of chromatids has doubled. Meiosis I is the separation of chromosomes (as chromatid pairs) into the daughter cells and meiosis II is the separation of chromatids into the grand-daughter cells. It might help to draw out this whole process, starting from a diploid cell in interphase with only one pair of (single-chromatid) chromosomes (one maternal and one paternal). p.s.: I think the question is a little bit misleading, since the total amount of DNA in each gamete is only *half* that present in the original (grand-mother) cell *during* interphase. You can only say that each gamete has a quarter of the DNA of the original cell if you’re starting from the amount of DNA *after* duplication, i.e. after interphase has finished and right before meiosis I. This is a weird way to think about ploidy, in my opinion!
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