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Imagine an isolated population in which each adult female has a distinct mitochondrial genome. In each generation, every adult female has two children (with a 50% chance of being male or female). After each generation, we will assume that all the adults die out, and all the children become adults.

After four generations, what is the expected percentage of mitochondria from the original population of females that will still exist in the population’s children? Express your answer as a decimal between 0 and 1, rounded to three decimal places.

Note: after one generation, there will be 100% of the mitochondria from the original population present in the population’s children since male children receive the mitochondria from their mothers (but do not pass them on to their own children.)

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closed as off-topic by Remi.b, anongoodnurse, canadianer, AMR, theforestecologist May 21 '17 at 5:26

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If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ Welcome to Biology.SE. Homework questions are off-topic on Biology unless you have shown your attempt at an answer. For more information see our homework policy. Also, the question has nothing to do with bioinformatics (unlike suggested by your tag). $\endgroup$ – Remi.b May 20 '17 at 23:03
  • $\begingroup$ I don't really get the question. Is it asking what fraction of the unique mitochondrial copies will remain after 3 generations. If it the case, it is impossible to answer without knowing the population size. I guess the question is weirdly formulated and it actually ask whether the allele frequency for this specific mitochondrial haplotype (that is 1 after the first reproductive event) will vary in the successive generations (and I suppose we assume, no mutation and no migration) but that sounds like a too simple and too unrelated to the special inheritance type of mitochondria $\endgroup$ – Remi.b May 20 '17 at 23:10
  • $\begingroup$ @Remi.b no, AFAICS the answer is independent of population size, and is equivalent to the asking "what is the probability that a female from the initial population has a daughter who has a daughter who has a daughter?" (which, aside from that realization, has nothing to do with bio at all). $\endgroup$ – hobbs May 21 '17 at 0:48
  • $\begingroup$ @adjan I removed my comment as it contained a math mistake. I tried to write an answer but realized the math are even a little more complex than I first thought (so I have deleted my wrong answer). I think the wording make the question more complex than it seems. What kind a course is it? Also, You are still suppose to show your effort at answering the question $\endgroup$ – Remi.b May 21 '17 at 3:54
  • $\begingroup$ @Remi.b I'm not the OP though $\endgroup$ – Adrian May 21 '17 at 4:20
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This is a question that is not as straightforward as it may seem.

One could make arguments, some better than others perhaps, for several different answers. The way it is worded, one could defend answers from 0.000 and 1.000 and many of the intermediate numbers as well.

After four generations, what is the expected percentage of mitochondria from the original population of females that will still exist in the population’s children?

0.000; the original women died; THEIR mitochondria died as well. None of the original mitochondria still exist.

That may seem, and it largely is, a matter of semantics, but in some ways, it is true without word games. Every time the mitochondria split, the copies are not EXACTLY the same. The changes may be so minute they are not always detectable with the current technology, but that does not mean they do not exist.

Some changes occur to the underlying genome; they are rare and may not be readily observed, but that does not mean they do not exist as well. When one of these changes occur, all subsequent mitochondria will have the new genome assuming, of course, that the genome is viable.

If the change will not allow the cell to function properly, this will undoubtedly affect whether the child, as a whole organism, is able to survive. Depending on the severity of the malfunction that results from the new genome, it may make it more difficult, perhaps impossible, for the offspring to thrive, to mate, and to produce their own offspring which can accomplish the same.

It is also likely that some of these genetic mutations will result in change that is too minute to have an effect on the mitochondria or how it functions. By the same token, it is likely that eventually there will be a mutation in the mitochondrial genome that will have a marked effect on cell function. The change may even improve the overall function of the organism to an extent that will enable the offspring to thrive, to mate, and to produce their own offspring at a greater rate than organisms that do not have this change. Needless to say, the 'improved offspring' will pass on their 'improved genome' to the lucky offspring that will be more likely to thrive and pass it on to the next ..... etc.

There are many factors influencing how well the new genome is going to spread. The population in this particular question was somewhat isolated; this will encourage the genomic change to spread through the general population more quickly. The rate of the spread, however, is affected by many variables.

So in a world with no mutations or any other factors that can result in changed mitochondrial DNA, it would be 1.000 as every offspring gets its mothers, who got it from hers, who got it from hers, so the four types, on an isolated island, would remain four types.

However, in reality, changes do happen. An error(s) in transcription would be one of the most common, but certainly not the only, process that could result in any DNA being changed in a heritable manner.

There is an average rate of mutations. In fact, one can look at the mitochondrial DNA of two individuals and calculate how long ago the genomes were essentially the same. In other words, one could look at a mitochondrial genome from some ancient fossil and tell how many generations it likely took for it to evolve in to the genome of a particular modern individual. However, as these changes start as mistakes, it can take several generations for a change that is adaptive and will spread to occur.

The only way humans can observe these changes are in animals with very short life spans, such as fruit flies.

There would be very little change likely in only four generations; therefore, unless you had a very large sample size, any prediction would have little more than a theoretical chance to be correct.

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    $\begingroup$ Please cite your source. $\endgroup$ – JM97 May 21 '17 at 3:36
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    $\begingroup$ I think there is an error in the following piece of reasoning: "So in a world with no mutations or any other factors that can result in changed mitochondrial DNA, it would be 1.000 as every offspring gets its mothers, who got it from hers, who got it from hers, so the four types, on an isolated island, would remain four types." There could be female that have 2 male offspring and others that have 2 female offspring. This phenomenon, called "drift" will cause some genotypes to increase their frequency, and others to decrease theirs, even in absence of selection. $\endgroup$ – bli May 21 '17 at 12:59

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