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I have one little issue with evolutionary theory that I have not been able to understand. Suppose genetic mutations happen from generation to generation. Nevertheless, from one generation to the next the mutation will present very small changes (I don't suppose a giraffe's neck would grow 10cm). If this were the case, then the advantages one gains from this mutation would be very small. So shouldn't it be the case that the mutation in the case of the giraffe and every other mutation for that matter present very very little advantage so shouldn't transmission of genes at this stage be random? If this were the case I don't see how natural selection could take place?

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In the long run (over hundreds or even millions of generations), small statistical advantages are bound to accumulate.

Even if a mutation gives only a +1% average reproductive advantage, it is still above chance and therefore this mutation is more likely to spread through the population. (If you can code, I have found it to be an interesting exercise to write scripts that simulate generations of evolution.)

It is also not necessarily true that effects of mutations have to be small. Single mutations can be deadly, they can change colors, create large morphological changes, and so on. It just happens to be the case that most mutations that have large effects are deleterious, and therefore won't generally spread for long throughout the population. But some mutations will be beneficial and therefore have improved odds of being passed on.

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Consider genetic drift: if a particular mutation is selectively neutral, it may persist indefinitely in the population, but it is subject to random changes in its frequency due to various non-selective influences. As a result of the random fluctuations in frequency, the allele may be eliminated from the population or may become fixed in the population despite having no influence on the natural selection of the individuals of the population.

Now consider if rather than being neutral, the mutation is slightly deleterious. Since its effect is only slight, it can persist in the population for a long time. Still, like a neutral mutation, it is subject to random fluctuations in frequency and so can be eliminated or fixed in the population. However since it is slightly deleterious, it is more likely that the fluctuations will eliminate the mutation.

Similarly, if a mutation is slightly selectively beneficial, it will still be subject to random fluctuations and can be eliminated or fixed, but in this case it is more likely to become fixed in the population.

One view of this process is formalized in the "nearly neutral theory of molecular evolution".

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