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Yes, I've heard that we have evolved from the common ancestor with primates as intesively, as the chimpanzees. Sometimes I read about some enormously complex traits, evolutionary psychologists think have evolved in humans, such like religion, night owls or art (which don't seem to require a specific complex mutation). On the other hand we still grow many unnecessary organs, so I really wonder: What is the percentage advantage a trait had to provide to humans (so that no other species share it) to actually evolve continuously?

OR (I'm not sure if it can be calculated generally) I can get by with this question: What is the correct formula how to calculate the average probability of survival a trait had to increase to preserve over some time (with the gene expression calculated in it)?

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  • $\begingroup$ "we still grow many unnecessary organs" - huh? Which organs are unnecessary? The liver? Kidneys? Stomach? $\endgroup$ – MattDMo Apr 24 '16 at 17:51
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I think a clear way to rephrase this question would be "How beneficial a mutation needs to be to behave really differently from neutral mutations?". I am answering to this question.

Neutral mutations and nearly neutral mutations

The probability of fixation of a new neutral mutation is $P_{neutral}=\frac{1}{2N}$, where $N$ is the population size. An intuitive way to understand why this is true is that, after an infinite amount of time (constant population size and in absence of speciation), the whole population will necessarily descend from a single individual. In absence of selection pressure every single individual has the same probability to be the ancestor. As a fraction of $\frac{1}{2N}$ of the population is carrying the mutant allele when it first occur, then the probability that his allele reaches fixation is $\frac{1}{2N}$. In fact, this result can be generalize to say that the probability of fixation of a neutral mutation present at frequency $p$ at a given time in the population has a probability $P_{neutral}=p$ to get fixed.

Given the selection coefficient $s$, a good approximation is that whenever $2Ns<<1$, then the probability of fixation is essentially not different from $P_{neutral}$.

This qualitative boundary ($2Ns<<1$ or $2Ns>>1$) is the boundary you were interested in. In your post you talk about "percentage advantage". This percentage advantage is just $s\cdot 100$.

Beneficial mutations

For "significantly" beneficial mutations, a good approximation to the probability of fixation of a newly arisen mutation given $s$ and $N$ is

$$\frac{1-e^{-s}}{1-e^{-2Ns}}$$

Source of information

Your question shows a few misunderstanding and is nested within the field of population genetics. Plus, in absence of good understanding equations and just vague symbols. I recommend that you have a look at an introductory source of information in population genetics. You will find recommendation of books in population genetics here. For a complete and relatively accessible (might still be a bit complicated) introduction to population genetics, I would recommend Gillespie's Population Genetics: A Concise Guide for you. This book will so offer proofs for the equations I gave you above.

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  • $\begingroup$ Sorry, I don't understand what does the N mean. But thanks for rewriting the question. And about the neutral mutation: Shouldn't the probability be just random? There is nothing else we can say about an individual with a neutral mutation, except from he has something that doesn't affect his fitnes. $\endgroup$ – Probably Apr 24 '16 at 19:17
  • $\begingroup$ Sorry, I forgot to indicate what $N$ means. $N$ is the population size. To make it more general $N$ should be replaced with the effective population size $Ne$. $\endgroup$ – Remi.b Apr 24 '16 at 21:05
  • $\begingroup$ You said Shouldn't the probability be just random?. This sentence makes no sense. You either don't understand the definition of "probability" or of "random" (or both). If a probability is different from 0 or 1, then there is randomness (=stochasticity). Yes, the probability of fixation of a mutation (neutral or not) is subject to certain level of stochasticity in finite populations (it is the very nature of genetic drift at play). $\endgroup$ – Remi.b Apr 24 '16 at 21:07
  • $\begingroup$ Yeah, sorry, I meant probability 0,5. It's the same probability that the bearer of my gene is a good one, as that he is a looser (comparing to the rest of the population). So the equation should somehow work only for population of 1 individual. $\endgroup$ – Probably Apr 25 '16 at 4:23
  • $\begingroup$ I added an intuitive explanation for why the probability of fixation of a newly arisen neutral mutation is $/frac{1}{2N}$. This equation holds true for a population of any size (however should be more correct to talk about "effective population size" but I did not want to add another concept you might not know of). $\endgroup$ – Remi.b Apr 25 '16 at 5:01

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