How long does it take for a genetic trait to dissipate if its no longer selected for?

Have their been any studies or experiments done that provide insight into the persistence of genetic traits if an environmental shift suddenly causes that trait to be neutrally selected for? Does it take 100s of generations to reach equilibrium or only a few?

For example, how long can we expect the effects of birth control to take in decoupling human behavior related to sex from human behavior related to having children?

• It depends on whether it is neutrally or negatively selected (and how strongly so), it depends on the population size, it depends on the mutation rate and mutational variance and - most important of all - it depends on the level of genetic variance for this trait to start with. This variance can be calculated at equilibrium (assuming no important demographic change "recently") from the above parameters though. It may take between 1 generation and a biliion generations. – Remi.b Oct 30 '15 at 23:21
• Lets say its neutral, not negative. I added an example case for reference. Of course it depends on those things, but I'm looking for a more quantitative answer. – B T Oct 30 '15 at 23:30
• The answer still varies between almost 1 generation to many generations. – Remi.b Oct 31 '15 at 0:29
• @Remi.b No it doesn't. There is literally no statistically probable way that a trait will be randomly removed in a single generation. Your comments aren't helpful at all. – B T Oct 31 '15 at 0:41
• If the population is 2, yes it is even quite likely. I wrote an answer to give you a hint about how variable it can be depending on the exact scenario of interest. – Remi.b Oct 31 '15 at 0:59

There is no way to answer this question as there are way too many factors influencing this time.

It depends on too many factors

It depends on:

• whether it is neutrally or negatively selected (and how strongly so)
• the population size
• mutation rate
• mutational variance
• This variance can be calculated at equilibrium (assuming no important demographic change "recently") from the above parameters though.

It may take between 1 generation and a billion generations.

For example

Consider for example that your trait is neutral. Assume that the trait can only take two binary state A and B and that only a single locus affect this trait, which two states are also named A and B for simplicity. Let's say A is the ancestral state and we want to know how much time it takes to have a population of B. Imagine the haploid population size is $N=10^5$. The mutation rate for the locus of interest is $\mu=10^{-9}$.

Slow Case

If at the start there are no alleles B, then you have to wait for a mutation to occur. The time for such a mutation to occur follows an exponential distribution with parameter $\mu=10^{-9}$. Because we assumed neutrality, the probability of fixation (fixation is the state when the whole population carry the same allele) is $\frac{1}{N}=10^{-5}$. Conditioning on fixation, the expected time for fixation to occur is $-4N \left(\frac{1-p_0}{p_0}\right)\ln(1-p_0)=399998$ generations. In consequence, the expected time to fixation in this case is $10^{5}*10^{9}+399998 ≈ 10^{14}$ generations, that is about 77 times the age of the earth assuming there is one generation per day! So Obviously, the environment has time to change again. Note that variance is about $10^{28}$ generations! Of course this example is just an extreme slow case, but I have been using realistic parameter values.

Fast Case

If you have a population size of $N=50$ and the B allele is already present at frequency 0.1 and that the B allele is beneficial with a selection coefficient of 1.5, then it might take about 100 generations.

• Thanks, this is much more informative. FYI, the answers I'm expecting are along the lines of equations, not a constant answer like "10-15 generations". – B T Oct 31 '15 at 1:00
• Happy that it helps. Note that there way too many processes in play and therefore too many equations (if you're looking for equations). I would recommend that you follow an introductory class to population genetics. – Remi.b Oct 31 '15 at 1:07