Genetic distance and FST

First off, I did a search for papers that used contextual analysis in some form or another to analyze experimental data. This is the list I came up with. It seems pretty pitiful for a statistical method that (1) works and (2) with the exception of Heisler and Damuth using a very small data set to demonstrate the technique, has been wildly successful at detecting multilevel selection. I am hoping that I missed some important references. If you know of any that I missed, please let me know! If I didn’t miss anything, well, it looks like it is time for us to get to work!

Aspi, J., A. Jåkålåniemi, J. Tuomi and P. Siikamåki (2003). “Multilevel phenotypic selection on morphological characters in a metapopulation of Silene tatarica.” Evolution 57: 509-517.

Donohue, K. (2003). “The Influence of Neighbor Relatedness on Multilevel Selection in the Great Lakes Sea Rocket.” American Naturalist 162(1): 77-92.

Donohue, K. (2004). “Density-dependent multilevel selection in the great lakes sea rocket.” Ecology 85: 180-191.

Eldakar, O. T., D. S. Wilson, M. J. Dlugos and J. W. Pepper (2010). “The role of multilevel seleciton in the evolution of sexual conflict in the water strider Aquarius remigis.” Evolution 64(11): 3183-3189.

Heisler, L. and J. D. Damuth (1987). “A method for analyzing selection in hierarchically structured populations.” American Naturalist 130: 582-602.

Herbers, J. M. and V. S. Banschbach (1999). “Plasticity of social organization in a forest ant species.” Behavioral Ecology and Sociobiology 45: 451-465.

Laiolo, P. and J. R. Obeso (2012). “Multilevel Selection and Neighbourhood Effects from Individual to Metapopulation in a Wild Passerine.” PLoS ONE 7(6): e38526.

Moorad, J. A. (2013). “Multi-level sexual selection.” Individual and Family-level selection for mating success in a historical human population 67(6): 1635-1648.

Pruitt, J. N. and C. J. Goodnight (2014). “Site-specific group selection drives locally adapted group compositions.” Nature 514: 359-362.

Stevens, L., C. J. Goodnight and S. Kalisz (1995). “Multi–Level Selection in Natural Populations of Impatiens capensis.” American Naturalist 145: 513-526.

Tsuji, K. (1995). “Reproductive conflicts and levels of seleciton in the ant pristomyrmex pungens: contextual analysis and partitioning of covariance.” American Naturalist 146: 587-607.

Weinig, C., J. Johnston, C. G. Willis and J. N. Maloof (2007). “Antagonistic multilevel selection on size and architecture in variable density settings.” Evolution 61: 58-67.

The second thing I wanted to talk about was that I was asked about the relationship between inbreeding coefficients and genetic distance. I thought I would share my answer, in part to be told where I was wrong. My disclaimer is that all I know about genetic distance, is that it is something I rarely care about. . .

Consider a metapopulation with M alleles, with the mth allele having a frequency of pm in the overall metapopulation. We would like to calculate d, which from I got a formula cited by Smouse and Peakall (1999, Heredity 561-573) to be:

Screen Shot 2014-12-17 at 11.43.46 AM

Here the summation is over the M possible alleles, and yijm is the number of alleles of type m in individual i in the jth deme. This takes on a value of 0, 1, or 2.

If we are interested in the average genetic distance between deme j and deme l then we would calculate this as:

Screen Shot 2014-12-17 at 11.44.02 AM

We can now define dmax to be the maximum value that can take on. This will occur when the FST = 1. In an infinite metapopulation this means that every population will be fixed for an allele, and pm of the populations will be fixed for the mth allele.

If demes j and l are fixed for the same allele the genetic distance is 0. For allele m this occurs with probability (pm)2. If deme j and l are fixed for different alleles the genetic distance is:

Screen Shot 2014-12-17 at 11.44.11 AM

For alleles m and n this occurs with probability pmpn, thus:

Screen Shot 2014-12-17 at 11.44.20 AM

We want a measure that is a function of FIT and FST (I just figured out that I have never talked about FIS,  FST and FITTry this) that goes from zero to 1. When FST = 0, dij,kl = 0, and when FST = 1 dij,kl =1.

Working this out (the excel worksheet is available here: genetic distance work sheet)

Screen Shot 2014-12-17 at 11.44.34 AM

If we assume random mating within demes then FIT = FIS.

Screen Shot 2014-12-17 at 11.44.44 AM

 

Note that when FST=0, d = 0, and when FST=1, d = 4. The problem, of course is that we want to multiply this by dmax. For this to work we need the equation to go from 0 to 1. Thus, we divide by 4:

Screen Shot 2014-12-17 at 11.44.54 AM

and

Screen Shot 2014-12-17 at 11.45.03 AM

OK, A lot of algebraic noise. What this is telling us is that using Smouse and Peakall’s formula, there is a fairly direct relationship between FST and Screen Shot 2014-12-17 at 11.45.14 AM. Basically the difference is that genetic distance is based on identity by state, whereas F is based on identity by descent. If, at the start, every allele is unique then Screen Shot 2014-12-17 at 11.45.23 AM. If not, then dmax will be some number smaller than 4, and Screen Shot 2014-12-17 at 11.45.32 AM. If you care here is a graph of my equation:

Screen Shot 2014-12-17 at 11.47.04 AM

Genetic distance standardized to a maximum value of one as a function of FST.  If mating is non-random then  FIT will not equal FST and the results will be somewhat different.

Finally, I was asked about our fly collecting trip. Well do to a whole bunch of odd events we are understaffed to take care of a new batch of flies, so the trip has been postponed until January. The other question was about how I was going about bringing flies back to the US. The answer is I am not. I strongly recommend doing research in Brazil, but if you do get a Brazilian collaborator, and do your experimental work in Brazil, and leave your samples there. The reason is simple. We, as in the US and other first world countries, have been pillaging countries like Brazil for too long, and they are, unsurprisingly, sensitive about this. Doing research in Brazil is dead easy IF you have a Brazilian collaborator and you do the work in Brazil.

OH, and yes, I am slowing down my posts for a while, but I will still be occasionally posting as the occasion arises.

Leave a Reply