That's a good question. Hedrick (2005. A standardized genetic differentiation measure. Evolution:1633-1638) discusses this a little bit. In practice, I think lots of people address this by having a suite of loci with varying #s of alleles so that you're not overly dependent on a single locus with a lot of potential noise. On the other hand, hyper-variable loci (assuming you can consistently and accurately genotype them) are excellent for parentage analyses.

You could try pooling alleles. Then for analysis treat the pooled alleles as a single "allele". Just make sure the same alleles are always pooled together in your analysis across all genotypes. Using this method you can easily reduce the number of observed alleles.

I would argue the opposite, that the high variability can be highly advantageous, allowing finer differentiation of divergent allele frequencies. But if you are concerned that this is depressing FST estimates for example (which it will), just use RST or Jost's D, and of course combine this with use of clustering software. The hypervariability can also be very useful in assignment tests, pinpointing the source population of migrants. So what exactly do you mean that hypervariability is a challenge/ concern? What is the goal of your study?

PS- one could also "bin" adjacent alleles to reduce the number of allelic categories but I'm not sure that is a good idea...

"Of course this is only true if sample sizes are large enough to accurately detect true population frequencies." This may well get to the point of the original question more than anything. For many studies of wild populations, this is the main challenge.

Even SNPs, which have very low variance on a per-marker basis (2 alleles, one of which is often rare), give me greater variation between individuals within a population than between populations. I study, a wind-pollinated, wind-dispersed grass species, so this makes sense biologically. So, seeing greater variation within than between populations doesn't necessarily mean that something is wrong with your markers.

Kevin mentioned diveRsity, but there is another package called mmod that calculates many of the same statistics. Not sure of all the advantages and disadvantages of either, but mmod integrates with adegenet, which is a fantastic package.

I agree to Lindsay Clark and others that high variability within population of cross-pollinating plants (and in many cases in self-pollinating too) is usual for PCR - based markers. SSR are often hypervariable if the repeat number is over 9 and locus is located near some retrotransposone. Usually, it is necessary to assess significant number of plants (more than 12 but less that 50) to find any difference between populations. Particular method of analysis can be important when the data set is on the edge of reliability, but most of methods will give similar result when plants and loci number approach 50

You raise two issues here that may not be necessarily related: working with SSR marker loci that have many alleles and detecting weakly differentiated populations. I say “weakly differentiated” because determining population structure for strongly differentiated populations is not, or should not be, challenging.

The only instance I can imagine when “far too many alleles” becomes a problem is when accurate genotyping of an SSR locus is not possible. When there are 18 and more alleles you are most probably dealing with dinucleotide SSR markers, right? In this case, mis-called genotypes will likely occur because not every allele can be detected, discriminated, or consistently called because of drop-out of larger alleles, null alleles, poor electrophoretic separation of similar allele lengths, variable allele stutter ratios, and possibly other technical reasons. If your set of SSR markers includes only some loci like this, then simply remove the troublesome ones from the analysis – bad genotypes will muck up any population genetic study. You can identify problematic markers with software that reports unexpected allele size distributions and homozygote frequencies and other metrics of genotyping errors, e.g., MicroChecker (Van Oosterhout et al. DOI: 10.1111/j.1471-8286.2004.00684.x), Alleleogram (Morin et al. DOI: 10.1111/j.1755-0998.2009.02672.x). Better yet, replace all dinucleotide SSR markers with tetranucleotide and higher repeat motif markers, as has been done for forensic applications. These days, plentiful DNA sequences can be obtained for just about any organism, which eliminates the need to restrict SSR marker development to the most frequent dinucleotide motif class; dinucleotide SSRs are just too problematic in general to bother with. Trinucleotide SSRs have similar types of problems, hence I recommend tetranucleotide and larger motifs. Moving on...

Assuming that every SSR marker yields nothing but 100% accurate genotypes, then you really can’t have too many alleles to foul up a population differentiation analysis. In fact, the more alleles genotyped, the more likely it is that you can detect true differentiation – just look for articles comparing isozymes, SSRs, and SNPs. For multiallelic loci, Jost’s Dest is more sensitive for detecting pairwise population differentiation than Fst or Gst (Jost DOI: 10.1111/j.1365-294X.2008.03887.x.; Gerlach et al. DOI: 10.1111/j.1365-294X.2010.04784.x; Lesser et al. DOI: 10.1111/mec.12280) and, in my opinion, provides more accurate comparisons of allele differentiation between populations, especially between those having different levels of inbreeding. Several genetic distance measures also are quite capable of detecting subtle population genetic differences. The important biological question, however, should be not whether the populations are different – that’s largely a sampling issue – but by what degree they differ and how different they need to be to conclude something interesting about their evolution, history, demography, conservation prospects, or whatever.

A final thought on accurate population structure analysis: you should select a set of markers with similar mutation rates, as approximated by their similar Na or Ne values. Population structure in many instances depends on population history or evolution, which are genome level processes. Genotyping a handful of marker loci is a way to sample the genomes from these populations. Depending on the particular process or timescale that interests you, you will want to compare populations from parts of the genome that are evolving not too fast, not too slow, but just right for your particular study. Goldilocks aside, the important thing is to obtain a statistically accurate genome sampling of the genomes. As with any sampling design, the more the better, but from practical considerations, I recommend no fewer than 24 SSR markers. See also Hale et al. DOI: 10.1371/journal.pone.0045170; Vali et al. DOI: 10.1111/j.1365-294X.2008.03876.x. ; DeFaveri et al. DOI: 10.1111/1755-0998.12071; Guichoux et al. DOI: 10.111/j.1755-0998.2011.03014.x.

Hope this helps.

Ok. More details to add to my question.

Say, I have 24 loci and population sizes are between 40 to 80 individuals. Now I use this loci set on populations A, B and C resulting in Na ranging from 2 to 8 and I get very good differentiation of populations. Using PCA and Structure.

Now I use this same loci set on three other populations D, E and F where they produce Na up to 32 (mode=21). No differentiation to be observed on PCA, Structure or sPCA (adegenet). Maybe its one pop? No! D, E, F are pops separated by 1000s of km.

So clearly hypervariable loci are not helping here. And no differentiation in contrast to many responses here.

There are many ways to calculate the diversity. Here I have attached a paper that calculate the diversity by other techniques

Article Comparative Assessment of Genetic Diversity in Tomato Cultiv...

Maybe this article can be of help for you.

Balloux F, Brunner H, Lugon-Moulin N, Hausser J, Goudet J (2000). MICROSATELLITES CAN BE MISLEADING: AN EMPIRICAL AND SIMULATION STUDY. Evolution 54(4): 1414–1422.

I don't get why highly variable loci could distort the genetic structure pattern... Is it possible that there is limited gene flow between populations A, B and C while the oposite happens between D, E and F? What happens if you analyze all populations together? Which species are you studing? Is all the distribution area of the species included in your data?

I would like to give Roy a little support with his original suggestion that it is possible to have too many alleles at an SSR locus, as there have been a number of responses suggesting the more alleles the better, or seeing no problem. I will illustrate with an extreme example, but the argument is the same for less extreme cases.

Suppose each of 10 SSRs have 100 alleles and we sample 40 individuals of a species and put their SSR data into an HWLE clustering algorithm like STRUCTURE... we are interested in whether there is any evidence of structure within the sample.

These clustering algorithms minimise signals of genetic disequilibria (Hardy Weinberg and Linkage disequilibria, HWLE) within clusters to estimate cluster membership Q. They use no model of mutation, so SSR alleles differing by 1 repeat are treated just the same as alleles differing by 100 repeats.

Given a high number of SSR alleles, most alleles will occur very few times in a small dataset, almost all loci will be heterozgous for unique allele pairs, and for the same reason each across-locus comparison will very likely be between unique combinations of alleles. To get any signal at all of genetic disequilibria in these difficult circumstances you really need to know the frequencies p of the allelic states in each proposed cluster... that is 10x100= 1000 p parameters per cluster to co-estimate along with the cluster memberships Q.... the clustering algorithms do attempt this co-estimation of p and Q but there is no such thing as a free lunch... for any reasonable number of clusters in the natural population our clustering algorithm will work better if our 10 SSRs had 3 states each, than if they had 100 states each (or 40, or 25...). What do I mean by work better? With large numbers of allelic states the necessary co-estimation of allele frequencies and cluster memberships blows up - to much is being attempted from a finite sample of individuals. The result is no clear signal of genetic disequilibria even when in nature there are distinct populations. The problem is resolved if, for the same sample of individuals, we had chosen SSRs of intermediate allele count (eg 3) - we are then less likely to miss structure that exists in nature.

Of course, lots of SSR states DO have their uses - they enable us to distinguish each individual from every other individual. But we should remember this may be of little relevance if what we actually want to do is group individuals together into clusters.

I fully endorse Stuart Baird's appraisal of the issue, which highlights a fundamental assumption of population genetics: the sample you take is representative for the population. Hypervariable markers require much larger sample sizes to ensure saturation of the allelic diversity and most of all richness in the sample compared to the actual population. In marine fish populations, which often have hypervariable microsatellites (100 alleles is no exception), sample sizes may have to reach 200 to 250 for mild saturation to occur.

Apart from this, there may be another problem already mentioned, but not covered completely. Genetic differentiation may take very long time to reach equilibrium, and reflect a pattern of gene flow. The time to reach migration-mutation-drift equilibrium (at which the genetic structure among populations stops increasing or decreasing; the loss of diversity by drift is exactly compensated by mutation and migration) is a function of the migration rate, mutation rate and the effective size. This can actually be deduced from Crow & Aoki 1984 (PNAS). The time to reach halfway equilibrium is t_(0.5)=Ln(2)/(2(µ+m)+1/2N). The time to 0.75 equilibrium is twice this time, and so on. Each further halving of the remaining march to equilibrium requires an additional time equal to t_(0.5).

Next, suppose two island populations were founded from a same mainland source by a considerable number of founders (e.g, 50 ind), quickly grew to a large effective size (say Ne=1000), and never exchanged migrants after this founding process. The expected differentiation of these new populations relative to the source population right after founding is 1/(2Ne), being Fst=0.01. It quickly grows to Ne=10000, meaning that very little drift occurs during this expansion. After 1000 generations, the neutral genetic differentiation caused by drift in the absence of any gene flow is still only Fst=0.058. Disregarding mutation, It requires more than 40 000 generations to reach 90% equilibrium, and full equilibrium (differentiation close to 1, as there is no gene flow) is only reached after nearly 100 000 generations. (ignoring the effect of mutation; at this temporal scale and in such large populations, however, mutation will have a considerable effect on diversity; but you get the picture).

So what does this tell you: genetic differentiation may sometimes take ages to reflect a pattern of gene flow, and many large populations never reach equilibrium. Even populations from around the globe that are completely isolated from each other may show little or no genetic differentiation, because the populations are so extremely far from equilibrium.

Guided by Stuart Baird’s example, I ran a simulation in EASYPOP to see just what would be the degree of population differentiation when 3 alleles per locus vs. 100 alleles per locus are used. I went with the assumption that the two sets of marker loci (SSRs) were selected from a much larger set derived from one evaluation population. The EASYPOP input parameters were: 2 diploid random mating populations each of 10000 individuals (Ne) in which 20 loci each had a mutation rate of 0.01 following a step-wise mutation model; genotypes were in an initial equilibrium state; the simulation ran for 1000 generations with no migration between the populations; genotypes were sampled from 30 individuals in the last generation to estimate Fst (from EASYPOP) and D-est (from the on-line implementation of SMOGD, but reported here as the locus arithmetic mean of D-est instead of the harmonic mean). The results from just one run:

# allelic states Fst D-est

3 0.002 0.026

100 0.004 0.496

I think Wright’s theory predicts that Fst between the two populations should be 0.05;

1 - Fst = (1 - 1/(2Ne))^ t, where here Ne = 10000 and t = 1000.

Thus, for a modest sample size from two isolated populations near equilibrium, a greater number of alleles per locus reveals greater differentiation, especially when Jost’s D is used. This contrasts from Stuart’s STRUCTURE clustering example where there would be no detectable population distinction when 100 alleles per locus are used. Unless I got something wrong in my simulation parameters, this contrast points to limitations of some clustering approaches for measuring population differentiation and to the importance of using marker loci with an appropriate level of polymorphism (whatever the heck that might be.)

Responding to Craig: there is indeed a strong distinction between the Fst-based analysis and the performance of clustering algorithms. That contrast is: the Fst based analysis assumes beforehand that we know which individuals belong to which populations (!)... that is, it does not have to work out which individuals group with which individuals.

The relevant comparison between the approaches would be to take the individuals from the 2 pops in Craig's simulation, remove their population labels, then sample two groups at random. Check the Fst (or Jost's D) between the random groups. Do this very many times. See if the original population labels can be worked out by favouring those random samples pairs with highest Fst. I am not even going to attempt that, but I would suggest that for large numbers of SSR alleles it is in principle exactly as hopeless as with a clustering algorithm, and would take a lot longer, and would not be based on any firm statistical model. There is a way of understanding this problem based only on Fst "the maximum value the Fst statistic can take depends on the number of alleles and their relative frequencies" (see Perspective: highly variable loci and their interpretation in evolution and conservation. PW Hedrick - Evolution, 1999)... with very many alleles all Fst values are constrained to a very small interval (the maximum is close to zero)... so distinguishing high from low Fst becomes difficult and arbitrary.

There is no such thing as a free lunch. In Craig's example the Fst based approach appears to work better only because it has been given most of the answer that the clustering approach is trying to work out. I would also suggest there will be a high rate of false positives in the Fst based approach ie when there are lots of alleles there will be many pairs of random groups (sampled blind to membership in the simulated populations) which will give higher Fst values than pairs of groups actually corresponding to the simulated populations. The noise due to small numbers of each allele obscures the signal of differentiation.

I agree with Kevin. Working with fish, though, some patterns can be different. High levels of variable alleles within a population have been seen as effects of population recovery after a bottleneck, for instance. Some species, with territorial habits and specialized reproduction habits (care of the fingerlings for example) are much more structured than species with annual and broad reproduction habits. Variability between and among populations will vary a lot. So, combining the data with the biological traits of the species in study will be essential to understand the numbers and apply the proper software to obtain statistical parameters.

Dear Roy,

I used different marker types (SSR, RAPD, STS) for characterization of barley varieties. You can find some information about it in this publication.

Mészáros K., Karsai I., Kuti Cs., Bányai J., Láng L., Bedő Z. (2007): Efficiency of different marker systems for genotype fingerprinting and for genetic diversity studies in barley (Hordeum vulgare L.). South African Journal of Botany, 73: 43-48