Bruvo's distance for microsatellites
Calculate the average Bruvo's distance over all loci in a population.
indicator to get the results per locus. The default setting
Bruvo's distance between two alleles is calculated as
d = 1 - (2^(-abs(x)))
, where x
is the number of repeat units between the two alleles (see the Algorithms
and Equations vignette for more details). These distances are calculated
over all combinations of alleles at a locus and then the minimum average
distance between allele combinations is taken as the distance for that
locus. All loci are then averaged over to obtain the distance between two
samples. Missing data is ignored (in the same fashion as
mean(c(1:9, NA), na.rm = TRUE)) if all alleles are missing. See the
next section for other cases.
Ploidy is irrelevant with respect to calculation of Bruvo's distance. However, since it makes a comparison between all alleles at a locus, it only makes sense that the two loci need to have the same ploidy level. Unfortunately for polyploids, it's often difficult to fully separate distinct alleles at each locus, so you end up with genotypes that appear to have a lower ploidy level than the organism.
To help deal with these situations, Bruvo has suggested three methods for dealing with these differences in ploidy levels:
Infinite Model - The simplest way to deal with it is to count all missing alleles as infinitely large so that the distance between it and anything else is 1. Aside from this being computationally simple, it will tend to inflate distances between individuals.
Genome Addition Model - If it is suspected that the organism has gone through a recent genome expansion, the missing alleles will be replace with all possible combinations of the observed alleles in the shorter genotype. For example, if there is a genotype of [69, 70, 0, 0] where 0 is a missing allele, the possible combinations are: [69, 70, 69, 69], [69, 70, 69, 70], and [69, 70, 70, 70]. The resulting distances are then averaged over the number of comparisons.
Genome Loss Model - This is similar to the genome addition model, except that it assumes that there was a recent genome reduction event and uses the observed values in the full genotype to fill the missing values in the short genotype. As with the Genome Addition Model, the resulting distances are averaged over the number of comparisons.
Combination Model - Combine and average the genome addition and loss models.
As mentioned above, the infinite model is biased, but it is not nearly as computationally intensive as either of the other models. The reason for this is that both of the addition and loss models requires replacement of alleles and recalculation of Bruvo's distance. The number of replacements required is equal to the multiset coefficient: choose(n+k-1, k) where n is the number of potential replacements and k is the number of alleles to be replaced. So, for the example given above, The genome addition model would require choose(2+2-1, 2) == 3 calculations of Bruvo's distance, whereas the genome loss model would require choose(4+2-1, 2) == 10 calculations.
To reduce the number of calculations and assumptions otherwise, Bruvo's distance will be calculated using the largest observed ploidy in pairwise comparisons. This means that when comparing [69,70,71,0] and [59,60,0,0], they will be treated as triploids.
an object of class
dist or a list of these objects if
by_locus = TRUE
Do not use missingno with this function.
Repeat Lengths (replen)
replen argument is crucial for proper analysis of Bruvo's
distance since the calculation relies on the knowledge of the number of
steps between alleles. To calculate Bruvo's distance, your raw allele calls
are first divided by the repeat lengths and then rounded. This can create a
problem with repeat lengths of even size due to the IEC 60559 standard that
says rounding at 0.5 is to the nearest even number, meaning that it is
possible for two alleles that are one step apart may appear to be exactly
the same. This can be fixed by subtracting a tiny number from the repeat
length with the function
fix_replen. Please consider using
this before running Bruvo's distance.
modify the model choice accordingly:
add = FALSE, loss = FALSE
Genome Addition Model:
add = TRUE, loss = FALSE
Genome Loss Model:
add = FALSE, loss = TRUE
Combination Model (DEFAULT):
add = TRUE, loss = TRUE
Details of each model
choice are described in the Details section, above. Additionally,
genotypes containing all missing values at a locus will return a value of
NA and not contribute to the average across loci.
If the user does not provide a vector of
appropriate length for
replen , it will be estimated by taking the
minimum difference among represented alleles at each locus. IT IS NOT
RECOMMENDED TO RELY ON THIS ESTIMATION.
Zhian N. Kamvar
Ruzica Bruvo, Nicolaas K. Michiels, Thomas G. D'Souza, and Hinrich Schulenburg. A simple method for the calculation of microsatellite genotype distances irrespective of ploidy level. Molecular Ecology, 13(7):2101-2106, 2004.
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# Please note that the data presented is assuming that the nancycat dataset # contains all dinucleotide repeats, it most likely is not an accurate # representation of the data. # Load the nancycats dataset and construct the repeat vector. data(nancycats) # Assume the alleles are all dinucleotide repeats. ssr <- rep(2, nLoc(nancycats)) test_replen(nancycats, ssr) # Are the repeat lengths consistent? (ssr <- fix_replen(nancycats, ssr)) # Nope. We need to fix them. # Analyze the first population in nancycats bruvo.dist(popsub(nancycats, 1), replen = ssr) ## Not run: # get the per locus estimates: bruvo.dist(popsub(nancycats, 1), replen = ssr, by_locus = TRUE) # View each population as a heatmap. sapply(popNames(nancycats), function(x) heatmap(as.matrix(bruvo.dist(popsub(nancycats, x), replen = ssr)), symm=TRUE)) ## End(Not run)
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