Tools for Analysing Forensic Genetic DNA Data.
DNAtools
There are two main features of this package:
- Computation of the distribution of the numbers of alleles in DNA mixtures.
- Empirical testing of DNA match probabilities.
Each is described in a separate vignette, and a small example given below under “Getting started”. The documentation (vignettes and manual) is both included in package and available for reading online at https://mikldk.github.io/DNAtools/.
Install
With internet access
To build and install from Github using R 3.3.0 (or later) and the R devtools package 1.11.0 (or later) run this command from within R:
devtools::install_github("mikldk/DNAtools",
build_opts = c("--no-resave-data", "--no-manual"))
You can also install the package without vignettes if needed as follows:
devtools::install_github("mikldk/DNAtools")
Without internet access
To install on a computer without internet access:
- Download
DNAtoolsas a.tar.gzarchive from GitHub, transfer to the destination computer, e.g. using removable media - Install
devtoolsandDNAtoolspre-requisites (multicool,Rcpp,RcppParallel,RcppProgress,Rsolnp) - Install
DNAtoolsinRusing thedevtools::install_local()function
Contribute, issues, and support
Please use the issue tracker at https://github.com/mikldk/DNAtools/issues if you want to notify us of an issue or need support. If you want to contribute, please either create an issue or make a pull request.
Getting started
Please read the vignettes for more elaborate explanations than those given below. The below example is meant to illustrate some of the functionality the package provides in a compact fashion.
Say that we have a reference database:
data(dbExample, package = "DNAtools")
head(dbExample)[, 2:7]
#> D16S539.1 D16S539.2 D18S51.1 D18S51.2 D19S433.1 D19S433.2
#> 1 11 11 15 21 14 14
#> 2 13 12 15 14 16 16
#> 3 9 9 13 17 14 14
#> 4 11 12 14 15 15 13
#> 5 12 12 17 12 15.2 13
#> 6 9 13 17 14 13 14
dim(dbExample)
#> [1] 1000 21
We now find the allele frequencies:
allele_freqs <- lapply(1:10, function(x){
al_freq <- table(c(dbExample[[x*2]], dbExample[[1+x*2]]))/(2*nrow(dbExample))
al_freq[sort.list(as.numeric(names(al_freq)))]
})
names(allele_freqs) <- sub("\\.1", "", names(dbExample)[(1:10)*2])
Number of alleles
One could ask: What is the distribution of the number of alleles observed in a three person mixture?
The distribution of the number of alleles in a three person mixture can be calculated by this package. We focus on the D16S539 locus:
allele_freqs$D16S539
#>
#> 8 9 10 11 12 13 14
#> 0.0005 0.1910 0.0195 0.2755 0.2860 0.2255 0.0020
noa <- Pnm_locus(m = 3, theta = 0, alleleProbs = allele_freqs$D16S539)
names(noa) <- seq_along(noa)
noa
#> 1 2 3 4 5 6
#> 0.001164550 0.089551483 0.492098110 0.389529448 0.027534048 0.000122361
This can be illustrated by a barchart:
Number of alleles Frequency
1
2 |||||||||
3 |||||||||||||||||||||||||||||||||||||||||||||||||
4 |||||||||||||||||||||||||||||||||||||||
5 |||
6
So it is most likely that a three person mixture on D16S539 has 3 alleles.
This can be done for all loci at once:
noa <- Pnm_all(m = 3, theta = 0, probs = allele_freqs, locuswise = TRUE)
noa
#> 1 2 3 4 5 6
#> D16S539 0.0011645502 0.089551483 0.4920981 0.3895294 0.02753405 1.223610e-04
#> D18S51 0.0002318216 0.017959845 0.1779391 0.4378291 0.31153235 5.450770e-02
#> D19S433 0.0035865859 0.089632027 0.3625087 0.3976107 0.13518050 1.148149e-02
#> D21S11 0.0038709572 0.096894566 0.3687696 0.3853717 0.13233905 1.275409e-02
#> D2S1338 0.0000431618 0.006746923 0.1068460 0.3899646 0.39812735 9.827197e-02
#> D3S1358 0.0016039659 0.078199562 0.3939623 0.4258141 0.09768694 2.733108e-03
#> D8S1179 0.0007349290 0.039905625 0.2705804 0.4539819 0.21275810 2.203902e-02
#> FGA 0.0000742453 0.010955567 0.1455096 0.4287449 0.34698332 6.773235e-02
#> TH01 0.0025373680 0.111902320 0.4515490 0.3761236 0.05783065 5.706482e-05
#> vWA 0.0008047420 0.054208046 0.3452015 0.4542519 0.13852872 7.005098e-03
We can also find the convolution and thereby the total number of distinct alleles:
noa <- Pnm_all(m = 3, theta = 0, probs = allele_freqs)
noa
#> 1 2 3 4 5 6
#> 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
#> 7 8 9 10 11 12
#> 0.000000e+00 0.000000e+00 0.000000e+00 2.891086e-32 2.089630e-29 6.726379e-27
#> 13 14 15 16 17 18
#> 1.282439e-24 1.625439e-22 1.457361e-20 9.605595e-19 4.777072e-17 1.827088e-15
#> 19 20 21 22 23 24
#> 5.455402e-14 1.287742e-12 2.429902e-11 3.702434e-10 4.597777e-09 4.693091e-08
#> 25 26 27 28 29 30
#> 3.968035e-07 2.798451e-06 1.656443e-05 8.274188e-05 3.504602e-04 1.263902e-03
#> 31 32 33 34 35 36
#> 3.894858e-03 1.028680e-02 2.334381e-02 4.560959e-02 7.684831e-02 1.117952e-01
#> 37 38 39 40 41 42
#> 1.405269e-01 1.526853e-01 1.433854e-01 1.163205e-01 8.143643e-02 4.912883e-02
#> 43 44 45 46 47 48
#> 2.548638e-02 1.133857e-02 4.311188e-03 1.394979e-03 3.821005e-04 8.802401e-05
#> 49 50 51 52 53 54
#> 1.691803e-05 2.685887e-06 3.478319e-07 3.616152e-08 2.955716e-09 1.846961e-10
#> 55 56 57 58 59 60
#> 8.484368e-12 2.703293e-13 5.435722e-15 5.774600e-17 2.098567e-19 1.565331e-22
This can be illustrated by a barchart:
Number of alleles Frequency
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32 |
33 ||
34 |||||
35 ||||||||
36 |||||||||||
37 ||||||||||||||
38 |||||||||||||||
39 ||||||||||||||
40 ||||||||||||
41 ||||||||
42 |||||
43 |||
44 |
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
So it is most likely that a three person mixture has 38 distinct alleles on all loci combined.
Empirical testing of DNA match probabilities
Another relevant questions is how many matches and near-matches there are. This can be calculated as follows:
db_summary <- dbCompare(dbExample, hit = 6, trace = FALSE)
db_summary
#> Summary matrix
#> partial
#> match 0 1 2 3 4 5 6 7 8 9 10
#> 0 102 1368 7122 21878 44189 59463 54601 34203 13571 3281 353
#> 1 206 2114 10013 26084 43656 47418 34320 15463 4145 472
#> 2 165 1477 5710 12566 17049 14642 7570 2220 310
#> 3 72 556 1821 3250 3361 2135 719 116
#> 4 22 149 360 493 379 156 34
#> 5 6 19 44 41 26 5
#> 6 0 2 3 0 0
#> 7 0 0 0 0
#> 8 0 0 0
#> 9 0 0
#> 10 0
#>
#> Profiles with at least 6 matching loci
#> id1 id2 match partial
#> 1 153 687 6 2
#> 2 625 641 6 2
#> 3 694 855 6 2
#> 4 379 560 6 1
#> 5 422 881 6 1
The hit argument returns pairs of profiles that fully match at hit (here 6) or more loci.
The summary matrix gives the number of pairs mathcing/partially-matching at ((i,j)) loci. For example the row
partial
match 0 1 2 3 4 5 6 7 8 9 10
5 6 19 44 41 26 5
means that there are 6+19+44+41+26+5 = 141 pairs of profiles matching exactly at 5 loci. Conditional on those 5 matches, there are 6 pairs not matching on the remaining 5 loci, 19 pairs partial matching on 1 locus and not matching on the remaining 4 loci, and so on.