Calculating Genotype Probabilities

Last updated on 2024-10-21 | Edit this page

Overview

Questions

  • How do I calculate QTL at positions between genotyped markers?
  • How do I calculate QTL genotype probabilities?
  • How do I calculate allele probabilities?
  • How can I speed up calculations if I have a large data set?

Objectives

  • To explain why the first step in QTL analysis is to calculate genotype probabilities.
  • To calculate genotype probabilities.

The first task in QTL analysis is to calculate conditional genotype probabilities, given the observed marker data, at each putative QTL position. For example, the first step would be to determine the probabilities for genotypes BR and RR at the locus indicated below.

Genotype probabilities must be calculated between typed markers; adapted from Broman & Sen, 2009{‘a chromosome with two typed markers labeled BR and RR with a locus of unknown genotype between them’}

The calc_genoprob() function calculates QTL genotype probabilities conditional on the available marker data. These are needed for most of the QTL mapping functions. The result is returned as a list of three-dimensional arrays (one per chromosome). Each 3d array of probabilities is arranged as individuals \(\times\) genotypes \(\times\) positions.

Figure showing three-dimensional array of genotype probabilities (genoprobs)
Three-dimensional genotype probabilities array

See this page for a graphical review of data structures in R{‘a web page showing R data structures including one-dimensional vectors and lists, two dimensional dataframes and matrices, and n-dimensional arrays’}.

We’ll use the Attie BL6/BTBR dataset from Tian et al (an intercross) as an example. In this study, circulating insulin levels were measured in an F2 cross between mouse strains C57BL/6J and BTBTR T+ .

First, we will load in the qtl2 library, which provides the functions that we will use for QTL analysis.

R 

suppressPackageStartupMessages(library(qtl2))

R 

cross <- read_cross2(file = 'data/attie_b6btbr_grcm39/attie_control.json')

To load your own data from your machine, you would use the file path to your data files. For example, if the file path to your data files is /Users/myUserName/qtlProject/data, the command to load your data would look like this:

R 

myQTLdata <- read_cross2(file = "/Users/myUserName/qtlProject/data/myqtldata.json" )

The JSON file contains all control information for your data, including names of data files, cross type, column specifications for sex and cross information, and more. This can also be in YAML format. Alternatively, all data files can be zipped together for loading.

R 

myQTLdata <- read_cross2(file = "/Users/myUserName/qtlProject/data/myqtldata.zip" )

Back to the BTBR data. Now look at a summary of the cross data and the names of each variable within the data.

R 

summary(cross)

OUTPUT 

Object of class cross2 (crosstype "f2")

Total individuals             490
No. genotyped individuals     490
No. phenotyped individuals    490
No. with both geno & pheno    490

No. phenotypes                  3
No. covariates                  8
No. phenotype covariates        0

No. chromosomes                20
Total markers                2057

No. markers by chr:
  1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19   X
156 135 157 126 125 102 109  91  93 123 124 116 116  91 102  66  60  95  50  20

R 

names(cross)

OUTPUT 

 [1] "crosstype"  "geno"       "gmap"       "pmap"       "pheno"
 [6] "covar"      "is_x_chr"   "is_female"  "cross_info" "alleles"

Have a look at the markers listed in the genetic map, gmap. Markers are listed by chromosome and described by cM position. View only the markers on the first two chromosomes.

R 

head(cross$gmap, n=2)

OUTPUT 

$`1`
rs13475697  rs3681603 rs13475703 rs13475710  rs6367205 rs13475716 rs13475717
 0.1881141  0.1920975  0.4167755  0.6488793  0.6555814  0.6638576  0.6676198
rs13475719 rs13459050  rs3680898 rs13475727 rs13475728 rs13475729 rs13475731
 0.6711377  0.6749344  0.6775292  1.8149573  1.9596637  2.3456569  2.7186389
rs13475737 rs13475744  rs6397513 rs13475747 rs13475748 rs13475749 rs13475750
 3.1059517  3.8222865  4.3094607  4.3120150  4.5098582  4.8154609  4.8853505
rs13475751 rs13475752 rs13475762 rs13475764 rs13475765 rs13475768 rs13475769
 4.8869793  4.8902179  7.2954871  8.2102887  8.3708197  8.7178703  8.8859153
rs13475771  rs6384194 rs13475790  rs3676270 rs13475794 rs13475801  rs4222269
 9.1374722  9.9295192  9.9970634 10.1508878 10.3962716 11.5981956 11.9606369
 rs6387241 rs13475822 rs13475824 rs13475826 rs13475827 rs13475834 rs13475880
16.8770742 16.9815396 17.4434784 18.0866148 18.6276972 19.2288050 27.4056813
rs13475883  rs6239834  rs3162895  rs6212146  rs3022802 rs13475899 rs13475900
28.4641674 30.8427150 31.1526514 31.2751278 31.3428706 31.8493556 31.8518088
rs13475906  rs3022803 rs13475907 rs13475909 rs13475912  rs6209698 rs13475929
32.2967145 32.3074644 32.3683291 32.8001894 33.6026526 36.5341646 37.6881435
rs13475931 rs13475933 rs13475934  rs4222476 rs13475939  rs8253473 rs13475941
37.7429827 38.0416271 38.0430095 38.9647582 39.4116688 39.4192277 39.4871064
rs13475944 rs13475947 rs13475948 rs13475950 rs13475951 rs13475954 rs13475955
39.7672829 40.2599440 40.3380113 40.3417592 40.3439501 41.1407252 41.2887176
rs13475963 rs13475966 rs13475967 rs13475970 rs13475960  rs6250696 rs13475973
42.4744416 42.5667702 42.9736574 43.1427994 43.5985261 43.5992946 43.6014053
 rs3691187 rs13475988 rs13475991 rs13476023 rs13476024  rs3684654  rs6274257
44.6237384 45.7855528 46.0180221 47.8579278 47.8600317 48.2423958 48.9612178
rs13476045 rs13476049  rs6319405 rs13476050 rs13476051 rs13476054 rs13476057
49.2018340 49.3701384 49.4261039 49.4275718 49.4323558 49.4972616 49.5031830
rs13476059 rs13476060 rs13476062 rs13476066 rs13476067  rs6259837 rs13476080
49.5084008 49.5113545 49.6085043 49.6644819 50.1779477 50.8256056 51.0328603
 rs6302966 rs13476085 rs13476089  rs3717360 rs13476090  rs6248251 rs13476091
51.3659553 51.6974451 52.3869798 52.3903517 52.3936241 52.4228715 52.5787388
 rs3088725  rs3022832  rs4222577 rs13476100  rs6263067  rs8256168  rs6327099
53.4044231 53.4129004 53.4189013 54.3267003 54.4193890 55.1459517 55.3274320
rs13476111 rs13476119  rs8236484  rs8270838  rs8236489 rs13476129 rs13476134
55.9050491 56.8936305 56.9852502 57.1870637 58.0248893 58.7605079 59.5401544
rs13476135 rs13476137 rs13476138 rs13476140 rs13476148  rs6202860 rs13476158
59.5426193 59.6023794 60.3355828 60.3439598 61.1791787 61.9905512 61.9930265
rs13476163 rs13476177 rs13476178 rs13476183 rs13476184  rs6194543 rs13476196
62.0039607 62.6243588 62.6269118 63.8101331 64.0856907 66.4047817 66.7425394
rs13476201  rs3685700  rs3022846 rs13476210 rs13476214 rs13459163  rs4222816
67.2638714 68.7230251 68.7246243 69.1209547 70.1550813 75.5548371 75.5593190
 rs4222820  rs3090340  rs8245949 rs13476242 rs13476251 rs13476254  rs6383012
75.5593202 75.5637846 76.7508053 79.0157673 79.7644000 79.8248805 85.3173344
rs13476279  rs6348421 rs13476290 rs13476300 rs13476302 rs13476304  rs3669814
86.7653503 88.2128991 89.0565541 94.6215368 94.8227821 94.8269227 95.5413280
rs13501301 rs13476316
96.0784002 96.9960494

$`2`
rs13476325 rs13476327 rs13476328 rs13476330  rs3695983 rs13476334 rs13476337
  1.329379   1.760872   1.839732   1.950151   1.954566   2.265170   3.619681
rs13476342  rs3696091 rs13476348  rs3681847 rs13476358 rs13476424 rs13476427
  4.113919   5.308337   6.708720   7.382269  10.053730  21.102901  21.547272
rs13476432 rs13476433 rs13476438 rs13476440 rs13476445 rs13476446 rs13476448
 22.457323  22.458829  22.472305  22.502827  22.703755  22.706606  22.809631
rs13476449 rs13476451 rs13476452 rs13476456  rs6333344 rs13476459  rs6288325
 22.811905  22.816989  22.917366  23.496527  23.499872  23.505774  23.764498
rs13476470 rs13476482  rs6203572 rs13476485 rs13476501 rs13476502 rs13476503
 25.671278  26.670288  26.702994  27.001404  29.014864  29.017621  29.019099
rs13476525 rs13476526 rs13476530  rs3660779 rs13476533 rs13476534  rs4223189
 31.635258  31.882499  32.606343  33.182340  33.622217  33.881289  33.886227
 rs6205317 rs13476536  rs3709716 rs13476538 rs13476540  rs6314726 rs13476543
 34.125908  34.182229  34.777129  35.011099  35.196852  35.859566  36.045536
rs13476544  rs6222797 rs13476546 rs13476553 rs13476554  rs8263229 rs13476565
 36.199822  36.656504  36.783097  37.624894  37.628034  38.509801  39.813261
rs13476566  rs3670631 rs13476583 rs13476586 rs13476592 rs13476595 rs13476645
 40.314536  41.215814  43.089828  43.274068  45.681933  46.026997  50.383519
rs13476655 rs13476660  rs6378047 rs13476661 rs13476666 rs13476667 rs13476669
 50.804234  51.471634  51.474692  51.557954  52.083779  52.257580  52.543537
rs13476672  rs3724460  rs3143279 rs13476687  rs6278009 rs13476693  rs3022892
 52.594599  53.100014  54.071835  54.256293  54.721524  55.005598  55.109510
rs13476700 rs13476702 rs13476703 rs13476705  rs4223406  rs3090608 rs13476739
 55.226885  55.233738  55.400903  55.678374  55.949739  57.841429  58.879499
rs13476747 rs13476754  rs6257970 rs13476758  rs3022901 rs13476769  rs4223486
 59.218037  59.231937  59.742629  60.304581  61.226450  61.739777  61.741096
rs13476774  rs4223511 rs13476778 rs13476783  rs6234650 rs13476784 rs13476786
 61.912021  62.703328  63.294674  63.904805  64.118754  64.219897  64.224107
rs13476788  rs3682725 rs13476801 rs13476803 rs13476816  rs6170159  rs3022909
 64.987248  65.971246  66.931607  67.071161  69.496928  69.584633  69.689891
rs13476819 rs13476822 rs13476823  rs3716380  rs6332517 rs13476826 rs13476827
 69.754708  71.191302  71.405084  71.816078  71.959179  72.019045  72.087910
rs13476830 rs13476831 rs13476832  rs4223605  rs3022932 rs13476872  rs3692409
 72.364799  72.368511  72.371502  76.460822  76.621947  78.531760  79.528125
 rs3726342 rs13476882  rs3673613  rs8260429  rs8275858 rs13476892 rs13476894
 80.337464  81.259831  82.295892  82.969957  83.669130  84.046818  84.787594
 rs3024096 rs13476907 rs13476910 rs13476918  rs3673248 rs13476928 rs13476934
 87.473424  87.498263  87.955210  92.672743  94.072805  96.238835  98.601444
rs13476935 rs13476936
 99.057281  99.455950

Next we use calc_genoprob() to calculate the QTL genotype probabilities.

R 

probs <- calc_genoprob(cross      = cross, 
                       map        = cross$gmap, 
                       error_prob = 0.002)

The argument error_prob supplies an assumed genotyping error probability of 0.002. If a value for error_prob is not supplied, the default probability is 0.0001.

Recall that the result of calc_genoprob, probs, is a list of three-dimensional arrays (one per chromosome).

R 

names(probs)

OUTPUT 

 [1] "1"  "2"  "3"  "4"  "5"  "6"  "7"  "8"  "9"  "10" "11" "12" "13" "14" "15"
[16] "16" "17" "18" "19" "X"

Each three-dimensional array of probabilities is arranged as individuals \(\times\) genotypes \(\times\) positions. Have a look at the names of each of the three dimensions for chromosome 19.

R 

dimnames(probs$`19`)

OUTPUT 

[[1]]
  [1] "Mouse3051" "Mouse3551" "Mouse3430" "Mouse3476" "Mouse3414" "Mouse3145"
  [7] "Mouse3656" "Mouse3242" "Mouse3427" "Mouse3527" "Mouse3281" "Mouse3405"
 [13] "Mouse3530" "Mouse3477" "Mouse3498" "Mouse3526" "Mouse3284" "Mouse3160"
 [19] "Mouse3655" "Mouse3615" "Mouse3491" "Mouse3603" "Mouse3191" "Mouse3130"
 [25] "Mouse3330" "Mouse3199" "Mouse3614" "Mouse3577" "Mouse3081" "Mouse3204"
 [31] "Mouse3513" "Mouse3219" "Mouse3331" "Mouse3301" "Mouse3503" "Mouse3083"
 [37] "Mouse3568" "Mouse3189" "Mouse3287" "Mouse3131" "Mouse3311" "Mouse3357"
 [43] "Mouse3149" "Mouse3256" "Mouse3644" "Mouse3217" "Mouse3212" "Mouse3082"
 [49] "Mouse3156" "Mouse3535" "Mouse3481" "Mouse3123" "Mouse3359" "Mouse3555"
 [55] "Mouse3597" "Mouse3624" "Mouse3314" "Mouse3128" "Mouse3531" "Mouse3295"
 [61] "Mouse3231" "Mouse3496" "Mouse3438" "Mouse3183" "Mouse3052" "Mouse3237"
 [67] "Mouse3462" "Mouse3293" "Mouse3543" "Mouse3276" "Mouse3200" "Mouse3502"
 [73] "Mouse3171" "Mouse3364" "Mouse3524" "Mouse3334" "Mouse3355" "Mouse3254"
 [79] "Mouse3358" "Mouse3468" "Mouse3192" "Mouse3214" "Mouse3536" "Mouse3606"
 [85] "Mouse3226" "Mouse3393" "Mouse3415" "Mouse3266" "Mouse3648" "Mouse3224"
 [91] "Mouse3474" "Mouse3381" "Mouse3138" "Mouse3660" "Mouse3616" "Mouse3425"
 [97] "Mouse3554" "Mouse3196" "Mouse3528" "Mouse3312" "Mouse3045" "Mouse3585"
[103] "Mouse3471" "Mouse3308" "Mouse3628" "Mouse3429" "Mouse3324" "Mouse3124"
[109] "Mouse3291" "Mouse3452" "Mouse3373" "Mouse3367" "Mouse3579" "Mouse3647"
[115] "Mouse3169" "Mouse3335" "Mouse3122" "Mouse3635" "Mouse3154" "Mouse3484"
[121] "Mouse3652" "Mouse3612" "Mouse3668" "Mouse3233" "Mouse3175" "Mouse3306"
[127] "Mouse3046" "Mouse3663" "Mouse3165" "Mouse3519" "Mouse3592" "Mouse3127"
[133] "Mouse3184" "Mouse3650" "Mouse3599" "Mouse3494" "Mouse3605" "Mouse3505"
[139] "Mouse3573" "Mouse3561" "Mouse3489" "Mouse3480" "Mouse3186" "Mouse3421"
[145] "Mouse3607" "Mouse3346" "Mouse3375" "Mouse3633" "Mouse3589" "Mouse3094"
[151] "Mouse3611" "Mouse3307" "Mouse3133" "Mouse3152" "Mouse3518" "Mouse3209"
[157] "Mouse3056" "Mouse3320" "Mouse3365" "Mouse3313" "Mouse3441" "Mouse3339"
[163] "Mouse3352" "Mouse3159" "Mouse3619" "Mouse3238" "Mouse3203" "Mouse3137"
[169] "Mouse3509" "Mouse3289" "Mouse3054" "Mouse3432" "Mouse3487" "Mouse3179"
[175] "Mouse3572" "Mouse3285" "Mouse3466" "Mouse3252" "Mouse3517" "Mouse3546"
[181] "Mouse3185" "Mouse3665" "Mouse3537" "Mouse3096" "Mouse3600" "Mouse3349"
[187] "Mouse3098" "Mouse3275" "Mouse3667" "Mouse3342" "Mouse3333" "Mouse3300"
[193] "Mouse3244" "Mouse3478" "Mouse3560" "Mouse3501" "Mouse3315" "Mouse3440"
[199] "Mouse3669" "Mouse3486" "Mouse3632" "Mouse3319" "Mouse3453" "Mouse3172"
[205] "Mouse3121" "Mouse3590" "Mouse3215" "Mouse3447" "Mouse3618" "Mouse3340"
[211] "Mouse3047" "Mouse3666" "Mouse3516" "Mouse3225" "Mouse3167" "Mouse3207"
[217] "Mouse3631" "Mouse3444" "Mouse3168" "Mouse3298" "Mouse3602" "Mouse3309"
[223] "Mouse3416" "Mouse3260" "Mouse3146" "Mouse3374" "Mouse3144" "Mouse3485"
[229] "Mouse3610" "Mouse3348" "Mouse3500" "Mouse3613" "Mouse3253" "Mouse3384"
[235] "Mouse3664" "Mouse3206" "Mouse3426" "Mouse3332" "Mouse3210" "Mouse3283"
[241] "Mouse3670" "Mouse3120" "Mouse3274" "Mouse3461" "Mouse3202" "Mouse3472"
[247] "Mouse3437" "Mouse3434" "Mouse3593" "Mouse3055" "Mouse3234" "Mouse3422"
[253] "Mouse3571" "Mouse3236" "Mouse3049" "Mouse3350" "Mouse3249" "Mouse3326"
[259] "Mouse3134" "Mouse3143" "Mouse3493" "Mouse3361" "Mouse3636" "Mouse3436"
[265] "Mouse3510" "Mouse3117" "Mouse3601" "Mouse3303" "Mouse3497" "Mouse3544"
[271] "Mouse3463" "Mouse3118" "Mouse3354" "Mouse3162" "Mouse3464" "Mouse3181"
[277] "Mouse3188" "Mouse3356" "Mouse3521" "Mouse3591" "Mouse3241" "Mouse3467"
[283] "Mouse3469" "Mouse3262" "Mouse3643" "Mouse3548" "Mouse3372" "Mouse3542"
[289] "Mouse3563" "Mouse3583" "Mouse3584" "Mouse3208" "Mouse3661" "Mouse3659"
[295] "Mouse3195" "Mouse3459" "Mouse3653" "Mouse3649" "Mouse3382" "Mouse3180"
[301] "Mouse3386" "Mouse3084" "Mouse3205" "Mouse3299" "Mouse3515" "Mouse3540"
[307] "Mouse3255" "Mouse3177" "Mouse3523" "Mouse3366" "Mouse3567" "Mouse3557"
[313] "Mouse3114" "Mouse3623" "Mouse3419" "Mouse3580" "Mouse3271" "Mouse3385"
[319] "Mouse3492" "Mouse3119" "Mouse3232" "Mouse3598" "Mouse3150" "Mouse3310"
[325] "Mouse3164" "Mouse3587" "Mouse3050" "Mouse3627" "Mouse3506" "Mouse3413"
[331] "Mouse3435" "Mouse3151" "Mouse3112" "Mouse3630" "Mouse3646" "Mouse3223"
[337] "Mouse3187" "Mouse3263" "Mouse3637" "Mouse3662" "Mouse3508" "Mouse3550"
[343] "Mouse3125" "Mouse3545" "Mouse3570" "Mouse3641" "Mouse3136" "Mouse3626"
[349] "Mouse3166" "Mouse3269" "Mouse3529" "Mouse3218" "Mouse3625" "Mouse3448"
[355] "Mouse3378" "Mouse3227" "Mouse3651" "Mouse3182" "Mouse3304" "Mouse3617"
[361] "Mouse3141" "Mouse3552" "Mouse3479" "Mouse3658" "Mouse3539" "Mouse3190"
[367] "Mouse3093" "Mouse3097" "Mouse3126" "Mouse3170" "Mouse3229" "Mouse3520"
[373] "Mouse3582" "Mouse3351" "Mouse3129" "Mouse3153" "Mouse3450" "Mouse3113"
[379] "Mouse3586" "Mouse3549" "Mouse3538" "Mouse3201" "Mouse3556" "Mouse3247"
[385] "Mouse3455" "Mouse3176" "Mouse3344" "Mouse3343" "Mouse3439" "Mouse3629"
[391] "Mouse3286" "Mouse3216" "Mouse3588" "Mouse3488" "Mouse3221" "Mouse3142"
[397] "Mouse3428" "Mouse3111" "Mouse3353" "Mouse3211" "Mouse3569" "Mouse3280"
[403] "Mouse3325" "Mouse3368" "Mouse3553" "Mouse3245" "Mouse3228" "Mouse3135"
[409] "Mouse3622" "Mouse3095" "Mouse3369" "Mouse3609" "Mouse3410" "Mouse3302"
[415] "Mouse3594" "Mouse3483" "Mouse3197" "Mouse3336" "Mouse3507" "Mouse3305"
[421] "Mouse3532" "Mouse3250" "Mouse3194" "Mouse3449" "Mouse3178" "Mouse3198"
[427] "Mouse3620" "Mouse3596" "Mouse3638" "Mouse3222" "Mouse3147" "Mouse3163"
[433] "Mouse3273" "Mouse3473" "Mouse3578" "Mouse3465" "Mouse3279" "Mouse3558"
[439] "Mouse3443" "Mouse3490" "Mouse3460" "Mouse3248" "Mouse3243" "Mouse3431"
[445] "Mouse3564" "Mouse3347" "Mouse3565" "Mouse3525" "Mouse3574" "Mouse3329"
[451] "Mouse3140" "Mouse3257" "Mouse3328" "Mouse3193" "Mouse3132" "Mouse3220"
[457] "Mouse3235" "Mouse3499" "Mouse3246" "Mouse3270" "Mouse3608" "Mouse3442"
[463] "Mouse3157" "Mouse3642" "Mouse3566" "Mouse3139" "Mouse3282" "Mouse3053"
[469] "Mouse3454" "Mouse3363" "Mouse3213" "Mouse3654" "Mouse3514" "Mouse3341"
[475] "Mouse3401" "Mouse3388" "Mouse3604" "Mouse3161" "Mouse3451" "Mouse3634"
[481] "Mouse3482" "Mouse3559" "Mouse3645" "Mouse3264" "Mouse3155" "Mouse3251"
[487] "Mouse3297" "Mouse3541" "Mouse3158" "Mouse3294"

[[2]]
[1] "BB" "BR" "RR"

[[3]]
 [1] "rs4232073"  "rs13483548" "rs13483549" "rs13483550" "rs13483554"
 [6] "rs13483555" "rs3090321"  "rs3090137"  "rs6309315"  "rs13483577"
[11] "rs3090325"  "rs13483579" "rs13483584" "rs13483586" "rs13483587"
[16] "rs13483589" "rs13483592" "rs13483593" "rs6344448"  "rs13483594"
[21] "rs13483595" "rs3705022"  "rs13483609" "rs13483612" "rs13483648"
[26] "rs13483650" "rs13483654" "rs13483658" "rs13483660" "rs13483664"
[31] "rs13483666" "rs13483667" "rs13483670" "rs8275553"  "rs8275912"
[36] "rs13483677" "rs13483679" "rs13483680" "rs13483681" "rs3660143"
[41] "rs13483682" "rs13483683" "rs13483685" "rs13483686" "rs6355398"
[46] "rs4222106"  "rs13483690" "rs13483693" "rs13483695" "rs13483699"

View the first three rows of genotype probabilities for the first genotyped marker on chromosome 19.

R 

(probs$`19`)[1:5,,"rs4232073"]

OUTPUT 

                    BB           BR           RR
Mouse3051 1.317728e-11 1.235895e-07 9.999999e-01
Mouse3551 9.999840e-01 1.595361e-05 5.027172e-08
Mouse3430 1.317728e-11 1.235895e-07 9.999999e-01
Mouse3476 9.999999e-01 1.235895e-07 1.317728e-11
Mouse3414 6.179474e-08 9.999999e-01 6.179474e-08

We can also view the genotype probabilities using plot_genoprob. The arguments to this function specify:

  1. probs: the genotype probabilities,
  2. map: the marker map,
  3. ind: the index of the individual to plot,
  4. chr: the index of the chromosome to plot.

R 

plot_genoprob(probs = probs, 
              map   = cross$pmap, 
              ind   = 1, 
              chr   = 19, 
              main  = rownames(probs[['19']])[1])

The coordinates along chromosome 19 are shown on the horizontal axis and the three genotypes are shown on the vertical axis. Higher genotype probabilities are plotted in darker shades. This mouse has a RR genotype on the proximal end of the chromosome and transitions to BR.

Challenge 1

1). Load a second dataset from Arabidopsis recombinant inbred lines (Moore et al, Genetics, 2013) in a study of plant root response to gravity (gravitropism).

grav <- read_cross2(file = system.file('extdata', 'grav2.zip', package = 'qtl2'))
2). How many individuals were in the study? How many phenotypes? How many chromosomes?
3). Insert pseudomarkers at 1cM intervals and save the results to an object called gravmap. Have a look at the first chromosome.
4). Calculate genotype probabilities and save the results to an object called gravpr. View the genotypes for the first three markers and pseudomarkers on chromosome 1 for the first five individuals.

1). grav <- read_cross2(file = system.file('extdata', 'grav2.zip', package = 'qtl2'))
2). summary(grav)
3). gravmap <- insert_pseudomarkers(map = grav$gmap, step = 1)
followed by head(gravmap, n=1)
4). gravpr <- calc_genoprob(cross = grav, map = gravmap) followed by
(gravpr$``1``)[1:5,,"PVV4"], (gravpr$1)[1:5,,"c1.loc1"], and
(gravpr$1)[1:5,,"c1.loc2"]

R 

m  = maxmarg(probs)
ph = guess_phase(cross, m)
plot_onegeno(ph, cross$pmap)

Challenge 2

Calculate genotype probabilities for a different data set from the qtl2 data repository, this one from a study of obesity and diabetes in a C57BL/6 (B6) × BTBR intercross.
1). Create a new script in RStudio with File -> New File -> R Script.
2) Download the B6 x BTBR zip file from the qtl2 data repository into an object called b6btbr by running this code:
b6btbr <- read_cross2(file = "https://raw.githubusercontent.com/rqtl/qtl2data/master/B6BTBR/b6btbr.zip")
3). View a summary of the b6btbr data. How many individuals? phenotypes? chromosomes? markers?
4). View the genetic map for the b6btbr data.
5). Insert pseudomarkers at 2 cM intervals. Assign the results to an object called b6btbrmap.
6). Calculate genotype probabilities assuming a genotyping error probability of 0.001. Assign the results to an object called b6btbrpr.
7). View the first several rows of genotype probabilities for any marker on chromosome 18.

1). Create a new script in RStudio with File -> New File -> R Script.
2). b6btbr <- read_cross2(file = "https://raw.githubusercontent.com/rqtl/qtl2data/master/B6BTBR/b6btbr.zip
3). summary(b6btbr) shows 544 individuals, 3 phenotypes, 20 chromosomes, 2057 markers.
4). b6btbr$gmap
5). b6btbrmap <- insert_pseudomarkers(map=b6btbr$gmap, step=2)
6). b6btbrpr <- calc_genoprob(cross=b6btbr, map=b6btbrmap, error_prob=0.001)
7). dimnames((b6btbrpr$18)) shows all marker names for chromosome 18. head((b6btbrpr$18)[,,"c18.loc48"]) gives genotype probabilities for an example pseudomarker, while head((b6btbrpr$18)[,,"rs6338896"]) gives genotype probabilities for a genotyped marker.

Parallel calculations (optional) To speed up the calculations with large datasets on a multi-core machine, you can use the argument cores. With cores=0, the number of available cores will be detected via parallel::detectCores(). Otherwise, specify the number of cores as a positive integer.

R 

probs <- calc_genoprob(cross = iron, map = map, error_prob = 0.002, cores = 4)

Allele probabilities (optional) The genome scan functions use genotype probabilities as well as a matrix of phenotypes. If you wished to perform a genome scan via an additive allele model, you would first convert the genotype probabilities to allele probabilities, using the function genoprob_to_alleleprob().

R 

apr <- genoprob_to_alleleprob(probs = probs)

The figure below shows genotype and allele probabilities for 3 samples. In the Diversity Outbred, there are 36 possible genotype states (AA, AB, AC, …, BB, BC, BD, …, CC, CD, CE, …, DD, DE, DF, …, EE,…) or 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1. The first SNP below has genotype BB. In the table describing alleles (8 state founder probabilities), the probability that this SNP has a B allele is 1. The 2nd SNP has genotype BH, so the allele table shows a probability of 0.5 for B and 0.5 for H. The third SNP is either BG or BH, and has a probability of 0.5 for each of these genotypes. The allele table shows a probability of 0.5 for allele B, and 0.25 for both G and H.

Genotype and allele probabilities{‘a table showing the probabilities for each of 36 genotypes in the Diversity Outbred followed by a second table showing probabilities for each of the 8 founder alleles’}

Key Points

  • The first step in QTL analysis is to calculate genotype probabilities.
  • Calculate genotype probabilities between genotyped markers with calc_genoprob().