Mixed effects models for quantitative trait loci mapping with inbred strains.
Fixed effects models have dominated the statistical analysis of genetic crosses between inbred strains. In spite of their popularity, the traditional models ignore polygenic background and must be tailored to each specific cross. We reexamine the role of random effect models in gene mapping with inbred strains. The biggest difficulty in implementing random effect models is the lack of a coherent way of calculating trait covariances between relatives. The standard model for outbred populations is based on premises of genetic equilibrium that simply do not apply to crosses between inbred strains since every animal in a strain is genetically identical and completely homozygous. We fill this theoretical gap by introducing novel combinatorial entities called strain coefficients. With an appropriate theory, it is possible to reformulate QTL mapping and QTL association analysis as an application of mixed models involving both fixed and random effects. After developing this theory, our first example compares the mixed effects model to a standard fixed effects model using simulated advanced intercross line (AIL) data. Our second example deals with hormone data. Here multivariate traits and parameter identifiability questions arise. Our final example involves random mating among eight strains and vividly demonstrates the versatility of our models.
Bauman
Lara E
LE
Department of Genetics, Southwest Foundation for Biomedical Research, San Antonio, Texas 78245-0549, USA. lbauman@sfbrgenetics.org
Sinsheimer
Janet S
JS
Sobel
Eric M
EM
Lange
Kenneth
K
D000818:Animals; D001947:Breeding; D002874:Chromosome Mapping; D019295:Computational Biology; D003198:Computer Simulation; D003433:Crosses, Genetic; D005260:Female; D008297:Male; D051379:Mice; D008954:Models, Biological; D015233:Models, Statistical; D010641:Phenotype; D040641:Quantitative Trait Loci
Genet Epidemiol. 2005 Jul;29(1):36-50
15834862
Genetics. 2001 Sep;159(1):371-87
11560912
Nat Rev Genet. 2005 Apr;6(4):271-86
15803197
Ann Hum Genet. 1982 Oct;46(4):373-83
6961886
Am J Hum Genet. 2000 Mar;66(3):1153-7
10712227
Hum Biol. 1993 Dec;65(6):941-66
8300087
Genetics. 2005 Mar;169(3):1699-709
15654110
Theor Appl Genet. 1990 Jul;80(1):11-6
24220804
Am J Med Genet. 1986 Jul;24(3):483-91
3728567
Genet Epidemiol. 1997;14(6):1053-8
9433623
Twin Res. 2002 Dec;5(6):572-6
12573188
Ann Hum Genet. 2005 Sep;69(Pt 5):590-611
16138917
Genetics. 2000 Oct;156(2):913-22
11014836
Bioinformatics. 2002 Feb;18(2):339-40
11847090
Genetics. 1999 Jul;152(3):1203-16
10388834
Mamm Genome. 1999 Apr;10(4):327-34
10087288
Hum Hered. 2001;51(3):133-44
11173964
Genetics. 1995 Nov;141(3):1199-207
8582624
Am J Hum Genet. 1994 Mar;54(3):535-43
8116623
Genetics. 1989 Jan;121(1):185-99
2563713
Bioinformatics. 2003 May 1;19(7):889-90
12724300
Ann Hum Genet. 1985 Oct;49(4):315-28
4073838
Genetics. 2001 Jan;157(1):445-54
11139524
Genet Epidemiol. 1997;14(6):959-64
9433607
Philos Trans R Soc Lond B Biol Sci. 2005 Jul 29;360(1459):1443-55
16048787
Genetics. 2007 Jan;175(1):321-33
17028314
Am J Hum Genet. 1993 Dec;53(6):1306-19
8250047
Genetics. 1998 Mar;148(3):1373-88
9539450
Genetics. 2005 Sep;171(1):365-76
15965257
Am J Med Genet. 1983 Mar;14(3):513-24
6859102
Proc Natl Acad Sci U S A. 1993 Dec 1;90(23):10972-6
8248199
Am J Hum Genet. 1996 Jun;58(6):1323-37
8651310
Genetics. 1998 Jun;149(2):1139-46
9611221
Genetics. 1999 Oct;153(2):825-35
10610347
Genetics. 1994 Nov;138(3):963-71
7851788
Genes Brain Behav. 2002 Nov;1(4):214-22
12882366
Behav Brain Res. 2001 Nov 1;125(1-2):279-84
11682119
Genet Res. 2000 Jun;75(3):345-55
10893870
Am J Hum Genet. 1999 Aug;65(2):531-44
10417295
Am J Hum Genet. 1990 Dec;47(6):957-67
2239972
Twin Res. 2002 Dec;5(6):554-71
12573187
Biometrics. 2002 Mar;58(1):157-62
11890311
Am J Hum Genet. 1996 Jun;58(6):1347-63
8651312
Genet Epidemiol. 2000;19 Suppl 1:S8-14
11055364
PLoS Biol. 2004 Dec;2(12):e393
15534693
Genetics. 2006 Mar;172(3):1783-97
16361245
Heredity (Edinb). 1992 Oct;69(4):315-24
16718932
Genetics. 2004 Aug;167(4):2055-65
15342540
Am J Med Genet. 1984 Jul;18(3):435-48
6476005
BMC Genet. 2005 Dec 30;6 Suppl 1:S57
16451669
Biostatistics. 2007 Apr;8(2):414-32
16928955
Physiol Genomics. 2003 Sep 29;15(1):44-51
12865502
Genetics. 1994 Apr;136(4):1457-68
8013918
Genet Epidemiol. 2000;19 Suppl 1:S22-8
11055366
Proc Natl Acad Sci U S A. 2000 Nov 7;97(23):12649-54
11050180
Theor Appl Genet. 1993 Sep;86(8):1014-22
24194011