Skip to main content
PMC home page
Genetics logoLink to Genetics
. 1995 Jan;139(1):445–455. doi: 10.1093/genetics/139.1.445

The Contribution of Quantitative Trait Loci and Neutral Marker Loci to the Genetic Variances and Covariances among Quantitative Traits in Random Mating Populations

A Ruiz 1, A Barbadilla 1
PMCID: PMC1206341  PMID: 7705644

Abstract

Using Cockerham's approach of orthogonal scales, we develop genetic models for the effect of an arbitrary number of multiallelic quantitative trait loci (QTLs) or neutral marker loci (NMLs) upon any number of quantitative traits. These models allow the unbiased estimation of the contributions of a set of marker loci to the additive and dominance variances and covariances among traits in a random mating population. The method has been applied to an analysis of allozyme and quantitative data from the European oyster. The contribution of a set of marker loci may either be real, when the markers are actually QTLs, or apparent, when they are NMLs that are in linkage disequilibrium with hidden QTLs. Our results show that the additive and dominance variances contributed by a set of NMLs are always minimum estimates of the corresponding variances contributed by the associated QTLs. In contrast, the apparent contribution of the NMLs to the additive and dominance covariances between two traits may be larger than, equal to or lower than the actual contributions of the QTLs. We also derive an expression for the expected variance explained by the correlation between a quantitative trait and multilocus heterozygosity. This correlation explains only a part of the genetic variance contributed by the markers, i.e., in general, a combination of additive and dominance variances and, thus, provides only very limited information relative to the method supplied here.

Full Text

The Full Text of this article is available as a PDF (1.1 MB).

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Aquadro C. F., Desse S. F., Bland M. M., Langley C. H., Laurie-Ahlberg C. C. Molecular population genetics of the alcohol dehydrogenase gene region of Drosophila melanogaster. Genetics. 1986 Dec;114(4):1165–1190. doi: 10.1093/genetics/114.4.1165. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Avery P. J., Hill W. G. Variability in genetic parameters among small populations. Genet Res. 1977 Jun;29(3):193–213. doi: 10.1017/s0016672300017286. [DOI] [PubMed] [Google Scholar]
  3. Avery P. J., Hill W. G. Variance in quantitative traits due to linked dominant genes and variance in heterozygosity in small populations. Genetics. 1979 Apr;91(4):817–844. doi: 10.1093/genetics/91.4.817. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Barker J. S. Inter-locus interactions: a review of experimental evidence. Theor Popul Biol. 1979 Dec;16(3):323–346. doi: 10.1016/0040-5809(79)90021-2. [DOI] [PubMed] [Google Scholar]
  5. Begun D. J., Aquadro C. F. Levels of naturally occurring DNA polymorphism correlate with recombination rates in D. melanogaster. Nature. 1992 Apr 9;356(6369):519–520. doi: 10.1038/356519a0. [DOI] [PubMed] [Google Scholar]
  6. Bodmer W. F., Felsenstein J. Linkage and selection: theoretical analysis of the deterministic two locus random mating model. Genetics. 1967 Oct;57(2):237–265. doi: 10.1093/genetics/57.2.237. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Boerwinkle E., Sing C. F. Bias of the contribution of single-locus effects to the variance of a quantitative trait. Am J Hum Genet. 1986 Jul;39(1):137–144. [PMC free article] [PubMed] [Google Scholar]
  8. Chakraborty R., Ferrell R. E., Barton S. A., Schull W. J. Genetic polymorphism and fertility parameters in the Aymara of Chile and Bolivia. Ann Hum Genet. 1986 Jan;50(Pt 1):69–82. doi: 10.1111/j.1469-1809.1986.tb01940.x. [DOI] [PubMed] [Google Scholar]
  9. Cockerham C C. An Extension of the Concept of Partitioning Hereditary Variance for Analysis of Covariances among Relatives When Epistasis Is Present. Genetics. 1954 Nov;39(6):859–882. doi: 10.1093/genetics/39.6.859. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Edwards M. D., Stuber C. W., Wendel J. F. Molecular-marker-facilitated investigations of quantitative-trait loci in maize. I. Numbers, genomic distribution and types of gene action. Genetics. 1987 May;116(1):113–125. doi: 10.1093/genetics/116.1.113. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Haley C. S., Knott S. A. A simple regression method for mapping quantitative trait loci in line crosses using flanking markers. Heredity (Edinb) 1992 Oct;69(4):315–324. doi: 10.1038/hdy.1992.131. [DOI] [PubMed] [Google Scholar]
  12. Karlin S. General two-locus selection models: some objectives, results and interpretations. Theor Popul Biol. 1975 Jun;7(3):364–398. doi: 10.1016/0040-5809(75)90025-8. [DOI] [PubMed] [Google Scholar]
  13. Knott S. A., Haley C. S. Maximum likelihood mapping of quantitative trait loci using full-sib families. Genetics. 1992 Dec;132(4):1211–1222. doi: 10.1093/genetics/132.4.1211. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Koehn R. K., Diehl W. J., Scott T. M. The differential contribution by individual enzymes of glycolysis and protein catabolism to the relationship between heterozygosity and growth rate in the coot clam, Mulinia lateralis. Genetics. 1988 Jan;118(1):121–130. doi: 10.1093/genetics/118.1.121. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Lande R., Thompson R. Efficiency of marker-assisted selection in the improvement of quantitative traits. Genetics. 1990 Mar;124(3):743–756. doi: 10.1093/genetics/124.3.743. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. Lander E. S., Botstein D. Mapping mendelian factors underlying quantitative traits using RFLP linkage maps. Genetics. 1989 Jan;121(1):185–199. doi: 10.1093/genetics/121.1.185. [DOI] [PMC free article] [PubMed] [Google Scholar]
  17. Nei M., Li W. H. Linkage disequilibrium in subdivided populations. Genetics. 1973 Sep;75(1):213–219. doi: 10.1093/genetics/75.1.213. [DOI] [PMC free article] [PubMed] [Google Scholar]
  18. Nodari R. O., Tsai S. M., Guzmán P., Gilbertson R. L., Gepts P. Toward an integrated linkage map of common bean. III. Mapping genetic factors controlling host-bacteria interactions. Genetics. 1993 May;134(1):341–350. doi: 10.1093/genetics/134.1.341. [DOI] [PMC free article] [PubMed] [Google Scholar]
  19. Paterson A. H., Damon S., Hewitt J. D., Zamir D., Rabinowitch H. D., Lincoln S. E., Lander E. S., Tanksley S. D. Mendelian factors underlying quantitative traits in tomato: comparison across species, generations, and environments. Genetics. 1991 Jan;127(1):181–197. doi: 10.1093/genetics/127.1.181. [DOI] [PMC free article] [PubMed] [Google Scholar]
  20. Pogson G. H., Zouros E. Allozyme and RFLP heterozygosities as correlates of growth rate in the scallop Placopecten magellanicus: a test of the associative overdominance hypothesis. Genetics. 1994 May;137(1):221–231. doi: 10.1093/genetics/137.1.221. [DOI] [PMC free article] [PubMed] [Google Scholar]
  21. Robinson W. P., Asmussen M. A., Thomson G. Three-locus systems impose additional constraints on pairwise disequilibria. Genetics. 1991 Nov;129(3):925–930. doi: 10.1093/genetics/129.3.925. [DOI] [PMC free article] [PubMed] [Google Scholar]
  22. Robinson W. P., Cambon-Thomsen A., Borot N., Klitz W., Thomson G. Selection, hitchhiking and disequilibrium analysis at three linked loci with application to HLA data. Genetics. 1991 Nov;129(3):931–948. doi: 10.1093/genetics/129.3.931. [DOI] [PMC free article] [PubMed] [Google Scholar]
  23. Ruiz A., Santos M., Barbadilla A., Quezada-Díaz J. E., Hasson E., Fontdevila A. Genetic variance for body size in a natural population of Drosophila buzzatii. Genetics. 1991 Aug;128(4):739–750. doi: 10.1093/genetics/128.4.739. [DOI] [PMC free article] [PubMed] [Google Scholar]
  24. Sax K. The Association of Size Differences with Seed-Coat Pattern and Pigmentation in PHASEOLUS VULGARIS. Genetics. 1923 Nov;8(6):552–560. doi: 10.1093/genetics/8.6.552. [DOI] [PMC free article] [PubMed] [Google Scholar]
  25. Sing C. F., Davignon J. Role of the apolipoprotein E polymorphism in determining normal plasma lipid and lipoprotein variation. Am J Hum Genet. 1985 Mar;37(2):268–285. [PMC free article] [PubMed] [Google Scholar]
  26. Sing C. F., Orr J. D. Analysis of genetic and environmental sources of variation in serum cholesterol in Tecumseh, Michigan. III. Identification of genetic effects using 12 polymorphic genetic blood marker systems. Am J Hum Genet. 1976 Sep;28(5):453–464. [PMC free article] [PubMed] [Google Scholar]
  27. Slatkin M. Linkage disequilibrium in growing and stable populations. Genetics. 1994 May;137(1):331–336. doi: 10.1093/genetics/137.1.331. [DOI] [PMC free article] [PubMed] [Google Scholar]
  28. Zapata C., Alvarez G. On the detection of nonrandom associations between DNA polymorphisms in natural populations of Drosophila. Mol Biol Evol. 1993 Jul;10(4):823–841. doi: 10.1093/oxfordjournals.molbev.a040045. [DOI] [PubMed] [Google Scholar]

Articles from Genetics are provided here courtesy of Oxford University Press

RESOURCES