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The Journals of Gerontology Series A: Biological Sciences and Medical Sciences 57:B409-B414 (2002)
© 2002 The Gerontological Society of America

Sex Specificity, Life-Span QTLs, and Statistical Power

James W. Curtsingera

a Department of Ecology, Evolution, and Behavior, University of Minnesota, St. Paul

James W. Curtsinger, 100 Ecology, 1987 Upper Buford Circle, St. Paul, MN 55108 E-mail: jwcurt{at}tc.umn.edu.

Decision Editor: James R. Smith, PhD


   Abstract
Top
 Abstract
Sampling Experiments
 Interval Mapping and Composite...
 General Considerations and...
 References
 
Most of the quantitative trait loci (QTLs) that have been found to influence life span in Drosophila and Mus organisms are reported to have genetic effects limited to one sex. Here I study the statistical properties of sex-limited QTLs by randomly sampling data from an exceptionally large Drosophila experiment, and then asking how sample size influences outcomes. The sampling study suggests that, for the particular data analyzed here, even moderately large experiments, of the order of 104 individuals, can have a high probability of detecting sex-limited effects when they are not actually present. If a particular QTL is present in both sexes, and if the probability of detecting it in each sex is moderately high, say 80%, then there is a 32% chance of erroneously concluding that there is sex specificity. A comparison of interval mapping and composite interval mapping methods of data analysis suggests that the latter can inflate the appearance of sex specificity and sexual antagonism, depending on the choice of number of background covariates in the analysis. Conclusive evidence for sex-limited QTLs will require demonstration that results are robust to methods of statistical analysis, and experimental replication.

QUANTITATIVE trait locus (QTL) mapping is a set of procedures for estimating the chromosomal locations of genes that contribute to variation in polygenic traits (1)(2). QTL mapping has been used to study many phenotypes in a variety of plant and animal species, often resulting in the detection of a small number of QTLs that, in combination, explain 20–60% of the total phenotypic variance (2). These studies offer the hope that complex polygenic traits can be broken down into component genetic parts.

Experimental gerontologists have used QTL mapping to localize chromosomal regions responsible for variations in life span and related traits in Caenorhabditis elegans (3)(4)(5)(6), Drosophila melanogaster (7)(8)(9)(10)(11)(12)(13)(14), and Mus musculus (15)(16)(17)(18). A striking feature of life-span QTLs in flies and mice is the predominance of genetic effects that are limited to one sex. Nuzhdin and colleagues (7) detected five QTLs for life span in a set of recombinant inbred lines of D. melanogaster, four male specific and one female specific. Subsequent work on the same lines of flies reported three sex-specific QTLs out of six total (11) and 14 sex-specific QTLs out of 17 total (12). Miller and colleagues (16) reported genetic marker associations with life span among the progeny of a four-way cross between two F1 hybrid mouse stocks. Although none of the associations attained experimentwise levels of statistical significance, seven cases were suggestive, all sex specific. Subsequent work with the same population of mice has provided additional support for two life-span QTLs that do attain experimentwise levels of statistical significance, both sex specific (17). Taken as a whole, these observations support the novel and very interesting hypothesis that modification of life span frequently occurs by different cellular and genetic mechanisms in males and females.

Observations in my laboratory suggest that the detection of sex-limited QTLs is affected by the design of the mapping experiment. Curtsinger and colleagues (8) reported four autosomal life-span QTLs in a backcross population of D. melanogaster, two of which were specific to males and two of which were shared by the sexes. Subsequent work with the same genetic material in the same laboratory environment found life-span QTLs with genetic effects expressed in both sexes (14)(18). The first experiments were done on a small scale, with no replication of recombinant genotypes, whereas the later experiments were large, employing 56 recombinant inbred lines, over 1000 life-span measurements per line, and fivefold replication of life-span measurements. The difference between earlier and later results suggests that either the QTLs changed from sex specific to sex shared over a brief period of time, which seems very unlikely, or that the smaller and less powerful experiment gave only partial and misleading information about the properties of life-span QTLs.

One definition of statistical power is the probability that a test will reject the null hypothesis when it is false. In the context of QTL mapping, power is the probability of detecting a QTL when it is actually present. Many factors influence the power associated with a particular mapping experiment, including the magnitude of genetic effects, the density and distribution of marker loci, the breeding design, the number of recombinant genotypes studied, and the method of data analysis (2). The most powerful breeding designs involve replicated progeny genotypes, such as recombinant inbred lines. For such designs, power can depend on both the number of recombinant genotypes studied and on the number of individuals measured per line (19).

Here I consider the issue of statistical power in the context of conclusions about sex-specific QTLs. I show that the probability of detecting sex-specific QTLs is rather sensitive to sample size, and that even moderately large mapping experiments can frequently come to an erroneous conclusion regarding sex specificity. This argument is developed by randomly sampling data generated in a large experiment, and then asking how conclusions are affected by sample size. I also show that one method of data analysis increases the chances of detecting spurious sex-specific and sexually antagonistic effects.


   Sampling Experiments
Top
 Abstract
 Sampling Experiments
Interval Mapping and Composite...
 General Considerations and...
 References
 
Khazaeli and colleagues (unpublished data, 2002) reported QTLs for life span in D. melanogaster, on the basis of observations of 157,000 flies in 56 recombinant inbred lines. Twenty QTLs were detected, only one of which showed evidence of sex specificity. Multiple closely linked QTLs were found in some regions of the genome, and they are not considered here because of complications arising from linkage. More useful for the present purposes are results for the left arm of chromosome 3, which carries a clearly defined QTL that increases life span in both males and females, observed in both sexes in each of five experimental replications. Also useful are several regions of the X chromosome, which were found to harbor no life-span QTLs in five large, replicated experimental blocks.

Sampling experiments were executed as follows. For each fly in the original experiment there is a record of line, sex, and age at death. For each line and sex, flies were randomly sampled from the original data, without replacement, using the "RAN0" random number generator ((20), p. 195), which is essentially free of sequential correlations. Line means were computed for the sampled data separately for males and females, and then analyzed by interval mapping, using QTL Cartographer WinQTL version 1.2 (21)(22) with the Ri2 design, Kosambi map function, walking speed of 2 centimorgans (cM), and window size of 10 cM. QTL peaks were scored on the X chromosome and the left arm of chromosome 3 (in the interval between 15 and 45 cM from the left telomere) on the basis of likelihood ratios greater than 11.5. Normally, thresholds for statistical significance in QTL mapping are determined by permuting and reanalyzing the data 1000 times. However, because there are 3500 sampled data sets to analyze here, the full permutation analysis is not feasible, so an arbitrary, conservative value was chosen. The sampling procedure was repeated for sample sizes 5, 10, 25, 50, 100, 200, and 300 flies per sex and genotype, with 500 replications per sample size.

Results of the sampling experiments are shown in Fig. 1. Power curves are smoothed by distance-weighted least squares (23) to clarify trends. Power to detect the life-span QTL on the left arm of chromosome 3 is clearly sensitive to sample size, particularly below 100 animals per sex and genotype (11,600 animals total per experiment). From the estimated power curves it is possible to calculate the probability of executing an experiment in which the QTL is observed in one sex but not the other. If the probability of detecting a particular QTL in males when it is actually present is µ, and the probability of detecting it in females, given that it is present, is {phi}, then the probability of detecting the QTL in just one sex is µ(1 - {phi}) + {phi}(1 - µ). The error rate calculated from estimates of µ and {phi} is shown in Fig. 1. It is nearly 60% for very small sample sizes, declines to 20% at sample sizes of 100 individuals for each sex and genotype, and reaches the 5% level at approximately 200 flies per sex and genotype. For extremely low sample size, fewer than 10 animals per sex and genotype, the error rate is very low (not shown), but the "accuracy" of such experiments is entirely illusory, arising from the low probability of detecting the QTL in either sex.



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  		Figure 1. Power curves and error rate for the Drosophila sampling experiment. The two upper curves show how power to detect a quantitative trait locus (QTL) that is present in both sexes varies with sample size. Power curves were estimated by randomly sampling data from an experiment with 56 inbred lines, five replicated blocks, and 157,000 individuals (19). The lower curve is the calculated probability of detecting the QTL in only one sex when it is actually present in both. The error rate declines to 5% only when sample sizes are ~200 animals per line per sex.

 
A second manner in which erroneous conclusions about sex specificity can arise is if there is no QTL at a particular chromosomal location in either sex, but a phantom QTL is detected in one sex. The probability of this Type I error, estimated by counting apparent X-linked QTLs in regions known to be devoid of QTLs, is negligible, of the order of 1% for small sample sizes and declining to zero at moderate sample sizes.


   Interval Mapping and Composite Interval Mapping
Top
 Abstract
 Sampling Experiments
 Interval Mapping and Composite...
General Considerations and...
 References
 
The most widely used method for statistical analysis of QTL data is interval mapping (IM) (24), a maximum-likelihood technique that involves testing for the presence of QTLs in each small segment of the genome considered one at a time. An important modification of the IM method is composite interval mapping (CIM) (25)(26)(27). In the CIM method, the analysis is similar to IM, but a subset of marker loci in the genetic background are included as covariates in the analysis. Under certain circumstances, CIM can greatly improve the resolution of QTL peaks by reducing residual variation and eliminating "ghost" peaks that arise from the overlap of true QTL peaks (2).

Although the CIM method is a significant advance in QTL methodology, there are unresolved problems in choosing the covariates. With too few covariates, CIM gives the same results as IM. With too many covariates, the results of CIM can become meaningless. Because it is not clear how the covariates should be chosen, CIM has been somewhat controversial. For example, Lynch and Walsh (2) support the method, but Broman (28) specifically recommends against its use.

All recent Drosophila experiments that report high levels of sex-specific life-span QTLs use CIM. This raises the possibility that the unresolved covariate problem might be influencing the interpretation of life-span QTL data. Nuzhdin and colleagues (7) were aware of this potential problem, which they addressed by comparing results obtained by CIM with regression of phenotypes on marker genotypes, a procedure that is very similar to IM when the marker map is dense. They found fairly good correspondence of results under the two methods. Subsequent studies with the same lines have addressed the possible biases of CIM by using additional, independent analyses for QTL mapping, including analyses of variance.

In order to further investigate the covariate problem, the data of Khazaeli and colleagues (unpublished data, 2002) have been reanalyzed by using both IM and CIM. IM was implemented as already described. CIM was implemented by using QTL Cartographer WinQTL version 1.2 (21)(22) with the Ri2 design, Kosambi map function, walking speed of 2 cM, forward regression, and a window size of 10 cM. CIM was executed with 5, 10, and 15 background covariates, spanning and exceeding the range normally reported in the literature. For each 2-cM segment of the genome, the additive effect on life span was estimated in both males and females, using both IM and CIM methods with all three levels of covariates. This procedure was repeated for five independent replicates of the mapping experiment, generating a total of 770 estimates of additive genetic effect in each sex by each method of data analysis.

Results of the different methods of data analysis are shown in Fig. 2, where additive effects in males are plotted against additive effects in females for each chromosomal segment. The IM method produces estimates that lie predominately in the upper right and lower left quadrants of Fig. 2, indicating similar genetic effects in males and females. There are three exceptional points in the lower right quadrant, suggesting a small degree of sex specificity. CIM with five covariates also produces estimates that are predominately positively correlated in males and females (Fig. 2), but more points lie in the lower right quadrant and along the axes far from the origin, suggesting a greater degree of sex-specific and sexually antagonistic genetic effects. CIM with 10 or 15 covariates (Fig. 2 and Fig. 2) produces many points in the lower right quadrant and many points along the y axis, suggesting a high degree of sex specificity and sexual antagonism. As the number of covariates increases from zero (equivalent to IM) to 5, 10, and then 15, the correlation of genetic effects across the sexes declines from 0.80 to 0.48, and the variance of estimated differences between male and female effects for each chromosomal segment increases more than threefold. Clearly, the degree of sex specificity detected by CIM is dependent on the number of covariates used in the analysis.



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  		Figure 2. Estimates of additive genetic effects on life span for males and females for each of 154 chromosomal segments studied in five replicated experimental blocks, from Khazaeli and colleagues (unpublished data, 2002). Genetic effects are estimated by interval mapping (IM) and composite interval mapping (CIM): A, IM, equivalent to CIM with zero background covariates; B, C, and D, CIM with 5, 10, and 15 background covariates, respectively. The number of covariates significantly influences the appearance of sex-specific and sexually antagonistic genetic effects.

 
At present, there is no simple solution to the CIM covariate problem. A conservative approach employed by Khazaeli and colleagues (unpublished data, 2002) is to avoid CIM altogether, using only IM. If CIM is used, QTL Cartographer suggests setting the number of covariates to the square root of the number of experimental lines, a suggestion followed in most Drosophila studies, including those reporting a high degree of sex specificity for life-span QTLs. One can also address the problem by employing additional analyses, including analyses of variance, for independent verification of sex-specific effects, as several of the Drosophila life-span QTL papers have done. Another strategy is to try to show that putative sex-specific effects are robust to changes in the parameters of the CIM analysis. For the data considered here, the putative sex-specific and sexually antagonistic effects are clearly not robust (Fig. 2), and they do not replicate well across experimental blocks. An analysis of variance on likelihood ratios observed for each chromosomal segment indicates that IM produces a high degree of repeatability across experimental blocks (chromosomal position explains 71% of the variance), whereas CIM with 15 parameters (twice the recommended number) produces dramatically lower repeatability (chromosomal position explains 20% of the variance across experimental blocks). For the data analyzed here, it appears that CIM produces unrepeatable artifacts with artificially exaggerated sex specificity and sexual antagonism.


   General Considerations and Conclusions
Top
 Abstract
 Sampling Experiments
 Interval Mapping and Composite...
 General Considerations and...
References
 
Consider again the general case in which the probability of detecting a hypothetical QTL in males, given that it is present, is µ, the probability of detecting it in females, given that it is present at the same chromosomal location, is {phi}, and the probability of erroneously concluding that there is a sex-specific QTL when it is actually present in both sexes is µ(1 - {phi}) + {phi}(1 - µ). The three-dimensional error surface, which shows the error rate as a function of µ and {phi}, is saddle shaped (Fig. 3). There is a saddle point at (0.5, 0.5) on the µ,{phi} plane. That point is a local maximum along the main diagonal, running from (0, 0) to (1)(1), and is a local minimum along the off-diagonal, from (0, 1) to (1, 0). If statistical power were similar in the two sexes, then a weak experiment with a power of 50% in each sex would produce a 50% error rate. A moderately powerful experiment, one with 80% power in each sex, would have a 32% error rate; 95% power in each sex would produce a 9.5% error rate. The situation becomes worse when power varies inversely in the sexes, as could arise in situations in which the variance in one sex is larger than the other; then the 50% error rate at the saddle point is a minimum.



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  		Figure 3. Theoretical probability of erroneously concluding that there is a sex-specific QTL, plotted as a function of statistical power in each sex. The surface is saddle shaped, with a saddle point at (0.5, 0.5) on the base plane. If power is similar in males and females, the error rate is maximal at 50% power and then declines as power increases to 100%.

 
The sampling experiments executed with Drosophila data show that, even for moderately large experiments involving several thousand animals, there can be an alarmingly high error rate. Khazaeli and colleagues (unpublished data, 2002) measured 157,000 animals total and over 1000 animals for each sex and genotype, but if sample sizes had been 50 animals per sex and genotype (5600 animals total), there would have been greater than a 40% error rate. With 100 animals per sex and genotype, the error rate would have been 20% (Fig. 1). These specific estimates cannot be directly extrapolated to experiments in other laboratories, but the general point still applies: any experiment that has less than the highest levels of statistical power is susceptible to producing an illusion of sex-specific QTLs. All of the recent reports of sex-specific life-span QTLs in Drosophila involve 20–30 animals per sex and genotype, and several thousand animals total per experiment, and are therefore potentially subject to this problem. Those reports also use CIM, which might exacerbate the problem. One argument in favor of those reports is that there is internal consistency: the observed correlations of life spans between the sexes are near zero, as one might expect if most of the genetic effects are sex limited. Unfortunately, low phenotypic correlations and sex-specific QTLs could both arise from the same root problem of limited statistical power.

There is no reason to think that these arguments apply only to Drosophila. Broman (28) discusses a backcross design appropriate for mice, and notes that with total sample sizes of 100–200 animals, and a phenotypic standard deviation of 11.5 units, power varies from 97% for QTLs of large effect (11 units) to 2% for QTLs of small effect (5 units). Clearly, the magnitude of genetic effect of a particular QTL, which is beyond the control of the experimenter, can have dramatic effects on power. This fact, plus logistical limitations on the size of mapping experiments, is likely to make the detection of sex-limited QTLs in rodents exceptionally difficult, unless QTLs with large effect are discovered.

QTL mapping experiments of moderate or less statistical power can be misleading in several ways. It is well known that even very weak mapping experiments have a high probability of detecting at least one QTL if many are present, and that the variance explained by detected QTLs is dramatically and systematically overestimated (2)(29). For an experimentalist it is comforting that the Type I error rate is low (when a QTL is detected by IM, it is very likely that one is actually present) but disconcerting that the Type II error rate is high (real QTLs are often undetected in one sex or the other). Altering the criteria for significance could help with the latter problem but also lead to an unwelcome increase in false positives. The only solution that I can see is replication: artifacts do not have a high probability of replicating. Because any mapping experiment might have appreciably less than 100% power, the only conclusive demonstration of sex-limited QTLs for life span or any other trait must come from replicated observations with the same genotypes studied in the same environment.

Replication will have its own special challenges. With recombinant inbred lines of Drosophila it is straightforward to replicate whole genomes, provided that one ignores recent spontaneous mutations. With the intercross and four-way cross designs used in mouse studies, exact replication of entire genomes at the level of individual experimental animals is not possible. In those cases it is necessary to define genotypes solely by marker loci, implicitly assuming that there is no effect of genetic background in unmarked regions of the genome. Both fly and mouse studies will be subject to microenvironmental differences between replicate experiments that are beyond the control of the experimenter, and the possibility of significant genotype by replicate interaction that obscures main effects. There is no clear consensus in the QTL literature about the magnitude of interaction that one might expect ((2), Table 15.6), but it is potentially large. Statistical power will also matter; if there are many QTLs, then small experiments will have a large chance of detecting some QTL, but they will have little chance of detecting the same QTL in replicated experiments. Considering all of these factors, it is clear that making replicated observations of a particular QTL and its gender-specific properties is potentially a daunting task, but is nevertheless one that can be accomplished, as demonstrated by Khazaeli and colleagues (unpublished data, 2002).


   Acknowledgments
 
This research was supported by Grants AG 09711 and AG 11722 from the National Institute on Aging at the National Institutes of Health.

I thank A. Galecki, R. Miller, and S. Nuzhdin for their critical comments.

Received May 24, 2002

Accepted August 13, 2002


   References
Top
 Abstract
 Sampling Experiments
 Interval Mapping and Composite...
 General Considerations and...
 References
 

  1. Tanksley SD, 1993. Mapping polygenes. Annu Rev Genet 27:205-233. [Medline]
  2. Lynch M, Walsh B. Genetics and Analysis of Quantitative Traits. Sunderland, MA: Sinauer Associates; 1988.
  3. Ebert RH, II Cherkasova VA, Dennis RA, et al. 1993. Longevity determining genes in Caenorhabditis elegans: chromosomal mapping of multiple noninteractive loci. Genetics 135:1003-1010. [Abstract]
  4. Shook DR, Brooks D, Johnson TE, 1996. Mapping quantitative trait loci affecting life history traits in the nematode Caenorhabditis elegans. Genetics 142:801-817. [Abstract]
  5. Shook DR, Johnson TE, 1999. Quantitative trait loci affecting survival and fertility-related traits in Caenorhabditis elegans show genotype-environment interactions, pleiotropy, and epistasis. Genetics 153:1233-1243. [Abstract/Free Full Text]
  6. Ayyadevara S, Ayyadevara S, Hou S, Thaden JJ, Reis RJS, 2001. Genetic mapping of quantitative trait loci governing longevity of Caenorhabditis elegans in recombinant-inbred progeny of a Bergerac-BO x RC301 interstrain cross. Genetics 157:655-666. [Abstract/Free Full Text]
  7. Nuzhdin SV, Pasyukova EG, Dilda CL, Zeng Z-B, MacKay TFC, 1997. Sex-specific quantitative trait loci affecting longevity in Drosophila melanogaster. Proc Natl Acad Sci USA 94:9734-9739. [Abstract/Free Full Text]
  8. Curtsinger JW, Fukui HH, Resler AS, Kelly K, Khazaeli AA, 1998. Genetic analysis of extended lifespan in Drosophila melanogaster. I. RAPD screen for genetic divergence between selected and control lines. Genetica 104:21-32. [Medline]
  9. Resler AS, Kelly K, Kantor G, Khazaeli AA, Tatar M, Curtsinger JW, 1998. Genetic analysis of extended lifespan in Drosophila melanogaster. II. Replication of the backcross test and molecular characterization of the N14 locus. Genetica 104:33-39. [Medline]
  10. Pasyukova EG, Vieira C, Mackay TFC, 2000. Deficiency mapping of quantitative trait loci affecting longevity in Drosophila melanogaster. Genetics 156:1129-1146. [Abstract/Free Full Text]
  11. Leips J, Mackay TFC, 2000. Quantitative trait loci for lifespan in Drosophila melanogaster: interactions with genetic background and larval density. Genetics 155:1773-1788. [Abstract/Free Full Text]
  12. Viera C, Pasyukova EG, Zeng S, Hackett JB, Lyman RF, Mackay TFC, 2000. Genotype-environment interaction for quantitative trait loci affecting lifespan in Drosophila melanogaster. Genetics 154:213-227. [Abstract/Free Full Text]
  13. Mackay TFC, 2002. The nature of quantitative genetic variation for Drosophila longevity. Mech Aging Dev 123:95-104.
  14. Curtsinger JW, Khazaeli AA, 2002. Lifespan, QTLs, age-specificity, and pleiotropy in Drosophila. Mech Aging Dev 123:81-93.
  15. Gelman R, Watson A, Bronson R, Yunis E, 1988. Murine chromosomal regions correlated with longevity. Genetics 118:693-704. [Abstract/Free Full Text]
  16. Miller RA, Chrisp C, Jackson AU, Burke D, 1998. Marker loci associated with lifespan in genetically heterogeneous mice. J Gerontol Med Sci 53A:M257-M263. [Abstract]
  17. Jackson AU, Fornes A, Galecki A, Miller RA, Burke DT, 1999. Multiple-trait quantitative trait loci analysis using a large mouse sibship. Genetics 151:785-795. [Abstract/Free Full Text]
  18. Jackson AU, Galecki AT, Burke DT, Miller RA, 2002. Mouse loci associated with life span exhibit sex-specific and epistatic effects. J Gerontol Biol Sci 57A:B9-B15. [Abstract/Free Full Text]
  19. Knapp SJ, Bridges WC, 1990. Using molecular markers to estimate quantitative trait locus parameters: power and genetic variances for unreplicated and replicated progeny. Genetics 126:769-777. [Abstract]
  20. Press WH, Flannery BP, Teukolsky SA, Vetterling WT. Numerical Recipes: The Art of Scientific Computing. Cambridge: Cambridge University Press; 1988.
  21. Basten CJ, Weir BS, Zeng Z-B. Zmap—A QTL cartographer. In: Smith C, ed. Proceedings of the 5th World Congress on Genetics Applied to Livestock Production: Computing Strategies and Software. Vol. 2. Guelph, Ontario, Canada: Organizing Committee; 1994:65–66.
  22. Basten CJ, Weir BS, Zeng Z-B. QTL Cartographer, version 1.13, Dept of Statistics, North Carolina State University, 1999.
  23. Wilkinson L. SYSTAT: The System for Statistics. Evanston, IL: Systat, Inc; 1988.
  24. Lander ES, Botstein D, 1989. Mapping Mendelian factors underlying quantitative traits using RFLP linkage maps. Genetics 121:185-199. [Abstract/Free Full Text]
  25. Jansen RC, 1993. Interval mapping of multiple quantitative trait loci. Genetics 135:205-211. [Abstract]
  26. Zeng Z-B, 1993. Theoretical basis for separation of multiple linked gene effects in mapping of quantitative trait loci. Proc Natl Acad Sci USA 90:10,972-10,976. [Abstract/Free Full Text]
  27. Jansen RC, Stam P, 1994. High resolution of quantitative trait loci into multiple loci via interval mapping. Genetics 136:1447-1455. [Abstract]
  28. Broman KW, 2001. Review of statistical methods for QTL mapping in experimental crosses. Lab Animal 30:44-52.
  29. Beavis WD. The power and deceit of QTL experiments: lessons from comparative QTL studies. In: Wilkinson DB, ed. 49th Annual Corn and Sorghum Research Conference. Washington, DC: American Seed Trade Association; 1994:252–268.



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