Interpreting the output files

When analyzing an $F_2$ design using composite interval mapping, QTL Cartographer reports 21 columns of information for each position in the walk along the chromosomes. Before enumerating those statistics, it's useful to point out that there are four hypotheses being examined at each position:

• $H_0$: $a=0, d=0$ - Both the additive allelic effect and the dominance deviation are zero.

• $H_1$: $a \ne 0, d=0$ - The additive allelic effect is distinguishable from zero, but the dominance deviation is zero.

• $H_2$: $a=0, d \ne 0$ - The additive allelic effect is zero, but the dominance deviation is distinguishable from zero.

• $H_3$: $a \ne 0, d \ne 0$ - Both the additive allelic effect and the dominance deviation are zero.

Many of the 21 columns in the output correspond to comparisons among these hypotheses or to estimates of additive and dominance effects under a particular hypothesis. Here's what each column in the output corresponds to:

1. Chromosome on which the test position is located.

2. Left flanking marker associated with the test position.

3. Absolute position of the test position from the left telomere of this chromosome (in Morgans).

4. Likelihood-ratio test statistic for $H_3$ versus $H_0$.

5. Likelihood-ratio test statistic for $H_3$ versus $H_1$.

6. Likelihood-ratio test statistic for $H_3$ versus $H_2$.

7. Estimate of the additive allelic effect, $a$, under $H_1$.

8. Estimate of the additive allelic effect, $a$, under $H_3$.

9. Estimate of the dominance effect, $d$, under $H_2$.

10. Estimate of the dominance effect, $d$, under $H_3$.

11. Likelihood-ratio test statistic for $H_1$ versus $H_0$.

12. Likelihood-ratio test statistic for $H_2$ versus $H_0$.

13. $r^2$ for $H_1$ versus $H_0$ - The extent to which $H_1$ reduces the residual variance,⁶ relative to the total variance.⁷

14. $r^2$ for $H_2$ versus $H_0$ - The extent to which $H_2$ reduces the residual variance, relative to the total variance.

15. $r^2$ for $H_3$ versus $H_0$ - The extent to which $H_3$ reduces the residual variance, relative to the total variance.

16. $r^2_t$ for $H_1$ versus $H_0$ - The extent to which $H_1$ reduces the total variance.⁸

17. $r^2_t$ for $H_2$ versus $H_0$ - The extent to which $H_2$ reduces the total variance.

18. $r^2_t$ for $H_3$ versus $H_0$ - The extent to which $H_3$ reduces the total variance.

19. A test statistic, $S$, for normality of the residuals under $H_1$.⁹

20. A test statistic, $S$, for normality of the residuals under $H_2$.

21. A test statistic, $S$, for normality of the residuals under $H_3$.

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