Table 1.

Conditional probabilities of QTL for two backcrosses populations from mating between DH (or RI) lines and parental lines (P₁ and P₂)

Backcross Types	Marker genotypes	Expected frequencya)
		DH			RI
		QiQi	Qiqi	qiqi	QiQi	Qiqi	qiqi
DH or RI×P1	Mi−Mi−Mi+Mi+	s1s2/s	r1r2/s	0	$\frac{1}{1+4r_1{r}_2}$	$\frac{4r_1{r}_2}{1+4r_1{r}_2}$	0
	Mi−Mi−Mi+Mi+	s1r2/r	r1s2/r	0	r2/(r1+r2)	r1/(r1+r2)	0
	Mi−mi−Mi+Mi+	r1s2/r	s1r2/r	0	r1/(r1+r2)	r2/(r1+r2)	0
	Mi−mi−Mi+mi+	r1r2/s	s1s2/s	0	$\frac{4r_1{r}_2}{1+4r_1{r}_2}$	$\frac{1}{1+4r_1{r}_2}$	0
DH or RI×P2	Mi−mi−Mi+mi+	0	s1s2/s	r1r2/s	0	$\frac{1}{1+4r_1{r}_2}$	$\frac{4r_1{r}_2}{1+4r_1{r}_2}$
	Mi−mi−mi+mi+	0	s1r2/r	r1s2/r	0	r2/(r1+r2)	r1/(r1+r2)
	mi−mi−Mi+mi+	0	r1s2/r	s1r2/r	0	r1/(r1+r2)	r2/(r1+r2)
	mi−mi−mi+mi+	0	r1r2/s	s1s2/s	0	$\frac{4r_1{r}_2}{1+4r_1{r}_2}$	$\frac{1}{1+4r_1{r}_2}$

^aThe putative QTL (Q_i) and two flanking marker are ordered along the chromosome as M_i−→Q_i→M_i+, where the recombination rate between M_i− and M_i+ is denoted as r, the one between M_i− and Q_i denoted as r₁, and the one between Q_i and M_i+ denoted as r₂; s=1−r, s₁=1−r₁, and s₂=1−r₂.