Experimental Design

The paradigm for the programs in the QTL Cartographer package is that of highly inbred lines with very little genetic variation within lines but variation between lines. We shall refer to these inbred lines as parental lines and denote them by the symbols $P_1$ and $P_2$. As a general rule, the $P_1$ lines will correspond to the ``high'' lines with respect to the trait of interest, that is they will have mean values larger than the $P_2$ or ``low'' lines. These parental lines can be crossed to produce $F_1$ lines which are heterozygous for both markers and QTLs. One can then cross the $F_1$ populations with either parental line to produce backcrosses. The symbols $B_1$ and $B_2$ will refer to backcrosses involving the $P_1$ and $P_2$ lines, respectively. Alternatively, the $F_1$ lines can be intercrossed to produce $F_2$ lines.

In each of these cases, the resultant lines will have variation in both the trait of interest and the underlying quantitative trait loci and marker genotypes. These crosses are illustrated in Figure 1.1. We can then look for correlations between the trait in question and marker genes that have been mapped previously.

Figure 1.1: Basic Cross

We have also included options for more complex experimental designs, including recombinant inbred lines, general $F_t$ lines produced by selfing or random crossing of $F_{t-1}$ lines, etc. The programs in the QTL Cartographer system will need to know the type of experimental design used to create the data. This design is encoded by a string of characters. If the letter $i$ stands for some integer, then the possible crosses will be $B_i$, $SF_i$, $RF_i$, $RI_i$, $T(XX)SF_i$ and $T(XX)RF_i$. The B stands for a backcross and the integer attached to it will indicate the parental line to which the $F_1$ line was crossed to (either 1 or 2). If there was repeated backcrossing to one of the parental lines, this can be indicated by attaching two integers to the B: $B_{ij}$ indicates that there were $j$ generations of backcrossing to parental line $i$. $B_{11}$ is equivalent to $B_1$. $SF_i$ stands for selfed intercross lines and the integer indicates the generation $(i = 2, 3, \ldots)$. $RF_i$ stands for randomly mated intercross lines. RI means recombinant inbred lines, and the integer can take on one of three values: 0, 1, and 2. A 1 indicates RI lines derived by selfing, a 2 by sib mating and a 0 means doubled haploid lines.

Table 1.1: Summary of Experimental Design Codes

Design	Code	Example
Backcross to $P_i$	$B_i$	B1
Backcross $j$ times to $P_i$	$B_{ij}$	B13
Selfed generation $i$ intercross	$SF_{i}$	SF3
Randomly mated generation $i$ intercross	$RF_{i}$	RF2
Doubled Haploid	$RI_0$	RI0
Recombinant Inbred via selfing	$RI_1$	RI1
Recombinant Inbred via sib mating	$RI_2$	RI2
Testcross of $SF_i$ to $P_j$	$T(B_j)SF_i$	T(B1)SF3
Testcross of $SF_i$ for $j$ generations	$T(SF_{i+j})SF_i$	T(SF4)SF3
Testcross of $RF_i$ to $P_j$	$T(B_j)RF_i$	T(B1)RF3
Design III	$T(D3)SF_i$	T(D3)SF5

The T indicates that the data are the result of a test cross. For a test cross, genotyping is done on an intercross ($SF_i$ or $RF_i$) and phenotyping on a cross derived from that intercross. The first part of the string, T(XX) indicates that phenotyping is done on the XX population and the second part ($SF_i$ or $RF_i$) indicates the genotyped population. XX can be a $B_1$, $B_2$, $SF_i$ or $D_3$ for $SF_i$ lines or $B_1$ or $B_2$ for $RF_i$ lines. $D_3$ stands for Design III experiments [Cockerham and ZengCockerham and Zeng1996].

All of the above experimental designs can be simulated, and all but the Design III experiments can be analyzed. Table 1.1 lists all the experimental designs and their QTL Cartographer codes. The experimental designs of Table 1.1 can be specified in Rcross for simulations or in certain data input files (see Section 6.3.2).