Experimental Design Considerations

Traits based on field, greenhouse or laboratory studies usually involve taking measurements on replications of the offspring lines. Many agronomic experiments involve random assignment of offspring within a block of field plots. The randomized complete block design (RCBD) provides a way to remove some of the larger field variation by blocking offspring in homogeneous units. The linear model for such a design can be written as

   trait = mean + block + geno + line(geno) + plot error ,

in which line(geno) is the effect of an offspring line with any given genotype and plot error is the unexplained variation from plot to plot. Note that there are as many plots, and hence trait measurements per offspring line as there are blocks.

It turns out that since the lines are usually assumed to be a random sample of possible offspring from a particular cross, that the appropriate error for assessing genotype effects is that attributed to line(geno). Put another way, if there were no missing data, then the trait could be examined by averaging across the blocks,

   traitave = mean + geno + error ,

in which error is actually the sum of the variation due to line(geno) and the average plot error.

proc glm;  /* randomized complete block design (RCBD) */
   class block line geno;
   model trait = block geno line(geno);
   random block line(geno) / test;
   lsmeans geno / stderr pdiff e=line(geno);

Missing field data upsets this somewhat, but analysis based on the average of the remaining measurements is a reasonable approximation if only a few values are missing. However, it is possible to use a statistical package such as SAS on marker loci to address concerns about a QTL package. Here is an appropriate way to analyze this problem using the recently released proc mixed in SAS:

proc mixed;  /* randomized complete block design (RCBD) */
   class block line geno;
   model trait = geno;
   random block line(geno);
   lsmeans geno;

Note that proc glm can only provide approximate F Values and standard errors for mixed models when there are missing data.

More complicated designs would require even more attention to data analysis. Few of the current QTL packages incorporate breeding designs used in the plant sciences. A promising package in this regard is QTLCart [\protect\citeauthoryearZengZeng1994], which is available from the author.