Punnett Square, Factors and Expected Sums of Squares for epistasis case c (<b>Fig. 1c</b>).

<p>Punnett Square, Factors and Expected Sums of Squares for epistasis case c (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0012264#pone-0012264-g001" target="_blank"><b>Fig. 1c</b></a>).</p

Performance of the BIC model selection procedure: number of loci selected.

<p>For each simulation setting, the percentage of iterations is given in which 0, 1, 2, or 3 loci were selected. Within each panel the six types of epistasis are as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0012264#pone-0012264-g001" target="_blank">Figure 1</a>. Upper panels show results for simulations with disparate allele frequencies within each locus (1%–10% for rare allele and 90% for the other allele); lower panels show results for simulations with allele frequencies within each locus closer to equal (20%–30% for one allele and 70%–80% for the other allele).</p

Goodness of fit for molecular epistasis.

<p>Proportion of variance explained by the QTL, estimated as the full model r2 of the correct model (averaged over 50 iterations). Panel A shows results for QTL with disparate allele frequencies (low minimum allele frequency); panel B shows results for QTL with more similar allele frequencies (high minimum allele frequency).</p

Punnett Square, Factors and Expected Sums of Squares for epistasis case d (<b>Fig. 1d</b>).

<p>Punnett Square, Factors and Expected Sums of Squares for epistasis case d (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0012264#pone-0012264-g001" target="_blank"><b>Fig. 1d</b></a>).</p

Punnett Square, Factors and Expected Sums of Squares for the additive model (<b>Fig. 1a</b>).

<p>The left Punnett Square gives genotypic means for the additive model as depicted in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0012264#pone-0012264-g001" target="_blank">Figure 1a</a>. Without loss of generality the genotypic means are centered. The last column and last row are the marginal effects, the average value of the cells in the rows and the columns. The right table gives the Expected Sum of Squares for the effect, effect, and interaction.</p

Factors and Expected Sums of Squares for the twoway fixed effects cell means model.

<p><i>The term involving the model error </i><i>, is omitted as it is present in all models.</i></p

Punnett Square, Factors and Expected Sums of Squares for epistasis case e (<b>Fig. 1e</b>).

<p>Punnett Square, Factors and Expected Sums of Squares for epistasis case e (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0012264#pone-0012264-g001" target="_blank"><b>Fig. 1e</b></a>).</p

Factors and Expected Sums of Squares for the twoway fixed effects cell means model when there is no interaction.

<p><i>Note that the identifiability constraint </i><i> implies </i><i>. The term involving the model error </i><i>, is omitted as it is present in all models.</i></p

Punnett Square, Factors and Expected Sums of Squares for recessive epistasis (<b>Fig. 1b</b>).

<p>The left Punnett Square gives genotypic means for the recessive epistasis case as depicted in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0012264#pone-0012264-g001" target="_blank">Figure 1b</a>. The last column and last row are the marginal effects, the average value of the cells in the rows and the columns. The right table gives the Expected Sum of Squares for the effect, effect, and the interaction.</p

Theoretical cell means corresponding to the nine genotypes.

<p><i>Without loss of generality it can be assumed that the values are centered so that the overall mean is zero, that is </i><i>.</i></p