Supplementary information: method to quantify population of starch granule types

Experimental Design The trait of interest in our experiment is the proportion of the granule types. This is estimated from the granule size distribution using the two methods described in the main paper, namely the size threshold measure and mixture measure. The distribution of the granule size is obtained from a multi-phase experiment. Specifically, the experiment involved four phases: grain samples taken from the field trial (Phase I); then milled to flour (Phase II); processed further for extraction in the laboratory (Phase III); and the run through Mastersizer (Phase IV). The treatment for our experiment is the genotype. To distinguish the sources of variation from genetic sources of variation, we require a separate randomisation and replication for each phase and an appropriate analysis that takes into account the blocking structures for each phase [1? –3]. The details of each phase are given below and factors that will be used to specify the model later are given in this font.