More Offspring and More Data

How can we determine for sure that linkage is responsible for what we see? Remember our planning involved making crosses with 30 females. The extra work of making multiple crosses between the F1 and the ccss parents was done to generate large numbers of offspring. In fact, in this experiment enough crosses were made to generate 7000 testcross offspring. Upon careful examination of the seeds on all the ears, we could observe Red, Shrunken and White, Plump kernels. The new combinations were rare but their appearance in the test cross progeny excludes some other ideas we could have had (like pleiotropy, where a single gene gives rise to multiple phenotypic changes in different traits).