Imagine you do a test cross between a purple-flowered pea plant having serrated leaves (a dominant trait) and a white-flowered pea plant having smooth edges. If the purple-flowered plant is heterozygous for both traits, the expected ratio in the offspring is 1 purple-serrated:1 purple-smooth:1 white-serrated:1 white-smooth. Instead, you see 4 purple-serrated:1 purple-smooth:1 white-serrated:4 white-smooth. What is the explanation of this ratio

test cross between a purple-flowered pea plant having serrated leaves and a white-flowered pea plant having smooth edges.
serrated leaves → dominant trait
smooth edges → recessive trait
purple color → dominant trait
white color → recessive trait
F1: 4 purple-serrated:1 purple-smooth:1 white-serrated:4 white-smooth.

There are two genes involved in the cross. The expected ratios are 1:1:1:1 because we assume genes assort independently. However, we see a different phenotypic distribution. When phenotypic ratios differ from the expected ones, it means that genes are linked.

To know if two genes are linked in the same chromosome, we must observe the progeny distribution. If individuals, whose genes assort independently, are test crossed, they produce a progeny with equal phenotypic frequencies 1:1:1:1. But if instead of this distribution, we observe a different one, that is that phenotypes appear in different proportions, we can assume that genes are linked in the double heterozygote parent