Final answer:
Chromosomes line up independently of one another during metaphase I of meiosis, through a process called independent assortment, contributing to genetic diversity.
Step-by-step explanation:
Each pair of chromosomes lines up independently of the other pairs during metaphase I of meiosis. This stage is crucial as it is responsible for the random orientation of homologous chromosomes, a process known as independent assortment. In each cell that undergoes meiosis, the orientation of the tetrads (groups of four chromatids, two from each homologous chromosome) on the metaphase plane is random, which means that each resulting gamete can have any possible combination of paternal and maternal chromosomes. This random partitioning is one of the mechanisms contributing to genetic diversity among offspring.