There are two main ways heritable variations can arise: independent assortment of genes during meiosis and fertilization, which introduces new combinations of parental genes, and spontaneous gene and chromosome mutations. Independent assortment occurs when parental chromosomes separate during meiosis and recombine in new configurations during fertilization. Gene mutations happen due to errors in DNA replication, while chromosome mutations result from changes like gains or losses of chromosomes. Both types of mutations can lead to new traits.