To increase genetic variation in offspring, the most relevant options would be those that involve processes that can change allele combinations or introduce new variations.
Among the options provided, a DNA replication error in a gamete of an individual during meiosis could potentially lead to increased genetic variation due to the introduction of mutations, which can create new alleles.
The other options, such as independent assortment and crossing over, are significant for increasing genetic variation during meiosis (not mitosis) as they involve the reassorting of alleles and combination of genetic material from homologous chromosomes. However, it is important to note that independent assortment and crossing over occur specifically during meiosis, not mitosis.
The statement regarding reproduction during asexual reproduction that results in genetically identical offspring is not relevant to increasing genetic variation since asexual reproduction generally produces clones.
In summary, a DNA replication error in a gamete during meiosis would lead to increased genetic variation in offspring compared to the other options.