Introduction:
Inheritance of genetic material from parents to offspring occurs through the process of gametogenesis, which involves the formation of gametes (sperm and eggs) with half the genetic material of the parent. The genetic material is randomly assorted and recombined during this process, leading to diversity in the offspring's genetic makeup. Phenotypic differences between siblings can arise from various factors, including mutation, recombination, independent assortment, and environmental influences. In this context, we will discuss which event during gametogenesis maximally contributes to the phenotypic differences between siblings.

Explanation:
Mutation:
- Mutations are changes in the DNA sequence that can occur spontaneously or due to environmental factors such as radiation or chemicals.
- While mutations can lead to phenotypic differences, they occur randomly and are relatively rare events during gametogenesis.
- Therefore, the contribution of mutations to the phenotypic differences between siblings is generally minimal.

Recombination:
- Recombination refers to the exchange of genetic material between homologous chromosomes during the formation of gametes.
- It leads to the creation of new combinations of alleles on chromosomes, increasing genetic diversity.
- However, recombination occurs independently for each chromosome pair, and the level of recombination is relatively consistent between siblings.
- Therefore, while recombination contributes to genetic diversity, it does not necessarily account for the phenotypic differences between siblings.

Independent Assortment:
- Independent assortment refers to the random alignment and separation of homologous chromosome pairs during meiosis.
- This process leads to the formation of gametes with a unique combination of chromosomes.
- Since chromosomes carry genes that code for different traits, independent assortment can result in the inheritance of different combinations of alleles for various traits.
- This random assortment of chromosomes during gametogenesis is a major contributor to the phenotypic differences between siblings.

Environment:
- The environment can also influence the expression of traits by interacting with genetic factors.
- However, since both siblings share the same environment, the environmental contribution to phenotypic differences between them is typically minimal.

Conclusion:
Among the given options, independent assortment of chromosomes during gametogenesis maximally contributes to the phenotypic differences between siblings. This process leads to the formation of gametes with unique combinations of chromosomes, resulting in the inheritance of different combinations of alleles for various traits. While mutation, recombination, and environmental factors can also contribute to phenotypic differences, their overall impact is usually less significant compared to the random assortment of chromosomes during independent assortment.