Final answer:
The hypotheses could include adoption, donor gametes, laboratory errors, or chimerism to explain the differing DNA results. A child's DNA must contain a combination of specific genetic markers from the mother and father. Historical studies on inheritance and DNA as genetic material, as well as HLA matching complexities, provide insight into DNA-related familial connections.
Step-by-step explanation:
To discern the hypotheses regarding why the children had DNA that did not match with Lillian's DNA, we need to consider several genetic scenarios. One hypothesis could be adoption or donor gametes, which would result in a child whose genetic material does not match that of the person they presume to be their biological mother. Another hypothesis might be a laboratory mix-up during the DNA testing process itself, leading to incorrect results. A less common hypothesis could include chimerism, a condition where an individual has two sets of DNA.
A child's DNA fingerprint must show a mix of genetic markers inherited from both biological parents to establish a biological relationship. Exploration of the chromosomal theory of inheritance and historical investigations, such as those conducted by Hershey and Chase with microbes, provide contextual evidence supporting the role of DNA as genetic material. The variations seen in human leukocyte antigen (HLA) matching highlight the complexity of finding a DNA match even among close relatives due to genetic diversity from crossing over and random assortment during gamete formation.