Final answer:
The genotype of the brown parent spider in your study is Bbg because it has one dominant B allele, which results in brown offspring, and one bg allele, which when combined with another bg from the green parent, can produce red offspring.
Step-by-step explanation:
You are studying body color in an African spider and have found that it is controlled by a single gene with 4 alleles: B (brown), br (red), bg (green), by (yellow). The B allele is dominant to all other alleles, and by is recessive to all other alleles. The bg allele is dominant to by but recessive to br. When a brown spider is crossed with a green spider and half of the offspring is brown and the other half red, it suggests that the brown parent must have had one dominant B allele and one recessive bg allele, hence the genotype was Bbg. This is because the only way to get red offspring from a brown and green parent is if the green allele (bg) is present in the brown parent, and the red allele (br) does not appear in the offspring at all.
For example, having two copies of one allele of a gene causes a certain trait and having two copies of another allele causes another trait. But having one copy of each of two different alleles may result in the dominant allele expressing its trait over the recessive one. Similarly, when discussing multiple alleles, like with blood type, certain combinations can lead to a codominance situation where both traits are expressed, such as AB blood type where A and B are codominant. However, in the case of the African spider, B is the only dominant allele, while by is the recessive one, with bg and br showing an intermediate inheritance pattern.