Final answer:
A genetic mutation or an unexpected occurrence during meiosis caused the production of a beetle with brown coloration from two green homozygous beetles. This is an exception to typical Mendelian inheritance patterns where offspring display the dominant trait in a homozygous fashion when both parents possess the same alleles.
Step-by-step explanation:
Genetic mutation or an unexpected occurrence during meiosis caused two beetles homozygous for green coloration to produce a single offspring with brown coloration. Beetle coloration typically follows Mendelian inheritance patterns, as demonstrated in Gregor Mendel's classic experiments with pea plants. In a monohybrid cross involving two homozygous parents, the offspring should display the dominant trait in a homozygous fashion if both parents possess the same alleles. However, if a mutation occurs or if there was an undetected heterozygosity in one of the parents, it is possible for an offspring to express a different trait, such as brown coloration in this case.
An example can be seen in Mendel's experiments, where true-breeding plants were crossed and the resulting F1 generation displayed the dominant phenotype. When F1 heterozygotes were crossed (as shown in the Punnett square scenario), a 3:1 phenotype ratio was observed. This same concept applies to the beetles mentioned in the question, where an unexpected brown offspring suggests a deviation from the typical inheritance pattern, potentially due to a mutation, non-Mendelian inheritance, or an undetected heterozygous state in the parents.