Final answer:
The probability of genetic drift fixing a mutant allele in a population is equal to its initial allele frequency. For the heterozygous bright blue cockroach in a diploid population of 100 individuals, this probability is 0.5% or 0.005 since the allele frequency of the blue allele is 1/200.
Step-by-step explanation:
The probability of the blue mutant allele becoming fixed in a population due to genetic drift can be initially approached by determining the allele frequency. Since we are starting with a single heterozygous individual in a population of 100 cockroaches, and knowing that cockroaches are diploid, we have exactly one copy of the blue allele among a total of 200 alleles (2 alleles per individual x 100 individuals). The initial frequency (p) of the blue allele is therefore 1/200 or 0.005.
Genetic drift refers to random changes in allele frequencies, which can result in an allele becoming fixed (reaching a frequency of 1) or being lost (frequency of 0). This process is particularly pronounced in small populations, where chance events can have a greater impact. The probability of the blue allele becoming fixed purely by chance is equal to its initial frequency, which is 0.005 or 0.5% in this scenario.
These principles of random fixation and loss of alleles are fundamental to understanding evolutionary processes such as natural selection, genetic drift, and population genetics. For example, if insecticide resistance conferred by the blue allele were to provide a selective advantage, the probability of fixation would likely increase, but since no such pressure exists in the student's environment, we rely solely on the process of genetic drift.