Final answer:
The gene order is straw body, Lobe, smooth abdomen with map distances of 23.6 cM between straw body and Lobe and 23.14 cM between Lobe and smooth abdomen. The coefficient of coincidence is approximately 0.46.
Step-by-step explanation:
The student's question relates to mapping gene order and calculating map units between loci in fruit flies (Drosophila melanogaster) based on a given set of offspring phenotypic ratios from a genetic cross. The observed phenotype ratios are indicative of crossovers between genes during meiosis. By identifying the parental, non-crossover, and double-crossover phenotypes, we can deduce the location of the genes and calculate the map distance between them.
First, we identify the parental (highest number) phenotypes, which are smooth abdomen, straw body (820) and Lobe (780). The double-crossover phenotypes (lowest number) are smooth abdomen, Lobe (42) and straw body (58). The non-parental single-crossover phenotypes are smooth abdomen (148) and Lobe, straw body (152). From these, we can deduce that the gene order is straw body, Lobe, smooth abdomen since the Lobe gene is involved in both single-crossover phenotypes.
To calculate the map distance:
1. Map distance between straw body and Lobe: (152 + 42) / total offspring * 100 = 23.6 cM.
2. Map distance between Lobe and smooth abdomen: (148 + 42) / total offspring * 100 = 23.14 cM.
Total map distance between straw body and smooth abdomen is 23.6 + 23.14 = 46.74 cM.
For coefficient of coincidence, it compares the observed number of double crossovers to expected:
Coefficient of coincidence = observed double crossovers / expected double crossovers.
Expected double crossovers = product of individual crossover frequencies for regions (0.236 * 0.2314) * total offspring.
E.g., Coefficient = (42 + 58) / (0.236 * 0.2314 * 1750) = 0.46 (rounded off).