Final answer:
The false statement is that double crossovers result in an overestimate of gene distances, as they typically lead to an underestimation. Recombination mapping accuracy decreases with increased gene distance, and generally, linkage maps show shorter genetic distances compared to actual physical distances.
Step-by-step explanation:
The statement that is false among the ones provided is that double crossovers result in an overestimate of gene distances. Double crossovers can actually lead to underestimating, not overestimating, the distance between genes because they may not be detected as recombination events. When this occurs, only the outermost genetic changes are observed, and the recombination between the inner genes goes undetected, which therefore suggests a shorter genetic distance than is actually the case.
Recombination mapping becomes less accurate as the distance between genes increases because it's harder to differentiate between genes very far apart and those on separate chromosomes, both can have similar high recombination frequencies. Positive interference takes place when a crossover in one region of a chromosome reduces the likelihood of a crossover in nearby regions. And generally, a linkage map represents distances based on recombination frequencies, which is shorter compared to the actual physical distances between genes on a chromosome.
Lastly, it's true that the higher the coefficient of coincidence, the lower the degree of interference because a high coefficient indicates that crossovers are occurring independently of each other.