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J.B.S. Haldane (1919) recognized that physical distance between gene loci was related to recombination rates between the loci, but that these two concepts were not interchangeable. He recognized that physical distance between loci on the same chromosome had to be quite large for the recombination rate to approach 50%, and that the recombination rate between any loci cannot be greater than 50% (which is the definition of unlinked genes).

To account for these issues, Haldane proposed an approximation of $n\alpha \approx 0.7r-0.15 \ln(1-2r)$ where:

• $n$ = number of factors between loci
• $α$ = probability of a crossover
• $r$ = recombination rate

Haldane used the term 'Morgans' for this approximation. Therefore, when this quantity is multiplied by 100, the units are referred to as 'centiMorgans' or cM (e.g., if the approximation calculation is 0.103, it is multiplied by 100 and expressed as 10.3 cM, etc.).

Use Haldane's approximation equation above to answer the two following questions (remember that $\ln$ in the formula indicates the natural log function).

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