Mendelian genetics formulas

For two independent events, e.g. the genotype at one unlinked locus combined with the genotype at another unlinked locus.

For mutually exclusive outcomes, e.g. two different genotypes that give the same phenotype.

n = number of heterozygous gene pairs. When all n loci assort independently, each gamete type has frequency $(1/2{)}^n$.

The probability that exactly s of n offspring are of one kind (probability p each) and t are of the other kind (probability q each), with s + t = n and p + q = 1. Each offspring is treated as an independent event.

O = observed count and E = expected count in each class under the hypothesised ratio. Use counts, not percentages. Degrees of freedom = number of classes − 1. If the calculated ${\chi }^2$ is below the tabulated critical value at the chosen significance level (commonly 0.05), the deviation is attributed to chance and the hypothesised ratio is not rejected.

Made up of n homozygotes and $\frac{n(n-1)}{2}$ heterozygotes. For n = 3 (ABO): 3 + 3 = 6 genotypes.

Measured in a testcross (heterozygote × fully recessive homozygote), where each offspring's phenotype shows the gamete it received from the heterozygote. The observed RF never exceeds 50%, the value for independent assortment. Over long intervals it underestimates the true map distance, because two (or any even number of) crossovers between the markers restore the parental combination and go undetected. Map distances are therefore built by adding short intervals.

r = observed recombination frequency as a fraction (r < 0.5); d = map distance in morgans (multiply by 100 for cM). Assumes crossovers occur independently along the chromosome (no interference). For small r, d ≈ r.

Expected double crossovers = RF(interval 1) × RF(interval 2) × total offspring. Both RFs are taken as fractions and each already includes the double-crossover classes. This expectation assumes that crossovers in the two intervals are independent.

I = 1: complete interference (no double crossovers observed). I = 0: crossovers in the two intervals occur independently (observed = expected). I < 0 (c.o.c. > 1): negative interference, more double crossovers than expected.