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BEGHIMNRS

Breeder's Equation

R=h2SR = h^2 S

Plant Breeding & GeneticsHow far a population moves in one generation of selection: the selection differential multiplied by narrow-sense heritability. The central equation of applied breeding.

Broad-Sense Heritability

H2=VGVPH^2 = \frac{V_G}{V_P}

Plant Breeding & GeneticsThe share of the variation you can see that is genetic rather than environmental. The starting question of any breeding programme: is this trait worth selecting on at all?

Effective Population Size

Ne=4NmNfNm+NfN_e = \frac{4 N_m N_f}{N_m + N_f}

Plant Breeding & GeneticsThe size of an idealised population that would drift as fast as the real one, from the numbers of male and female parents. Unequal sex ratios shrink it sharply.

Genetic Gain per Year

ΔG=RL\Delta G = \frac{R}{L}

Plant Breeding & GeneticsResponse to selection divided by the years one breeding cycle takes. The figure that decides whether a programme is actually improving anything at a useful rate.

Hardy–Weinberg Heterozygote Frequency

H=2p(1−p)H = 2p(1-p)

Plant Breeding & GeneticsThe proportion of heterozygotes expected in a population at Hardy–Weinberg equilibrium, from one allele's frequency. The null model every real population is compared against.

Inbreeding Coefficient after Selfing

F=1−(12)nF = 1 - \left(\tfrac{1}{2}\right)^{n}

Plant Breeding & GeneticsHow homozygous a line has become after a number of self-pollinated generations. Halving the remaining heterozygosity each generation is what turns a cross into a fixed line.

Mid-Parent Heterosis

MPH=100 F1−MPMPMPH = 100 \, \frac{F_1 - MP}{MP}

Plant Breeding & GeneticsHow far an F₁ hybrid exceeds the average of its two parents, as a percentage — the measure of hybrid vigour that justifies the whole hybrid seed industry.

Narrow-Sense Heritability

h2=VAVPh^2 = \frac{V_A}{V_P}

Plant Breeding & GeneticsThe additive share of phenotypic variance — the only part that reliably passes from parent to offspring, and the one the breeder's equation uses.

Recombination Frequency and Map Distance

RF=100 nrnRF = 100 \, \frac{n_r}{n}

Plant Breeding & GeneticsThe share of offspring showing a recombinant genotype, which for closely linked markers is read directly as map distance in centimorgans.

Recurrent Parent Recovery in a Backcross

R=1−(12)n+1R = 1 - \left(\tfrac{1}{2}\right)^{n+1}

Plant Breeding & GeneticsThe expected share of the recurrent parent's genome recovered after a number of backcrosses — the arithmetic behind moving a single trait into an established variety.

Selection Differential

S=xˉs−xˉS = \bar{x}_s - \bar{x}

Plant Breeding & GeneticsHow much better the selected parents are than the population they were chosen from — the input to the breeder's equation, and the part the breeder actually controls.