(An “allele” is a single gene within any gene pair that can exchange at conception)
There are two kinds of cattle—“horned” and “polled”.
Horns are “recessive” (both parents must transmit horn gene)
Polled is “dominant” (one parent can transmit polled gene)
There are two levels of polled genotypes—“heterozygous” and “homozygous”
Heterozygous = Pp (or Ph) = one Polled, one horned gene in the pair
Homozygous = PP = two polled genes in the pair (no horn gene remains)
If a polled cow (or bull) produces a horned calf, the polled gene is LOST.
This is demonstrated as below:
Heterozygous Polled bull to horned cow: (OR horned bull to polled cow)
P1h2 x h3h4 = P1h3 = polled calf Four possible gene pairings:
= P1h4 = polled calf 50% polled, 50% horned calves
= h2h3 = horned calf (expressed at random)
= h2h4 = horned calf the polled calves would be heterozygous
Heterozygous Polled bull to Heterozygous horned cow:
P1h2 x P3h4 = P1P3 = homozygous polled calf (25% chance)
P1h4 = heterozygous polled calf (50% chance)
h2P3 = heterozygous polled calf
h2h4 = horned calf (25% chance)
Homozygous Polled bull to horned cow:
P1P2 x h3h4 = P1h3 = heterozygous polled calf (100% chance)
P1h4 = heterozygous polled calf
P2h3 = heterozygous polled calf
P2h4 = heterozygous polled calf
Homozygous polled bulls and homozygous polled cows mated together will always give homozygous polled calves, thus matings on horned cows will always produce polled BUT such heterozygous animals can revert to horned calves if bred as above (Ph or hh mates), allowing the recessive horn condition to assert itself.
Beta Casein – neither recessive OR dominant
Kappa Casein --
Most gene pairs identified with selection traits are just “pairs of genes”, are neither single-allele “dominant” or dual-gene “recessive”.
Thus, if you are selecting in favor of caseins that affect the quality or the use potential of the milk produced, it is a simple process of accumulation.
Let us say you have a Holstein herd, and at random, it matches the breed’s “normal” distribution of 50% A2 Beta Casein (25% A2A2 Beta casein).
You would have A1A1 cows (lacking A2 Beta casein)
You would have A1A2 cows (heterozygous for Beta casein)
You might have A2A2 cows (homozygous for Beta casein)
To improve accumulation of A2, you first need to avoid A1A1 sires. Then you may wish to test your cows for the A2 gene frequency. Depending on the sires available (some breeds have few A2A2 sires identified in AI) your strategy may be as follows:
Breed all A1A1 cows to available A2A2 sires only.
The resulting calves will ALL be A1A2, thus heterozygous A2 Beta casein.
Breed all A1A2 cows to A2A2 sires only.
Even though two thirds of all calves produced will be A2A2, you will still have some born A1A2. Mainly you avoid making more A1A1cows this way.
Breed all A2A2 cows as you please (for added genetic selection reasons).
You may also be selecting for polled heads, in a breed that has few polled sires.
If the polled sires are not A2A2, at least all their [polled] calves will be at least A1A2, half from A1A2 mates will be homozygous A2, and in the next generation you may have enough sire choices to go all the way with both traits.
In spite of your desires to become an “all A2A2” (or all polled) herd, it is never necessary to make all matings to A2A2 (or polled) sires. In the case of A2A2, calves from mixed matings can be tested and only the A2A2 calves saved for the herd (do you really need all the heifers you produce each year?). Likewise, by the magic of polled “dominance” you will still get some polled calves when only one parent is polled. Again, keep the polled ones, dehorn the A2A2 horned ones, sell the A1A2 horned ones. Avoid single trait selection[inbreeding] traps!!