A question on genetics?

Question

The hornless condition in cattle is dominant over horned. A cattleman hasd a herd of hornless cattle only, but some horned cattle occasionally appear. These are removed from the range before they can produced. Assuming that this man has good fences that can keep out stray bulls, how could this be explained?

Answer 1

We know that there are at least 2 (N for hornless and n for horns) Some of his cattle including a bull would have to be Nn and when bred together an offspring could be nn and therefore have horns.
If this only happens 'occasionally' I would guess that there are more than 2 that are responsible for whether or not horns are present...NN, Nn, Nn, and nn are the possible offspring so it should happen 25% of the time with only N or n being responsible for horns or hornless.

Answer 2

Most of the herd has only hornless genes. However, some of the herd has the recessive allele for hornless. Without expensive genetic testing, the cattleman wouldn't be able to tell which hornless cattle were heterozygous and were carrying the hornless allele. So the horned trait can show up now and then. If he has only one or two bulls, one of the bulls must also be heterozygous.

Answer 3

Let H be the dominant allele for hornless.
Let h be the recessive allele for horned.

If a herd of hornless cattle can produce horned cattle, this means that some of the hornless cattle are heterozygous (Hh). When 2 hetrozygotes mate, the possible genotypes of the offspring are HH, Hh and hh. Cattle with HH and Hh will be hornless while those with hh are horned.

Answer 4

there could be a large number of heterozygous cattle

Answer 5

presence of heterozygous cattles.