The inheritence of poll and scur genes in cattle of European origin (Bos taurus) is outlined below:
Genotype / Phenotype: The genes contain the instructions for making all living things. The genes an animal has are it's genotype. Not all genes can be expressed, for example black coated cattle can carry the gene for a red coat, but as black is a dominant gene, the red gene is not expressed. The phenotype is what is expressed in an individual.
Heterozygous or Homozygous: The sperm and the ovum each contain half the genes of the parent, and therefore the genes of each calf come half from each parent. A horned calf has inherited one horn gene from its father and one horn gene from its mother. To express the phenotype of horns, the calf must be carrying two horned genes.
Approximately 1:25000 calves are born with a random mutation of the horn gene, which converts it into a poll gene (known as a "sport"). Such a calf would have one horn gene and one poll gene. As the poll gene is dominant, the calf would not grow horns, and would express the phenotype of being polled. This calf is heterozygous polled.
Once a mutation has happened, and if the animal reaches maturity, then 50% of its calves will inherit the poll gene, and therefore will not grow horns, and these in turn will pass on the poll gene to 50% of their calves. Of course, in the wild, a cow or bull without horns would be at a huge disadvantage, and would be unlikely to successfully breed, therefore natural selection would strongly favour horned cattle, which is why the original wild cattle were horned.
If two heterozygous polled animals breed together, there is a 1 in 4 chance that the calf will inherit a poll gene from each parent, to have two poll genes and no horn genes. This is known as homozygous polled. A homozygous animal must always pass a poll gene to it's calves, and therefore 100% of its calves will be phenotypically polled, even if mated to horned cattle.
Scurs: Polled cattle can grow what look like rudimentary horns. They are distinguished from real horns in that real horns are firmly attached to the skull of the animal, whereas scurs grow in the skin and are "loose".
The scur gene is separate to the poll gene. As the phenotype of scurs cannot be expressed when an animal has horns, there is no natural selective pressure on the scur gene, so it tends to be randomly distributed in any population of horned cattle.
A polled animal is either smooth polled (polled but not scurred), or scurred (polled and scurred). In either case the inheritence of the poll gene by its calves is the same, ie a scurred bull/cow can produce smooth polled calves and vice versa according to the presence or absence of the scur gene in the other parent.
Impact on other qualitites: There are "old wives tales" that polled cattle are inherently poorer than horned cattle in some important aspects, such as growth rate. Current science tells us this is incorrect. There is no loss of economic performance connected with the poll gene. However, what may happen in practice is that a breeder will retain a poorer quality polled animal for reproduction which they would have rejected if it had horns, simply because it is polled. This is a mistake of the breeder, and not a feature of the poll gene.
