Final answer:
Beard growth in goats, as described, is a sex-influenced trait because the same autosomal gene causes different phenotypes depending on the sex of the goat. It is not sex-linked as it is not located on sex chromosomes, and it is not sex-limited since it can be expressed in both sexes.
Step-by-step explanation:
Sex-Linked, Sex-Limited, or Sex-Influenced?
The traits of having a beard in goats as described in the question are not sex-linked because the genes responsible are not located on the sex chromosomes. Instead, this is an example of a sex-influenced trait. The autosomal gene behaves differently depending on the sex hormones within the organism which influence the expression of the gene, hence it is not sex-limited because it does express in both sexes but differently.
For male goats, the presence of a beard is influenced by the genotypes B+Bb and BbBb which result in a beard. The homozygous dominant B+B+ genotype, however, does not have a beard. On the other hand, female goats exhibit beards only if they are homozygous recessive (BbBb). The different expressions of the beard trait depend on the amount and effect of male sex hormones, which makes it a sex-influenced trait. Beard growth in goats, in this case, is not limited to one sex nor is it linked to the sex chromosomes like the traits associated with human sex-linked disorders such as red-green color blindness and hemophilia which are found on the X chromosome.