Final answer:
The scenario described indicates a pattern of sex-linked inheritance, where the trait of heavy beard appears in males but not in females due to the presence of a gene on the sex chromosomes.
Step-by-step explanation:
The scenarios described suggest a pattern of sex-linked inheritance, as the trait of having a heavy beard, which is absent in the woman but present in her father and son, is typically carried on genes located on the sex chromosomes. This is a characteristic example of an X-linked trait, where a phenotypic expression appears more frequently in one sex due to the presence of a gene on the X chromosome. Women, having two X chromosomes, would not display the beard trait if it is recessively linked, because they would have a second, typically dominant allele to mask the recessive one. On the other hand, men, having only one X chromosome, would express the trait if they inherit a recessive allele for it from their mothers, hence, the son having a heavy beard like his grandfather. So, contrasting beard growth between the father/grandfather and the female in the scenario points to a sex-linked inheritance. Sex-limited or sex-influenced traits are not suggested in this scenario because they refer to traits that are physically capable of expression in both sexes but are only expressed in one sex due to hormonal differences (sex-limited) or vary in expression intensity between sexes (sex-influenced).