In what animal species is the sex ratio skewed in favour of the fertile female?
It is advantageous to have a skew towards more males. Males can be expendable as they are only required briefly for impregnation and can then focus on providing resources for the mother and young and protection. This breaks down when this is no longer the case, for example in humans we are closer to a 50/50 divide. 

This article notes that in aphids, there are twice as many females as males, the same is true for daphnia. I don't think the reason behind this is known. In reptiles, the female to male ratio can depend on temperature of incubation thus this can lead to strong fluctuations.

An interesting principle is Fisher's principle:


  Fisher’s principle explains why for most species, the sex ratio is
  approximately 1:1. Bill Hamilton expounded Fisher’s argument in his
  1967 paper on “Extraordinary sex ratios” as follows, given the
  assumption of equal parental expenditure on offspring of both sexes.
  Suppose male births are less common than female. A newborn male then
  has better mating prospects than a newborn female, and therefore can
  expect to have more offspring. Therefore parents genetically disposed
  to produce males tend to have more than average numbers of
  grandchildren born to them. Therefore the genes for male-producing
  tendencies spread, and male births become more common. As the 1:1 sex
  ratio is approached, the advantage associated with producing males
  dies away. The same reasoning holds if females are substituted for
  males throughout. Therefore 1:1 is the equilibrium ratio.
  Source