Many Pokemon fans know that in the video game series it is more likely to find a male Eevee than a female. A quick check to Bulbapedia confirms that the gender ratio for Eevees is 87.5% male, 12.5% female[1]. In real-world biology, the sex of a baby is determined mostly from the sex chromosome contributed by the male. This is the reason why Henry VIII, no matter how many wives he had, only had healthy daughters. If this fact is also present in the Pokemon world, the sex of a baby Eevee would be determined by the male.
Now, let's say that hundreds of years ago, the gender ratio for Eevees was 50/50, there were around the same number of male and female Eevees. Let's say that, at this time, the male Eevee had a mutation that in a gene that influences the ratio of y chromosome-carrying gametes to x chromosome carrying gametes, resulting in a new allele of that gene, one that imparts a predisposition towards producing less gametes containing the x chromosome in its (still haploid) genome and more of the y carrying ones, which would result in a tendency passed down father to son towards producing more male offspring (a trend that is often observed in humans and research suggests is caused by inheriting a certain allele of a hypothetical gene that determines such a predisposition).
Anyway, this would make certain Eevee more likely to produce male offspring. That vital allele would be passed down to his offspring, say two males and one female. The three children would posses this allele, but it would only affect the males, as it is their contribution of a sex chromosome that determines their offspring's biological sex.
Now, let's say that these three Eevees grow up and reproduce. The two males with the genetic allele will birth two sons and one daughter each, and the female will birth, say a son and a daughter. These numbers are highly exaggerated, as the mutated genes would be passed down much more gradually, but this current generation contains five males and three females, where the past generation had two males and one female and the first had one male and one female.
If this trend continues, eventually the allele would become fixed (100% frequency in the population) and the birth of a female Eevee would become so unlikely that the species would be in danger of extinction, as you cannot produce offspring with no females (or Dittos :P). Only Eevees who do not have this allele could continue to thrive without human intervention, assuming it's not too late.
For example, if you were a Pokemon breeder in charge of breeding Eevees, you would want to catch purebred Eevees, ones without the new allele, so you could keep the Eevee population alive and save them from extinction. So if you see a female Eevee in the tall grass, don't catch it. Instead, wait for a male. Protect the Eevee population--they're too cute to go extinct!