Nature has a fickle way of removing the wheat from the chaff. When organisms are less suited to survival, their chances of lasting long enough to reproduce may be in serious jeopardy. If the deleterious traits are genetic in nature, then there is limited chance they will be handed off to future generations. We call this process natural selection.
One example proving that humans can act as a shaping force similar to mother nature by chiseling the genetic outlook of a creature is presented in this recent Independent article.The piece describes how African elephants in some regions are being born with smaller tusks or entirely without them, presumably in response to the selective pressure of poaching. While there always have been an elephant here or there born without tusks, the preferential culling of ivory has increased the prevalence of tuskless elephants.
However, as Snopes suggests (not a source I was expecting to comment on the issue), this particular phenomenon has been noted and written about for years prior. A 1995 paper published in the African Journal of Ecology noted in Queen Elizabeth National Park had jumped from 3-4% up to 9-25%. Collectively in South Luangwa National Park and nearby Lupande Game Management Area, the change was from 10% up to 38% in a 20 year period.
While elephants may be the charismatic mascot for poaching issues, undoubtedly it is an issue that for a multitude of animal species reverberates well beyond just their population size and deeply into the very tapestry of their DNA.