I wish I could describe epigenetics in detail, but I cannot. It is an extremely complicated topic and as of yet, not a fully understood process. But in a nutshell, during times of physical/nutritional stress, proteins can become attached to an individuals DNA. As that DNA replicates, it carries the attached protein with it. These proteins can drastically alter the function of the DNA (preventing genes from turning on or off at the correct time). And since these proteins are attached to the DNA, they are heritable, and that's the critical part - they can be passed on to offspring.
Epigenetics was discovered while researching the effects of famine in Scandinavian countries. It seemed to be a strange coincidence that women who had experienced severe nutritional deficiencies during a famine, no matter how much later after the famine was over and how great their health was at the time of pregnancy, produced a much higher percentage of underperforming children (low birth weights, poor health through life), than women who had never experienced a famine. It was found that the periods of famine produced these epigenetic proteins that attached themselves to the women's DNA, and these proteins were passed down to their children, causing poor health and underdevelopment.
A few years back, in a university study (may have been Univ of SD), researchers looked at the white-tailed deer of the Black Hills versus white-tailed deer farther east in the state in the Plains. It was noted deer in the Plains were much larger in body and antler than deer from the Black Hills. Wanting to show these differences were caused just by differences in food quality, deer captured from the Black Hills were moved to a facility in the Plains, and raised side by side with local deer (although the two groups were not allowed to interbreed). The researchers assumed that as soon as the Black Hills deer had been eating the same food sources as the Plains deer, and living in the same environment, the differences between the two groups would vanish. But they didn't. At least not for several years. It took at least 3 years before Black Hills does bred to Black Hills bucks began growing close in size to the local Plain deer (and they never caught up in body size). This is where the idea came about that a does health - long before she becomes pregnant - is such an important factor in producing bucks that can express their full potential at maturity. However, although their observations were correct, their theory on why it took so long for the Black Hills deer to start catching up to the Plains deer was wrong. It wasn't just the condition of doe before pregnancy. It was epigenetics. Due to the lower nutrition and higher stress life of living in the Black Hills, DNA altering proteins were attaching themselves to the Black Hills deer' genetics and that was being passed on to their offspring, lower the offspring's life-long growth potential.
As far as I know, the Miss. State is the only university currently studying the role of epigenetics in white-tailed deer, and their finding some fascinating things.
But epigenetics is probably a major contributing factor into why sudden improvements in herd dynamics and habitat quality often DON'T produce the dramatic improvements in deer performance many landowners expect. It often takes many years - even decades - basically a number of generations of deer, to lose the negative influence of epigenetics on the local population.