We know that socializing puppies is incredibly important if we want them to grow up friendly to everyone they meet and relaxed in unfamiliar surroundings. High quality early socialization provides a lifelong solid behavioral foundation to help a dog deal with whatever life might throw at him. But could it last longer than a lifetime? Could socialization actually extend to the behavior of a dog’s puppies?
DNA is like a Recipe Book and Socialization is Which Recipes Get Used
A dog’s DNA contains lots of genes which are relevant to how friendly they are and how they react to strangers. Socialization doesn’t modify these genes directly, but it might affect which ones a dog uses, or how many of a particular one a dog uses. So if DNA is like a recipe book, then an unsocialized dog might use one set of recipes (like a person who frequently makes donuts and deep-fried twinkies), while a dog who was successfully socialized might use a different set (such as grilled salmon and chicken soup).
All the recipes are still unchanged in the cookbook before and after the dog is socialized, but which ones get used are changed as the dog’s brain is modified by the socialization process. And this means that the original recipes get passed on unchanged to the dog’s puppies, whether or not the parent dog was socialized. Changing the brain doesn’t change DNA sequences, and it’s DNA sequences that are passed on to puppies.
Learning from Mom
We’re not the only ones who train puppies; their mothers do as well. Sometimes they do it intentionally, as when they discipline a puppy who’s being a little too obnoxious. And sometimes puppies just learn by watching. One study showed that puppies who were allowed to watch their mothers do narcotics detection work were significantly faster at learning this somewhat complicated job themselves. The trainers attributed this improvement to observational learning: the puppies watched what mom did and learned from it. Maybe they learned that the scent sachets that mom hunted for were interesting, and the puppies were more likely to pay attention to them in their own training. Maybe they actually learned search techniques from mom. Either way, they learned something compared to puppies who were not allowed to watch their dams work.
What might puppies learn from their mother’s interactions with humans, just by observing? If you have a bitch who has impeccable genetics but who is poorly socialized, could she pass a fear of strange people on to her puppies, just by her behavior in front of them? Inheritance isn’t always entirely about genetics.
Early Maternal Care
Maybe that answer was cheating (although I prefer to say it was thinking outside the box). Moms can’t actually affect their puppies’ DNA, which is what the question was about. Right?
It’s true that moms can’t change their offspring’s DNA sequence (beyond passing on a selection of their own genes, which so far as we know are selected at random). But they can change their offspring’s epigenetics, as suggested in the socialization example above. Epigenetics is a new branch of genetics studying modifications made to the physical DNA strand. If DNA is a mammoth book of recipes, then traditional genetics is about the recipe content (to make cookies, use this much flour, this much sugar…) and epigenetics is about the book itself. Maybe the page with your favorite cookie recipe is stuck to the page next to it so you can’t get at it easily, and you end up using another recipe instead. Maybe the words are blurred out from an old spill. Maybe the book is on a high shelf that you can’t reach. There are lots of ways that your access to the recipe can be affected which have nothing to do with the recipe itself. This is what epigenetics is about: access to particular DNA sequences.
Some already classic studies on how maternal care can affect epigenetics were done by Michael Meaney’s laboratory using rats. These studies showed that the amount of licking and grooming that mother rats performed on their babies affected the personalities of those young rats for the rest of their lives, even as adults. Rats who got a lot of licking from their moms were more confident, and those that got less were more anxious and fearful. Meaney’s team traced the changes in these rats’ brains down to a particular region of their DNA. The DNA sequence was unchanged. But the accessibility of this particular recipe was increased or decreased, so that the brain could make more or less of a particular protein that turns out to be important in personality. And these rats passed their personality changes on to their offspring — if their mom licked them a lot, then they licked their offspring a lot. Even if their mom was actually a foster mom who wasn’t genetically related to them, and even if their genetic mom tended to lick her own pups less. 
Unfortunately, these studies don’t exactly answer the question of whether a mother dog’s level of socialization can be passed on to her offspring. We aren’t even sure if the amount mom dogs lick their puppies affects the puppies’ personalities (but it might). If there is some way that socialization is passed on by moms through epigenetic mechanisms, we don’t know it yet. But we’re just starting to learn about all the ways epigenetics affects personalities, and I think we’ll start finding these mechanisms in animals other than rats once we start looking for them.
Now here’s the crazy thing. A study that was published in late 2013 suggests that learned fears can be passed along to offspring in sperm. This isn’t socialization, exactly, but it’s getting closer. And it’s so weird to think that this kind of information could be passed along in the sperm — little cells almost as far away physically from the brain as you can get, very simple cells with very little cellular machinery, unlike the relatively large and complicated egg cell.
In this study, which I posted about in detail at the time (http://dogzombie.blogspot.com/2013/12/the-epigenetics-of-fear.html), male mice were conditioned to fear a particular smell. Their offspring were then tested, and showed fearful reactions to the same smell — specifically, they were more easily startled after smelling it than a control smell. Epigenetic changes were found in their brains which helped them make more receptors for that particular smell. All this even though the father mice had no interaction with their offspring at all — they just passed along the sperm!
It makes sense at some level that, while mothers have plenty of opportunities to pass along information about the world to their offspring, fathers might have much more limited chances — maybe just whatever information they can cram into their sperm. But what a crazy idea, to think that this information can turn into actual behavior in adult offspring. I’m still waiting for new studies to confirm this one; maybe it will end up not being reproducible. But for now we’re left to wonder. Can fathers pass along socialization epigenetically in their sperm? Maybe they can.
 Slabbert, J. M., and O. Anne E. Rasa. “Observational learning of an acquired maternal behaviour pattern by working dog pups: an alternative training method?.” Applied Animal Behaviour Science 53.4 (1997): 309-316.