I was just talking about this subject with someone today. When it comes to morals, developmental psychology has an interesting and useful framework for this. They have 6 levels of moral composition that are linked to development. Now, I don't fully buy into psych models because they are too categorical and hierarchical, but they do provide some insight.
The first morality that we learn in life is level 1 which is punitive morality. It means that you lack the cognitive development to understand the reasons behind rules, so you simply follow the rules in order to avoid negative stimulus (punishment). Without the negative stimulus, you may harm others. I don't fully buy this, like I said, because some infants display empathy without being told to. But nonetheless, I think level 1 is the level that most animals are operating on, and frankly a lot of humans. They won't do something because they'll be punished.
I don't remember all of the levels just now, but there is the reputation level... where you follow rules because you care what your community might think of you if you don't. Level 6 is apparently the highest, where you break or follow a rule based on collective benefit. It goes beyond just you and yours. Most people are only out for themselves, then their families, then maybe their close friends, and then maybe society beyond that... but most people will not stick their necks out for total strangers.
So most of humanity is kind of middle range, which is a product of our social nature. The only asset we have is big brains and we use those to collectivize safety, resources, etc... which means we have to get along... which means there is a personal and collective interest in maintaining certain moral values.
Morals are different than ethics though. Ethics are more actionable. Morals are just an idea. You may have a moral but your ethical behaviour is different. Maybe you're a hypocrite or maybe circumstances (i.e. poverty) force you to behave outside of your morals. Maybe your morals are just a show and your ethics reveal something else, or vice versa: you behave ethically but deep down you believe something else.
I think animals are a good template for examining the so-called "lower levels" of moral development, especially the other social animals. I don't think they are totally useful though because 1) animals deal with scarcity issues that humans no longer face as hardcore and 2) they are not intelligent in the way that we are intelligent. If you look to animals for morality, then you are forming morals on the basis of survival threats.
Over all, human war, violence, depravity, etc... has declined a lot in the past 200 years. It's because we removed the natural stressors that test our moral imperatives. It's easy to be moral and ethical if you have all your needs met.
Sorry to write a novel, but I'll say one more thing: not every culture orients morals the same way. In the west, our morals are more justice oriented. In other cultures, care matters more. In one culture it may be wrong to steal but in another stealing is bad unless it's to care for someone. In the animal kingdom, there are too many environmental stressors for us to fully comprehend what their internal morals really are. We only have their ethics to go on, which seem to involve a lot of killing and stealing.