The Anna Karenina Principle, which Diamond uses to explain the success of certain societies as opposed to others by suggesting that Tolstoy's first line of his great novel which tries to explain why some relationships work and others fail also applies to the process of domesticating animals. Just like relationships fail for many different reasons, certain societies failed to domesticate the animals in their geographic regions for different reasons. He is also trying to say that relationships that succeed have a lot of common factors that contribute to their success.
There are many contributing factors which make a family, or a marriage happy, if one of those key components fails, the whole thing falls apart or loses its ability to be considered happy.
"Happy families are all alike; every unhappy family is unhappy in its own way." (Diamond)
Diamond is trying to make a point that there are no single factors that contribute to failure.
"The Anna Karenina principle explains a feature of animal domestication that had heavy consequences for human history, namely that so many seemingly suitable wild mammal species, such as zebras and peccaries have never been domesticated"
Diamond tries to explain how some species of mammals were not domesticated because they were not a good fit with man. For example, according to the Anna Karenia principle, which says that if one of the basic factors of a good relationship fails, the marriage or the relationship will not succeed, applying this to the domestication of animals goes like this: if the animals in an environment were not a good fit for domestication than the society could not access this resource in the same way that the successful Eurasians did because they had animals in their geographic region that were easy to domesticate.
For example, just like happy marriages that have certain factors for success, domesticating animals also have to fit into certain categories in order to succeed in becoming domestic and therefore assisting man in his survival.
1. Diet - It matters what they eat and how much, if the animal eats too much than it isn't worth the effort to domesticate
2. Growth Rate - to be worth keeping or domesticating, animals must grow quickly
3. Problems of Captive Breeding- the animals must be able to successfully breed in captivity, have live births
4. Disposition - if the animal is nasty or capable of killing humans and are really dangerous, that disqualifies them for domestication
5. Tendency to panic - some species of large animal tend to get nervous and run, this is counter productive to domestication
6. Social Structure - if the animal lives in groups then it tends to be more easily domesticated, rather than animals who live alone and prowl