One interesting mathematical idea
drawn by W. D. Hamilton
and Richard Dawkins
based on the Selfish Gene
model is the idea that people are altruistic in proportion to how closely they are related to someone. So I am 100% altruistic to myself (duh), and in comparison I am 100% altruistic to an identical twin, 50% altruistics to a parent or sibling or offspring, 25% altruistics to an uncle or aunt or nephew or nice, 12.5% altruistic to a cousin, etc. I think it was the biologist J. B. S. Haldane
who said, "Would I die for my brother? No, but i would for two brothers. Or eight cousins."
Of course this completely ignores other factors like attachments made through lifetime (friendship, marriage), cultural norms and social pressures, morality, etc. I still think it's interesting and a useful model, especially in studying social insects. No naturalist, the above included, believes this model alone can explain human behavior.