It is hard to imagine that anyone thinks of goodness as a problem, but evolution pioneer Charles Darwin did. The little worker bees that sacrificed themselves to protect their hives -- the ultimate example of animal goodness -- kept Darwin up at night.
If Darwin's ideas about evolution and natural selection were correct -- and, of course, they are -- then this sort of altruism should be extraordinarily rare in nature. If increased reproduction is the ultimate end all and be all of evolution by natural selection, then altruists should disappear -- and fast.
But they don't disappear, and Darwin was so puzzled by this that he spoke of altruism as a problem that could prove fatal to his whole theory of evolution.
Then a solution to this nasty conundrum hit Darwin like a ton of bricks. Worker bees weren't helping just any old bunch of bees, they were protecting their hive. And their hive contained special individuals: blood relatives.
Blood relatives are, by definition, very similar to one another. So even though the little worker bees may have been giving up their lives, by doing so they were potentially saving hundreds of blood relatives. In modern parlance, we'd say that the worker bees were helping blood kin, because blood kin are genetically related. By helping your blood relatives, you are indirectly promoting the reproduction of copies of your own genes -- copies that just happen to reside inside your kin.
Darwin wasn't the only scientist who was fascinated with the question of the evolution of goodness. His good friend and colleague, Thomas Henry Huxley, was as well. Huxley got himself into a heated argument over whether blood kinship could or could not explain altruism.
Huxley's opponent was Prince Peter Kropotkin, ex-page to the Czar of Russia, naturalist and arguably the most famous anarchist of the 19th century. Huxley argued that all goodness could be traced to blood kinship, while Kropotkin argued that goodness and blood kinship were completely divorced from one another.
Neither was right, as it turned out, but it would take almost a hundred years before a shy, reserved and brilliant British biologist named William Hamilton would settle all the arguments about blood kinship and altruism by coming up with a simple, but elegant mathematical equation.
Instead of asking whether blood kinship is the single factor explaining altruism, Hamilton approached the question from a different perspective. He began by defining three terms: the genetic relatedness between individuals (labeled r), the cost of an act of goodness (c), and the benefit that a recipient obtained when someone was nice to him or her (b). Using some beautiful mathematics, in the early 1960s Hamilton discovered that altruism and blood kinship are not linked by an all-or-nothing relationship.
Instead, what is now known as "Hamilton's Rule" states that altruism evolves whenever r times b is greater than c. In other words, if enough relatives receive benefits from altruism to outweigh the cost of altruism, then altruism spreads; otherwise, it does not.
Phrased in the cold language of natural selection, blood relatives are worth helping in direct proportion to their genetic (blood) relatedness, weighted by how great a benefit they received.
Literally thousands of experiments with both nonhumans and humans show the power of Hamilton's Rule. This little equation is evolutionary biology's version of E = mc2.