Final answer:
Hamilton's Rule expresses that altruism will increase in a population when the relatedness of the beneficiary to the actor times the benefit is greater than the cost to the actor, expressed as rB > C. This biological principle intersects conceptually with the economic metaphor of the invisible hand, where individual self-interest potentially leads to collective social benefit.
Step-by-step explanation:
Hamilton's Rule is a fundamental concept in evolutionary biology that describes the conditions under which altruistic behavior would likely evolve and become more frequent within a population. According to Hamilton's Rule, altruism is favored by natural selection when the genetic relatedness of the recipient to the actor (r), multiplied by the benefit to the recipient (B), exceeds the cost to the actor (C). In mathematical terms, this is expressed as rB > C. This principle highlights the idea that the reproductive success of an organism's relatives can contribute to its own genetic legacy, thereby incentivizing actions that may seem altruistic on the surface.
The metaphor of the invisible hand, by contrast, is a concept from economics that suggests individuals acting in their own self-interest can lead to a collective benefit for society as a whole. While this idea might appear to be at odds with altruism, it shares the underlying principle that behaviors which may not seem beneficial at the individual level can result in positive outcomes at the group level. Thus, both Hamilton's Rule and the invisible hand metaphor explore the broader social good that can unexpectedly arise from individual actions.