This problem continued to challenge biologists until W. D. Hamilton, in 1964, addressed this question in quantitative terms (and J. B. S. Haldane, who foreshadowed the logic behind kin selection in the 1930's). These findings introduce a new term -- inclusive fitness -- which maintains the logic of genetics over evolutionary time.

Provided that there is a genetic basis for altruistic tendencies, Mendelian genetics should - via the principle of independent assortment - produce siblings with a particular probability for sharing genes. For example, siblings will share approximately 50% of total genetic makeup, parent-offspring (50%), 1st cousins (12.5%), and so forth, depending upon the degree of relatedness. Hamilton took this degree of relatedness into account when addressing altruistic social encounters, stating it in a formula called "Hamilton's Rule":

where (in terms of fitness) c indicates the cost to the actor, b indicates the benefit to the recipient, and r indicates the degree of relatedness between actor and recipient. By this formulation, actors can be expected to gain fitness by assisting relatives, provided that the cumulative benefit to the recipients is greater than the cost to the actor. Now this logic, coupled with the fact that interaction between individuals will likely be biased towards kin rather than non-kin (particularly those of an altruistic nature), provides a theory in which altruism and evolutionary success are no longer at odds.

Example

Imagine a situation in which the threat of predation can evoke one of two possible responses in a vigilant monkey: give an alarm call, whereupon the caller will incur a cost (being eaten) at the benefit of the others (pictured at right, below); or, remain silent, whereupon some of the other members will be eaten while the actor escapes unharmed (pictured at right, top). If the beneficiaries of this act of ultimate altruism are close relatives, it would actually benefit the inclusive fitness of that individual to give the call and save their kin rather than themselves. Because relatives will have a higher tendency to share similar genetic material, the total genetic benefit for this behavioral strategy would exceed a selfish strategy. Therefore, natural selection has provided a mode by which group fitness is augmented by individuals acting, really, in their own self interest.

Kin selection is not the only reason why cooperative and seemingly altruistic behavior may have evolved. Reciprocal altruism - the continued, mutually beneficial interaction between individuals over time - is another behavioral strategy that has been tested in a simulated evolutionary forum. For reciprocal altruism to work as a strategy, several conditions are required:

• frequent interaction
• recognizing individuals
• remembering past interactions with individuals
• assisting only those who provided past assistance

Given these conditions, the strategy of reciprocating altruistic behavior has proven to be both successful and evolutionarily stable. In a simulated computer environment organized by Robert Axelrod, different programs were placed in an arena where they could interact with each other. The product of interactions between any two programs could result in:

This payoff matrix is known as the Prisoner's Dilemma. There are four types of payoffs, given in the parenthetical numbers in the matrix above, in the form (Payoff to: Individual #1, Individual #2). These are basically:

• you take advantage of the other person's altruism: payoff is greatest, at the expense of the other individual
• you both cooperate and benefit, although this is somewhat less than defecting against a cooperating individual
• you cooperate and the other individual takes advantage of this at your expense (the so-called, "Sucker's Payoff")
• both individuals attempt to defect, and each receives little or nothing

Axelrod then took various interactional algorithms submitted by programmers, game theorists, and non-academic dabblers, and pitted them against one another in a simulated computer environment. The victorious program - which also was simplest program - was called, "Tit-for-Tat". This program interacted cooperatively at first, and for each subsequent interaction, copied what the individual did in the previous encounter. This simple rule fulfills the above requirements to restrict altruistic behavior to only cooperators, and thus avoids exploitation by opportunists. While a purely defective (i.e., exploitative) strategy might appear to be successful as well, it is dependent upon having exploitable individuals in the population. In a situation where there are numerous "Tit-for-Tat" strategists, the population is expected to remain stable and resistant to invasion by exploiters.