Final answer:
Altruistic alleles can survive through kin selection and inclusive fitness, where helping relatives indirectly aids in one's own gene propagation. Concepts such as the Selfish Gene and evolutionary game theory further explain how natural selection may favour such alleles.
Step-by-step explanation:
The survival of an allele that codes for altruism can be understood through the concept of kin selection, where organisms increase their own genetic success through the success of their relatives. Altruistic behaviours can aid the survival and reproduction of close relatives who share many of the same genes, thereby indirectly passing on the altruistic individual's genes. A famous example is the concept of the Selfish Gene introduced by Richard Dawkins, which suggests that genes act to preserve and multiply themselves through generations, not necessarily the individual organism.
Moreover, evolutionary game theory, drawing from mathematics, challenges the idea of altruism by suggesting that behaviours often have "selfish" components that benefit the individual's genetic fitness. The studies within population genetics also demonstrate how behaviours that increase the likelihood of gene transmission are favoured by natural selection, whether directly or indirectly.
Considering these factors, altruistic behaviour could evolve and be maintained in a population if it contributes to an individual's inclusive fitness, thereby influencing allele frequencies and leading to a genetic basis for seemingly altruistic actions.