Hamilton's rule states that an altruistic allele could spread in a population if Br > C, where B represents the fitness benefit to the recipient, r is the coefficient of relatedness between altruist and recipient, and C represents the fitness cost to the altruist. If r=0.5 between the altruist and the recipient, what would the ratio of costs to benefits have to be for the altruistic allele to spread? a. C/B > 0.5 b. C/B > 0 c. C/B < 0.5 d. C/B < 0

Verified step by step guidance

1. Step 1: Understand the problem. Hamilton's rule states that an altruistic allele could spread in a population if Br > C. Here, B represents the fitness benefit to the recipient, r is the coefficient of relatedness between altruist and recipient, and C represents the fitness cost to the altruist. We are given that r=0.5 and we need to find the ratio of costs to benefits (C/B) for the altruistic allele to spread.
2. Step 2: Substitute the given value of r into the inequality. This gives us 0.5B > C.
3. Step 3: To find the ratio of costs to benefits (C/B), we need to rearrange the inequality. Divide both sides by B to isolate C/B on one side. This gives us C/B < 0.5.
4. Step 4: Look at the answer choices and find the one that matches our result. The correct answer is c. C/B < 0.5.
5. Step 5: Therefore, for the altruistic allele to spread in the population, the ratio of costs to benefits must be less than 0.5.

Key Concepts

Hamilton's Rule

Hamilton's rule is a principle in evolutionary biology that predicts when altruistic behavior will evolve. It states that an altruistic allele can spread in a population if the fitness benefit to the recipient (B), multiplied by the coefficient of relatedness (r) between the altruist and recipient, exceeds the fitness cost to the altruist (C). This relationship is expressed mathematically as Br > C.

Coefficient of Relatedness (r)

The coefficient of relatedness (r) quantifies the genetic relatedness between individuals. It ranges from 0 to 1, where 0 indicates no genetic relationship and 1 indicates identical genetic makeup. In the context of Hamilton's rule, a value of r = 0.5 suggests that the altruist and recipient are siblings, sharing approximately half of their genes, which influences the potential for altruistic behavior to be favored by natural selection.

Fitness Cost and Benefit

In evolutionary terms, fitness cost refers to the reduction in an individual's reproductive success due to an altruistic act, while fitness benefit refers to the increase in reproductive success for the recipient of the altruistic behavior. For an altruistic allele to spread, the ratio of costs to benefits (C/B) must be such that the benefits, adjusted for relatedness, outweigh the costs, specifically requiring C/B < r for the allele to be favored.