J.B.S. Haldane reportedly quipped he would lay down his life for eight cousins. Which version of Hamilton's rule correctly captures why eight cousins (but not seven) meets the threshold?
Ar = 0.5 for cousins, so 8 × 0.5 = 4 > 1, giving a large fitness surplus
Br = 0.125 for first cousins, so 8 × 0.125 = 1.0 ≥ c (=1 life), exactly meeting the rb ≥ c threshold
Cr = 0.25 for cousins, so 8 × 0.25 = 2 > 1, well exceeding the threshold
DHaldane's quip doesn't satisfy Hamilton's rule — he was speaking metaphorically
First cousins share on average r = 0.125 of their genes by common descent (one of eight possible shared great-grandparent alleles). With eight cousins: rb = 8 × 0.125 = 1.0, which exactly equals the cost c = 1 (one life). This is the break-even point — the allele for this altruism neither spreads nor declines. With even slightly higher benefit (nine cousins) or lower cost, the allele would spread. r = 0.5 applies to full siblings (two brothers is sufficient for Haldane), and r = 0.25 applies to half-siblings or grandchildren.
Question 2 Multiple Choice
Worker bees in a haplodiploid (Hymenoptera) colony are sterile females who help their mother (the queen) produce more sisters rather than reproducing themselves. Hamilton's rule explains this because:
AWorkers cannot reproduce physiologically, so Hamilton's rule does not apply — this is a case of constraint, not selection
BDue to haplodiploidy, workers share r = 0.75 with their sisters but only r = 0.5 with their own daughters, so helping raise sisters yields more inclusive fitness than personal reproduction
CThe queen has higher fitness than workers, so workers defer to her reproductive advantage
DWorkers benefit by receiving food and protection from the colony in exchange for their labor
In haplodiploid species, females develop from fertilized diploid eggs and males from unfertilized haploid eggs. Because the father is haploid, all daughters share identical paternal genes (r = 0.5 from father) plus an average of 0.25 from the mother — giving r = 0.75 between sisters. But a worker's own daughters would share only r = 0.5 with her. Since rb for sisters (0.75 × b) exceeds the equivalent for daughters (0.5 × b) for the same b, Hamilton's rule predicts workers gain more inclusive fitness by raising sisters than by reproducing directly. This is Hamilton's original explanation for eusociality — one of evolutionary biology's most elegant applications of the rule.
Question 3 True / False
Hamilton's rule only applies to behaviors that benefit the altruist's direct offspring.
TTrue
FFalse
Answer: False
Hamilton's rule applies to any social behavior where costs and benefits can be quantified in fitness terms and where the recipient is a genetic relative. The 'r' in rb > c is the coefficient of relatedness between the altruist and the recipient — not restricted to offspring (where r = 0.5). The rule predicts altruism toward siblings (r = 0.5), cousins (r = 0.125), and any relatives. It also predicts when altruism should NOT evolve (when rb < c). The rule is a general framework for kin-selected social evolution, covering alarm calls, food sharing, cooperative breeding, and sterile castes.
Question 4 True / False
Hamilton's rule predicts that, most else being equal, organisms should be more willing to help more distantly related individuals than closely related ones.
TTrue
FFalse
Answer: False
The opposite is true. In Hamilton's rule rb > c, the r term (coefficient of relatedness) weights the benefit b. Higher r means a higher rb, making it easier for the inequality to be satisfied. An altruistic act toward a close relative (high r) propagates more copies of the altruism allele per unit of benefit than the same act toward a distant relative (low r). Hamilton's rule therefore predicts that organisms should be MORE altruistic toward close relatives and LESS altruistic toward distant ones — exactly what is observed in kin-biased helping behavior across species.
Question 5 Short Answer
Why can an allele that causes its bearer to pay a personal fitness cost still spread through a population?
Think about your answer, then reveal below.
Model answer: Natural selection tracks the fate of alleles, not individuals. An allele for altruism can spread if it increases the reproductive success of enough relatives who carry copies of that same allele. Because relatives share genes by common descent, a copy of the altruism allele in the altruist can propagate through the reproductively successful relatives it helped — even if the altruist itself has fewer offspring. Hamilton's rule quantifies when this happens: rb > c means that the expected number of extra copies of the altruism allele transmitted through helped relatives (r × b) exceeds the copies lost because the altruist paid a personal cost (c). Inclusive fitness, not personal reproductive success, is what selection maximizes.
This insight — that the unit of selection is the allele, not the organism — is the core of kin selection theory and resolves what Darwin saw as a major puzzle: how sterile castes evolve in social insects. The sterile worker 'loses' personal reproduction but 'wins' in terms of allele propagation through the fertile relatives it helps. Hamilton's rule makes this intuition precise and testable.