← all lessons

Scaffold S12 — Hamilton's rule

Five scenarios. Given relatedness r, benefit to the recipient B, and cost to the helper C, decide whether an allele for helping will spread. The reveal simulates the trajectory of the helping allele's frequency across generations, and shows whether rB > C for each case. Same rule across four levels of biological organization plus one negative control.

Locked — answer the pretest above first.

Running tally — rB − C across rounds (positive means helping spreads)

What you just did has a name

rB > C is the whole of Hamilton's rule. You applied it five times across wildly different levels of biological organization — alarm-calling mammals, cooperating bacteria, cooperating gametes, and a negative control where relatedness was zero. The unit of selection changed every round; the rule did not.

Inclusive fitness counts gene copies in the next generation, including copies carried by relatives. A prairie dog that gives an alarm call and dies has zero offspring — but if it saves four full siblings, those siblings carry r = 0.5 × 4 = 2 genome-equivalents, and helping is net positive. The same accounting works for a bacterium that shares iron with clonal neighbors and for a sperm cell that hooks onto its brother-sperm to swim faster. Kinship is kinship.

Round 2 (cousins, rB < C) and round 5 (strangers, r = 0) did not favor helping. These are not exceptions — they are the test. If the rule "worked everywhere" it would not be a rule, it would be an assumption. The point of Hamilton's rule is the boundary: when does the inequality flip?