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Figure S1. The direction of selection acting at a locus encoding greenbeard (G), falsebeard (F), and nonbeard (N) phenotypes, where the production of beards is costless (k = 0).

Figure S2. The direction of selection acting at a locus encoding greenbeard (G), falsebeard (F), and nonbeard (N) phenotypes, where the production of beards is costly (k = 0.1 in all panels).

Figure S3. The direction of selection, approximated at quasi-linkage equilibrium, acting at two loci: a greenbeard locus, with greenbeard allele at frequency pG, and a modifier locus, with partial-suppressor allele at frequency p".

Figure S4. Frequency-dependent selection on facultative helping greenbeards in a population of kin groups with average genealogical relationship R.

Figure S5. The direction of selection acting at a locus encoding greenbeard (G), defecting falsebeard (F), and defecting nonbeard (D) phenotypes in a structured population of kin groups, where it is assumed that Rb < c (b = 0.6, c = 0.35, R = 0.5).

Figure S6. The direction of selection acting at a locus encoding facultative or obligate helping greenbeard (G), unconditionally helping falsebeard (F), and unconditional helping nonbeard (H) phenotypes in a structured population of kin groups, where it is assumed that Rb > c (b = 0.6, c = 0.25, R = 0.5).

Table S1. Payoffs (PXY) to type X individuals (greenbeard [G], nonbeard [N], or falsebeard [F]) for interacting with type Y partners in a class-structured population of individuals that can only ever perform a behaviour (class A) or only ever receive the behaviour (class B).

Table S2. Payoffs (PXY) to type X individuals (helping greenbeard [G], nonbeard [N], or falsebeard [F]) for interacting with type Y partners in kin groups.

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