Supplementary material:
1. Simulation model
The genetic simulations began by establishing colonies with one queen, mated randomly
to one or five males, and 50 workers. Workers receive one allele each from the queen and a
father (randomly selected with polygamy). Queens produce at least 50 offspring, sex randomly
determined. Each worker can produce one offspring. If producing daughters, workers randomly
mate with a male from the population. Queens homozygous for ‘manipulation’ suppress all
worker reproduction, regardless of worker genotypes. Heterozygous queens have a 50%
probability of suppressing any given worker from reproducing. With ‘altruistic’ alleles,
homozygous workers always cede their reproduction to queens, and heterozygous workers have
a 50% probability of doing the same. With ‘sibsocial’ alleles, worker genotypes are summed to
generate a cumulative colony suppression level. Thus, if 50% of all worker alleles are for
sterility, any given worker has a 50% chance of ceding reproduction to the queen. Therefore,
sibsociality is like pre-emptive worker policing, where workers prevent others from laying eggs
by rendering them incapable of reproducing. Across sibsocial scenarios workers can either
produce both daughters and sons, or only sons because they do not or cannot mate. All
suppressed reproduction in every scenario is replaced by some number of queen-derived
offspring as described in the main text.
All colonies contribute their reproductive offspring into one general pool, where mating occurs by
random. I randomly draw from this pool the mated queens that will be progenitors of the next
generation’s colonies. Because matedness level is assumed to not affect colony initiation, growth,
survival, or the working quality of daughters, the model does not address how colonies start and grow to
reproductive size, as getting to this point is not under selection relative to mating behavior. For
computational simplicity I assume a 100% turnover of colonies across generations (rather than each
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colony having some stochastically determined and variable lifespan). I maintain populations at a constant
100 per generation to avoid the complication of selection in increasing or declining populations.
For each combination of conditions, the interbreeding population of 100 colonies was
simulated for 1000 generations from a starting condition where sterility alleles initially occurred
at low frequency (and replicated 100 times). A strict monogamy window would be evident if
sterility allele frequencies always increase over a wider range of starting conditions or spread
demonstrably faster under monogamy rather than polygamy. The simulations were replicated for
diploidy with the manipulation and altruism scenarios.
2. Model assuming diploid sexes.
When both sexes are diploid the results do not qualitatively differ from an assumption of
haplodiploidy for either the maternal manipulation or daughter altruism cases (Fig. S1). With
manipulation, sterility alleles always spread in the population even when worker sterility does
not add any extra offspring (i.e., b = c) to the colony output (Fig. S1a). Under this scenario, the
number of mates has no effect on the spread of sterility. With daughter altruism, sterility
increases in frequency more rapidly under monogamy than with polygamy, and this effect is
similar for both haplodiploidy or diploidy (Fig. S1b). For both genetic systems, daughter
altruistic sterility can only be favored when there is a net colony-level benefit in reproductive
output (i.e., b > c).
Although diploidy does not produce qualitatively different outcomes from haplodiploidy,
there does appear to be a consistent negative effect on the rate at which sterility increases in
populations for both the manipulation and altruism scenarios (Fig. S1). This suggests that under
similar levels of cost, benefit and relatedness, haplodiploidy is initially more conducive for the
appearance and spread of obligate sterility.
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Figure S1. Changes in sterility allele mean frequencies under haplodiploidy and diploidy.
Monogamy and polygamy are represented by black and gray lines, respectively, with 100
replicates for each set of conditions. Solid and dashed lines are from simulations assuming
haplodiploidy and diploidy, respectively. Results are given for the range of added benefit
sterility could provide in the simulations (from 0 to 100%). Alleles produce sterility through
maternal manipulation (a), or altruism (b).
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