Forsyth (1981) has studied the sex ratio in colonies of the hymenopteran ant, Apterostigma dentigerum. Mating, colony initiation, and sexual production occur throughout the year, so that, at any time, a sample should reveal a typical cross-section of the population. Colonies are started by a queen who produces workers and reproductives. If the queen dies or fails to function, at least one worker will develop ovaries and lay (unfertilized) male eggs. Forsyth found that queens produced reproductives with a female-biased sex ratio. He suggested that this bias might have evolved to compensate for the all male production of workers in colonies which had lost their queen. My purpose is to build a simple model to see how such sex ratio compensation might work. Forsyth ascertained that male and female alates had the same dry weight, hence assumed that they were equally expensive to make, and that ratios of investment in the two sexes could be calculated by counting individuals. Of 53 colonies sampled containing sexual alates, 35 had a functional queen and had produced 269 female and 164 male alates, and the remaining 18 had no functional queen and had produced 121 males. The observed sex ratio of queen production is 164/433 = .38 males/total giving an overall population sex ratio of 285/554 = .51. To construct a simple model for this situation, let /3 denote the ratio of worker reproductive output to queen reproductive output in the population. Forsyth's estimate of /8 would be 121/433 = .279. Denote by r the equilibrium sex ratio (proportion of males) of queen produced offspring. In a steady state situation each queen expects to contribute to the next generation, 1 daughter, r/(l r) sons and ,B(1 + r/ (1 r)) = ,3/(1 r) grandsons (by a worker), and each male expects to mate with (1 r)/(/3 + r) queens. Following the standard ESS argument, we suppose the sex ratio r is controlled by an allele t which is expressed in the queen. We postulate a rare mutant allele T, dominant over t, which codes for an alternative ratio s. Then r is the equilibrium value if for every s $ r, the allele T has no selective advantage over t. The rarity of T allows us to ignore matings between Tt females and T males, and hence ignore the existence of TT females. If we denote by x and y the numbers of Tt queens and T males, respec-