Colony sex ratios vary with breeding structure but not relatedness asymmetry in the facultatively polygynous ant Pheidole pallidula

We investigated sex allocation in a Mediterranean population of the facultatively polygynous (multiple queen per colony) ant Pheidole pallidula. This species shows a strong split sex ratio, with most colonies producing almost exclusively a single-sex brood. Our genetic (microsatellite) analyses reveal that P. pallidula has an unusual breeding system, with colonies being headed by a single or a few unrelated queens. As expected in such a breeding system, our results show no variation in relatedness asymmetry between monogynous (single queen per colony) and polygynous colonies. Nevertheless, sex allocation was tightly associated with the breeding structure, with monogynous colonies producing a male-biased brood and polygynous colonies almost only females. In addition, sex allocation was closely correlated with colony total sexual productivity. Overall, our data show that when colonies become more productive (and presumably larger) they shift from monogyny to polygyny and from male production to female production, a pattern that has never been reported in social insects.

Cannibal Animal Games: A new variant of Tic-Tac-Toe

This paper presents a new partial two-player game, called the cannibal animal game, which is a variant of Tic-Tac-Toe. The game is played on the infinite grid, where in each round a player chooses and occupies free cells. The first player Alice can occupy a cell in each turn and wins if she occupies a set of cells, the union of a subset of which is a translated, reflected and/or rotated copy of a previously agreed upon polyomino P (called an animal). The objective of the second player Bob is to prevent Alice from creating her animal by occupying in each round a translated, reflected and/or rotated copy of P. An animal is a cannibal if Bob has a winning strategy, and a non-cannibal otherwise. This paper presents some new tools, such as the bounding strategy and the punching lemma, to classify animals into cannibals or non-cannibals. We also show that the pairing strategy works for this problem.