Multiple queens means fewer mates

SummaryObligate multiple mating by social insect queens has evolved in some derived clades where higher genetic diversity is likely to enhance colony fitness [1–3]. The rare and derived nature of this behaviour is probably related to copulations being costly for queens, but fitness trade-offs between immediate survival and future reproductive success are difficult to measure and not well understood [1]. A corollary of this logic, that multiple mating should be less common or lost when genetic diversity among workers is achieved through multiple queens per colony, was suggested more than ten years ago [4]. However, large scale comparative analyses did not support this prediction, quite possibly because they did not contain any informative contrasts [1,2]. Only comparisons between closely related species with similar ecology and high queen-mating frequencies as ancestral state would provide decisive information, but such species pairs are exceedingly rare so that no case studies have been conducted and a comparative statistical approach [5] is impossible. Here we document for the first time that there is a clear link between the number of queens and the average number of matings of these queens, using the army ant Neivamyrmex carolinensis as a model system

The Webster scalar curvature and sharp upper and lower bounds for the first positive eigenvalue of the Kohn-Laplacian on real hypersurfaces

Let $(M,\theta)$ be a compact strictly pseudoconvex pseudohermitian manifold which is CR embedded into a complex space. In an earlier paper, Lin and the authors gave several sharp upper bounds for the first positive eigenvalue $\lambda_1$ of the Kohn-Laplacian $\Box_b$ on $(M,\theta)$. In the present paper, we give a sharp upper bound for $\lambda_1$, generalizing and extending some previous results. As a corollary, we obtain a Reilly-type estimate when $M$ is embedded into the standard sphere. In another direction, using a Lichnerowicz-type estimate by Chanillo, Chiu, and Yang and an explicit formula for the Webster scalar curvature, we give a lower bound for $\lambda_1$ when the pseudohermitian structure $\theta$ is volume-normalized.Comment: 11 page