Is big best? Queen size, usurpation and nest closure in a primitively eusocial sweat bee (Lasioglossum malachurum).

For primitively eusocial insects in which a single foundress establishes a nest at the start of the colony cycle, the solitary provisioning phase before first worker emergence represents a risky period when other, nestless foundresses may attempt to usurp the nest. In the primitively eusocial sweat bee Lasioglossum malachurum (Hymenoptera, Halictidae), spring foundresses compete for nests which are dug into hard soil. Nest-searching foundresses (‘floaters’) frequently inspected nests during this solitary phase and thereby exerted a usurpation pressure on resident queens. Usurpation has been hypothesised to increase across the solitary provisioning phase and favour closure of nests at an aggregation, marking the termination of the solitary provisioning phase by foundresses, before worker emergence. However, our experimental and observational data suggest that usurpation pressure may remain constant or even decrease across the solitary provisioning phase and therefore cannot explain nest closure before first worker emergence. Levels of aggression during encounters between residents and floaters were surprisingly low (9% of encounters across 2 years), and the outcome of confrontations was in favour of residents (resident maintains residency in 94% of encounters across 2 years). Residents were significantly larger than floaters. However, the relationship between queen size and offspring production, though positive, was not statistically significant. Size therefore seems to confer a considerable advantage to a queen during the solitary provisioning phase in terms of nest residency, but its importance in terms of worker production appears marginal. Factors other than intraspecific usurpation need to be invoked to explain the break in provisioning activity of a foundress before first worker emergence.

Polynomials on Banach spaces with unconditional bases

We study the classes of homogeneous polynomials on a Banach space with unconditional Schauder basis that have unconditionally convergent monomial expansions relative to this basis. We extend some results of Matos, and we show that the homogeneous polynomials with unconditionally convergent expansions coincide with the polynomials that are regular with respect to the Banach lattices structure of the domain.