European Hornet Vespa crabo

I am an amateur naturalist trying to learn something about everything alive in my garden.

Photo 1 (click to enlarge) shows the handsome insect I found lying dead on a windowsill in my house some months ago. I am not expert at insect identification so at first I wasn't sure what I was looking at, but a little internet browsing and I'm confident I've found a European Hornet (Vespa Crabo): of the half dozen-or-so social wasps one might encounter in a British garden, the hornet is the only one with a distinctly brown coloured thorax. Much the most extensive introductory source I've come across online is Dieter Kosmeier's excellent hornet website.

Despite their fearsome reputation hornets are no more likely to attack humans than other wasps, nor is their sting notably worse. They are voracious predators of other insects however; a nest colony can take up to half-a-kilo a day. There are even records of hornets taking down pairs of copulating dragon flies (see Dijkstra et. al., Int. J. of Odonatol. 4(1),17-21, 2001).

Queen hornets hibernate over winter - the site of the Bees, Ants and Wasps Recording Society gives a record of a queen discovered beneath a rotting branch of cherry wood. She emerges around May and begins the process of constructing a nest and egg laying. By mid summer the nest is in full swing and may contain in excess of 500 individuals. Nests of one species of hornet (Vespa wilemani) have been recorded at altitudes of 2300m (Martin, Jpn.J.Ent.61(4), 679-682,1993). Come winter the nest is permanently abandoned (hornets do not reuse a nest the next year).

Figure 2 (click to further enlarge - if you dare!) shows a close up of my hornet's feasome jaws and, atop the head, the circle of small primitive light sentive 'eyes' (ocelli). Counting the number of segments on the antennae (=12) tells me my hornet is a female (males have 13)

A debate amongst professional naturalists concerns the mechanism and role of 'brood policing' in Vespa crabo. In brief the debate surrounds the question of why only the eggs of the queen, and not of the workers, are allowed to hatch (I was surprised to learn that the workers are not in fact sterile, and are quite capable of producing progeny). In the 60's the British evolutionary theorist W.Hamilton, argued mathematically that, other things being equal, in order to benefit their gene-line organisms ought to behave in ways that favour their close relatives (kin). Genetically however, a Vespa crabo worker is closer to its own offspring or indeed the offspring of a fellow worker than that of the queen. Despite this, workers ruthlessly seek out the eggs of fellow workers and discard them. Foster et.al. argue (Molecular Ecology (2000) 9, 735-742) that this may be due to the queen chemically controlling the 'minds' of the workers, hence the title of their paper 'Do hornets have zombie workers?' - although overall the jury seems still out.

Or at least that's my loose understanding of things. As I say often, I'm not a professional. I'm happy to be corrected and in particular I've not managed to follow the quantitative aspects of this debate. For example, Foster et. al. begin:

"In a colony headed by a singly mated queen, workers should prefer rearing sons (r= 0.5) and other workers’ sons (r= 0.375) to their mother’s sons(r= 0.25)'

I get the general idea, but can anyone give me a simple explanation of what these numbers mean and how they're calculated?