I'm sorry Derek but your 'simplistic' approach doesn't entirely cut it. It is more than just insulation and I would concur with MBC that the overwhelming factor influencing survival is the size of the cluster and it's relative health. In the UK we rarely see temperatures fall consistently below 0°C for extended periods. Contrast that with the likes of Finland and other parts of North Scandinavia, Canada and the North US where temperatures fall consistently well below -10°C for long periods which according to your 'simplified' model would result in high colony mortality rates. This is a point well made by Finman.
Using macro thermodynamics fails to appreciate the microdynamics of the cluster. It is not a uniform body and it is highly unlikely that individual bees will be generating heat constantly. They will take it in turns and I suspect will change position so that the centre of the cluster generates heat and the peripheral bees will huddle to help insulate the 'generators' and at the same time stay warm themselves. Moreover, microdynamics of convection and conduction are probably going to be far more important than the overall thermometric properties of the 'space' that the bees are contained in, and the critical factor will be the amount of air that the cluster captures within its structure. This is where critical mass comes in. A small cluster will be flat with a large surface area to volume ratio whereas a large cluster is more likely to form the most optimum shape of a ball, i.e. smallest surface area to volume ratio with optimal radial insulation and conduction. Essentially, a large cluster will be much more efficient in generating AND insulating the heat that is generated and will have proportionately smaller heat losses (per unit bee) than a small cluster.
And it is important to understand that survival is a complex interaction between individual bees and the cluster. In small clusters the loss of a single bee 'generating unit' will cause far more strain on the remaining units because the contribution from each individual bee generating unit has to increase significantly more than in a large cluster. Consequently, the bees in a smaller cluster have to work much harder for longer periods and therefore 'burn out' quicker. This is an inverse geometric relationship to cluster size which is why I agree with MBC. In terms of microdynamics this is also where dampness and drafts are far more likely to cause problems particularly in those diseases which result in 'wet' clusters, for example Nosema and this is simply because dampness reduces micro-insulation and promotes heat losses. It is also at this level that sub-lethal diseases/toxins are likely to have far reaching effects because it's not just about the ability of the bees to generate heat (i.e. the amount of paralysis), it is also about their ability to co-ordinate the higher level social functionality of the cluster i.e. co-ordinate swopping turns and rotating from feeding to generating to insulating/huddling etc.
I absolutely agree that better insulation will improve survival chances but it does not explain the relative increase in colony deaths in both insulated and uninsulated populations on a like for like basis and I repeat my earlier statement that there is much more going on than just the amount of insulation. I do agree with you that much more needs to be done to understand the thermodynamic profile of clusters but I don't believe it needs to be limited to insulated environments. I think it would be far more advantageous to understand cluster performance in stressed conditions especially with respect to exposure to drafts, damp, disease and poisoning.
Kind regards,
Karol
