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I have been reading through Peter Kropotkin's Mutual Aid: A Factor of Evolution and he mentions a curious fact about bees (bolding by me for emphasis):

predatory instincts and laziness continue to exist among the bees as well, and reappear each. time that their growth is favoured by some circumstances. It is well known that there always are a number of bees which prefer a life of robbery to the laborious life of a worker; and that both periods of scarcity and periods of an unusually rich supply of food lead to an increase of the robbing class. When our crops are in and there remains but little to gather in our meadows and fields, robbing bees become of more frequent occurrence; while, on the other side, about the sugar plantations of the West Indies and the sugar refineries of Europe, robbery, laziness, and very often drunkenness become quite usual with the bees. We thus see that anti-social instincts continue to exist amidst the bees as well;

He does not provide a citation for this (and even if he did, it would be something from the late 1800s). Is there a good modern reference for the above behavior?

I would in particular be interested in something like a graph of %-robber-bees vs. plentiness-of-food (in some abstract measure of the latter) so that I could intuitively see the increase in lazy/robber bees as the environment is low on food, or as it is overly abundant and compare it to 'typical levels'.

Theories that explain this behavior are of interest, as well, but I am primarily after experimental measures/observations to support and quantify the above quote.

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Can you define what you think he means by Robbery? Is it robbing from the plant or raiding other colonies? – niallhaslam Oct 31 '12 at 20:29
@niallhaslam that is his full treatment of the subject. He says nothing more on it in terms of defining things. – Artem Kaznatcheev Oct 31 '12 at 20:58
@niallhaslam I think we can assume that he's referring to what we would call today "cheat" or "selfish" individuals, rather than nectar robbers. – Oreotrephes Jul 28 '13 at 1:24

The quote refers to 'robber' bees, but in today's terminology, there are actually three separate phenomena. "Cheating" in bees and other social animals refers to the exploitation of a social contract for one's own benefit. Example: bee workers lay their own eggs rather than tending those of the queen. "Laziness" or "inactivity" of bee or other social insect workers is incredibly widespread, but it is not clear that it is selfish: it may be a side-effect of imperfect task allocation, or those individuals may be a reserve work force. "Robbing" in bees usually refers to removal of nectar or pollen from flowers without pollinating them.

"Cheating" associated with illicit reproduction is widespread in social insects, including in bees, and there's a broad literature on it (search terms "anarchist" "queenright", "policing") but it sounds like your question concerns differential effort and environmental resources specifically.

Differential effort in labor ("laziness vs. busynesss") has been seen in many social animals. The way you frame the question seems to be in terms of:

"how many lazy individuals can a society tolerate given environmental conditions?"

Most observational/experimental studies seem to have approached the question in terms of:

"how can what appears to be cheating actually be adaptive?"

For instance, Kukuk et al. suggest that in Halictine bees, lazy bees who avoid the high-mortality-risk foraging tasks are actually acting as caretakers and orphan-rearers for the brood of the foraging busy bees. It's also been proposed that apparently lazy insects act as a "defensive reserve" for the nest, although at least in Bombus impatiens, experiments show no evidence that lazy bees defend any more than busy bees (Jandt et al.)

Lazy individuals could also be acting a labor reserve ("substitute helpers"), in case of food or colony depletion. To me, this scenario is the closest to what you mention – the idea that lazy individuals become busier, either voluntarily or through coercion, in time of need. Baglione et al. show that this is the case for carrion crows, and quantify it to some degree along the terms you suggest. On the other hand, Cartar (cited in Jandt and Dornhaus) shows that for a number of bumblebee species, it was more likely that busy bees would work harder or switch tasks than it was that the lazy bees would become busy!

In sum, what you/Kropotkin suggest exists in all social insects, although the mechanisms of sociality and of laziness are diverse and various among species.

Also see: Jandt JM, Dornhaus A 2011 ‘Competition and cooperation: bumblebee spatial organization and division of labor may affect worker reproduction late in life’, Behavioral Ecology and Sociobiology 65: 2341-2349. - shows that selfishness/cheating may actually play a role

Dornhaus A, Holley J-A, Pook VG, Worswick G, Franks NR 2008 'Why do not all workers work? Colony size and workload during emigrations in the ant Temnothorax albipennis' Behavioral Ecology and Sociobiology 63: 43-51 - this paper reviews other literature about how many bees/ants in a colony are lazy; up to 75% or even more at a time!

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