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
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.
- Baglione V, Canestrari D, Chiarati E, Vera R, Marcos JM. 2010. Lazy group members are substitute helpers in carrion crows. Proc Biol Sci 277: 3275–3282. (free)
- Cartar RV. 1992. Adjustment of foraging effort and task switching in energy-manipulated wild bumblebee colonies. Animal Behaviour. (full text not online?)
- Jandt JM, Robins NS, Moore RE, Dornhaus A. 2012. Individual bumblebees vary in response to disturbance: a test of the defensive reserve hypothesis. Insectes sociaux. (behind paywall, buy Jandt kindly has uploaded for free on her site)
- Jandt, Dornhaus. 2009. Spatial organization and division of labour in the bumblebee Bombus impatiens. Animal Behaviour 77: 11–11. (behind paywall, but also free on Jandt's site)
- Kukuk PF, Ward SA, Jozwiak A. 1998. Mutualistic benefits generate an unequal distribution of risky activities among unrelated group members. Naturwissenschaften. (Behind paywall, but this free article by Forbes et al. reports similar information)
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!