Explaining workers’ inactivity in social colonies from first principles

Abstract

Social insects are among the ecologically most successful collectively living organisms, with efficient division of labour a key feature of this success. Surprisingly, these efficient colonies often have a large proportion of inactive workers in their workforce, sometimes referred to as lazy workers . The dominant hypotheses explaining this are based on specific life-history traits, specific behavioural features or uncertain environments where inactive workers can provide a ‘reserve’ workforce that can spring into action quickly. While there is a number of experimental studies that show and investigate the presence of inactive workers, mathematical and computational models exploring specific hypotheses are not common. Here, using a simple mathematical model, we show that a parsimonious hypothesis can explain this puzzling social phenomenon. Our model incorporates social interactions and environmental influences into a game-theoretical framework and captures how individuals react to environment by allocating their activity according to environmental conditions. This model shows that inactivity can emerge under specific environmental conditions as a by-product of the task allocation process. Our model confirms the empirical observation that in the case of worker loss, prior homeostatic balance is re-established by replacing some of the lost force with previously inactive workers. Most importantly, our model shows that inactivity in social colonies can be explained without the need to assume an adaptive function for this phenomenon.

Social Learning versus Individual Learning in the Division of Labour

“…This refers to the fact that in numerous efficient colonies, a significant portion of the workforce is comprised of inactive workers. This is a frequent occurrence in social organisations, including social insects, animals, humans, etc., which has been observed empirically and explained through modelling studies [35,[54][55][56][57][58].…”

“…As ∀i : x i + y i + z i = 1, we can model a population of N workers as a two-dimensional vector of trait values (x j , y j ) j=1,••• ,N . As we are predominantly interested in the emergence of inactivity, we model inactivity as a third "pseudo-task" that does not generate benefit and has no cost (see [35]). We thus have to have two "normal" tasks (X and Y) with collective benefits and inactivity as a third "pseudo" task (Z).…”

“…Details are given in Appendix A. (We follow [35]: X is a task with a concave benefit shape and marginally decreasing cost such as thermoregulation tasks in an ant colony; Y is a task with sigmoidal (thresholding) benefit shape and marginally decreasing costs such as brood care or defence tasks; and Z indicates inactivity (forgone effort), which produces no benefit and bears no cost.) Appendix B also explains the theoretical analysis and updating rules of adaptive dynamics.…”

“…We have previously established that certain empirically observed characteristics of colony behaviour, including task specialisation and the emergence of inactive subgroups can arise as a by-product of social learning mechanisms [35]. However, despite the wellestablished existence of social interactions in colonies, it is uncertain whether these behavioural phenomena can be attributed to mechanisms of social learning with certainty.…”

“…Evolutionary game theory was initially developed to model changes across evolutionary timescales, where the payoff represents fitness. However, this conceptual framework is not restricted to this timescale and can also be used to model faster processes that involve changes on colony lifetime scales, where payoffs are interpreted as feedback signals instead of fitness [35,42,43]. Our study is explicitly only concerned with these colony lifetime timescales.…”