Extracting individual characteristics from population data reveals a negative social effect during honeybee defence

Abstract

Honeybees protect their colony against vertebrates by mass stinging and they coordinate their actions during this crucial event thanks to an alarm pheromone carried directly on the stinger, which is therefore released upon stinging. The pheromone then recruits nearby bees so that more and more bees participate in the defence. However, a quantitative understanding of how an individual bee adapts its stinging response during the course of an attack is still a challenge: Typically, only the group behaviour is effectively measurable in experiment; Further, linking the observed group behaviour with individual responses requires a probabilistic model enumerating a combinatorial number of possible group contexts during the defence; Finally, extracting the individual characteristics from group observations requires novel methods for parameter inference. We first experimentally observed the behaviour of groups of bees confronted with a fake predator inside an arena and quantified their defensive reaction by counting the number of stingers embedded in the dummy at the end of a trial. We propose a biologically plausible model of this phenomenon, which transparently links the choice of each individual bee to sting or not, to its group context at the time of the decision. Then, we propose an efficient method for inferring the parameters of the model from the experimental data. Finally, we use this methodology to investigate the effect of group size on stinging initiation and alarm pheromone recruitment. Our findings shed light on how the social context influences stinging behaviour, by quantifying how the alarm pheromone concentration level affects the decision of each bee to sting or not in a given group size. We show that recruitment is curbed as group size grows, thus suggesting that the presence of nestmates is integrated as a negative cue by individual bees. Moreover, the unique integration of exact and statistical methods provides a quantitative characterisation of uncertainty associated to each of the inferred parameters.

Fig 1. Modelling stinging response for n = 2.

A) Probability density function of aggressiveness. B) Four different situations for a group of two bees. Simulation of different stinging behaviour across time for four different initial aggressiveness situations. C) A Markov chain model of four different stinging scenarios for a group of two bees. D) An example trace of a Markov chain model generated for n = 10.

Fig 2. Experimental data with Agresti-Coull confidence intervals (using Dunn’s correction) and 90% confidence level.

Frequencies of the number of stinging bees (22, 14, 19, 11, 4, 10, 8, 2, 2, 0, 0) resulting from 92 repeated experiments.

Fig 3. Single point estimation (parametrisation minimising the L2 distance between the rational functions and data).

(A). For comparison, rational function values (coloured lines), data (dashed line), and 90% confidence intervals computed from data points (black error bars) (B). On each graph, the results are shown for the agnostic model (green), a linear regression on the agnostic points (yellow), the linear model (red) and the sigmoidal model (blue).

Fig 4. Metropolis-Hastings results of the agnostic (A), linear (B), and sigmoidal (C) model: Set of accepted points.

Each accepted point shown as a line with values of respective parameter point. Burn-in period selected as 25%. We run the agnostic model for twice many iterations to check the convergence of the method. The black line shows the respective optimised point.

Fig 5. Likelihood to sting as a function of alarm pheromone units, based on optimisation of the parameter points with a linear model.

The optimisation was run separately for each group size, for the 3 datasets available.

Fig 6. Slopes, intercepts and r0 values of the alarm pheromone dose-response curve as a function of group size, for all 3 datasets.

The slopes and intercepts are based on the linear model, while the r0 value is estimated from the agnostic model. Pearson’s r test; dataset 1 (A): slopes ρ = −0.9332609, p = 0.1169501, intercepts ρ = 0.7495004, p = 0.7697062, r0 ρ = 0.2101355, p = 0.6050677; dataset 2 (B): slopes ρ = −0.8315731, p = 0.0404234, intercepts ρ = −0.8248105, p = 0.04283618, r0: ρ = −0.8208478, p = 0.02263414; dataset 3 (C): slopes ρ = −0.9426515, p = 0.1083237, intercepts ρ = −0.730198, p = 0.2394278, r0 ρ = −0.4074521, p = 0.296274.