Task allocation and site fidelity jointly influence foraging regulation in honeybee colonies

Variation in behaviour among group members often impacts collective outcomes. Individuals may vary both in the task that they perform and in the persistence with which they perform each task. Although both the distribution of individuals among tasks and differences among individuals in behavioural persistence can each impact collective behaviour, we do not know if and how they jointly affect collective outcomes. Here, we use a detailed computational model to examine the joint impact of colony-level distribution among tasks and behavioural persistence of individuals, specifically their fidelity to particular resource sites, on the collective trade-off between exploring for new resources and exploiting familiar ones. We developed an agent-based model of foraging honeybees, parametrized by data from five colonies, in which we simulated scouts, who search the environment for new resources, and individuals who are recruited by the scouts to the newly found resources, i.e. recruits. We varied the persistence of returning to a particular food source of both scouts and recruits and found that, for each value of persistence, there is a different optimal ratio of scouts to recruits that maximizes resource collection by the colony. Furthermore, changes to the persistence of scouts induced opposite effects from changes to the persistence of recruits on the collective foraging of the colony. The proportion of scouts that resulted in the most resources collected by the colony decreased as the persistence of recruits increased. However, this optimal proportion of scouts increased as the persistence of scouts increased. Thus, behavioural persistence and task participation can interact to impact a colony's collective behaviour in orthogonal directions. Our work provides new insights and generates new hypotheses into how variations in behaviour at both the individual and colony levels jointly impact the trade-off between exploring for new resources and exploiting familiar ones.


Recruitment by recruits
Our simulations include only recruitment by scouts, here we note the effects of adding recruitment by recruits to our model. Recruitment by recruits has the same impact on collective foraging as increasing the rate of recruitment by scouts (see above). To avoid instantaneous depletion of available recruits in the hive, the probability that a recruit will recruit new foragers once it returned to the hive ranged from 0 to 0.5. Adding recruitment by recruits does not change the relationship between the proportion of scouts that results in the maximum amount of food collected and the persistence of foragers in returning to the same food source ( Figure S1a). However, the optimal proportions of scouts are smaller than those reported in the main text, when recruits do not recruit ( Figure S1b) and the amounts of resources collected are larger ( Figure S1c). Furthermore, adding recruitment by recruits does not change the opposite relationship between the optimal proportion of scouts and the persistence of scouts vs. the persistence of recruits that we report in the main text ( Figure S1d,e). When the persistence of recruits is fixed, the optimal proportion of scouts grows almost linearly with the persistence of scouts ( Figure S1f); when the persistence of scouts is fixed, the optimal proportion of scouts decays with the persistence of recruits and plateaus between 20% and 40% ( Figure S1g).

Boundary conditions
Making bees that reach the boundary of the simulated foraging area fly back to the hive in a straight line did not change our findings compared with returning them to the hive instantaneously.
Including this trip back to the hive created a time delay during which scouts that go beyond the simulated area cannot recruit. This time delay is a function of the distance of foragers from the hive and their flight velocity. Assuming that the average velocity remains the same throughout the simulation, then this time delay has a similar effect as reducing the recruitment rate (compare Figures S9a with S1 and S6). The relationship between the optimal proportion of scouts and colony persistence remains the same as in all the various iterations of our model ( Figure S9b). Furthermore, the total amount of collected resources will increase monotonically with this delay ( Figure S9c). For a small distance such as 50m, no difference was observed when adding a return trip, compared with returning bees to the hives instantaneously. Figure S2. The effect of the distance that a simulated bee flies before returning to the hive to start foraging again. (a) Total amount of resource collected as a function of the proportion of scouts in the colony for different values of persistence. Distance was set to 500m. Bars represent the standard deviation across all simulation runs. (b) The optimal proportion of scouts slowly increases with the total distance explored by the simulated bees, saturating when this distance approaches 500m. Orange circles are the results shown in the paper ( Figure  3d). (c) The maximum amount of resources collected by the colony decreases with the total distance explored by the simulated bees. Green circles are the results shown in the paper (Figure 3e).

Experiments with feeders at different distances
To fit the average velocity of the simulated honey bees and the time that they spend in the hive recruiting other foragers, we empirically determined the time interval between consecutive visits when feeders were positioned at four different distances from the hive (3, 5, 10 and 15m). The observed intervisit interval < > was linearly related to the distance between hive and feeder (R = 95%, Figure S3a): We used these empirical values to set the parameters of our model. Persistence was not affected by distance from the hive ( Figure   S3b).  Comparing predictions between the System Dynamics and Agent-

Based Models
The curvature of the dependence between the amount of resources collected and the proportion of scouts slightly differs between the Agent-Based and the Systems Dynamics models ( Figure S4). These

Increasing the rate of recruitment
Increasing the rate of recruitment decreased the proportion of scouts that resulted in the maximum amount of food collected ( Figure S5a), regardless whether recruitment takes place only during the first return trip or during all return trips. Recruitment rate was measured as the average number, K, of bees that were recruited by each waggle dance. When K was greater than 40, the optimal proportion of scouts became very small (below 10% for all persistences). Although the values of the optimal proportion of scouts became smaller, the relationship with colony persistence remained unchanged compared to what we report in the main text. At K=25 the optimal proportion of scouts ranged between 20% and 40% ( Figure S5a), in agreement with the estimated percentage of scouts in honeybee colonies [2]. The relationship between the optimal proportion of scouts and the maximum amount of resources collected as a function of the colony persistence remained the same as reported in the main text ( Figures   S5b,c).

Colony size
Regardless of colony size, the proportion of scouts required for collecting the maximum amount of resources (optimal composition) decreased with persistence ( Figure S6a). In the main text, we show results from simulations with 300 scouts. The exponential decays for all colony sizes were very close to 40 ± 5 (% scouts/persistence). Although colonies of different sizes showed slightly different optimal compositions, these differences saturated above 900 bees ( Figure S6b). Regardless, larger colonies always collected more resources than small ones when given the same amount of time to forage ( Figure S6c). For all colony sizes, the maximum amount of resources collected can be approximated by a saturating exponential model, / (1 − 34 ), with being persistence (see lines in Figure S6c). Including recruitment by recruits did not change our findings ( Figure S8).  The optimal proportion of scouts grows linearly with colony size. The rate at which the proportion of scouts change is faster than that of the results without recruitment by recruits. Persistence for all foragers in both panels was set to = 5.

Increasing flight precision in response to finding a resource
Removing the increase in flight precision after detecting a new resource did not change our main findings. The increase in flight precision that we included in our model reflects the communication of information about distance and direction between scouts and recruits [1]. The proportion of scouts that led to an optimal amount of resources collected decreased with persistence in the presence and absence of increasing flight precision ( Figure S7a). However, the total amount of resources that a colony collected when there was an increase in flight precision after finding a resource was substantially larger than without this increase ( Figure S7b). In both cases, the maximum amount of resources collected can be approximated by a saturating exponential model, / (1 − 34 ), with being persistence, and / and fitted using the simulated results (see lines in Figure S7b).

Figure S9. The effect of increasing flight precision after finding a new resource. (a)
The relationship between optimal colony composition and behavioral persistence was not affected by increasing (light green) flight precision after finding a resource. (b) Total amount of resources collected with an increase in flight precision (light green) was on average 2.5 larger than without this increase (dark green). Lines represent the exponential fit to the simulated data.