Pollinating bees develop foraging circuits (traplines) to visit multiple flowers in a manner that minimizes overall travel distance, a task analogous to the travelling salesman problem. We report on an in-depth exploration of an iterative improvement heuristic model of bumblebee traplining previously found to accurately replicate the establishment of stable routes by bees between flowers distributed over several hectares. The critical test for a model is its predictive power for empirical data for which the model has not been specifically developed, and here the model is shown to be consistent with observations from different research groups made at several spatial scales and using multiple configurations of flowers. We refine the model to account for the spatial search strategy of bees exploring their environment, and test several previously unexplored predictions. We find that the model predicts accurately 1) the increasing propensity of bees to optimize their foraging routes with increasing spatial scale; 2) that bees cannot establish stable optimal traplines for all spatial configurations of rewarding flowers; 3) the observed trade-off between travel distance and prioritization of high-reward sites (with a slight modification of the model); 4) the temporal pattern with which bees acquire approximate solutions to travelling salesman-like problems over several dozen foraging bouts; 5) the instability of visitation schedules in some spatial configurations of flowers; 6) the observation that in some flower arrays, bees' visitation schedules are highly individually different; 7) the searching behaviour that leads to efficient location of flowers and routes between them. Our model constitutes a robust theoretical platform to generate novel hypotheses and refine our understanding about how small-brained insects develop a representation of space and use it to navigate in complex and dynamic environments.
Pollinating bees, along with bats, hummingbirds, rodents and primates, typically develop circuits (traplines) to visit multiple foraging sites in an efficient stable sequence. The question of how animals encode and process spatial information to develop these impressive foraging patterns remains poorly understood. Previously we showed that an iterative improvement heuristic model of bumblebee traplining can replicate the establishment of stable routes by bees between flowers distributed over several hectares. Here we tested the model against a variety of datasets with different configurations of flowers and found it to give good agreements with all these observations. We have thus shown how these complex dynamic routing problems can be solved by small-brained bees using simple learning heuristics and without acquiring a ‘map-like’ memory. The proposed heuristic shows how bees develop optimal routes simply by following multi-segment journeys composed of learnt flight routines (local vectors), each pointing towards target locations (flowers) and coupled to a visual context (landmarks or panoramas). Such a decentralized representation of space relying on learnt sensorimotor routines is akin to ‘route-based’ navigation as described in desert ants, where spatial information is thought to be processed by separate, potentially modular, guidance systems.