Analysing Head-Thorax Choreography During Free-Flights in Bumblebees

Figure 1. Experimental setup and example flight. (A) Virtual setup of the arena. Bee enters the flight arena through the hole at the bottom, that connects to the hive. (B) Marker positions on head and thorax. (C) Top view of real world arena. (D) Example of a learning flight in 3d space. (E) Temporal structure of a section of a leaning flight as lollipop plot, with each sticks pointing direction indicating thorax orientation and color indicating movement classification (green = intersaccade; purple = saccade).

Figure 2. Example of the decision process done by a decision tree. The thorax angular z-velocity (in blue) within a given time window Δt (e.g., red and green dotted rectangle), is the input of the classifier. A decision tree is composed of nodes (circles), with input xi (gray arrows). If the input xi is greater or equal to a learned threshold ϵ, the right node is selected, otherwise the left (see example in the gray square). The process is repeated until a decision saccade/intersaccade can be drawn. The red (resp. green) node highlights the decision path for an intersaccade (resp. for a saccade).

Figure 3. Time course of yaw angles and ωz(t) of the head and thorax of a learning flight. Head saccades (blue regions) are extracted with manually chosen thresholds (red dotted line). Body saccades (red regions) are extracted with thresholds to best match the head saccades.

Figure 4. Time course of head saccades (blue) and predicted head saccades (orange and green) from thorax angular velocity ωy). Thorax saccades (in red) are extracted with a double thresholds (as in Figure 3). Two trained classifiers (a decision Tree, in green, and a Random Forest, in orange) were applied to the learning flight (which was not used for training) to predict head saccades.

Figure 5. Area under the curve between saccade/intersaccade classifications from classifier or double thresholds on thorax angular velocity and head saccade/intersaccade classification as a function of frame rate. The benchmark is the classification from ωz of the thorax based on the optimally chosen double threshold at 500 fps. The classifier outperform the benchmark for frame rates above 40 fps even when angular velocity of the thorax is determined by assuming zero pitch and roll orientation (classifier followed by 2D).

Figure 6. Predicting head and thorax angular velocity (without temporal shift) on a given flight not seen during training of the artificial neural network. (A) Prediction, in blue, of the thorax angular velocity from head angular velocity (orange). (B) Prediction, in blue, of the head angular velocity from thorax angular velocity (orange). (C,D) Zoom on (A,B), respectively. The prediction (blue line) follow the target (green line). (E) Schematic of a prediction at a given time point. (F,G) distribution of error between predictions and targets.

Figure 7. Error for one flight (validation set) for thorax to head (A) and head to thorax (B) prediction. Time course of the head and thorax angular velocity (C) are shown in blue and orange, respectively. (D,F) Example of a positive and negative shift of ±τ11 time steps of the observation. (E) Correlation between target and prediction for different temporal shifts.