Fig 1.
(A) Example of theoretical trajectory. Blue line: Trajectory during the exploration phase. Black line: Trajectory during the return phase. Black circle: bee. Black square: nest. H is the homing vector pointing towards the nest. is the velocity of the bee. φ is the angle between
and
. (B) Evolution of the return strength (η) over time. At time = τ, η switches from 0 (no attraction) to η*. (C) Example of an experimental trajectory [71]. Each dot represents the position of a bee recorded by a harmonic radar approximately every 3s. Different colors represent different flight loops around the nest. The sequential order of the loops is represented by the color gradient where the first loops have lightest colors (yellow to purple). (D) Same as C, but for a simulated trajectory with parameters γ = 1.0 s−1, σ = 0.37 rad/ s1/2, preturn = 1/30 s−1 and η* = 0.2 s-1.
Fig 2.
Distributions of the four observables, for experimental and simulated data.
Black lines: experimental data. Red lines: model predictions using the optimal γ = 1.0 s−1, σ = 0.37 rad/s1/2, preturn = 1/30 s−1 and η* = 0.2 s-1. Insets: Schematic of each observable. (A) Cumulative distribution function of loop lengths for our full dataset. (B) Same as A, but for the loops extension. (C) Probability distribution of the number of trajectories intersects per 100m traveled. (D) Same as C, but for the number of re-departures per 100 m traveled.
Fig 3.
Probability of presence of a bee around the nest.
(A) Overlay of 1000 trajectories with attraction to the nest (η* = 0.2 s−1) simulated during 900 s. (B) Example trajectories with and without attraction, simulated during 500 s. The nest is located at (0,0). Blue: model with attraction. Orange: model without attraction. (C) Same as A but without attraction to the nest (η* = 0). (D) Probability to find a bee below a given distance to the nest (i.e., inverse cumulative probability distribution for the distance to the nest) after different amounts of time. Blue: model with attraction (stationary distribution of bees). Orange: model without attraction (non-stationary distribution of bees).
Fig 4.
Probability that flowers are discovered.
(A) Probability that a flower is found as a function of its distance to the nest. We simulated exploration trips in a field of uniformly distributed flowers with density 1.3 10−4 flowers/m2 and flower size 70 cm. For each flower, we computed the probability that it was found in each exploration trip, and we show this probability as a function of the distance between the flower and the nest. Results were computed over 6000 simulated trips of 900s in 10000 environments for each density (negligible bar errors not reported). Red line: Probability calculated without taking into account the masking effect. Blue line: Probability calculated taking into account the masking effect (i.e., only counting the first flower that was discovered in each trip). (B) Illustration of the masking effect. The probability of discovering a flower depends on the presence of other flowers. In a scenario where there are just 2 flowers equidistant to the nest, both flowers should be visited equally (top). However, if another flower is added, it can capture visits that would otherwise visit one of the original flowers (bottom). Black square: nest. (C) Same as (A), but for different flower densities. Red dotted line: Probability calculated without taking into account the masking effect. This probability is independent of the density of flowers. Solid lines: Probability calculated taking the masking effect into account. Black dotted line: threshold probability at which we consider an area that has a high probability of being pollinated. (D) Radius of the area around the nest that has a high probability of being discovered (i.e., where the probability that flowers are discovered is above 10−2) as a function of flower density.
Fig 5.
Number of different flowers discovered by a group of bees as a function of flower density.
(A) Number of different flowers discovered in 100 exploration trips of 900 s, in an environment with randomly distributed flowers. Results are averaged over 80 simulations, keeping the environment stable for every simulation. Solid lines: Number calculated taking into account the masking effect (i.e., only counting the first flower that was discovered in each trip). Dotted lines: Results without taking into account the masking effect. (B) Same as A but for a given flower size (50 cm), and assuming that each bee will return to the nest only after having discovered a number of flowers (F) (note that box A corresponds to F = 1 for the simulations with masking effect, and F = ∞ for the simulations without masking effect). Line colors represent the maximum number of flowers discovered by each bee (F).