Honey bees and social wasps reach convergent architectural solutions to nest-building problems
Fig 4
Modeling different merge strategies.
(A-C) Connection pattern for transition between worker and reproductive cells, where the center of each additional reproductive cell is offset by Δ, the mismatch between worker and reproductive cells. (A) Lateral displacement of cell centers increasing left to right. The gray disks show the circumscribing circles for center triplets that would be connected in a regular lattice. Note that the disk on the right violates the Delaunay condition (disk contains 4, not 3, cell centers). (B) This lateral displacement introduces a 5–7 pair. (C) A transition region introduces intermediate-sized hexagonal cells, but no non-hexagonal cells (3 transition layers, in green). (D) Observed transition in A. florea showing a sudden transition between worker and reproductive cells, which includes 5–7 pairs (unshaded cells). (E) Observed transition in V. shidai showing a transition that uses intermediate-sized hexagonal cells, and no 5–7 pairs. (F) Observed rate of non-hexagonal cells per worker cell as a function of the observed size dimorphism (n = 115 images). The red line is the predicted rate based on a one-step worker-to-reproductive transition for an average transition length (strategy shown in A and B). The shaded area corresponds to transitions that outperform the best one-step transition in terms of non-hexagonal cells. Species with high size dimorphism do not build transition layers (A. andreniformis, A. florea; D), whereas species with moderate-sized dimorphism produce fewer non-hexagonal cells (“better than optimal” shaded region), by employing intermediate-sized cells across the transition region (strategy shown in C, E). (G) Regression of predicted non-hexagonal cells based on the following: size dimorphism, observed merge length, and depth of the transition region, versus the observed non-hexagonal cells, for each image. Marker size corresponds to the number of data points that fall on the same coordinate. In the model prediction (x-axis), each 5–7 pair produces 2 non-hexagonal cells. The observed non-hexagonal cells (y-axis) counts all non-hexagonal cells, including 4-sided, 8-sided, and unpaired cells. Underlying data can be found at http://dx.doi.org/10.35099/aurora-605.