Figure 2. Interaction volume is the dominant component of unloading rate.

(a) Interaction rate (blue) and interaction volumes (red) both decline with increasing colony state. Binned data is presented by mean $\pm$ SEM. Interaction rate was calculated as the inverse of all intervals between interactions. The intervals were binned according to the colony state at which they occurred (n = 49, 79, 101, 170, 240 for bins 1–5, respectively. See Figure 2—figure supplement 1 for raw data and Figure 2—source data 1 for binning sensitivity analysis). Blue line depicts a linear fit $r(F)=0.032-0.017F$, $R^2=0.96$. Interaction volumes were measured in units of pixel intensities, normalized between experiments (see Methods, Data Analysis), and binned into equally-spaced colony state bins (n = 84, 137, 165, 274, 496 for bins 1–5, respectively. See S4). Red line represents the predicted relationship between the mean interaction volume and the colony state from Equation 9, with $C_0=1.14$ and $\frac{1}{{\lambda }_0}=0.14$ as obtained from the fit in Figure 3a. (b) Foragers’ unloading rates at each visit in the nest were binned according to colony state (black, mean $\pm$ SEM for each bin, n = 26,26,28,39,57 for bins 1–5, respectively). Mean unloading rate values were fitted by three functions: the blue line represents a model which includes the effect of interaction rates only ($unloadingrate\propto 0.032-0.017F$, function obtained from fit in panel a, $R^2=0.52$), the red line represents a model which includes the effect of interaction volumes only ($unloadingrate\propto 0.2-0.2F$, function obtained from fit in Figure 2—figure supplement 2, $R^2=0.96$), and the black dashed line represents a model that incorporates the combined effects of interaction volumes and interaction rates ($unloadingrate\propto (0.032-0.071F)\cdot (0.2-0.2F)$, $R^2=0.99$). All panels in this figure represent pooled data from all three observation experiments. For raw data see Figure 2—figure supplement 3. Source file is available in Figure 1—source data 1.

Figure 2—figure supplement 1. Raw (gray) and binned (black) data of interaction rates.

Each data point is the inverse of an interval between two consecutive interactions of a single forager. Binned data and linear fit are as presented in Figure 2a. The figure relates to the pooled data from all three observation experiments.

Figure 2—figure supplement 2. Raw data pooled from all three observation experiments (gray) and binned (black) data of interaction volumes.

Negative values represent interactions in which the forager was the receiver. Binned data and linear fit are as presented in Figure 2a. Linear fits to the raw data (red, $y=0.185-0.178x$, $R^2=0.10$), and to the binned data (blue, $y=0.200-0.201x$, $R^2=0.90$), are similar to each other and close to the prediction (black, $y=0.163-0.163x$, $R^2=0.73$).

Figure 2—figure supplement 3. Raw (gray) and binned (black) data of unloading rates.

Each data point is the unloading rate of a forager in a single visit in the nest, calculated as the amount of food she transferred in that visit (in normalized units, see Methods: Data Analysis), divided by the duration of that visit. Binned data and fits are as presented in Figure 2b. The figure relates to the pooled data from all three observation experiments.