including communication effects were derived [@ellison2016cell; @mugler2016limits]. Communication was modeled using a multicellular version of the local excitation–global inhibition (LEGI) paradigm [@levchenko2002models], in which each cell produces a “local” and a “global” molecular species in response to the chemoattractant, and the global species is exchanged between cells to provide the communication (Fig. \[sensing\]C). The difference between local and global molecule numbers in a given cell provides the readout. A positive difference informs the cell that its detected chemoattractant concentration is above the spatial average among its neighbors, and therefore that the cell is located up the gradient, not down. In this model, the relative error of gradient sensing was shown [@mugler2016limits] to be limited from below by $$\label{eq:G2}
\frac{\sigma_g}{\bar{g}} \sim \sqrt{\frac{\bar{c}}{a(n_0a\bar{g})^2DT}},$$ where $n_0^2$ is the ratio of the cell-to-cell exchange rate to the degradation rate of the global species. Comparing Eq. \[eq:G1\] to Eq. \[eq:G2\], we see that without communication the error decreases indefinitely with the size $Na$ of the collective, whereas with communication the error is bounded by that of a collective with effective size $n_0a$. Evidently, communication defines an effective number of cells $n_0$ over which information can be reliably conveyed, and a collective that grows beyond this 