that cells on the ends act as the molecule-counting compartments, $s \to a$, and that the entire collective acts as the detector, $a \to Na$, where $N$ is the number of cells in the gradient direction, then we have [@mugler2016limits] $$\label{eq:G1}
\frac{\sigma_g}{\bar{g}} \sim \sqrt{\frac{\bar{c}}{a(Na\bar{g})^2DT}}.$$ We see that, as expected, the relative error goes down with the size $Na$ of the multicellular collective.

However, there is a crucial point that is overlooked in formulating Eq. \[eq:G1\]: the larger the group of cells, the more difficult it is for cells on either end to communicate the measurement information. This fact is not accounted for in Eq. \[eq:G1\]. Instead, we see that the relative error decreases with the separation $Na$ between the end cells without bound, which is unrealistic. For a single cell it may be a reasonable approximation to assume that compartments quickly and reliably communicate information across the cell body, but for a multicellular collective, the communication process cannot be overlooked. Importantly, the communication mechanism of multicellular collectives may introduce additional noise into the gradient sensing process. Therefore, it is imperative when considering collective sensing to properly account for the effects of communication.

Recently, the physical limits to collective gradient sensing 