A cluster formation model in which the member galaxies formed over the course of 2-3Gyr, with galaxy formation peaking at $z=3$ predicts an average red sequence colour of $i'-J=2.7$mag, consistent with the data [@Cooke2015].

We define “red" galaxies as those that lie within 0.5mag of (or redder than) the red sequence (shown by the lower, grey, dotted line in Figure \[fig:CMD\]); this cleanly divides the red sequence from the blue cloud. We calculate the red fraction for 7C, statistically removing the expected number of field contaminants as: $$f_{\rm red} = \langle\frac{(N^{\rm 7C1753}_{\rm red} - N^{\rm field}_{\rm red})}{(N^{\rm 7C1753}_{\rm total} - N^{\rm field}_{\rm total})}\rangle_{\rm median}$$

where $N^{\rm field}_{\rm red}$ and $N^{\rm field}_{\rm total}$ are the measured number of “red" and total galaxies that satisfy our colour criteria in $\sim400$ random 0.9arcmin field regions from the UDS. The uncertainty is the $1\sigma$ standard deviation in the calculated red fractions for 7C.

The fraction of red galaxies in the protocluster is significantly larger than in the blank field. The red fraction of 7C, after statistically removing field contaminants, is $f_{\rm red} = 0.66 \pm 0.13$, compared to the average fraction of $1.5<z<1.7$ galaxies in the UDS control field, which is $f_{\rm red} = 