(a) Fitted patch-specific lionfish incidences Ji (i.e. the fraction of time a reef patch was occupied by lionfish) plotted across a map of the study patch reef network, where warmer colours indicate higher incidence than cooler colours. (b) Relative network-wide benefits, in terms of reduced lionfish incidence, gained from the removal of lionfish from each individual patch, as measured by the AUC of ΔJi over distance from the target patch. As examples, change in the mean patch-specific incidences following removal of lionfish from (c) patch 15, a large well-connected patch, and (d) from patch 24, a small, less well-connected patch. Patches (circles) are numbered for easy reference in the text. Circle sizes are proportional to patch size, but are not drawn to scale, and patches that appear to overlap on these plots do not in reality. x and y axes represent Universal Transverse Mercator (UTM) coordinates (in m).