a, Local population growth; b, market gravity; c, nearest settlement gravity; d, tourism; e, nation/state population size; f, Human Development Index; g, high compliance marine reserve (0 is fished baseline); h, restricted fishing (0 is fished baseline); i, low-compliance marine reserve (0 is fished baseline); j, voice and accountability; k, reef fish landings; l, ocean productivity; m, depth (−1 = 0–4 m, 0 = 4–10 m, 1 = >10 m); n, reef flat (0 is reef slope baseline); o, reef crest flat (0 is reef slope baseline); p, lagoon/back reef flat (0 is reef slope baseline). All variables displayed on the x axis are standardized. Red lines are the marginal trend line for each parameter as estimated by the full model. Grey lines are 100 simulations of the marginal trend line sampled from the posterior distributions of the intercept and parameter slope, analogous to conventional confidence intervals. Two asterisks indicate that 95% of the posterior density is in either a positive or negative direction (Fig. 1b–d); a single asterisk indicates that 75% of the posterior density is in either a positive or negative direction.