Three-stage joint least-squares regression.

Results of three-stage joint least-squares regression analyses testing the response of urchin density as a function of lobster catch (in number of individuals km−2; our proxy for lobster abundance), and the response in macroalgal biomass as a function of urchin density across the eight sites from 2000–2008 (n = 61 observations). Site and year were fixed factors in Model 1. Model 2 had year as a fixed factor, but used reef rugosity as a covariate for each site, instead of fixing site as a factor. Model 3 was the same as Model 2, but included water depth as a covariate at each site. Numbers in the table are regression coefficients. Standard errors of the regression coefficients are shown in parenthesis.* = P** = P