Sensitivity of seabird distribution to presence or absence of rats on nearby islands. Partial dependence plot (a, c, e, g) of the effects of rat-free (blue lines) and rat-invaded (red lines) islands contrasted with the original distribution model (green lines). Stippled line denotes location of the breaking point that denotes a threshold in distribution. Comparison of the break point regression using the 95% confident intervals calculated in the Davies’ test is shown (b, d, f, h)