where b0 and b1 are coefficients, Xi is the value for one of the predictors of specialization (i.e. crop area harvested, observed parasite herbarium occurrence, or host-specific ENM contrast), S0j is the random effect of host genotype j, I0i is the random effect of region (Western, Central, or Eastern) for S. hermonthica population i, R0i is the random effect of study (i.e. publication) for S. hermonthica population i ,and 𝜖ij is the residual error. To assess the significance of our specialization predictors (Xi) as fixed effects, equation 1 was compared to the intercept-only model: