where band b1 are coefficients, Xis 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 jI0i 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: