Critical values in Bak-Sneppen type models

In the Bak-Sneppen model, the lowest fitness particle and its two nearest neighbors are renewed at each temporal step with a uniform (0,1) fitness distribution. The model presents a critical value that depends on the interaction criteria (two nearest neighbors) and on the update procedure (uniform). Here we calculate the critical value for models where one or both properties are changed. We study models with non-uniform updates, models with random neighbors and models with binary fitness and obtain exact results for the average fitness and for $p_c$.