Figure 4

The behavior of the stochastic transition model for different parameter values. (A) and (B) potential barrier for different parameter values (black lines) and the resulting dynamics (red lines). Time is on the y axis and x values are on the x axis. For low β and high σ transition to high shedding will be very rapid (A), while for high β and low σ it may never happen (or may take a very long time) (B). (C) Fraction of cows reaching high shedding at t = 1000. For high σ and low β the fraction is close to 1 (orange), while for low σ and high β the fraction is close to zero (blue). There is an intermediate region, where a limited fraction of cows becomes high shedders. The black line represents the parameter values that equal to the distance between the low attractor and the unstable fixed point.