Figure 1.

The stochastic Gompertz growth generated by the prior $N_e(t)={\left[\frac{1}{1+exp\{-X(t)\}}\right]}^{-1}$, where X(t) is the OU process presented in equation 4. N_e(t) is the diffusion with infinitesimal mean given by equation 6. The solid black line is the equivalent translated Gompertz trajectory (see equation 7). The horizontal dashed line corresponds to (1/λ) + (1/(κλ)) exp(β²/θ). Values of the parameters used in the plot are β² ≈ 0.002630, κ = 3.9140, θ = 0.2876, N_e(0) = 0.0678. This plot was done by first simulating trajectories according to the OU process (equation 4), applying the prior transformation to these and then overlaying the infinitesimal mean calculation from equation 6 (as well as equation 7) as a check of calculations for the SDE transformation.