Likelihood surfaces for simulated time series, where the inset of each shows the underlying time series (black/grey line) and its sampling (red circles); (a) sampling time Δt = 100 generations, (b) Δt = 1000 generations, and (c) Δt = 2500 generations. The black dotted lines represent contours of Ns = 1 (lower contour), which is the boundary between weak and strong selection and Ns = 10 (higher contour), which is the strength of selection used in the simulations. The likelihoods are scaled to their maximum value for each sampling period and contours show lines of equal likelihood, separated by values of 0.05 in likelihood, where magenta is the largest likelihood and cyan the smallest likelihood; in each case the L = 0.05 contour corresponds approximately to 95% of the integral of the likelihood. The green dashed lines represent the parameter values used to generate the simulated data, while the red dashed lines represent those values that maximise the likelihood; the maximum likelihood parameters are (a) N* = 1.8 × 104, and s* = 1.3 × 10−3, (b) N* = 1.7 × 104, and s* = 1.1 × 10−3, (c) N* = 2.6 × 104, and s* = 1.3 × 10−3.