Fig. 1

Homoplasy values in the stepwise demographic expansion model for different values of the expansion time parameter τ. The points in each plot are the average values for each statistic across 100 simulations for plots (a-c), those average values were used to calculate the mean values of the homoplasy index (P), mean size homoplasy (MSH) and distance homoplasy (DH) that are plotted as points in (d). The dashed lines are the approximated expected values estimated from our derivations. a π _ISM and π _SMM ; b \( {F}_{ISM}^i \) and \( {F}_{SMM}^i \); c F _ISM and F _SMM d P, MSH and DH