Figure A2.

Scale factor choice. (A) Simplest case. The scale factor is the inverse of the smallest non-scaled value. (B) If A is not applicable, the scale factor is chosen such that the initial conditions are centered inside the range of acceptable values. The mid-point (on a log scale) of this interval is approximately 1. (C) Last case, if all scaled values cannot fit at once inside the range of accepted values, the lowest non-scaled values are dropped and set to zero so that the problem is simplified to case 1 (panel A) or 2 (panel B). In all panels, the white rectangle represents values that can be represented using DPFP. Dots represent the values of initial conditions for the differential equations of the multi-type birth–death model, before (1) and after (2) scaling. Red dots represent values that are initially outside the window of values that can be represented using DPFP.