  Cheek and Johnston (Journal of Mathematical Biology, 2023) consider a
continuous-time Bienaym\'e-Galton-Watson tree conditioned on being alive at
time $T$. They study the reproduction events along the ancestral lineage of an
individual randomly sampled from all those alive at time $T$. We give a short
proof of an extension of their main results to the more general case of
Bellman-Harris processes. Our proof also sheds light onto the probabilistic
structure of the rate of the reproduction events. A similar method will be
applied to explain (i) the different ancestral reproduction bias appearing in
work by Geiger (Journal of Applied Probability, 1999) and (ii) the fact that
the sampling rule considered by Chauvin, Rouault and Wakolbinger (Stochastic
Processes and their Applications, 1991) leads to a time homogeneous process
along the ancestral lineage.
