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Cheek and Johnston (Journal of Mathematical Biology, 2023) consider acontinuous-time Bienaym\'e-Galton-Watson tree conditioned on being alive attime $T$. They study the reproduction events along the ancestral lineage of anindividual randomly sampled from all those alive at time $T$. We give a shortproof of an extension of their main results to the more general case ofBellman-Harris processes. Our proof also sheds light onto the probabilisticstructure of the rate of the reproduction events. A similar method will beapplied to explain (i) the different ancestral reproduction bias appearing inwork by Geiger (Journal of Applied Probability, 1999) and (ii) the fact thatthe sampling rule considered by Chauvin, Rouault and Wakolbinger (StochasticProcesses and their Applications, 1991) leads to a time homogeneous processalong the ancestral lineage.

Ancestral reproductive bias in continuous time branching trees under various sampling schemes