  In this article, we consider time-changed models of population evolution
$\mathcal{X}^f(t)=\mathcal{X}(H^f(t))$, where $\mathcal{X}$ is a counting
process and $H^f$ is a subordinator with Laplace exponent $f$. In the case
$\mathcal{X}$ is a pure birth process, we study the form of the distribution,
the intertimes between successive jumps and the condition of explosion (also in
the case of killed subordinators). We also investigate the case where
$\mathcal{X}$ represents a death process (linear or sublinear) and study the
extinction probabilities as a function of the initial population size $n_0$.
Finally, the subordinated linear birth-death process is considered. A special
attention is devoted to the case where birth and death rates coincide; the
sojourn times are also analysed.
