  We study a class of multi-species birth-and-death processes going almost
surely to extinction and admitting a unique quasi-stationary distribution (qsd
for short). When rescaled by $K$ and in the limit $K\to+\infty$, the
realizations of such processes get close, in any fixed finite-time window, to
the trajectories of a dynamical system whose vector field is defined by the
birth and death rates. Assuming that this dynamical has a unique attracting
fixed point, we analyzed in a previous work what happens for large but finite
$K$, especially the different time scales showing up. In the present work, we
are mainly interested in the following question: Observing a realization of the
process, can we determine the so-called engineering resilience? To answer this
question, we establish two relations which intermingle the resilience, which is
a macroscopic quantity defined for the dynamical system, and the fluctuations
of the process, which are microscopic quantities. Analogous relations are well
known in nonequilibrium statistical mechanics. To exploit these relations, we
need to introduce several estimators which we control for times between $\log
K$ (time scale to converge to the qsd) and $\exp(K)$ (time scale of mean time
to extinction).
