Consider a continuous time process {Y t = Z N t , t ≥ 0}, where {Z n } is a supercritical Galton– Watson process and {N t } is a renewal process which is independent of {Z n }. Firstly, we study the asymptotic properties of the harmonic moments E(Y −rt) of order r > 0 as t → ∞. Then, we obtain the large deviations of the Lotka-Negaev estimator of offspring mean.