  We consider an interacting particle system on trees known as the frog model:
initially, a single active particle begins at the root and
i.i.d.~$\mathrm{Poiss}(\lambda)$ many inactive particles are placed at each
non-root vertex. Active particles perform discrete time simple random walk and
activate the inactive particles they encounter. We show that for Galton-Watson
trees with offspring distributions $Z$ satisfying $\mathbf{P}(Z \geq 2) = 1$
and $\mathbf{E}[Z^{4 + \epsilon}] < \infty$ for some $\epsilon > 0$, there is a
critical value $\lambda_c\in(0,\infty)$ separating recurrent and transient
regimes for almost surely every tree, thereby answering a question of
Hoffman-Johnson-Junge. In addition, we also establish that this critical
parameter depends on the entire offspring distribution, not just the maximum
value of $Z$, answering another question of Hoffman-Johnson-Junge and showing
that the frog model and contact process behave differently on Galton-Watson
trees.
