  Species subject to predation and environmental threats commonly exhibit
variable periods of population boom and bust over long timescales.
Understanding and predicting such behavior, especially given the inherent
heterogeneity and stochasticity of exogenous driving factors over short
timescales, is an ongoing challenge. A modeling paradigm gaining popularity in
the ecological sciences for such multi-scale effects is to couple short-term
continuous dynamics to long-term discrete updates. We develop a data-driven
method utilizing weak-form equation learning to extract such hybrid governing
equations for population dynamics and to estimate the requisite parameters
using sparse intermittent measurements of the discrete and continuous
variables. The method produces a set of short-term continuous dynamical system
equations parametrized by long-term variables, and long-term discrete equations
parametrized by short-term variables, allowing direct assessment of
interdependencies between the two time scales. We demonstrate the utility of
the method on a variety of ecological scenarios and provide extensive tests
using models previously derived for epizootics experienced by the North
American spongy moth (Lymantria dispar dispar).
