The identification of key environmental forcings responsible for population
patterns is a pervasive ecological problem and an important application of
time series analysis. A common approach, implemented with methods such as
cross-correlation and cross-spectral analysis, relies on matching scales of
variability. This approach concludes that a population pattern is caused b
y a physical factor if their variances share a dominant period. In a nonlin
ear system, however, forcing at one temporal period can produce a response
with variability at one or more different periods. Thus, scale-matching met
hods will be most successful at establishing cause-effect relationships in
linear systems, or close to equilibria, where nonlinear systems are well ap
proximated by linear ones. Here, we propose an alternative approach that do
es not assume linearity and relies on time series models that are both nonl
inear and nonparametric. We specifically apply these models to determine th
e correct but unknown frequency of a periodic forcing. The time series are
generated by simulation of a predator-prey model. Under periodic forcing, t
his type of model is known to be capable of different dynamic regimes, incl
uding chaos and quasiperiodicity, in which the power spectra of population
numbers exhibit variance at frequencies other than that of the forcing. We
show that nonlinear time series models, built with feedforward neural netwo
rks, are able to distinguish the correct forcing period in the predator-pre
y simulations. These results hold under two common limitations of ecologica
l data: the presence of dynamical and measurement noise, and the availabili
ty of time series data for only one variable. We discuss future application
s of the approach to more general environmental forcings, other than period
ic.