How does environmental variation translate into biological processes?

Birth and death rates, as so many other biological processes, are usually not linearly related to environmental variation. Common examples of non-linear response forms include unimodal "optimum-type" responses and various saturating responses. These responses filter the signal coming from the environment to a corresponding biological process. We explored how different types of environmental signal may be transformed to a biological process. We were interested in the effect of the filter on modulation of (1) the variance of the signal, on (2) the variance-covariance structure between the signal and the filtered signal, and on (3) the match between the power spectra of the signal and the filtered signal. We found that the filters will change the frequency distribution (mean, variance, modality) of the signal. Especially symmetric filters that have a single peak of optimum will change signal structure so that there either exists or does not exist a correlation between the signal and the filtered signal. When the correlation exists it may be either positive or negative depending on the signal's mode relative to the filter structure. Also, the power spectrum properties of the signal may be dramatically transformed after passing the filter, e.g., blue noise can turn into red noise. Our results strongly suggest that studies on the influence of external signals on biological processes, such as population dynamics, should explicitly consider how the signal is transferred to biological processes.