How does environmental variation translate into biological processes?

Birth and death rates, as so many other biological processes, are usually n ot linearly related to environmental variation. Common examples of non-line ar response forms include unimodal "optimum-type" responses and various sat urating responses. These responses filter the signal coming from the enviro nment to a corresponding biological process. We explored how different type s of environmental signal may be transformed to a biological process. We we re 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. Especi ally symmetric filters that have a single peak of optimum will change signa l structure so that there either exists or does not exist a correlation bet ween 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 infl uence of external signals on biological processes, such as population dynam ics, should explicitly consider how the signal is transferred to biological processes.