Approximate aggregation techniques allow one to transform a complex system involving many coupled variables into a simpler reduced model with a lesser number of global variables in such a way that the dynamics of the former can be approximated by that of the latter. In ecology, as a paradigmatic example, we are faced with modelling complex systems involving many variables corresponding to various interacting organization levels. This review is devoted to approximate aggregation methods that are based on the existence of different time scales, which is the case in many real systems as ecological ones where the different organization levels (individual, population, community and ecosystem) possess a different characteristic time scale. Two main goals of variables aggregation are dealt with in this work. The first one is to reduce the dimension of the mathematical model to be handled analytically and the second one is to understand how different organization levels interact and which properties of a given level emerge at other levels. The review is organized in three sections devoted to aggregation methods associated to different mathematical formalisms: ordinary differential equations, infinite-dimensional evolution equations and difference equations.

Mouse models are key tools for studying cochlear alterations in noise-induced hearing loss (NIHL) and for evaluating new therapies. Stimuli used to induce deafness in mice are usually white and octave band noises that include very low frequencies, considering the large mouse auditory range. We designed different sound stimuli, enriched in frequencies up to 20 kHz (“violet” noises) to examine their impact on hearing thresholds and cochlear cytoarchitecture after short exposure. In addition, we developed a cytocochleogram to quantitatively assess the ensuing structural degeneration and its functional correlation. Finally, we used this mouse model and cochleogram procedure to evaluate the potential therapeutic effect of transforming growth factor β1 (TGF-β1) inhibitors P17 and P144 on NIHL. CBA mice were exposed to violet swept-sine noise (VS) with different frequency ranges (2–20 or 9–13 kHz) and levels (105 or 120 dB SPL) for 30 min. Mice were evaluated by auditory brainstem response (ABR) and otoacoustic emission tests prior to and 2, 14 and 28 days after noise exposure. Cochlear pathology was assessed with gross histology; hair cell number was estimated by a stereological counting method. Our results indicate that functional and morphological changes induced by VS depend on the sound level and frequency composition. Partial hearing recovery followed the exposure to 105 dB SPL, whereas permanent cochlear damage resulted from the exposure to 120 dB SPL. Exposure to 9–13 kHz noise caused an auditory threshold shift (TS) in those frequencies that correlated with hair cell loss in the corresponding areas of the cochlea that were spotted on the cytocochleogram. In summary, we present mouse models of NIHL, which depending on the sound properties of the noise, cause different degrees of cochlear damage, and could therefore be used to study molecules which are potential players in hearing loss protection and repair.