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Searching for the fractal dimension of ecology : Bubbles, Zooplankton, and Things that go Bump in the Night

Conférence de Karen Fisher Favret, chercheure invitée au Département de sciences biologiques de l’Université de Montréal.

Fractal statistics succinctly describe many natural distributions, in both space and time. When Mandelbrot asked, forty years ago, 'How long is the coastline of Britain?' he meant to bring the concepts of statistical self-similarity, and fractional dimensions into the toolbox of all working scientists. The fractal dimension of a time series or spatial transect characterizes the variance and multi-fractals characterize higher-order moments.

Many systems have critical scales at which these dimensions change. A critical scale indicates a switch from one mix of biological, chemical, and physical factors to another. The wavelet transform offers a straight-forward way to determine local fractal dimensions in large datasets. This tool is extremely useful in ecology, and offers a way to interrogate remote-sensing data where in-situ data is lacking. It can then be used to generate interpolated fields that reflect observed characters of the variance in the data. Here, I will present results using the wavelet transform to characterize phytoplankton, zooplankton, and a number of physical features in their environments, like bubbles and abrupt temperature gradients.

I will show how this method applies to flow-through fluorometers and high frequency acoustic backscatter (sonar). I will also outline my plan to apply this approach to analyzing passive acoustics, recordings of the soundscape above and below the water in Lac Cromwell at the SBL.

Conférence présentée par le Département de sciences biologiques de l’Université de Montréal dans le cadre de la série « Midi Écologique ».