Showing posts from February, 2017

The Mysterious Taylor’s Power Law – Part III

Taylor’s power law regards the statistical relationship between population variance and population abundance, V = aMb. I refer to Parts I–II for background information. Whether V(M) is studied at a given spatial resolution or from varying abundance M in a sample by changing grid resolution the still unresolved problem is that animal populations (covering a wide range of taxa) upon re-scaling tend to show b≈2. Typical range is 1.5<≈b<≈2.2 rather than b≈1. In other words, due to the power law structure population dispersion seems to be scale-invariant; also called self-similar and thus compliant with a statistical fractal (aggregations within aggregations within…). In this post, I illustrate how V(M) in the Zoomer model becomes compliant with real-life V(M) patterns when the model is parameter-tuned towards its default condition – scale-free population dynamics!

Many model proposals exist for V(M) when sampling at a given spatial resolution, but despite thousands of papers over a …

The Mysterious Taylor’s Power Law – Part II

In a previous post I introduced the empirically observed Taylor’s power law, by referring to some of its history and one of its paradoxical properties: population abundance typically seems to satisfy a very aggregated pattern, V = aMb with b≈2, which seems to be self-similar (satisfying a statistical fractal) over a wide range of spatial resolutions. I also hinted towards chapters of my book, where I describe and discuss this and other strange statistical aspects relative to expectation from traditional population-dynamical models. In this post I study how my Zoomer model for scale-free population dynamics behave with respect to compliance with Taylor’s power law if I parameter-tune it towards more standard assumptions.

Consider the generic statistical pattern that would be expected from a “well mixed” population (satisfying, for example the default assumption for a standard differential or difference equation model). In this case, which by the way also makes the model population comp…