# earth and environmental sciences

## Rast Holbrook Seminar- Deep, Deep Down: Convection in the Lower Mantle

“Deep, Deep Down: Convection in the Lower Mantle”

## Rast Holbrook Seminar- Living Large: the paleobiology of Diplodocus and other long-necked dinosaurs

## Rast-Holbrook Seminar Series

" Deep crustal structure, processes, and properties from xenoliths and seismic observations in the Rocky Mountains "

## Rast-Holbrook Seminar Series

“Dissolved Trace Elements in Rivers: Problems and Perspectives”

## Rast-Holbrook Seminar Series

“Invasive species, mass extinction, and speciation: How biogeography impacts the history of life”

## The Dubious Power of Power Laws

Everyone knows the classic normal distribution—the “bell curve,” where most observations cluster around the mean, and the frequency falls off toward either end, with well known statistical properties. Lots of things in nature are more-or-less normally distributed, but lots of things are not. In some cases distributions are “heavy-tailed,” such that for example there are many of the small ones, and increasingly fewer as size increases. Famous examples are the distribution of earthquake magnitudes, rank-size distributions of cities, and the distribution of wealth in societies.

*Models of avalanche size distributions in (mathematically-simulated) sand piles were seminal in developing ideas about self-organized criticality and power laws, both in geomorphology and in general. Unfortunately even real sandpiles, much less more complex systems, are not necessarily well described by the models.*

## Convergence, Divergence & Reverse Engineering Power Laws

Landform and landscape evolution may be convergent, whereby initial differences and irregularities are (on average) reduced and smoothed, or divergent, with increasing variation and irregularity. Convergent and divergent evolution are directly related to dynamical (in)stability. Unstable interactions among geomorphic system components tend to dominate in earlier stages of development, while stable limits often become dominant in later stages. This results in mode switching, from unstable, divergent to stable, convergent development. Divergent-to-convergent mode switches emerge from a common structure in many geomorphic systems: mutually reinforcing or competitive interrelationships among system components, and negative self-effects limiting individual components. When the interactions between components are dominant, divergent evolution occurs. As threshold limits to divergent development are approached, self-limiting effects become more important, triggering a switch to convergence. The mode shift is an emergent phenomenon, arising from basic principles of threshold modulation and gradient selection.