Power Law
A mathematical relationship where one quantity varies as a power of another: y = x^k. Power laws appear as straight lines on log-log plots and produce highly skewed distributions with many small values and few large ones.
Used in the Books
This term appears in 6 chapters:
"...fore moving far - Optimal when resources are clustered and predictable Example: Ants searching near nest (food likely nearby) 2. Lévy Flight (Power Law Distribution) - Mostly short steps, occasional very long jumps - Cover more ground, find distant patches - Optimal when resources are sparse and un..."
"Large events (building-sized) happen monthly. Gigantic events (stadium-sized) happen annually. The distribution follows a power law: The number of events decreases exponentially as size increases. If you observe 1,000 car-sized calving events, you'll observe ~100 house-sized, ~10 ..."
"...nding metabolic scaling theory to ecological phenomena including population density and trophic structure. Glazier, D.S. (2005). Beyond the '3/4-power law': Variation in the intra- and interspecific scaling of metabolic rate in animals. Biological Reviews, 80(4), 611-662."
"..., March 27, 2021. Fractal Analysis and Measurement 21. Feder, J. (1988). Fractals. Plenum Press. 22. Schroeder, M. (1991). Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise. W.H. Freeman. 23. Falconer, K. (2003). Fractal Geometry: Mathematical Foundations and Applications (2nd ed.)...."
"...networks, most nodes have few connections while a few "hubs" have many - creating a highly heterogeneous structure. Mathematically, this follows a power law: the distribution of node connections (degree k) follows P(k) ∝ k^(-γ), where γ typically ranges from 2 to 3."
And 1 more chapter...
Biological Context
Species abundance, body size, metabolic rate, and extinction frequency all follow power laws. Power law distributions have 'fat tails'—extreme events are more common than normal distributions predict. Power laws often arise from multiplicative processes or preferential attachment.
Business Application
Business outcomes follow power laws: a small fraction of products generate most revenue, a few employees drive most value, and rare events dominate long-term results. Averages mislead.