Fluctuation Scaling, Taylor’s Law, and Crime

Abstract

Fluctuation scaling relationships have been observed in a wide range of processes ranging from internet router traffic to measles cases. Taylor’s law is one such scaling relationship and has been widely applied in ecology to understand communities including trees, birds, human populations, and insects. We show that monthly crime reports in the UK show complex fluctuation scaling which can be approximated by Taylor’s law relationships corresponding to local policing neighborhoods and larger regional and countrywide scales. Regression models applied to local scale data from Derbyshire and Nottinghamshire found that different categories of crime exhibited different scaling exponents with no significant difference between the two regions. On this scale, violence reports were close to a Poisson distribution (α = 1.057±0.026) while burglary exhibited a greater exponent (α = 1.292±0.029) indicative of temporal clustering. These two regions exhibited significantly different pre-exponential factors for the categories of anti-social behavior and burglary indicating that local variations in crime reports can be assessed using fluctuation scaling methods. At regional and countrywide scales, all categories exhibited scaling behavior indicative of temporal clustering evidenced by Taylor’s law exponents from 1.43±0.12 (Drugs) to 2.094±0081 (Other Crimes). Investigating crime behavior via fluctuation scaling gives insight beyond that of raw numbers and is unique in reporting on all processes contributing to the observed variance and is either robust to or exhibits signs of many types of data manipulation.

Rural to Urban Population Density Scaling of Crime and Property Transactions in English and Welsh Parliamentary Constituencies

“…Complex scaling has been observed in other types of scaling. For example, it has been noted in fluctuation scaling of crime [ 39 ], disease [ 40 ], and a variety of physical processes [ 41 ] and scientists have been encouraged to test alternative models to power laws when appropriate [ 42 ]. Here, visually inspired by the behavior of our data, we tested whether a double power-law provided a significantly better fit between a density metric ( y ) and the population density ( d ) than a single power law, that is, where d * is a population density threshold, β L ( β H ) is the power-law exponent for low (high) population density, y 0 and y 1 are constants.…”

The scaling of crime concentration in cities

“…The characterization of crime concentration paves the way for unveiling the very mechanisms that underlie the phenomenon in cities. Yet, an unbiased assessment of any regularity in crime needs to consider the relationship between population and crime, and thus an ideal framework must employ aggregation units that take into account the population in each unit [ 6 , 12 , 43 – 45 ].…”

Taylor’s Power Law for Leaf Bilateral Symmetry

“…Then, fixing the exponent of TPL to 2.0, the estimate of the logarithm of the constant α in TPL was demonstrated to be a logarithmic function of the time interval division. These studies related to TPL have added to our understanding of the variation of a large number of ecological and non-ecological measures, for example, animal and plant population density, biomass, poikilothermic developmental rate, crime, precipitation, released energies of aftershocks, trading activity of stock, and so on [13,[18][19][20][21][22]. In our recent studies, weight is a typical representative of energy for biological measures, so the variance-mean relationship based on weight measures should reflect TPL well [23].…”