This paper presents a comprehensive mathematical test of Quetelet's biological explanation for the age crime curve, connecting criminological theory to methods developed in germ science through the application of probit analysis. It represents the most complete and technically developed version of the theoretical framework elaborated in Arnold (2012), Some Preliminary Thoughts on a Biological Explanation for the Age Crime Curve, and Arnold (2013), Testing Quetelet's Biological Explanation for the Age Crime Curve, and provides the mathematical foundation for Arnold (2016), The Criminological Puzzle. The age crime curve — the well documented population level pattern of rising criminal activity in adolescence followed by decline in adulthood — has resisted explanation for nearly two centuries. This paper proposes and tests a two factor biological model in which the interaction of developmental trajectories of physical strength and brain capacity, operating through the normal distribution of criminal propensity in the population, produces the age crime curve. The connection between germs and criminals lies in the fact that a germ's propensity to resist antiseptics and a person's propensity to commit crimes are both normally distributed in their respective populations — a statistical similarity that makes probit analysis the appropriate mathematical framework for modeling the age crime curve. Using U.S. arrest data from the National Incident Based Reporting System (NIBRS) for the eleven year period from 1996 to 2006, a Z-score model based on linear trajectories of strength and brain capacity is shown to fit the age crime curve with R² values of .999836 for males and .999736 for females — far superior to all standard curve fitting alternatives including linear, quadratic, cubic, exponential, and growth models tested using SPSS. The model demonstrates that the age crime curve consists of three sections — ages 0-18, 19-45, and 46-98 — each requiring separate explanations corresponding to different phases of the interaction between strength and brain capacity trajectories over the life course. Seven key propositions underlie the model: criminal propensity is normally distributed in the population; the mean and standard deviation of this distribution vary due to biological, psychological, and sociological factors; individual levels of criminal propensity are highly dynamic; the life course trajectories of strength and mental capacity interact to create the age crime curve; physical strength is directly related to criminal propensity; mental capacity is inversely related to criminal propensity; and the shape of the age crime curve results from the intersection of the normal distribution of criminal propensity with the age distributions of physical strength and mental capacity. These findings directly refute the conclusion of Sweeten, Piquero, and Steinberg (2013) that a simple solution to the age crime curve is unlikely — demonstrating that two biological variables explain what 40 criminological variables operating together could not. The results support Hirschi and Gottfredson's (1983) contention that the age crime curve operates independently of psychological and sociological factors, while providing the explicit biological explanation they declined to offer. This paper forms the mathematical foundation of the broader theoretical framework of The Physics of Living Systems, which proposes that living systems across multiple domains follow predictable distributional patterns governed by propensity selection thresholds in normally distributed propensity pools. The same mathematical framework applied here to criminal propensity has been applied to healthcare risk assessment in Arnold (2017, 2018), producing comparable breakthrough results.
Thomas K. Arnold (Wed,) studied this question.