How Predictable modeling rates of change in individuals and populations

Krumme, K. "How Predictable modeling rates of change in individuals and populations"


This thesis develops methodologies to measure rates of change in individual human behavior, and to capture statistical regularities in change at the population level, in three pieces: i) a model of individual rate of change as a function of search and finite resources, ii) a structural model of population level change in urban economies, and iii) a statistical test for the deviation from a null model of rank churn of items in a distribution.

First, two new measures of human mobility and search behavior are defined: exploration and turnover. Exploration is the rate at which new locations are searched by an individual, and turnover is the rate at which his portfolio of visited locations changes. Contrary to expectation, exploration is open-ended for almost all individuals. A present a baseline model is developed for change (or churn) in human systems, relating rate of exploration to rate of turnover. This model recasts the neutral or random drift mechanism for population-level behavior, and distinguishes exploration due to optimization, from exploration due to a taste for variety. A relationship be- tween the latter and income is shown.

Second, there exist regular relationships in the economic structure of cities, with important sim- ilarities to ecosystems. Third, a new statistical test is developed for distinguishing random from directed churn in rank ordered systems. With a better understanding of rates of change, we can better predict where people will go, the probability of their meeting, and the expected change of a system over time. More broadly, these findings propose a new way of thinking about individual and system-level behavior: as characterized by predictable rates of innovation and change.

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