Using geometry to rank evenness measures: Towards a deeper understanding of divergence.

While recent work has established divergence as a key framework for understanding evenness, there is currently no research exploring how the families of measures within the divergence-based framework relate to each other. This paper uses geometry to show that, holding order and richness constant, the families of divergence-based evenness measures nest. This property allows them to be ranked based on their reactivity to changes in relatively even assemblages or changes in relatively uneven ones. We establish this ranking and explore how the distance-based measures relate to it for both order q = 2 and q = 1. We also derive a new family of distance-based measures that captures the angular distance between the vector of relative abundances and a perfectly even vector and is highly reactive to changes in even assemblages. Finally, we show that if we only require evenness to be a divergence, then any smooth, monotonically increasing function of diversity can be made into an evenness measure. A deeper understanding of how to measure evenness will require empirical or theoretical research that uncovers which kind of divergence best reflects the underlying concept.

A behavioural dynamic model of the relative age effect.

The relationship between date of birth and success in a variety of sports, including hockey, is well established. This phenomenon is known as the relative age effect (RAE). We model the RAE in Canadian youth hockey as a positive feedback loop where an initial age advantage is reinforced through additional training and playing opportunities based on perceived skill superiority. The same causal mechanism leads to a higher quit rate for relatively younger players. Our model effectively replicates the birth month distribution of Canadian National Hockey League players (R2 = 86.79%) when driven by Canadian birth distributions. We use this model to evaluate three policies that aim to lessen the RAE. All of the policies reduce the RAE with a significant delay. The most effective policy is a combination of providing additional support to age disadvantaged children and rotating the cut-off date for youth leagues between January 1st and July 1st annually. In equilibrium, this approach leads to a 96% reduction in the RAE compared to the base case.

Building a richer understanding of diversity through causally consistent evenness measures.

Causally consistent evenness measures can only be changed when the populations they refer to change. This novel property is deeply important for making causal inferences, and yet every prominent evenness measure is not causally consistent. This paper proposes a family of causally consistent evenness measures, and while any evenness measure can be made to be causally consistent, the family I introduce has the added benefit of a straightforward interpretation as a percentage evenness. I go on to illustrate the performance of these measures, and demonstrate the importance of causal consistency not only for causal inference but also for correctly reflecting the evenness of ecological communities. I also present several alternative transformations of my preferred measures, which work to address potential critiques in advance, communicate evenness to nontechnical audiences, and connect my work to more familiar ecological indicators.

The Government Finance Database: A Common Resource for Quantitative Research in Public Financial Analysis.

Quantitative public financial management research focused on local governments is limited by the absence of a common database for empirical analysis. While the U.S. Census Bureau distributes government finance data that some scholars have utilized, the arduous process of collecting, interpreting, and organizing the data has led its adoption to be prohibitive and inconsistent. In this article we offer a single, coherent resource that contains all of the government financial data from 1967-2012, uses easy to understand natural-language variable names, and will be extended when new data is available.