Creagar, M., Tenhumberg, B., and Rebarber, R. (2024). "A Spatially Explicit Game-Theoretic Model of Optimal Defense Strategies in Herbaceous Plants with Herbivore Movement". Soon to be submitted.

Abstract: Insect behavior has been demonstrated to be influenced by the presence of certain chemicals in herbaceous plants. In particular, host plant choice by insect herbivores has been shown to depend on the the presence and odor of chemical in the plant. Thus, if the chemical plume reaches far enough, allocation to defense may also be influenced by defense strategies employed by other plants in the environment. We incorporate a neighborhood defense effect by applying spatial evolutionary game theory to optimal resource allocation in plants where cooperators are plants investing in defense and defectors are plants that do not. We use a stochastic dynamic programming model, along with ideas from game theory, to examine how defense strategies in individual plants influence population outcomes in herbaceous plants. We incorporate an individual-based model for the herbivore population and allow the herbivores to move between plants. In this case, defense is only a neighborhood benefit, and this approach yields the possibility of a population evolving to consist of only cooperators or only defectors (pure stable strategy), as well as the possibility of a mixed stable strategy. We show that our model offers a theoretical explanation for the neighborhood effect seen in empirical evidence.

Creagar, M., Tenhumberg, B., and Rebarber, R. (2023). "Spatial Evolutionary Public Goods Game Theory Applied to Optimal Resource Allocation and Defense Strategies in Herbaceous Plants". Soon to be submitted.

Abstract: Empirical evidence suggests that the attractiveness of a plant to herbivores can be affected by the investment in defense by neighboring plants, as well as investment in defense by the focal plant. Thus, allocation to defense may not only be influenced by the frequency and intensity of herbivory but also by defense strategies employed by other plants in the environment. We incorporate a defense effect by applying spatial evolutionary game theory to optimal resource allocation in plants where cooperators are plants investing in defense and defectors are plants that do not. Our model builds on a stochastic dynamic programming model that accounts for metabolic cost of maintenance of stored resources when predicting optimal resource allocation to growth, reproduction, and storage; this cost is not commonly accounted for in previous models. For both annual and perennial plants, our model predicts an evolutionarily stable proportion of cooperators and defectors (mixed stable strategy), but the proportion of cooperators is higher in a population of perennial plants than in a population of annual plants. We also show that including a metabolic cost of maintaining stored resources does not change the proportion of cooperators but does decrease plant fitness and allocation to overwinter storage.

Jones, R.M., Creagar, M., Musty, M., Reynolds, R., Slone, S.M., and Barbato, R. (2022). "A k-Means Analysis of the Voltage Response of a Soil-Based Microbial Fuel Cell to an Injected Military-Relevant Compound (Urea)". USACE ERDC CRREL Technical Report. https://dx.doi.org/10.21079/11681/45940

Abstract: Biotechnology offers new ways to use biological processes as environmental sensors. For example, in soil microbial fuel cells (MFCs), soil electrogenic microorganisms are recruited to electrodes embedded in soil and produce electricity (measured by voltage) through the breakdown of substrate. Because the voltage produced by the electrogenic microbes is a function of their environment, we hypothesize that the voltage may change in a characteristic manner given environmental disturbances, such as the contamination by exogenous material, in a way that can be modelled and serve as a diagnostic. In this study, we aimed to statistically analyze voltage from soil MFCs injected with urea as a proxy for gross contamination. Specifically, we used k-means clustering to discern between voltage output before and after the injection of urea. Our results showed that the k-means algorithm recognized 4–6 distinctive voltage regions, defining unique periods of the MFC voltage that clearly identify pre- and postinjection and other phases of the MFC lifecycle. This demonstrates that k-means can identify voltage patterns temporally, which could be further improve the sensing capabilities of MFCs by identifying specific regions of dissimilarity in voltage, indicating changes in the environment.

Creagar, M., Wakefield, N., Smith, W.M., Apkarian, N., and Voigt, M. (2022). "Developing the Student Postsecondary Instructional Practices Survey in Mathematics for Measuring Student Experiences in Introductory Mathematics Courses." Investigations in Mathematics Learning, https://doi.org/10.1080/19477503.2022.2060023

Abstract: Active Learning is becoming a standard method of delivering instruction in mathematics courses across the country. Researchers, administrators, policy makers, and instructors all need access to valid means of measuring practices used in the classroom. Drawing on the Postsecondary Instructional Practices Survey, the Student Postsecondary Instructional Practices Survey in Mathematics (SPIPS-M) was developed to measure the undergraduate student perspective of active learning. Factor analysis from 10 institutions (N=16,495 surveys) supports a 4-factor model with a plausible theoretical foundation connected to the four pillars of Inquiry-Based Mathematics Education, by measuring the degree to which students perceive 1) their own engagement with meaningful mathematics, 2) collaboration to process mathematical ideas, 3) participation and formation of community, and 4) contribution of their own ideas for immediate instructor feedback. The instrument provides a new mechanism for program evaluation and course formative feedback. Ultimately the SPIPS-M instrument will allow a better understanding of the nuances of student experiences in their mathematics courses.

Devlin, S., Treloar, T., Creagar, M. and Cassels, S. "An iterative Markov rating method." Journal of Quantitative Analysis in Sports, vol. 17, no. 2, 2021, pp. 117-127. https://doi.org/10.1515/jqas-2019-0070.

Abstract: We introduce a simple and natural iterative version of the well-known and widely studied Markov rating method. We show that this iterative Markov method converges to the usual global Markov rating, and shares a close relationship with the well-known Elo rating. Together with recent results on the relationship between the global Markov method and the maximum likelihood estimate of the rating vector in the Bradley–Terry (BT) model, we connect and explore the global and iterative Markov, Elo, and Bradley–Terry ratings on real and simulated data.