Black and Latinx students are underrepresented on most public university campuses. At the same time, affirmative action policies are controversial and legally fraught. The Supreme Court has ruled that affirmative action should help a minoritized group achieve a critical mass of representation. While the idea of critical mass is frequently invoked in law and in policy, the term remains ill-defined and hence difficult to operationalize. Motivated by these challenges, we build a mathematical model to forecast undergraduate student body racial/ethnic demographics on public university campuses. Our model takes the form of a Markov chain that tracks students through application, admission, matriculation, retention, and graduation. Using publicly available data, we calibrate our model for two different campuses within the University of California system, test it for accuracy, and make a 10-year prediction. We also propose a coarse definition of critical mass and use our model to assess progress towards it at the University of California-Berkeley. If no policy changes are made over the next decade, we predict that the Latinx population on campus will move towards critical mass but not achieve it, and that the Black student population will decrease, moving further below critical mass. Because affirmative action is banned in California and in nine other states, it is worthwhile to consider alternative policies for diversifying a campus, including targeted recruitment and retention efforts. Our modeling framework provides a setting in which to test the efficacy of affirmative action and of these alternative policies.
Mutualisms are ubiquitous in nature, provide important ecosystem services, and involve many species of interest for conservation. Theoretical progress on the population dynamics of mutualistic interactions, however, has comparatively lagged behind that of trophic and competitive interactions. Consequently, ecologists still lack a generalized framework to investigate the population dynamics of mutualisms. Here, we propose extensible models for two-species mutualisms focusing on nutritional, protection, and transportation mechanisms and evaluate the population-level consequences of those mechanisms. We introduce a novel theoretical framework that highlights characteristic dynamics when the effects of mutualism are directly dependent or independent of recipient density and when they saturate due to inter- or intra-specific density-dependence. We end by integrating our work into the broader historical context of population-dynamic models of mutualism and conclude that a general ecological theory of mutualism exists.
<p style='text-indent:20px;'>The disparity in the impact of COVID-19 on minority populations in the United States has been well established in the available data on deaths, case counts, and adverse outcomes. However, critical metrics used by public health officials and epidemiologists, such as a time dependent viral reproductive number (<inline-formula><tex-math id="M1">\begin{document}$ R_t $\end{document}</tex-math></inline-formula>), can be hard to calculate from this data especially for individual populations. Furthermore, disparities in the availability of testing, record keeping infrastructure, or government funding in disadvantaged populations can produce incomplete data sets. In this work, we apply ensemble data assimilation techniques which optimally combine model and data to produce a more complete data set providing better estimates of the critical metrics used by public health officials and epidemiologists. We employ a multi-population SEIR (Susceptible, Exposed, Infected and Recovered) model with a time dependent reproductive number and age stratified contact rate matrix for each population. We assimilate the daily death data for populations separated by ethnic/racial groupings using a technique called Ensemble Smoothing with Multiple Data Assimilation (ESMDA) to estimate model parameters and produce an <inline-formula><tex-math id="M10000">\begin{document}$R_t(n)$\end{document}</tex-math></inline-formula> for the <inline-formula><tex-math id="M2000">\begin{document}$n^{th}$\end{document}</tex-math></inline-formula> population. We do this with three distinct approaches, (1) using the same contact matrices and prior <inline-formula><tex-math id="M30000">\begin{document}$R_t(n)$\end{document}</tex-math></inline-formula> for each population, (2) assigning contact matrices with increased contact rates for working age and older adults to populations experiencing disparity and (3) as in (2) but with a time-continuous update to <inline-formula><tex-math id="M4">\begin{document}$R_t(n)$\end{document}</tex-math></inline-formula>. We make a study of 9 U.S. states and the District of Columbia providing a complete time series of the pandemic in each and, in some cases, identifying disparities not otherwise evident in the aggregate statistics.</p>
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