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.

No abstract

<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>

The COVID-19 pandemic has imposed many strenuous effects on the global economy, community, and medical infrastructure. Since the out- break, researchers and policymakers have scrambled to develop ways to identify how COVID-19 will affect specific sub-populations so that good public health decisions can be made. To this end, we adapt the work of Evensen et al [1] which introduces a SEIR model that incorporates an age-stratified contact matrix, a time dependent effective reproduction number R, and uses ensemble data assimilation to estimate model parameters. The adaptation is an extension of Evensen’s modeling framework, in which we model sub-populations with varying risks of contracting SARS-CoV-2 (the virus that causes COVID-19) in a particular state, each with a characteristic age-stratified contact matrix. In this work, we will focus on 9 U.S. states as well as the District of Columbia. We estimate the effective reproductive number as a function of time for our different sub-populations and then divide them into two groups: frontline communities (FLCs) and the complement (NFLCs). Our model will account for mixing both within populations (intra-population mixing) and between populations (inter-population mixing). Our data is conditioned on the daily numbers of accumulated deaths for each sub-population. We aim to test and demonstrate methodologies that can be used to assess critical metrics of the pandemic’s evolution which are difficult to directly measure. The output may ultimately be of use to measure the success or failures of the pandemic response and provide experts and policymakers a tool to create better plans for a future outbreak or pandemic. We consider the results of this work to be a reanalysis of pandemic evolution across differently affected sub-populations which may also be used to improve modeling and forecasts.

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 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.

Pollination and seed dispersal mutualisms are critical for biodiversity and ecosystem services yet face mounting threats from anthropogenic perturbations that cause their populations to decline. Characterizing the dynamics of these mutualisms when populations are at low density is important to anticipate consequences of these perturbations. We developed simple population dynamic models detailed enough to distinguish different mechanisms by which plant populations benefit from animal pollination or seed dispersal. We modeled benefits as functions of foraging rate by animals on plant rewards and specified whether they affected plant seed set, germination, or negative density dependence during recruitment. We found that pollination and seed dispersal mutualisms are stable at high density but exhibit different dynamics at low density, depending on plant carrying capacity, animal foraging efficiency, and whether populations are obligate upon their partners for persistence. Under certain conditions, all mutualisms experience destabilizing thresholds in which one population declines because its partner is too rare. Plants additionally experience Allee effects when obligate upon pollinators. Finally, both pollination and seed dispersal mutualisms that reduce mortality during recruitment can exhibit bistable coexistence at low or high density. Insights from our models can inform conservation efforts, as mutualist populations continue to decline globally.