Simple Mechanisms of Plant Reproductive Benefits Yield Different Dynamics in Pollination and Seed Dispersal Mutualisms.

AbstractPollination 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 on 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 on pollinators. Finally, pollination mutualisms can exhibit bistable coexistence at low or high density when plants are facultative on pollinators. Insights from our models can inform conservation efforts, as mutualist populations continue to decline globally.

Affirmative action, critical mass, and a predictive model of undergraduate student body demographics.

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.