Since 2006, the North American bat population has been in rapid decline due to white-nose syndrome (WNS), which is caused by an invasive fungus (Pseudogymnoascus destructans). The little brown bat (Myotis lucifugus) is the species most affected by this emerging disease. We consider how best to prevent local extinctions of this species using mathematical models. Development began in 2017 of a new vaccine for WNS and thus, we analyze the effects of implementing vaccination as a control measure. We create a Susceptible-Exposed-Infectious-Vaccinated hybrid ordinary differential equation and difference equation model informed by the phenology of little brown bats. We compare the effectiveness of annual, biennial, and one-time vaccination programs for multiple durations of immunity length. We also determine the optimal time to vaccinate, if vaccinating only once, as a function of average duration of immunity. Next, we perform a sensitivity analysis to determine the robustness of our results. Finally, we consider other possible control measures together with vaccination to determine the optimal control strategy. We find that if the vaccine offers lifelong immunity, then it will be the most effective control measure considered thus far.

Black-tailed prairie dogs (Cynomys ludovicianus) are a keystone species of shortgrass and midgrass prairies, and they are essential for successful reintroduction efforts of endangered black-footed ferrets (Mustela nigripes). Sylvatic plague extirpates black-tailed prairie dog colonies. We present a model to determine optimal

Differences in pollen performance, often revealed during pollen competition, have long been recognized as evolutionarily significant and agriculturally important. Though we have sophisticated models for the growth of individual pollen tubes, we have no robust models for larger scale pollen competition, a process that has been linked with inbreeding avoidance, sexual selection, reproductive barrier reinforcement, and speciation. Here we use existing data on pollen performance traits to develop an agent-based model of pollen competition. We calibrate our model parameters to empirical data found in the literature of seed siring proportions from mixed pollinations and pollen tube length distributions from single accession pollinations. In this model, parameters that influence pollen tube movement and sensing of ovules were found to be primary factors in competition. Our model also demonstrates that interference competition emerges as a property of pollen competition, and suggests a potential mechanism for this phenomenon. This study integrates pollen performance measures with mathematical modeling conducted on a simplified and accessible system. This represents the first mechanistic agent-based model for pollen competition. Our model may be extended to predict seed siring proportions for other accessions of Arabidopsis thaliana given data on their pollen performance traits.

No abstract