Search

We study the equilibrium dynamics of a Lur’e system modelling a structured population, where adult conspecifics are assumed to have a negative density-dependent feedback on the recruitment of possible recruits. We find that, depending on the model’s parameter values, the population either goes extinct or has a positive equilibrium that is asymptotically stable, globally attracting or globally asymptotically stable. We apply our results to an integral projection model for the Platte thistle (Cirsium canescens) and highlight open aspects of this problem for future work.

Mathematical and computational methods are vital to many areas of contemporary biological research, such as genomics, molecular modeling, structural biology, ecology, evolutionary biology, neurobiology, and systems biology. As such, the contemporary life science student needs to be exposed to, if not well-versed in, many areas of mathematics to keep pace. However, traditional ways of teaching mathematics may not be able to provide life science majors the skills and experiences necessary to effectively use mathematics in their careers as practitioners and/or researchers, as these skills and experiences (for example, mathematical modeling and interdisciplinary collaboration) are difficult to teach using lecture-style approaches. In this paper the authors describe the implementation and assessment of a flipped-classroom approach to teaching a sophomore-level mathematical biology course for life science majors.

American chestnuts, Castanea dentata, were once a dominant tree in eastern deciduous forests of the United States before the chestnut blight fungus, Cryphonectria parasitica, was introduced unintentionally in the early 1900s in New York. This fungus rapidly devastated American chestnut populations until a hypovirus infection of the fungus began to reduce pathogen virulence on chestnut trees. The subsequent reappearance of large reproducing chestnut trees, associated with a large proportion of blight-infected isolates being parasitized by this hypovirus, is currently taken to indicate recovery of American chestnut populations. We explore, using previously-established matrix population models, the dynamics of healthy, fungus-infected, and hypovirus-infected American chestnut populations to test the efficacy of this recovery. Our main result is that populations transitioning from being fungus-infected to hypovirus-infected are predicted to show large transient amplifications as a result of demographic transitions, only to decline asymptotically to zero, and this result is robust to uncertainty in fecundity values. Our results suggest that the current recovery of the American chestnut population may be a transient phenomenon and that more conservation efforts may be necessary to ensure its long-term persistence.