Collaborative research: coexistence of competing structured populations: delineating mechanisms of niche differentiation

The National Science Foundation Division of Mathematical Sciences awarded $180,000 to the University of Louisiana at Lafayette on September 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop novel mathematical models describing how population structure—including size structure and patch-age structure—enables competing species to coexist. The research team will create analytical and computational techniques to analyze these models and apply them to understand how niche differentiation mechanisms allow closely competing species to persist together in ecological communities, addressing a central challenge in theoretical and mathematical ecology. The award funds work at the University of Louisiana at Lafayette's Research Office in Lafayette, Louisiana, with a period of performance through August 31, 2029.

Abstract

In nature, a dizzying array of closely competing species is at times observed coexisting together?they are repeatedly present together in the same locales. IT remains a puzzle for ecologists to fully explain how one species does not gain a foothold and take over. In many cases, there are potentially important types of ?structure? To the populations of species living together. For example, in a forest, each tree species has individuals of different sizes?the population has ?size structure?. Another type of structure is that some individuals live in ?gaps? Newly formed by a treefall from a disturbance like a storm, and others live in spots in the forest filled in with trees because they have not been disturbed in a long time. This other type of structure is ?patch-age structure?, where ?patch-age? Is how old the spot or ?patch? Is since IT was a new GAP created by disturbance. These types of ?structure? In populations importantly govern how individuals of the different species compete for light, nutrients, and water, and hence including them when using mathematical models to understand competitive coexistence may be essential. In this project, the investigators develop novel mathematical models to describe such interactions. However, analyzing these models presents significant mathematical challenges and requires the development of analytical and numerical tools. Accordingly, the research team also develops mathematical and computational techniques for analyzing these models and apply them to gain new insights into how population structure shapes the differences between species that enable their coexistence. The question of how competing species coexist remains a major challenge for theoretical and mathematical ecology. Size, age, stage, and other types of structure are thought to be critical features of biological populations, and they may importantly shape how species exploit different opportunities and as a result stably live together, but their incorporation into the theory of competitive interactions is so far limited. Our proposed research will develop and analyze mathematical models describing the coexistence of competing populations with (1) patch-age structure, (2) size structure, and (3) both patch-age and size structure, with a particular focus on identifying potential ?niche mechanisms? (i.e., types of differences between species that allow coexistence) at play among tree species in forests. The investigators will formulate partial differential equation models that capture these structures and use them to build, step by step, an understanding of the niche differentiation mechanisms that can arise from variation in life-history strategies, and the structural forces needed for these mechanisms to act. The research team will use analytical methods to derive conditions for feasible and stable coexistence whenever possible, extending the existing semigroup framework to establish stability results for our models. The project will also significantly extend recently developed higher-order finite difference numerical schemes and use them to analyze the likely large number of cases that are not analytically tractable but are essential for developing a more comprehensive understanding of coexistence in structured populations. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the foundation's intellectual merit and broader impacts review criteria.- subawards are not planned for this award.