LEAPS-MPS: Predator Competition in Systems with Seasonal Birth

In many ecosystems, seasonal processes are experienced as sudden events, disrupting continuous processes. These disparate processes are closely linked, for example when resource consumption (a continuous behavior) determines reproductive capacity (a seasonal event). Describing the links between these processes is fundamental to long-term descriptions of seasonal ecosystems.

This project bridges a gap between common mathematical methods which describe these processes separately, combining them into a hybrid framework. The framework permits long-term models of seasonal ecosystems. Long-term models are necessary for ecological forecasts and seasonal behavior is especially relevant for incorporating sensitivities to annual climate.

Hybrid models are therefore broadly applicable to a range of ecological problems. This project focuses on hybrid descriptions of competition between predatory insects which consume pests in agricultural ecosystems, with attention to how changing temperatures affect pest control. The project also assesses hybrid model performance in arbitrary ecosystems, building broader capacity to address conservation and management problems.

The project is hosted at a Hispanic Serving Institution and supports undergraduate research in ecological modelling, which is an accessible entry point to mathematical research and fosters computational skills applicable to a multitude of technical careers. Participation includes travel to a scientific conference for postgraduate planning and community building among groups underrepresented in mathematics, where the PI will also seek applicants for supported graduate student research.

The project improves institutional capacity to support students from groups underrepresented in mathematics through the development of tailored resources for retention and job placement, which also amplifies existing initiatives broadening participation in mathematics.

Describing the interface between long-term (discrete) and short-term (continuous) changes to an ecological population requires mathematical models which couple continuous differential equations and discrete difference equations. This coupling results in a hybrid model, which incorporates population processes over disparate timescales and describes seasonal ecosystems’ long-term development.

However, dynamics of such models are difficult to assess if the continuous equations incorporate complex behaviors, as is necessary for the target model of predator-prey interactions in a community of generalist predators. This project investigates the effects of competition and seasonal birth on long-term prey abundance and predator coexistence in hybrid models in three stages: (1) through the analysis of simple, two-predator models to build intuition for the interplay between predator competition and seasonal birth; (2) by extending the hybrid model to investigate the effects of predator diversity and temperature variability on pest control in a real agricultural ecosystem; and (3) through the numerical simulation of many complex, theoretical ecosystems to compare persistence outcomes between hybrid and continuous models.

Preliminary theoretical analysis of fixed points and other stable outcomes yields a thorough understanding of how specific behaviors influence population trajectories, facilitating later work. Parameterizing the hybrid competition model from prior abundance data and empirical observations provides insight into the effects of similar behaviors in real agricultural ecosystems.

Simulating hybrid models for a range of parameters and feeding interactions establishes the conditions under which species persistence is affected by seasonal behaviors. Together, the three stages establish a foundational understanding of hybrid models in seasonal ecosystems.

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.