Dr. Yu Jin, University of Nebraska-Lincoln

Abstract: The study of population persistence and spread in river ecosystems is key for understanding river population dynamics and invasions as well as instream flow needs. We develop process-oriented reaction-diffusion-advection equations that couple hydraulic flow to population growth and analyze the models theoretically and numerically to assess the effects of hydraulic, physical, and biological factors on population dynamics. We present a mathematical framework, based on the fundamental niche, the source and sink metric, and the net reproductive rate, to determine local and global persistence of a population in a spatially heterogeneous one-dimensional or two-dimensional river. To investigate the influence of the geometric structure of river networks on population dynamics, we establish the fundamental theories of the corresponding parabolic and elliptic problems, and then derive the persistence thresholds by using the principal eigenvalue of the associated eigenvalue problem and the net reproductive rate. Furthermore, we present a hybrid modeling approach to explicitly link the flow regime with ecological dynamics. That is, we derive the water depth and current from hydrodynamic equations for one-dimensional or two-dimensional depth-averaged river flows, and then feed these quantities into population models to study the impact of spatial heterogeneity and temporal variability on population dynamics. We couple a benthic-drift model into the two-dimensional computational river model “River2D” to analyze the impact of river morphology on population persistence in a realistic river.

Bio: Dr. Yu Jin’s research is in applied mathematics with the main focus on dynamical systems and mathematical biology. This includes the establishment of appropriate mathematical models (mainly differential equations and difference equations) for phenomena in spatial ecology, population dynamics, and epidemiology, as well as mathematical and computational analysis for models. In recent years, she has been mainly interested in spatial dynamics of populations in advective environments, such as streams or rivers with temporal fluctuations and spatial heterogeneities, by virtue of studies of reaction-diffusion-advection equations. Her aim is to develop results to serve as theoretical basis for ecologists and water managers for decision making on biological invasion control and water resource management in complex river systems.

• For Zoom meeting information, please contact Dr. Jia Gou