# Population dynamics in river networks

## TL;DR

This paper develops a mathematical framework to analyze how the structure of river networks influences population persistence, incorporating models, eigenvalue analysis, and numerical simulations to identify key factors affecting species survival.

## Contribution

It introduces a process-oriented model for population dynamics in river networks, establishing fundamental theories and deriving thresholds for persistence based on eigenvalue analysis.

## Key findings

- River network structure significantly impacts population persistence.
- Hydrological, physical, and biological factors influence species survival.
- Eigenvalue-based thresholds can predict population extinction or persistence.

## Abstract

Natural rivers connect to each other to form networks. The geometric structure of a river network can significantly influence spatial dynamics of populations in the system. We consider a process-oriented model to describe population dynamics in river networks of trees, establish the fundamental theories of the corresponding parabolic problems and elliptic problems, derive the persistence threshold by using the principal eigenvalue of the eigenvalue problem, and define the net reproductive rate to describe population persistence or extinction. By virtue of numerical simulations, we investigate the effects of hydrological, physical, and biological factors, especially the structure of the river network, on population persistence.