The supplementary materials for the article "Dams trigger exponential population declines of migratory fish" by Zhenli Huang and Haiying Li provide detailed supplementary text, figures, tables, and references. The supplementary text covers several key aspects: 1. **Yangtze Dams and Major Fish Rescue Objects**: It discusses the historical context of fish rescue programs (FRPs) in the Yangtze River, focusing on the challenges of balancing hydropower development with fish conservation. The text outlines the development of FRPs for major dams such as the Gezhouba Dam (GD), Three Gorges Dam (TGD), and others, and the scientific and policy efforts to protect migratory fish species. 2. **Three-tiered Framework of Fish Migration Taxonomy**: This section proposes a three-tiered framework for classifying fish migration patterns, including diadromy, potamodromy, and oceanodromy. It provides detailed lifecycle models for each category, emphasizing the importance of understanding fish migration patterns for effective conservation measures. 3. **A Simplified Model for Quantifying the Barrier Effects of Dams**: This part introduces an age-structured population model to quantify the impact of dams on fish populations. The model considers natural mortality, fishing mortality, and the effects of dams on survival rates. It defines "invalid stock" and "valid stock" to assess the long-term impacts of dam construction on fish populations. The supplementary materials aim to provide a comprehensive understanding of the challenges and solutions related to the conservation of migratory fish species in the Yangtze River, particularly in the context of dam construction and operation.The supplementary materials for the article "Dams trigger exponential population declines of migratory fish" by Zhenli Huang and Haiying Li provide detailed supplementary text, figures, tables, and references. The supplementary text covers several key aspects: 1. **Yangtze Dams and Major Fish Rescue Objects**: It discusses the historical context of fish rescue programs (FRPs) in the Yangtze River, focusing on the challenges of balancing hydropower development with fish conservation. The text outlines the development of FRPs for major dams such as the Gezhouba Dam (GD), Three Gorges Dam (TGD), and others, and the scientific and policy efforts to protect migratory fish species. 2. **Three-tiered Framework of Fish Migration Taxonomy**: This section proposes a three-tiered framework for classifying fish migration patterns, including diadromy, potamodromy, and oceanodromy. It provides detailed lifecycle models for each category, emphasizing the importance of understanding fish migration patterns for effective conservation measures. 3. **A Simplified Model for Quantifying the Barrier Effects of Dams**: This part introduces an age-structured population model to quantify the impact of dams on fish populations. The model considers natural mortality, fishing mortality, and the effects of dams on survival rates. It defines "invalid stock" and "valid stock" to assess the long-term impacts of dam construction on fish populations. The supplementary materials aim to provide a comprehensive understanding of the challenges and solutions related to the conservation of migratory fish species in the Yangtze River, particularly in the context of dam construction and operation.