Earth is home to an extraordinary diversity and abundance of organisms, among them fish that provide us with food, recreation, and other services. The ability of aquatic ecosystems to sustainably provision these services is shaped by human influences such as harvest, species invasions, and habitat alteration. Effective management to maintain healthy fish populations requires at its most basic level an understanding of species distribution and abundance, which is made challenging by the expansive, diverse, and ever-changing nature of ecological communities. It also benefits from a mechanistic understanding of ecological dynamics, so that we can correctly anticipate population responses to environmental change and the outcomes of management interventions. This dissertation uses quantitative tools to contribute to these management needs in three ways: developing statistical methods capable of leveraging data from emerging environmental DNA (eDNA) technologies to estimate species distributions (mapping); improving animal migration models to help forecast ecological and evolutionary responses to environmental change (modeling); and applying optimization methods that draw upon dynamic models to directly formulate effective management strategies (managing). Chapter 1 explores how invasive species control can be optimized to restore native species by leveraging species traits and accounting for collateral damage. We apply optimal control theory to a two-species model, demonstrating how to maximize native population sizes by making careful choices about which removal methods to employ and when, where, and how intensely to apply them. Chapter 2 illustrates the potential utility of this approach with a case study aimed at restoring populations of an endemic freshwater goby (Sicyopterus stimpsoni) whose populations are depressed by invasive live-bearing fishes (poeciliids) in Hawaiian streams. Chapter 3 lays statistical groundwork for using aquatic eDNA to quickly and cost-effectively estimate spatial patterns of species abundance. Unlike traditional count and capture data, the interpretation of eDNA concentration data is complicated by dilution, transport, and loss processes that modulate concentrations and cause the eDNA collected from a water sample to be derived from a mixture of organisms both near and far from the collection point. We develop a hierarchical linear model that accounts for these processes and apply it across a large number of simulated stream networks that vary realistically in their topological and hydrologic properties. We determine how eDNA’s potential accuracy to estimate species-environment relationships depends on stream network properties, and we find optimal sampling designs with consistent features that offer rules of thumb about how eDNA surveys can position their samples most effectively. Finally, Chapter 4 extends existing theory about the evolution of partial migration, a phenomenon in which some individuals in a population migrate while others remain residents. Previous work on this topic has generally assumed that migration is a decision made by the organism, but in some taxa and life stages—especially larval fishes—external forces also influence an organism’s destination. In our model, migration is jointly determined by a migration propensity trait and environmental forcing conditions, which may either compel or impede movement. We found that weak, consistent forcing can be compensated for by evolution, but that strong or variable forcing cannot.