We implement a newly developed framework, expressed as a mathematical model that we solve numerically, for understanding environmental sex determination in populations with consistent trends in abundance. Though broadly applicable, the analysis here focuses on the steadily declining North Atlantic eel populations. This enables us to show how the eco-evolutionary dynamics of eels reflect sex-specific and habitat-specific relationships among demographic features. When increasing stress levels resulting from Human-Induced Rapid Environmental Change are imposed on these populations, they become increasingly vulnerable to highly biased sex ratios. Our analysis is both prescriptive (identifying the key components and the priorities for deepening our understanding of them) and predictive (indicating expected qualitative patterns to be tested in future work). Priorities include establishing sex ratios and age/sex structure by habitat, measuring the magnitude and effects of social and individual stress levels, estimating effects of fishing pressure, and investigating reproduction in the Sargasso Sea. Key predictions address expected biases and trends in sex ratios, habitats more likely to be population sources (e.g. river basins) or sinks (e.g. estuary), expected trends in bimaturism (sex-specific maturation times), implications of the relative speed of adaptation and of environmental deterioration, and fitness responses to stress levels, early-stage mortality, and female demographic parameters.