Developing fast, cost-effective assessments of wild animal abundance is an important goal for many researchers, and environmental DNA (eDNA) holds much promise for this purpose. However, the quantitative relationship between species abundance and the amount of DNA present in the environment is likely to vary substantially among taxa and with ecological context. Here, we report a strong quantitative relationship between eDNA concentration and the abundance of spawning sockeye salmon in a small stream in Alaska, USA, where we took temporally- and spatially-replicated samples during the spawning period. This high-resolution dataset suggests that (1) eDNA concentrations vary significantly day-to-day, and likely within hours, in the context of the dynamic biological event of a salmon spawning season; (2) eDNA, as detected by species-specific quantitative PCR probes, seems to be conserved over short distances (tens of meters) in running water, but degrade quickly over larger scales (ca. 1.5 km); and (3) factors other than the mere presence of live, individual fish — such as location within the stream, live/dead ratio, and water temperature — can affect the eDNA-biomass correlation in space or time. A multivariate model incorporating both biotic and abiotic variables accounted for over 75% of the eDNA variance observed, suggesting that where a system is well-characterized, it may be possible to predict species' abundance from eDNA surveys, although we underscore that species- and system-specific variables are likely to limit the generality of any given quantitative model. Nevertheless, these findings provide an important step toward quantitative applications of eDNA in conservation and management.