To promote understanding of fish population dynamics in tropical river-floodplains, we have synthesized existing information by developing a largely empirical population model for arapaima (Arapaima sp.). Arapaima are characterized by very large bodies, relatively late sexual maturity, small clutches, and large parental investment per offspring, and their populations are overexploited and even declining due to overfishing. We used unparalleled time series data on growth, reproduction, catch-at-age, and size-class abundance estimates for a population that has increased several-fold and undergone drastic changes in fishing practices in the Amazon, Brazil. Model population numbers were close to observed numbers, with generally low mean absolute percentage errors for juveniles (16%), adults (30%), and catch (18%). In using the model to test ecological hypotheses and to investigate management strategies, we found the following: (1) Annual recruitment is directly and positively related to spawner abundance, and it appears to be density-compensatory following a Beverton–Holt relation (R2 = 0.85). (2) Fishing-selectivity of arapaima caused by use of harpoons and gillnets can lower yield potentials dramatically through removal of the faster-growing individuals of the population. That is in part because fewer individuals live long enough to reproduce and survivors take longer to reach reproductive age. (3) Arapaima populations can sustain annual catches of up to 25% of the number of adults in the population the previous year if minimum size (1.5 m) and closed season (December–May) limits are met. (4) When 25% of the number of adults in the population the previous year is harvested under a 1.6 m minimum size limit of catch, catches are slightly smaller but abundance of adults in the population is considerably greater than under a 1.5 m limit. These findings can be used in ongoing management initiatives, but caution is needed because of present biological and ecological uncertainty about these fishes.