Scientists and resource managers need to know life history parameters (e.g., average mortality rate, individual growth rate, maximum length or mass, and timing of maturity) to understand and respond to risks to natural populations and ecosystems. For over 100 years, scientists have identified “life history invariants” (LHI) representing pairs of parameters whose ratio is theorized to be constant across species. LHI then promise to allow prediction of many parameters from field measurements of a few important traits. Using LHI in this way, however, neglects any residual patterns in parameters when making predictions. We therefore apply a multivariate model for eight variables (seven parameters and temperature) in over 32,000 fishes, and include taxonomic structure for residuals (with levels for class, order, family, genus, and species). We illustrate that this approach predicts variables probabilistically for taxa with many or few data. We then use this model to resolve three questions regarding life history parameters in fishes. Specifically we show that (1) on average there is a 1.24% decrease in the Brody growth coefficient for every 1% increase in maximum size; (2) the ratio of natural mortality rate and growth coefficient is not an LHI but instead varies systematically based on the timing of maturation, where movement along this life history axis is predictably correlated with species taxonomy; and (3) three variables must be known per species to precisely predict remaining life history variables. We distribute our predictive model as an R package, FishLife, to allow future life history predictions for fishes to be conditioned on taxonomy and life history data for fishes worldwide. This package also contains predictions (and predictive intervals) for mortality, maturity, size, and growth parameters for all described fishes.