Initial paper presenting the Schaefer Biomass Dynamics assessment method: From morphometric data, tagging results and reaction of the stock to fishing, it is inferred that the yellowfin tuna of the Eastern Pacific form a distinct population which intermingles little, if at all, with populations to the westward. Excellent statistics of catch and effort, and records of total catch, available since 1934, during rapid growth of the fishery, have made possible application of a generalized mathematical predator-prey model to estimate the effect of fishing on the population, and the average abundance and yield corresponding to different amounts of fishing effort, and also to estimate the rate of fishing mortality per unit of effort. From serial samples of size composition of catches, and from tagging experiments, it has been possible to determine rates of growth and of total mortality. These kinds of information permit application of the catch-per-recruit model of Beverton and Holt. Combination of the results of application of the Beverton and Holt model and of the generalized predator-prey model, leads to inference of the relationship between stock size and recruitment. The form of the relationship is remarkably similar to the theoretical model developed by W. E. Ricker. These studies, based on the data of the near-surface fishery by baitboats and purse seiners, indicate clearly that the increased intensity of fishing has caused diminution of the stocks to the point where they are somewhat "overfished"-that is, incapable of supporting the maximum sustainable average harvest.