The history of human harvests of seals, whales, fish and krill in the Antarctic is summarised briefly, and the central role played by krill emphasised. The background to the hypothesis of a krill surplus in the mid-20th century is described, and the information on population and trend levels that has become available since the postulate was first advanced is discussed. The objective of the study is to determine whether predator–prey interactions alone can broadly explain observed population trends without the need for recourse to environmental change hypotheses. A model is developed including krill, four baleen whale (blue, fin, humpback and minke) and two seal (Antarctic fur and crabeater) species. The model commences in 1780 (the onset of fur seal harvests) and distinguishes the Atlantic/Indian and Pacific Ocean sectors of the Southern Ocean in view of the much larger past harvests in the former. A reference case and six sensitivities are fitted to available data on predator abundances and trends, and the plausibility of the results and the assumptions on which they are based is discussed, together with suggested further areas for investigation. Amongst the key inferences of the study are that: (i) species interaction effects alone can explain observed predator abundance trends, though not without some difficulty; (ii) it is necessary to consider other species, in addition to baleen whales and krill, to explain observed trends – crabeater seals seemingly play an important role and constitute a particular priority for improved abundance and trend information; (iii) the Atlantic/Indian Ocean sector shows major changes in species abundances, in contrast to the Pacific Ocean sector, which is much more stable; (iv) baleen whales have to be able to achieve relatively high growth rates to explain observed trends; and (v) Laws’ (1977) estimate of some 150 million tonnes for the krill surplus may be appreciably too high as a result of his calculations omitting consideration of density-dependent effects in feeding rates.