Specialist predators per definition show numerical responses to changes in food supply. Numerical responses are broadly divided into a reproductive response, where reproductive output increases with increased food supply, and an aggregative response caused by breeding suppression and movements. Numerical responses are crucial for understanding predator-prey relations, and also for appropriate management of predator populations. Declining populations of keystone herbivores (voles and lemmings) have been described as a widespread pattern in Europe. Negative effects of dampened small mammal cycles on numerical responses, and thereby population dynamics, have been predicted but so far demonstrated for relatively few specialist predators. We therefore monitored relationships between a common sub-arctic avian predator, the rough-legged buzzard Buteo lagopus, and small rodents in NW Sweden for 19 years (1970-1978 and 2001-2010, 369 observed breeding attempts). Rough-legged buzzards were food-limited and exhibited aggregative and reproductive responses to current rodent abundance in both study periods, but with a weaker coupling in recent years. Density of breeding pairs in rodent peak years was 32-50 % lower in the 2000s than in the 1970s. Further, reproductive output was lower in the 2000s, possibly preventing a population increase. Mean clutch size decreased with 0.77 eggs/clutch (from 4.53 to 3.73, an 18 % reduction), and mean number of fledglings per breeding attempt decreased with 1.08 juveniles/pair (from 3.88 to 2.80, a decrease of 28%). Hatching success and brood survival did not change between 1970s and 2000s, which suggests that reproductive output is constrained by clutch size, rather than by nestling mortality. The observed changes in reproductive parameters support a long-term change in food supply at the onset of breeding as the causal factor. Our study demonstrates the link between predator-prey theory and the declining population-paradigm of conservation biology, illustrating how estimation of numerical responses can be used to predict the outcome of perturbations to predator-prey systems.