Populations of large grazing birds have increased in Europe during the past five decades, raising conflicts between conservation and farming interests. Managing these conflicts requires knowledge about the currently unknown relationship between population sizes and crop damage levels. We analysed unique data on reported, inspected and compensated crop damage caused by geese, swans and cranes together with data from population surveys in Sweden to investigate how bird abundance is related to damage levels at the national scale between 2000 and 2015. Over the study period, the annual number of damage reports, yield loss and costs for compensation increased. These crop damage levels were positively related to national population indices of common crane, barnacle and greylag goose. The shape of these relationships varied between species and encompassed considerable uncertainty. However, on a year‐to‐year basis (detrended data) we found no evident association between damage levels and bird numbers. Yield loss and compensation costs per reported damage did not increase with higher population indices of greylag goose, but they did so for barnacle goose. Synthesis and applications. We present a novel study of the relationships between different crop damage level indicators (damage reports, yield loss and compensation costs) and population numbers of large grazing birds. We identified a positive relationship with high uncertainty for all cases. We also identified the need to (a) better synchronize the monitoring of damages and bird numbers in time and space and (b) further study the relationships between damage levels and bird numbers at smaller (local and regional) and larger (flyway) spatial scales to reduce the uncertainty of the relationship and to gain a more holistic understanding of the system.

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