Using independent discovery and target subpopulations to generate and test risk scores, we found that the association of low FEV1 versus average FEV1 with the risk score became stronger for increasingly liberal p value thresholds of association in the discovery population (p=6·24 × 10−16 for a p value threshold of 0·5). This finding suggests a polygenic component to low FEV1, in which many variants of individually small effect size contribute to the risk of low FEV1. We found substantial sharing of genetic causes across thousands of genetic variants between low FEV1 in heavy smokers and low FEV1 in never smokers (p=2·29 × 10−16; p value threshold <0·5; figure 2; appendix p 30). Similarly, we found substantially overlapping genetic causes for low FEV1 in participants reporting a history of doctor-diagnosed asthma and low FEV1 in those without asthma (p=6·06 × 10−11; p value threshold <0·5; figure 2; appendix p 31). Finally, overlapping genetic causes were shown for high FEV1 and low FEV1 (p=1·64 × 10−22; p value threshold <0·5; figure 2; appendix p 30).