Crop diversification affects weed communities and densities in organic spring cereal fields in northern Europe

•The utilization frequency of crop diversity measures is diverse and region dependent.•Weed densities are reduced by short term management such as weed harrowing and crop choice.•Cover cropping is a long-term crop diversity measure that increases weed diversity, but does not affect their densities.•Fields under organic management become more diverse over time, without weed densities increasing.•In addition to weed densities and diversity, communities as a whole are affected by the use of crop diversity measures.