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Maize (Zea mays ssp.mays) is a major staple crop,with the highest tonnage among cereal crops worldwide (FAO 2o14).Over the past century,maize yields have increased about 8-fold in the US central C Belt (from 1,287 kg/ha in the 1930s to 11,084 kg/ha in 2017,http://www.fao.org,Duvick 2005b) due to a combination of genetic gain resulting from breeding efforts and improved management practices (such as application of synthetic nitrogen fertilizers,weed,and pest control,increased efficiency of harvest equipment,etc.).A major management practice that contributed to the continuous yield increase is continual increases in planting density (from 30,000 plants per hectare or less in the 1930s to 80,000 plants per hectare or higher in the 1980s,Duvick 2005a,2005b).A series of retrospective studies have suggested that newer hybrids yield more than older hybrids because of improved plant architecture better adapted to high density planting and increased ability to withstand various biotic and abiotic stresses associated with high density planting (Tollenaar and Wu 1999;Duvick 2005a,2005b).Although lagging behind the United States,increasing planting density has been a popular practice in other countries as well for increasing grain yield per unit land area in the last few decades (Li et al.2011).For example,maize planting densities have increased 2.1-fold over the last 60 years in China,with the yield increase kept in pace with increasing planting densities (Li et al.2013).