The conflict between the Mendelian theory of participate inheritance¹ and the observation of continuous variation for most traits in nature was resolved in the early 1900s by the concept that quantitative traits can result from segregation of multiple genes, modified by environmental effects^2–5. Although pioneering experiments^6–9 showed that linkage could occasionally be detected to such quantitative trait loci (QTLs), accurate and systematic mapping of QTLs has not been possible because the inheritance of an entire genome could not be studied with genetic markers⁷. The use of restriction fragment length polymorphisms¹⁰ (RFLPs) has made such investigations possible, at least in principle. Here, we report the first use of a complete RFLP linkage map to resolve quantitative traits into discrete Mendelian factors, in an interspecific back-cross of tomato. Applying new analytical methods, we mapped at least six QTLs controlling fruit mass, four QTLs for the concentration of soluble solids and five QTLs for fruit pH. This approach is broadly applicable to the genetic dissection of quantitative inheritance of physiological, morphological and behavioural traits in any higher plant or animal.