Long after triumph of the central dogma of molecular biology, which is often equated with the idea that the DNA of a cell alone determines its fate, it was the fact that the cell plasm of an egg cell, whose composition can influence the early stages of a developing embryo, is in part derived from the diploid cells of the parent, which will have a different genotype, that to look for examples where this is important.
It is important because now the offspring will have the same traits. In a separate development, it was realised in quantitative genetics that models that included a maternal effect made more accurate predictions.
The original idea of inheritance of acquired characters has survived as a proverb, "use it or lose it". But this phrase does not usually refer to the inheritance of traits. Instead, it is applied to the maintenance of attributes in an individual.
In the 1920s, Harvard University researcher William McDougall, studied the abilities of rats to correctly solve mazes. He found that offspring of rats that had learned the maze were able to run it faster. The first rats would get it wrong 165 times before being able to run it perfectly each time, but after a few generations, it was down to 20. McDougall attributed this to some sort of Lamarckian evolutionary process.
In the USSR during the rule of Joseph Stalin in the 1930s, the theory of inheritance of acquired characteristics was central to the dogma put forth by Trofim Lysenko, president of the Soviet Academy of Agricultural Sciences. Lysenkoism was advanced primarily in service to Soviet agriculture, always resulting in dismal failure. But its implications for human biology were not lost on the Soviet leadership. Although Lysenkoism was discredited in the USSR by the mid-1960s, it still finds favor in Marxist circles.