Final answer:
The theory that acquired characteristics can be inherited is known as the inheritance of acquired characteristics, proposed by Jean-Baptiste Lamarck, but this has been discredited by modern genetics in favor of gene theory.
Step-by-step explanation:
The theory that characteristics acquired during the lifetime of an individual could be passed on to that individual's offspring is termed inheritance of acquired characteristics. This concept was proposed by French naturalist Jean-Baptiste Lamarck in the early 19th century. Lamarck suggested that if an organism changes during life in order to adapt to its environment, those changes are passed on to its offspring. However, this theory has been largely discredited by modern genetics, which shows that genetic changes (mutations) are the basis of inheritance, not the alterations acquired over the course of an individual's life.
The gene theory, by contrast, explains that characteristics are controlled by genes that are inherited from parents to offspring. This theory aligns with the work of Gregor Mendel and was later confirmed with the discovery of DNA as the genetic material responsible for heredity. Modern understanding of heredity is based on this gene-centric view, where genetic material is not altered by an organism's lifestyle or experiences in a way that can be passed on to offspring.