Final answer:
Lamarck supported the theory of inheritance of acquired characteristics, suggesting that modifications due to an organism's environment could be passed on to offspring, resulting in evolutionary change. This idea has since been largely discredited, but echoes of it persist in the study of epigenetics.
Step-by-step explanation:
Jean Baptiste Lamarck was a supporter of the inheritance of acquired characteristics theory of how mutations occurred in a population. Lamarck's theory of heritability, which predated Darwinian evolution, posited that organisms could pass on traits to their offspring that they acquired during their lifetime. An example commonly associated with Lamarck's hypothesis is the idea that giraffes acquired longer necks through stretching to reach high leaves and then passed this trait onto their offspring, leading to evolutionary changes.
However, the inheritance of acquired characteristics has largely been discredited in favor of genetics and Darwin's theory of natural selection. Despite this, some aspects of Lamarck's ideas have experienced a resurgence in the context of epigenetics, where changes in gene expression caused by mechanisms other than changes in the underlying DNA sequence can be influenced by environmental factors and, in some cases, be heritable.