The naturally occurring process used to isolate and study specific genes is called gene cloning. In this mechanism, a segment of DNA containing a desired gene is replicated and inserted into a vector such as a plasmid or virus, which can then be transferred to a host organism. This process allows for the examination of gene function, the production of proteins, and can be instrumental in biotechnology and medical research. Gene cloning is also significant in the field of genomics which aims to understand the structure and function of genomes.