It just does not work that way. Mutations could be favorable and unfavorable, but there is no mechanism that "adaptations" are encoded back into genome.
Some random mutation which persisted in one population and wiped out in another has been selected due to environmental factors, such as climate and availability of food sources, does not imply that it is necessarily better or advantageous for a different environment.
And, of course, a diet could not cause genetic changes. Mutations could be selected in a population within some particular environment or wiped out in another.