Epigenetics refers to a special kind of hereditary mechanism. Epigenetic changes do not change the DNA nucleotide sequence, yet their effect on gene expression can last for several generations. In one surprising study, it was found that the grandsons of men who suffered a famine were less likely to die of cardiovascular disease. The experience of famine made some cardio-protective change in the sperm of those grandfathers that was passed on. What type of change was likely responsible?

Histone acetylation or DNA methylation.

Explanation:

The epigenetics may be defined as the genetic phenomena that might cause mutation in the organism's genome. The DNA sequence of the organisms do not get changed in epigenetics.

This phenomena is limited whether the gene is herited from the mother ot the father. The phenomena like acetylation of histones increase the gene expression. The DNA methylation and histone deacetylation at specific residues reduces the gene expression.

Thus, the answer is histone acetylation or DNA methylation.