He said: "Knowing what your parents were doing before you were conceived is turning out to be important in determining what disease risk factors you may be carrying.
"A major and underappreciated aspect of what is transmitted from parent to child is ancestral environment.
"Our findings suggest there are many ways that parents can 'tell' their children things.
"We often look at a patient's behaviour and their genes to assess risk. If the patient smokes, they are going to be at an increased risk for cancer.
"If the family has a long history of heart disease, they might carry a gene that makes them more susceptible to heart disease.
"But we're more than just our genes and our behaviour.
"Knowing what environmental factors your parents experienced is also important."
The phenomenon, called epigenetic inheritance – where changes in gene expression not caused by changes to the underlying DNA sequence are passed from a parent to a child – may be relevant to a number of illnesses.
Researchers fed different diets to two groups of male mice – the first set receiving a standard diet, while the second received a low-protein diet.
All females were fed the same, standard diet.
They observed that offspring of the mice fed the low-protein diet exhibited a marked increase in the genes responsible for lipid and cholesterol synthesis in comparison to offspring of the control group fed the standard diet – indicating an increased risk of heart disease.
Previous studies have suggested a father's lifestyle can come back to genetically affect his kids – but were unable to rule out socioeconomic factors.
Professor Rando went on: "Our study begins to rule out the possibility that social and economic factors, or differences in the DNA sequence, may be contributing to what we're seeing.
"It strongly implicates epigenetic inheritance as a contributing factor to changes in gene function."
Dr Hans Hofmann, associate professor of integrative biology at the University of Texas at Austin and a co-author of the study, said the study could help our understanding of how evolution works.
He said: "It has increasingly become clear in recent years that mothers can endow their offspring with information about the environment, for instance via early experience and maternal factors, and thus make them possibly better adapted to environmental change.
"Our results show that offspring can inherit such acquired characters even from a parent they have never directly interacted with, which provides a novel mechanism through which natural selection could act in the course of evolution."
Professor Rando said: "We don't know why these genes are being reprogrammed or how, precisely, that information is being passed down to the next generation.
"It's consistent with the idea that when parents go hungry, it's best for offspring to hoard calories, however, it's not clear if these changes are advantageous in the context of a low-protein diet."
The study was published this week in the journal Cell