There are a few comments talking about epigenetics, and there seems to be a bit of error in explanation, so I wanted to try and clarify.

Historically, it has been understood that an organism will not pass on traits that arose as a product of environmental input (you wouldn’t pass along a broken arm to your child, just like you wouldn’t pass down decreased height as a result of malnourishment).

This is where things get interesting though. Epigenetics is the modification of a genome given environmental conditions. Modification of a genome means that offspring will contain the genetic modifications even in the absence of the environmental conditions that brought them about.

For example, an experiment was conducted on rats, in which the first experimental generation (F1) were exposed to jet fuel hydrocarbons (bad toxins). As one might expect, the offspring of these rats was also negatively affected by these toxins. The interesting part though, is that the F3 generation (not exposed to hydrocarbons and not developed in an adult with exposure to hydrocarbons) also showed increased abnormalities -to kidney function, specifically - which was a product of exposure to the toxins. This means that environmental changes to the F1 generation were seen in generations further down the line which had no environmental exposure to these toxins.

If you care about the mechanics of it, the jet fuel hydrocarbons methylated regions of DNA, essentially changing how the script is read by the molecular machinery expressing that DNA and making proteins with the instructions from it. Methylation alters the instructions that the gene is giving to the protein making complex. This methylation (attaching of a methyl group to a nucleic acid) was a direct result of the exposure to harmful chemicals. This methylation is often passed down to offspring, and can have an effect on how the organism grows, develops and responds to external stimulus.

So, the gene itself has not been altered in any way. The organisms DNA is the same. It’s only the amounts of methylation that have changed. The genome now simply contains extra instructions on how to read and express it.

So, it could be possible that one’s height is affected by malnourishment in parents. If a parent experienced high enough environmental stress levels (constant hunger) to lead to modification of how their body responds to food, they could pass that down.

Epigenetics is barely starting to be understood, however, so it is difficult to make accurate claims about whether someone height could be affected by a parents malnutrition (during pregnancy is different obviously).

While it is difficult to make a direct claim, I would be genuinely surprised if there wasn’t some modification to the musculoskeletal development in offspring of malnourished parents.