There is good evidence that we inherit characteristics that may make individuals more or less prone to being anxious. Depending on what they are exposed to this may lead to phobias and anxiety disorders or just make the person one of life's worriers. This is based on now long-accepted theories of inheritance going back to Darwin.
One of the key concepts in Darwin's theory of natural selection is that change happens across generations because those genes that most help an organism survive and have descendants are more likely to be passed on to the next generation.
A competing theory at the time of Darwin was Lamarkism. Jean Baptiste Lamark proposed that organisms changed to fit their environment rather than as with Darwin being selected for by the environment. He thought that if an animal learned a new trick over its life-time and that proved to be a valuable trick this will be passed on to the next generation.
With our developing understanding of DNA as the mode of genetic transmission it became clear that Lamarkism was apparently impossible. A giraffe stretching to reach a branch doesn't change its DNA to result in a longer neck in the generation. Rather those giraffes with longer necks are more successful, produce more offspring and hence the species gradually develops longer necks.
All this makes the recent study carried out by Brian Dias and Kerry Ressler the more interesting. They took a group of male mice and got them to smell acetophenone. At the same time they gave them an electric shock. The mice learned (via classical conditioning) to associate the shock with the smell and so became scared of it. As a result they would react fearfully to it even in the absence of the shock. So far nothing astounding.
The researchers then got the fearful mice to have some baby mice. They got the offspring to smell the acetophenone scent and here is where it gets interesting. They found that the offspring mice were scared of the smell even though they had never been shocked. Also they did not watch their fathers react fearfully to the smell, in case you were wondering. This shouldn't be the case according to our current Darwinian model and it has the potential to dramatically shift our view of inheritance.
The authors suggest the effect is transmitted not by a change in the actual DNA or genes, but rather that how genes are expressed; something called 'epigenetics'.
As with all studies which challenge a long held theory this one needs to be replicated and the mode of transmission understood, but if confirmed it has major implication for human behaviour and how it is inherited.