No, I mean direct environmental effect on deep DNA.
When people use "deep" like that, I tend to take them as signalling that they don't know what they are talking about but want to sound impressive.
"The stress of fear, lack of food, lack of mating opportunities etc., are the main causes of soft or deep changes. As these stresses are empathetically transmitted not only to life peers, but to extant population in wild areas, and to proximal generations , the resultant beneficial mutations are fairly quickly established, reducing the time needed by natural selection to do its work. This long time effect is the main cause of speciation as it expresses deep survival needs."
Much of that might be correct. But that is what I would call "environmental". The biochemical environment has changed, which has effects on development.
Personally, I have been a critic of biological determinism. There's nothing in that Time article (thanks for the link, Percy) that particularly surprises me. However, to make a case of Lamarckian inheritance, you would really need to see these effects transmitted to many generations, not only to the immediate next generation.
There's another effect that I didn't see in that Time report (or perhaps I missed it). Namely that some of these stress conditions are known to increase mutation rates, which can affect the rapidity of evolution.
Jesus was a liberal hippie