In 2004, I went on a doctor supervised Optifast diet (about 400-500 calories a day and lost 70+ pounds in about 9 months). I mentioned to the doc about 2 months in that I was loosing a lot of hair (I had long hair then, and it seemed to be coming out in clumps). If I recall correctly, he said it was a reaction to the starvation, and recommended Zinc. I started supplementing and a little while later, the loss slowed down.
In the last few years I've kept my hair very, very short, so it would be hard to notice if it was shedding more. But I started growing it out last fall, and ever since starting LCHF, I've been noticing the comb has many more strands than usual. I am going to add a small amount of Zinc to my mineral regimine (potassium, magnesium, calcium).
I hope this information helps. I don't have any links to include, but you can Google Zinc and hair loss, and check it out.