do red-headed dogs require more anaesthetic?

When we first saw Penny we decided to name her after the copper coin because of the reddish colour of her coat the fur on her head, and we've always thought of her as a 'red-head' even though, over time, she's shifted somewhat towards blonde. I was fascinated, therefore, to hear a discussion on the radio today about the fact that red-headed humans need a greater dose of anaesthetic than others when they are having surgery, because they feel pain more than others do. The person who said this was a professor of anaestheology at a local university. There's an article about it in New Scientist of 15 October 2002.

A listener rang in to say that it's the same for ginger cats. Interesting. But I'd need to hear some scientific backup to this suggestion. A look around the Net doesn't throw up any immediate information. I can't see that it would logically follow, that the reddish colour in cats comes from a gene that operates in the same way as the gene for red hair in the human genome. The New Scientist article says:

In people with red hair, the cells that produce skin and hair pigment have a dysfunctional melanocortin 1 receptor. Liem says this dysfunction triggers the release of more of the hormone that stimulates these cells, but this hormone also stimulates a brain receptor related to pain sensitivity

Of course, now I wonder about ginger(ish) dogs...