Are these two meanings of "brood" related?

I am aware of two meanings of the word "brood". One is to do with children:

the young of an animal or a family of young

the other is to do with being in a bad mood:

a: to dwell gloomily on a subject,
b: to be in a state of depression

(both these definitions are given at Merriam-Webster).

I am wondering whether there is a relationship between these two meanings. I’m no etymologist, but usually when I look up the root of a word with two meanings like this I can sort of see how it could be interpreted in the two different meanings (even if they are quite different). But in this case all I can see is a root to do with breeding. So I can’t see how the other meaning came about.