Lonesome Pigeon

I'm not a fan of woodpigeons, but I can't help feeling sorry for this one as its partner was torn to pieces in front of my eyes by a large ginger cat.  Woodpigeons apparently mate for life, and certainly this one has seen off all other pigeons: whether singles looking for a mate or doubles looking for a garden.  How do birds choose who has what garden?  I've no idea.