Apparently it can start even before the new sibling has arrived. My daughter has been very excited about having a baby brother and she's been worried about him since I landed in the hospital. Nenertheless, I guess there's some part of her that's beginning to realize that having another child in the family will affect the existing family dynamic, specifically my relationship with her.
My little Ladybug can be super stubborn and disobedient, but she is nothing if not affectionate. Kisses, hugs, and "I love yous" are dispensed pretty liberally in our house. Sometime in the past couple of years the Ladybug has gotten into the habit of saying to me "I love you more than anyone else" and I respond in kind. So... the other night she called me to say goodnight and when I said "I love you" she asked "do you love me more than the Bumblebee?"