Are you aware of any research papers that have explored a multi-type Galton-Watson process in which only particles of the majority type are permitted to reproduce in each generation?
I've been unable to find relevant literature; it's possible I'm using incorrect keywords.
In the most basic scenario, you'd have just two particle types, type-1 and type-2. A particle of a given type will generate a single offspring only if its type is predominant in that generation (ties are broken at random). In that case, a type-i particle would produce another type-i offspring with probability $p_i$, and an offspring of the opposite type with probability $1-p_i$.
