Self-localization of directed polymers and oppressive population control

We construct a phenomenological theory of self-localization of directed polymers in d+1 dimensions. In d=1 we show that the polymer is always self-localized, whereas in d=2 there is a phase transition between localized and free states. We also map this system to a model of population dynamics with fixed total population. Our previous results translate to static and expanding population clusters, depending on the birth and death rates. A novel ``pseudo-travelling wave'' is observed in some sectors of parameter space.