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We consider several one-species population dynamics model with finite andinfinite carrying capacity, time dependent growth and effort rates and solvethem analytically. We show that defining suitable scaling functions for a giventime, one is able to demonstrate that their ratio with respect to its initialvalue is universal. This ratio is independent from the initial condition andfrom the model parameters. Although the effort rate does not break the modeluniversality it produces a transition between the species extinction andsurvival. A general formula is furnished to obtain the scaling functions.

Scaling Function, Universality and Analytical Solutions of Generalized One-Species Population Dynamics Models