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