  Here we show that a particular one-parameter generalization of the
exponential function is suitable to unify most of the popular one-species
discrete population dynamics models into a simple formula. A physical
interpretation is given to this new introduced parameter in the context of the
continuous Richards model, which remains valid for the discrete case. From the
discretization of the continuous Richards' model (generalization of the
Gompertz and Verhuslt models), one obtains a generalized logistic map and we
briefly study its properties. Notice, however that the physical interpretation
for the introduced parameter persists valid for the discrete case. Next, we
generalize the (scramble competition) $\theta$-Ricker discrete model and
analytically calculate the fixed points as well as their stability. In contrast
to previous generalizations, from the generalized $\theta$-Ricker model one is
able to retrieve either scramble or contest models.
