  We consider a generalized two-species population dynamic model and
analytically solve it for the amensalism and commensalism ecological
interactions. These two-species models can be simplified to a one-species model
with a time dependent extrinsic growth factor. With a one-species model with an
effective carrying capacity one is able to retrieve the steady state solutions
of the previous one-species model. The equivalence obtained between the
effective carrying capacity and the extrinsic growth factor is complete only
for a particular case, the Gompertz model. Here we unveil important aspects of
sigmoid growth curves, which are relevant to growth processes and population
dynamics.
