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On infinitesimally short time interval various processes contributing topopulation change tend to operate independently so that we can simply add theircontributions (Metz and Diekmann (1986)). This is one of the cornerstones fordifferential equations modeling in general. Complicated models for processesinteracting in a complex manner may be built up, and not only in populationdynamics. The principle holds as long as the various contributions are takeninto account exactly. In this paper we discuss commonly used approximationsthat may lead to dependency terms affecting the long run qualitative behaviorof the involved equations. We prove that these terms do not produce sucheffects in the simplest and most interesting biological case, but the generalcase is left open.

Logistic approximations and their consequences to bifurcations patterns and long-run dynamics