  The idea of incompetence as a learning or adaptation function was introduced
in the context of evolutionary games as a fixed parameter. However, live
organisms usually perform different nonlinear adaptation functions such as a
power law or exponential fitness growth. Here, we examine how the functional
form of the learning process may affect the social competition between
different behavioral types. Further, we extend our results for the evolutionary
games where fluctuations in the environment affect the behavioral adaptation of
competing species and demonstrate importance of the starting level of
incompetence for survival. Hence, we define a new concept of learning
advantages that becomes crucial when environments are constantly changing and
requiring rapid adaptation from species. This may lead to the evolutionarily
weak phase when even evolutionary stable populations become vulnerable to
invasions.
