In temporally or spatially varying environments species often evolve different phenotypes in response to this variety of niches. Such a phenotypic polymorphism can either be due to different genotypes present in the population or due to a mechanism that allows a single genotype to produce different phenotypes. Both possibilities were subject to many studies but rarely have they been combined in a single analysis. Here, an eco-evolutionary model for the evolution in time-varying environments is studied by means of individual based simulations. This model has been introduced by Rueffler et al. and initially been studied by using the adaptive dynamics approximation. In this model different mechanisms of phenotype determination are allowed to evolve simultaneously. The alternatives are a canalised genotype-phenotype map, phenotypic plasticity where an environmental cue is used to produce an adapted phenotype and bet-hedging (randomisation). The simulations presented here relax the assumptions of the adaptive dynamics approximation and show that the analytical results remain valid under more general conditions. Additionally, cases are treated in which the model is not analytically tractable. Contrary to preceding work we find that genetic polymorphisms can outcompete a bet-hedging strategy if a certain mutational correlation is introduced and mutational step sizes are limited. Comparing canalised genotypes and phenotypic plasticity we find that, depending on model parameters, different outcomes - ranging from polymorphisms of canalised phenotypes to evolutionary cycles - are possible. When canalised genotypes, phenotypic plasticity and bet-hedging are all allowed for simultaneously, we find that the strategy approached by evolution is a mixture of phenotypic plasticity and bet-hedging.