Despite the advances in understanding molecular evolution, current phylogenetic 
methods barely take account of a fraction of the complexity of evolution. We are 
chiefly constrained by our incomplete knowledge of molecular evolutionary 
processes and the limits of computational power. These limitations lead to the 
establishment of either biologically simplistic models that rarely account for a 
fraction of the complexity involved or overfitting models that add little 
resolution to the problem. Such oversimplified models may lead us to assign high 
confidence to an incorrect tree (inconsistency). Rate-across-site (RAS) models 
are commonly used evolutionary models in phylogenetic studies. These account for 
heterogeneity in the evolutionary rates among sites but do not account for 
changing within-site rates across lineages (heterotachy). If heterotachy is 
common, using RAS models may lead to systematic errors in tree inference. In 
this work we show possible misleading effects in tree inference when the 
assumption of constant within-site rates across lineages is violated using 
maximum likelihood. Using a simulation study, we explore the ways in which gamma 
stationary models can lead to wrong topology or to deceptive bootstrap support 
values when the within-site rates change across lineages. More precisely, we 
show that different degrees of heterotachy mislead phylogenetic inference when 
the model assumed is stationary. Finally, we propose a geometry-based approach 
to visualize and to test for the possible existence of bias due to heterotachy.