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Orientation selectivity in the visual cortex has been extensively studied since it was disovered in 1959. In this article we demonstrate that current mechanistic explanations of orientation selectivity in the visual cortex, which appear to work in simplified models, do not suffice when embedded in a more realistic network. Up to now, orientation selectivity has only been reproduced in models with distance-dependent connectivity and limited cellular diversity. We therefore constructed a mouse primary visual cortex model with, among other refinements, realistic neuronal diversity and morphologically constrained connectivity. We implemented proposed mechanisms of orientation selectivity - specifically the organization of thalamocortical input into elliptical subfields and peferential connectivity between neurons with similar receptive fields - within this model. In the process we explored limitations of pure anatomy in predicting the connectivity and function of the cortex. Simulations of our model did not reproduce realistic levels of orientation selectivy. This indicates that these mechanisms, despite working well in simpler models, are not sufficient to explain orientation selectivity in real brain networks. On the basis of our results, we suggest the hypothesis that homeostatic plasticity is necessary to reconcile orientation selectivity with realistic connectivity.