Where do you think behavioural characteristics come from then? For instance, schizophrenia is arguably a 'behavioural characteristic' as is autism - yet it is established that these have a strong genetic component. Behaviour isn't some abstract notion that is completely detached from our physical (i.e. neurological) and thus genetic nature.
As long as you agree that behaviour is derived from brain activity, and that the brain is composed of neurones whose activity is to an extent genetically controlled, then you can't really escape that all behavioural characteristics are to some extent genetically determined (as far as I can see).
