Why are the Big Five factors of personality correlated? One of main characteristics of Five Factor Model is that factors are not orthogonal as in some other personality models.


Why it is tolerated that those factors are not independent?
Is it possible to find biological basis if factors are not independent?
There are no personality models in which the factors are orthogonal in the strict sense of being at 90 degrees from one another, unless an orthogonal rotation method is used to extract them. I think you meant to say that the Big Five factors are less independent (or more strongly inter-correlated) relative to the factors in other models. 

Whether or not one wants to obtain orthogonal factors depends on what one is trying to achieve. In most cases, you want an orthogonal solution if you want simple structure, i.e. you want to figure out which factor indicators unambiguously cluster together to form a relatively independent factor. But in general, factors are allowed to correlate because that just happens to be the "reality" and there is no theory suggesting that they should be completely independent. There are of course plenty of reasons why relatively independent factors might correlate and it doesn't mean that biological bases cannot be found; it could mean that there are biological bases that are shared among traits and there are those that are unique to each trait. For example, the relationship between Openness and Extraversion could in part be due to shared genes related to exploration (I forget the source for this).