Generally, the aim is to minimize BIC, so if you are in a negative territory, a negative number that has the largest modulus (deepest down in the negative territory) indicates the preferred model. Hence, in your plot the best case would appear to be "2".

Can information criteria be negative?

Generally, it is assumed that AIC (and so AICc) is defined up to adding a constant, so the fact if it is negative or positive is not meaningful at all. So the answer is yes, it is valid.

Can BIC values be negative?

The BIC values are always negative, e.g. [-2000, -3000, -3300, ..] . In the documentation of the method bic() , it says "The lower the better".