The question is obvious.
Actually, they were mentioned in the anime. So, I believe that they would exist. Examples were Sophocle's Charjabug had a mild nature and when Horacio said that his shiny Charjabug had a Timid nature. These were the only instances nature were mentioned, but they were taken out in the dub from Japanese to the other languages. So, you can take that how you want, but I still believe they exist.
Hope I helped!