Salmon oil - should I refrigerate?

[JMSA]

I've recently started giving my Shih Tzu a couple of pumps of salmon oil in his dry food. He is loving it. I've looked up storage recommendations online, but it's mixed. There's nothing on the bottle.
What do you do with yours?
Thanks

Wild salmon is very high in Omega 3 which goes rancid very easily so would need refrigeration.

However, farmed salmon, which your mix likely is, is fed food high in Omegas 6 and 9 to reduce the rancid problem and increase stability and shelf life.

Thank you very much. If there's no harm in refrigerating either way, then it's likely I'll do that.

I don’t. I’ve not killed my dog or cat yet 😉

Edit. My bottle says 9 months from opening and store in a cool place

The bottle I had soon went rancid & off smelling, I hadn't kept it in the fridge, obviously a mistake.