Growth & Science (Like a horse and carriage right?)

I find that I often have difficulty keeping up with other players in terms of the growth of my cities, and subsequently, my science.

I'm an average player, so I know all the basics, but I wonder if there's any tricks out there that I'm missing?

Last night I had a game where I was in a quiet corner of the map and the only one not at war for almost the entire game and I was still behind the others on population and science. I had six cities, researched the top branches of the tree to get those science buildings quick, filled out the Tradition tree (after Liberty). Am I missing something guys?

If you have BNW I believe people are sending many food trade routes to their own capital so that it grows ludicrously quickly. Makes sense I suppose because if war breaks out it stops your trade routes getting plundered.

You might struggle for gold though, I don't know, I have yet to play BNW on multiplayer because my friends all own G&K, so my multiplayer experiences are mainly with G&K.

Other than that I can't think of much except the basic stuff, build food buildings, keep your empire happy to stop growth impairment, ally with maritime city states, try to get 'we love the king day', etc. I'm far from an expert. Someone else can probably offer you better advice than me.

You can send food to your cap, yes. But that requires a granary in the city you are sending the food from, and that is not always a prioritized building unless perhaps you are aiming for quick growth.
You still do get some science from trade routes with other major civs so you can keep up a little better even if you dont have the really big cities. It's a good way to introduce proper diplo in a mp ffa instead of the all out war kind of game. You can't fight without gold and you don't have any gold if you don't make friends. Atleast at the start of the game up to trade posts.

One thing that is easy to miss is running scientist specialists. In the city screen you can add citizens to the University to get tech and great scientists. You can also try for a quick national college. And consider going into rationalism immediately when it is available.If you want trade routes try to make sea conections to make them 2x effective.