Disentangling effect of different players

Hi everybody,

I am new to the forum, greetings to everybody and thank you in advance for your help!
I have a question about how to approach an ecological dataset:

I have data on the number of animal species visiting sites.
I also have data on the total consumption of a common prey item.
Now, I would like to indirectly estimate the importance of each species on total consumption.
I would like to know whether lions, tigers, or leopards are driving consumption, or if they have a similar effect.

The question is whether it would be ok to run individual models for each species, e.g. one looking at lion abundance and total prey consumption, one looking at tiger abundance and total prey, and so one, or whether I have to include all of them in one model and see which one has a stronger effect...?

Maybe it is easier to understand if I visualize it... My dataset looks like this:

Site | Date | lions_seen | tigers_seen | leopards_seen | prey_items_consumed
1 | 03/20/2015 | 2 | 0 | 5 | 26
1 | 03/28/2015 | 3 | 3 | 2 | 17

In R, is it ok to model it like this:
glmer(prey_items_consumed ~ lions_seen + (1|Site), data=L, family="poisson")
glmer(prey_items_consumed ~ tigers_seen + (1|Site), data=L, family="poisson")
glmer(prey_items_consumed ~ leopards_seen + (1|Site), data=L, family="poisson")

Or should I do something like this?
glmer(prey_items_consumed ~ lions_seen + tigers_seen + leopards_seen + (1|Site), data=L, family="poisson")

Thanks a lot