I'm writing a science paper for school, and my teacher said I need a
short title (running title) and a long title that uses active voice (a sentence).
How do I write the long title?
The short title is: Effect of Climate on Deer Population Density
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Summarise the paper's findings in one sentence.
Every one-sentence scientific fact you've ever read either had a citation or could have had one, depending on where you read it. That citation world be to a paper whose research showed as much, and possibly other things besides. It's routine for papers' findings to be described in this way, and clearly we know as a people how to do it. (Sometimes it's as a headline, but grammatically that's often just a sentence without a full stop.)
If you're struggling to summarise your paper's findings in this way, practise with a few existing papers. You only need to get the hang of condensing the abstract to a sentence, not the paper itself. The abstract typically says, "A has been investigated for reason B. There has been agreement on C but controversy on D. We illuminate this by looking at E with F, which builds on prior use of G in respect H. We found I. Further study could use J to check K." You only need the "I" part.
So what is the effect of climate on deer population density?
I'll leave that to you, since you're the one who knows. But that's what the sentence should be about. Try not to repeat too many words from the previous title. You'll probably say something like, "Warming in region L has already taken species M below replacement rate, with species N predicted to do the same if warming passes O" (or whatever the facts of it may be; maybe the effect is now global or at the genus-level, I wouldn't know).
For active voice, just get the verbs the right way round.
In other words, say climate change has reduced populations, not that populations were reduced by climate change. If nothing else, it's more concise (and yes, short and long titles alone need concision).