Howdy! I think that I might be able to help with this one.
But with a closer inspection I noticed something. We have to look at the larger structure of the sentence to see what is going on. We have two phrases that are describing the anthropologists. "...studying..." is a present participle phrase and "Influenced by..." is a past participle phrase. So actually this question is a little more complex than I originally thought.
Here is some info about different participle phrases:
"The -ing ending is added to the root of a verb to create a present participle (e.g., play becomes playing). Its function, explained below, is to form the progressive tense or to act as a verbal (a verb used as a noun or adjective). The -ed (sometimes -en) ending is added to the root of a verb to create a past participle (e.g., play becomes played). Its function is to form the simple past tense (e.g., played), the perfect tense (have, had, or will have played) or to act as a verbal."
Here is where I found the info: http://writingcenter.tamu.edu/2006/composing-process/grammar-composing-process/participles-%E2%80%9C-ing%E2%80%9D-and-%E2%80%9C-ed%E2%80%9D-endings/
Thanks for the question! It was a good one!
Best of luck with your studies!