Structure
What are the elements that make up this word's structure?
This word has some common elements I can "peel off:"
in + carcer + ate/ + ed
The suffix <-ed> is found on verbs to indicate the past; however, the past participle form can also be used to modify nouns, like adjectives do. We see it before the noun in the collocation "incarcerated population" above.
The suffix <-ate> forms many different word classes. Here it may have been added to my hypothesized base to create a verb, incarcerate.
Can we remove an incarcerated involves being "in jail," I'm not sure which sense it has here.
That leaves me with a proposed base of comparative adjective suffix you find on words like bigger and greater. I also do not think it is the agent <-er> suffix you find on farmer or teacher. Of course, it may be some other suffix <-er>, but I'm going to leave it intact for now until I find evidence.
For that evidence, let's look at Etymonline. There we can see the root. From the root, we can work out the spelling of our English base.
The entry for incarcerate says it is a back-formation of incarceration. A back-formation is a word where an assumed or actual suffix has been removed so that a new word is formed. The word edit is a back-formation of editor. It was assumed that's an agent <-or> suffix, and so it was removed to obtain the verb edit. Perhaps someone removed the <-ate> and <-ion> suffixes to arrive at
It also says it is a past participle of Latin incarcerare. The <-are> at the end of that word is a Latin infinitive suffix. We can remove it to arrive at incarceration just to be sure.
That entry says that the carcer which meant "prison; enclosed space."