If a sentence ends with a question offset by an em-dash does it end with a period or a question mark? This is the example:
Lucy scans for forgotten manglow mentions, but the margin notes contain only her data for resolving Mangifera humboldtensis’ central question— how did a subtropical angiosperm survive cold damp Humboldt County?
The direct question at the end of the sentence licenses a question mark. Even if you thought that the first part of the sentence (a statement) justified a period at the end, the question mark would override it. The Chicago Manual of Style says:
When more than one mark of punctuation (excepting quotation marks, parentheses, brackets, and sometimes dashes) is called for at one location in a sentence, only the stronger or more necessary mark is retained. (CMOS 14th ed., section 5.135)
It then gives two examples, the second of them demonstrating that "the period . . . is omitted in deference to the question mark". This suggests that a question mark is "stronger" than a period and is the mark that is retained.
Note that although this answer cites only CMOS, I'm fairly confident (based on experience) that most major style guides would recommend including a question mark (rather than a period) at the end of your example sentence.
By the way, I agree with Hot Licks (in a comment above) that a colon would work better than a dash here. Capitalizing the following letter is optional.
