Choice B is the best answer. The convention being tested is the punctuation of items in a complex series (a series including internal punctuation). The semicolon after “nonnative” is correctly used to separate the first item (“growing diverse plant species, both native and nonnative”) and the second item (“fostering scientific research”) in the series of things that botanical gardens are dedicated to. Further, the comma after “species” is correctly used to separate the noun phrase “diverse plant species” and the supplementary phrase “both native and nonnative” that modifies it.
Choice A is incorrect because a comma (specifically, the comma after “nonnative”) can’t be used in this way to separate items in a complex series. Choice C is incorrect because a semicolon can’t be used in this way to separate the noun phrase “diverse plant species” and the supplementary phrase “both native and nonnative” that modifies it. Further, a comma can’t be used in this way to separate items in a complex series. Choice D is incorrect because it fails to use appropriate punctuation to separate the noun phrase “diverse plant species” and the supplementary phrase “both native and nonnative” that modifies it. Further, a comma can’t be used in this way to separate items in a complex series.