Step 1: Examine each statement.
\[
\begin{aligned}
I. &\text{True }(\text{tropical regions possess maximum biodiversity})
II. &\text{False }(\textit{Vinca rosea}\text{ yields vincristine/vinblastine, not digitalin})
III. &\text{True }(\text{Alien invasive species threaten native species})
IV. &\text{False }(\text{Sacred groves are an example of \emph{in-situ} conservation})
\end{aligned}
\]
Step 2: Identify the correct statements.
The correct statements are
\[
\boxed{I and III.}
\]
Step 3: Choose the correct option.
Hence,
\[
\boxed{(D)}
\]
is the correct answer.