Identify the correct statements from the following:
$(1)$ Succession occurring in dry areas is called xerarch succession.
$(2)$ The stage where plants can survive in open conditions throughout the year is the herb stage.
$(3)$ Ecological succession leads to a decrease in the net primary productivity of the community.
$(4)$ Primary succession takes an average of $1000$ years to complete.

• A
  Only $1$ and $3$ are correct
• B
  Only $1$ and $2$ are correct
• C
  $1, 2, 3$ are correct
• D
  $1, 2, 3, 4$ are correct