Step 1: Understanding the Concept
An evolutionarily stable strategy (ESS) is a strategy that, once common, cannot be bettered by another strategy.
Step 2: Apply to sex ratio
If one sex becomes rarer, parents who produce that sex have more grandchildren, so its numbers rise again.
Step 3: Stable point
The only stable point is equal production of both sexes, a 1 : 1 ratio. So the ratio is 1000 : 1000.
Final Answer:
The ESS sex ratio of males to females is 1000 : 1000.
\[ \boxed{\text{(A) }\text{1000 : 1000}} \]