Initially, assume the population is 1. Each year, 1/3rd of the population migrates, leaving 2/3rd of the population. After the 1st year, the remaining population = $\frac{2}{3}$. After the 2nd year, the remaining population = $\frac{4}{9}$. After the 3rd year, the remaining population = $\frac{8}{27}$. After the 4th year, the remaining population = $\frac{16}{81}$. After the 5th year, the remaining population = $\frac{32}{243}$. After the 6th year, the remaining population = $\frac{64}{729}$. Therefore, the remaining population after the sixth year is $\frac{64}{729}$, which corresponds to option D.