Interesting question I would recommend the effective population size $N_{e}$, and error bars around this. Ne can be calculated via $F_{st}$ and is perhaps the most important parameter to determine the genetic population size.
Under the Fisher definition $N_{e}$ is the number of breeding individuals in the population.
The central issue with the approach you are suggesting is that population size does not equate to genetic population size. Thus the population could be huge, but if it is genetically homogeneous it will appear very small. In contrast the number of individuals could be very small, but the genetic variation between between them very large so $N_{e}$ would be huge.