Is there a statistical analysis test I can perform that will give me a estimate of total population from my own smaller data sets?
I'm assuming you're asking how to estimate population size based on numbers of individuals you capture. Yes, there are many approaches to this. The R library SPECIES-R offers a number of methods of calculating this. They are described in the manuscript SPECIES: An R Package for Species Richness Estimation. Some of the methods described are:


Chao, A. (1984), Nonparametric Estimation of the Number of Classes in a Population, Scandinavian Journal of Statistics, 11, 265-270.
Norris, J. L. I., and Pollock, K. H.(1998), Non-Parametric MLE for Poisson Species Abundance Models Allowing for Heterogeneity Between Species, Environmental and Ecological Statistics, 5, 391-402.
Chao, A., and Bunge, J. (2002), Estimating the Number of Species in a Stochastic Abundance Model, Biometrics, 58, 531-539.


and many more.