Before revision:  In a bid to resolve this conundrum we are inspired by de Finetti's Theorem, and we exhibit equivalence classes of meta-population models that are orbits of the symmetric group.
After revision:  This paper utilizes a result from the theory of interest rate modeling, namely a bond pricing formula of Vasicek, and an approach inspired by a foundational result in statistics, de Finetti's Theorem, and we exhibit equivalence classes of meta-population models that are orbits of the symmetric group.