def chao1_uncorrected(observed, singles, doubles):
    """Calculates chao1 given counts. Eq. 1 in EstimateS manual.

    Formula: chao1 = S_obs + N_1^2/(2*N_2) where N_1 and N_2 are
    count of singletons and doubletons respectively.

    Note: this is the original formula from Chao 1984, not bias-corrected,
    and is Equation 1 in the EstimateS manual.
    """
    return observed + singles**2/float(doubles*2)