def chao1_var_no_doubletons(singles, chao1):
    """Calculates chao1 variance in absence of doubletons.

    From EstimateS manual, equation 7.

    chao1 is the estimate of the mean of Chao1 from the same dataset.
    """
    s = float(singles)
    return s*(s-1)/2 + s*(2*s-1)**2/4 - s**4/(4*chao1)