def _chao1_var_no_doubletons(s, chao1):
    """Calculates chao1 variance in absence of doubletons.

    From EstimateS manual, equation 7.

    `s` is the number of singletons, and `chao1` is the estimate of the mean of
    Chao1 from the same dataset.

    """
    return s * (s - 1) / 2 + s * (2 * s - 1) ** 2 / 4 - s ** 4 / (4 * chao1)