def crown_capture_probability(n, k):
    """
    Calculate the probability that a sample of `k` taxa from a clade
    of `n` total taxa includes a root node, under a Yule process.

    This equation is taken from:

    Sanderson, M. J. 1996. How many taxa must be sampled to identify
    the root node of a large clade? Systematic Biology 45:168-173
    """
    if n < k:
        raise Exception('n must be greater than or equal to k (n={}, k={})'
            .format(n, k))
    if n == 1 and k == 1:
        return 0
    return 1 - 2 * (n - k) / ((n - 1) * (k + 1))
