def phi_1D_snm(xx, nu=1.0, theta0=1.0, theta=None, beta=1):
    """
    Standard neutral one-dimensional probability density.

    xx: one-dimensional grid of frequencies upon which phi is defined
    nu: size of this population, relative to the reference population size Nref.
    theta0: scaled mutation rate, equal to 4*Nref * u, where u is the mutation 
            event rate per generation for the simulated locus and Nref is the 
            reference population size.
    theta: deprecated in favor of distinct nu and theta0 arguments, for 
           consistency with Integration functions.

    Returns a new phi array.
    """

    if theta is not None:
        raise ValueError('The parameter theta has been deprecated in favor of '
                         'parameters nu and theta0, for consistency with the '
                         'Integration functions.')
    # Protect from division by zero errors
    if xx[0] == 0:
        phi = 0*xx
        phi[1:] = nu*theta0/xx[1:]
        phi[0] = phi[1]
    else:
        phi = nu*theta0/xx
    return phi * 4.*beta/(beta+1.)**2