def inject_mutations_1(phi, dt, x, dx, y2, theta1):
    """
    new mutations injected along phi[1,:] against a background given by y2
    phi - numerical density function
    dt - given time step 
    x, dx - one dimensional grid and grid spacing
    y2 - the biallelic density function
    theta1 - population scaled mutation rate for mutation 1
    """
    phi[(1), 1:-1] += y2[1:-1] / dx[1] * 1.0 / x[1] * dt * theta1 / 2
    return phi
