Before revision:  However we show that measures of ` lived population density', which capture density as perceived by a randomly chosen person, do a better job of explaining variations in the rate of spread , achieving R^2 = 0.45 in Europe.
After revision:  However we show that measures of ` lived population density', which capture density as perceived by a randomly chosen individual. These measures of population density can significantly explain variation in the initial rate of spread , achieving R^2 = 0.45 in Europe.