This paper includes an estimate of what we need to know for predicting the spreading rates of introduced animal and plant species. The models although catching the principal aspects of the spreading process, still prove to be too simple. Yet even in their initial state of development, they require an amount of biological and environmental information that cannot be reasonably supplied. However, as such, they can indicate the kind of information needed to make statistical prediction reliable. These models also indicate the limits of prediction beyond which extrapolations from simpler models should not be made. It thus appears that the limits of prediction are very restrictive about the fate of species accidentally or deliberately introduced into an area.