Thus, although the fertility of each species is, as a matter of fact, precisely regulated, a low rate of multiplication is not in itself sufficient to prevent the excessive increase of any species, nor is the quantity of the relevant food-supply. Whether this be very large or very small, we see that in reality it is never entirely used up, that, as a matter of fact, a much greater quantity is always left over than has been consumed. If increase depended only on food-supply, there would, for instance, be food enough in their tropical home for many thousand times more elephants than actually occur; and among ourselves the cockchafers might appear in much greater numbers than they do even in the worst cockchafer year, for all the leaves of all the trees are never eaten up; a great many leaves and a great many trees are left untouched even in the years when the voracious insects are the most numerous. Nor do the rose-aphides, notwithstanding their enormously rapid multiplication, ever destroy all the young shoots of a rose-bush, or all the rose-bushes of a garden, or of the whole area in which roses grow. At the same time it must be noted, that the number of individuals in a species undoubtedly does bear some relation to the amount of the food-supply available; for instance, it is very low among the large carnivores, the lion, the eagle, and the like. In our Alps the eagles have become rarer with the decrease of game, and where one eagle pair make their eyrie they rule alone over a hunting territory of more than sixty miles, a preserve on which no others of the same species are allowed to intrude. If there were several pairs of eagles in such a preserve, they would soon have so decimated the food-supply that they would starve. On the other hand, numerous herbivores, e.g. chamois and marmots, live within the bounds of the pair of eagles' hunting grounds, since the food they require is present in enormously greater quantity.