As to the facts of an extremely rapid increase of horses and cattle in America, of pigs and rabbits in New Zealand, and even of wild animals imported from Europe (where their numbers are kept down by man, not by competition), they rather seem opposed to the theory of over-population.  If horses and cattle could so rapidly multiply in America, it simply proved that, however numberless the buffaloes and other ruminants were at that time in the New World, its grass-eating population was far below what the prairies could maintain.  If millions of intruders have found plenty of food without starving out the former population of the prairies, we must rather conclude that the Europeans found a want of grass-eaters in America, not an excess.  And we have good reasons to believe that want of animal population is the natural state of things all over the world, with but a few temporary exceptions to the rule.  The actual numbers of animals in a given region are determined, not by the highest feeding capacity of the region, but by what it is every year under the most unfavourable conditions.  So that, for that reason alone, competition hardly can be a normal condition. but other causes intervene as well to cut, down the animal population below even that low standard.  If we take the horses and cattle which are grazing all the winter through in the Steppes of Transbaikalia, we find them very lean and exhausted at the end of the winter.  But they grow exhausted not because there is not enough food for all of them—­the grass buried under a thin sheet of snow is everywhere in abundance—­ but because of the difficulty of getting it from beneath the snow, and this difficulty is the same for all horses alike.  Besides, days of glazed frost are common in early spring, and if several such days come in succession the horses grow still more exhausted.  But then comes a snow-storm, which compels the already weakened animals to remain without any food for several days, and very great numbers of them die.  The losses during the spring are so severe that if the season has been more inclement than usual they are even not repaired by the new breeds—­the more so as all horses are exhausted, and the young foals are born in a weaker condition.  The numbers of horses and cattle thus always remain beneath what they otherwise might be; all the year round there is food for five or ten times as many animals, and yet their population increases extremely slowly.  But as soon as the Buriate owner makes ever so small a provision of hay in the steppe, and throws it open during days of glazed frost, or heavier snow-fall, he immediately sees the increase of his herd.  Almost all free grass-eating animals and many rodents in Asia and America being in very much the same conditions, we can safely say that their numbers are not kept down by competition; that at no time of the year they can struggle for food, and that if they never reach anything approaching to over-population, the cause is in the climate, not in competition.