But even with these examples we have not reached the highest elimination number, for many of the lower animals—not to speak of many plants—produce an even greater number of offspring. Leuwenhoek calculated the fertility of a thread-worm at sixty million eggs, and a tape-worm produces hardly less than 100 millions.

There exists, therefore, a constant relation between fertility and the ratio of elimination; the higher the latter is, the greater must the former be, if the species is to survive at all. The example of the tape-worm makes this very obvious, for here we can readily understand why the fertility must be so enormous, as we are aware of the long chain of chances on which the successful development of this animal depends. The common tape-worm of Man, Tænia solium, does not lay its eggs, they remain enclosed within one of the liberated joints or 'proglottides.' Only if this liberated joint or one of the embryos within it happens to be fortuitously eaten by a pig or other mammal can there be successful development, and even then under difficulties and possible failures, and not right away into adult animals, but first into microscopically minute larvæ which may bore their way into the walls of the intestine, or, if they are fortunate enough, may get into the blood-stream and be carried by it to a remote part of the body. There they develop into 'measles,' the so-called bladder-worms, within which the head of the tape-worm arises. But in order that this may become a complete and reproductive adult worm the pig must die, and the next step necessary is that a piece of the flesh of the infected first host must happen to be swallowed raw by a man or other mammal! Only then does the fortunate bladder-worm—swallowed with the flesh—attain the goal of its life, that is, a suitable place to mature in, the food-canal of a human being. It is obvious that countless eggs must be lost for one that succeeds in getting through the whole course of a development depending so greatly on chance. Hence the necessity for such enormous productivity of eggs.

In many cases the causes of elimination, which keep a species within due bounds, are very difficult to determine. Enemies, that is to say, other species which use the species in question as food, play an important rôle; often, however, the cause lies in the unfavourableness of external conditions, in chance, which is favourable only to one of a thousand. The oak would only require to produce one seed in the 500 years of its life, if it were certain that that one would grow into an oak-tree; but most of the little acorns are eaten up by pigs, squirrels, insects, &c., before they have had time to sprout, thousands fall on ground already thickly covered with growth where they cannot take root, and even if they do succeed in finding an unoccupied space in which to germinate, the young plants are still surrounded by a thousand dangers—the possibility of being devoured by many animals large and small, of being suffocated by the surrounding vegetation, and so on. We can thus understand, to some extent, though only approximately, why it is that the oak must year by year produce thousands of seeds in order that the species may maintain its normal number, and not be exterminated; for it is obvious that a constant, even though slow diminution of the normal number, a regular deficit, so to speak, can end in nothing else than the gradual extinction of the species.

But even this prodigality of seeds is not the greatest reach of fertility that we meet with in nature; it is, perhaps, amongst the simpler flowerless plants that we find the climax. It has been calculated that a single frond of the beautiful fern so common in our woods, Aspidium filix mas, produces about fourteen million spores. They serve to distribute the species, and are carried as motes by the wind, but comparatively few of the millions ever get the length of germinating at all, much less of attaining to full development into adult plants. Thus we see that the apparent prodigality of nature is a real necessity, an indispensable condition of the maintenance of the species; the fertility of each species is related to the actualities of elimination to which it is exposed. This is clearly seen when a species is placed under new and more favourable conditions of life, in which it has an abundant food-supply and few enemies. This was the case, for instance, with the horses introduced from Europe into South America, where they reverted to a feral state, and are now represented by herds of many thousands roaming the great grassy plains. If the small singing-birds of a region diminish in number, there is a great increase of caterpillars and other injurious insects which form part of their food-supply. The colossal destruction which the much-dreaded nun-moth from time to time brings about in our woods probably depends in part on the diminution of one or another of the many animals inimical to insects; but the occurrence of several years of weather-conditions favourable to the larvæ must also be taken into account. How enormously, indeed almost inconceivably, the number of larvæ may increase under favourable conditions is shown by such devastations as that in Prussia in 1856, when many square miles of forest were absolutely eaten up. The caterpillars were so numerous that even from some distance the falling excrement could be heard rustling like rain, and ten hundredweights of the eggs were collected, with an average of 20,000 eggs to the half-ounce!

But it would be a great mistake to conclude, from this enormous and sudden increase in the number of individuals, that the normal number of individuals is determined by the number of enemies alone. The average number of individuals in a species depends on many other conditions, especially on the extent of the available area, and on the amount of the food-supply in relation to the size of body in the species. I cannot dwell on this now, but I wish to point out that, for the continuance of a species, it is indifferent whether it is 'frequent' or 'rare,' if we presuppose that its normal number remains on an average constant for centuries, that is, that its fertility suffices to make good the continual losses through enemies and other causes of elimination. One would be inclined to conclude from such cases of sudden and enormous increase in the number of individuals as these caterpillar-blights, that enemies and other causes of destruction played the major part in the regulation of the normal number of the species. But this is only apparently the case. Enemies necessitate a certain fertility in the species on which they prey, so that the elimination in each generation may be made good; but the number of pairs capable of reproduction is not thereby decisively determined. We must not forget that the number of enemies is also, on the other hand, dependent on the number of victims, and that the normal number of enemies must rise and fall with that of the species preyed upon.

For this reason, such an enormous increase as that of the caterpillars cannot last long; it carries its corrective in itself. The appearance of the caterpillars in such enormous numbers in itself increases the host of their enemies; singing-birds, ichneumon-flies, beetle-grubs, and predaceous beetles find abundant and available food, and therefore reproduce and multiply so rapidly, that, with the help of the caterpillar's plant-enemies, especially the insect-destroying fungi, they soon reduce the caterpillars to their normal number, or even below it. But then the reverse process begins; the enemies of the caterpillars diminish because their food has become scarce, and their normal number is lowered, while that of the caterpillars gradually rises again.

When the number of foxes in a hunting district increases, the number of the hares that they prey upon diminishes, and, on the other hand, the decimating of the foxes by Man brings about an increase in the number of hares in the district. Under natural conditions, that is, without the intervention of Man, there would be a constant balancing of the numbers of hares and foxes, for every noteworthy increase of the hares would be followed by a similar increase of foxes, and this, in its turn, would diminish the number of hares, so that they would no longer suffice for the support of so many foxes, and these would decrease in number again, until the number of hares had again increased because of the lessened persecution and elimination. In nature the case is not quite so simple, because the fox does not live on hares alone, and the hare is not preyed upon only by the fox; but the illustration may serve to elucidate the point that a moving equilibrium is maintained between the species of a district, between persecutors and persecuted, in such a way that the number of individuals in the two species is always varying a little up and down, and that each influences the other so that a regulative process results. Throughout periods of considerable length the average remains the same; that is to say, a normal number is established. This normal strength of population is the mean above and below which the number of individuals is constantly varying. It is, of course, seldom that the mutual influences and regulations are so simple as in the example given; usually several or even many species interact upon each other, and not beasts of prey and their victims alone, but the most diverse species of animals and plants, which do not stand in any obvious relation to one another at all. Moreover, the physical, and especially the climatic conditions, also cause the normal number of the species to rise and fall.

The inter-relations between species living together on the same area are so intricate that I should like to give two other illustrations. Let us first take Darwin's famous instance of the fertility of clover, which depends on the number of cats. It is of course only an imaginary one, but the facts it is based upon are quite correct. The number of cats living in a village to a certain extent determines the number of field-mice in the neighbourhood. These again destroy the nests of the humble-bees, which live in holes in the ground, and thus the number of humble-bees depends on that of the field-mice and cats. But the clover must be pollinated by insects if it is to produce fertile seed, and only the humble-bee has a proboscis long enough to effect the pollination. Therefore the quantity of clover-seed annually produced depends on the number of humble-bees, and ultimately upon the number of cats. And, as a matter of fact, humble-bees were introduced into New Zealand from England, because without them the clover would produce no fertile seeds.

On the grassy plains of Paraguay there are no wild cattle and horses, because of the presence of a fly which has a predilection for laying its eggs in the navel of the newly-born calves and foals, with the result that the calves or foals are killed by the emerging maggots. We may reasonably assume that the numerical strength of this fly-species depends on the distribution of insect-eating birds, whose numbers in turn are determined by certain beasts of prey. These again vary in number in relation to the extent of the forest-land, and this is determined by the number of ruminants which browse on the young growth of the woods (Darwin).

That forests can actually be totally destroyed by ruminants is proved by the case of the island of St. Helena among others. On its discovery the island was covered with thick wood, but in the course of 200 years it was transformed into a bare rock by goats and pigs, which devoured the young growth so completely that trees which were felled or which died were not replaced.