This needs two conditions to hold at once: organisms breed extremely fast, yet populations stay roughly stable. Together they mean that the great majority of individuals never reach breeding age, and everyone is competing for limited places. Darwin called this the "struggle for existence". Individuals of the same species have the most similar needs, so competition among them is fiercest. It is, he said, "the doctrine of Malthus applied with manifold force to the whole animal and vegetable kingdoms".

Given that competition is unavoidable and that individuals differ in heritable ways, an individual with even a slight advantage is more likely to survive, leave offspring and pass that advantage on, while harmful differences are eliminated along with their bearers. Darwin called this "preservation of favourable variations and the rejection of injurious variations" natural selection.

As natural selection accumulates its effects, the descendants of one ancestor diverge more and more: varieties become species, species become genera. Darwin called this "divergence of character". There are two reasons: the more diverse they are, the more each can hold its own place and all can live together; and the intermediate forms lose out in the competition. The living world therefore looks like an ever-branching tree.

People cannot create differences; they can only select the ones nature offers and accumulate them generation after generation. By that alone they have produced pigeons, dogs and livestock of enormously different appearance. This proves two things: the differences really exist, and selection can pile them up into great change. If people can do it, nature, with countless generations at its disposal, has no reason not to.

The patterns naturalists found when classifying organisms are the traces common ancestors left behind: there is no sharp line between species and varieties, and all organisms can be arranged in groups nested within groups, like a family tree. If each species had been created independently, neither fact could be explained.

The patterns in the fossil record match descent through generations: the ancient inhabitants of a region most resemble the living ones of the same region, and once a species goes extinct it never reappears.

Where organisms are found has little to do with climate and environment, and much to do with routes and barriers to migration. Island species always resemble the nearest mainland, not some distant place with similar conditions. Only "migration from a neighbouring source, followed by modification on the spot" explains it.

Organs with different uses share the same arrangement of bones; the embryos of different animals resemble one another; and some organs persist although plainly useless. All of this shows that body structure is set first by ancestry and only then altered for use.

If every species had been designed for its environment, structure and habit should match everywhere and adaptation should be perfect. Yet nature is full of mismatch and imperfection. Natural selection asks only that an organism be a little better than its competitors, not perfect, so under it these facts are exactly what one would expect.

If species changed little by little, the rocks should be full of transitional fossils, yet they are rarely found. Darwin admitted this is "the most obvious and forcible" objection. His answer: the fossil record is extremely incomplete. Only a few organisms ever become fossils, only a small part of the strata has been explored, and vast blank intervals separate the formations; compared with the life that once existed, the specimens in museums are "absolutely as nothing".

The eye can focus, regulate the light it admits and correct aberrations. Darwin admitted that to say it was formed by natural selection "seems absurd in the highest degree". His answer: between the simplest light-sensitive structure and a complex eye, nature shows many intermediate stages, each useful to its owner; and eyes do vary in small, heritable ways. If those points hold, the eye can form step by step. This is the old maxim: "Nature makes no leaps."

The cells bees build are as exquisite as a precomputed mathematical optimum; sterile worker ants come in several castes of sharply different form, and since they never breed, how is their instinct passed on? Darwin's answer: instincts, like body structure, vary and are inherited, and gradations from simple to complex can be found; as for sterile workers, selection can act on the whole family, just as a gardener who eats the tastiest cabbage still sows seed from the same stock.

Crosses between different species are mostly sterile, or produce sterile offspring; crosses between varieties of one species are usually fertile. It looks like something designed specifically to keep species apart. Darwin's answer: sterility comes in every degree and is not universal, and the same two species can give completely different results depending on which is the father and which the mother. Sterility is "not a specially acquired or endowed quality"; like the failure of two kinds of tree to graft, it is a by-product of differences in constitution between the two species.

If all individuals of a species descend from a common ancestor, they must have travelled from one place to another, yet some species live in regions extremely far apart and cut off from each other. Darwin's answer: species can persist unchanged for a long time, and over such spans there is always a chance to migrate by one route or another; extinction in the intervening regions makes a range look broken; and the climate changes of the Ice Age spread many species across the world.