There are very good reasons for rejecting all such saltationist theories of evolution. One rather boring reason is that if a new species really did arise in a single mutational step, members of the new species might have a hard time finding mates. But I find this reason less telling and interesting than two others are referred to in our discussion elsewhere of why major jumps across gene space are to be ruled out. The first of these points was put by the great statistician and biologist R. A. Fisher. Fisher was a stalwart opponent of all forms of saltationism, at a time when saltationism was much more fashionable than it is today, and he used the following analogy. Think, he said, of a microscope which is almost, but not quite perfectly, in focus and otherwise well adjusted for distinct vision. What are the odds that, if we make some random change to the state of the microscope (corresponding to a mutation), we shall improve the focus and general quality of the image? Fisher said:
It is sufficiently obvious that any large derangement will have a very small
probability of improving the adjustment, while in the ease of alterations
much less than the smallest of those intentionally effected by the maker or
the operator, the chance of improvement should be almost exactly one half.
I have remarked elsewhere that what Fisher found 'easy to see' could place formidable demands on the mental powers of ordinary scientists, and the same is true of what Fisher thought was 'sufficiently obvious'. Nevertheless, further cogitation almost always shows him to have been right, and in this case we can prove it to our own satisfaction without too much difficulty. Remember that we are assuming the microscope to be almost in correct focus before we start. Suppose that the lens is slightly lower than it ought to be for perfect focus, say a tenth of an inch too close to the slide. Now if we move it a small amount, say a hundredth of an inch, in a random direction, what are the odds that the focus will improve? Well, if we happen to move it down a hundredth of an inch, the focus will get worse. If we happen to move it up a hundredth of an inch, the focus will get better. Since we are moving it in a random direction, the chance of each of these two eventualities is one half. The smaller the movement of adjustment, in relation to the initial error, the closer will the chance of improvement approach one half. That completes the justification of the second part of Fisher's statement.
But now, suppose we move the microscope tube a large distance - equivalent to a macromutation - also in a random direction; suppose we move it a full inch. Now it doesn't matter which direction we move it in, up or down, we shall still make the focus worse than it was before. If we chance to move it down, it will now be one and one-tenth inches away from its ideal position (and will probably have crunched through the slide). If we chance to move it up, it will now be nine-tenths of an inch away from its ideal position. Before the move, it was only one-tenth of an inch away from its ideal position so, either way, our 'macromutational' big move has been a bad thing. We have done the calculation for a very big move ('macromutation') and a very small move ('micromutation'). We can obviously do the same calculation for a range of intermediate sizes of move, but there is no point in doing so. I think it really will now be sufficiently obvious that the smaller we make the move, the closer we shall approach the extreme case in which the odds of an improvement are one-half; and the larger we make the move, the closer we shall approach the extreme case in which the odds of an improvement are zero.
