My dear Sir

Though I have been fortunate enough to meet you only once many years ago I am led to address you at the suggestion of my friend D^r Hooker with reference to a subject on which I have addressed a letter to ‘Nature’ which may probably appear next Thursday.²

I should probably have done better to send the letter in the first instance for your consideration but in truth I did not think myself justified in taking up your time in that way and if I am led to write now with a view to supply the obvious deficiencies of a short letter where the subject demanded much fuller treatment I do so without expecting you to take the trouble of replying unless you see any occasion to do so.

The subject in question is the application of the theory of probabilities to estimate the chance of survival of a new variety appearing in a given species of plant or animal— The argument first used by a writer in the North British Review has been adopted by M^r Mivart and others and its validity has been admitted by yourself—as I understand your remarks—to a greater extent that I think it fairly deserves.³

You probably recollect the original passage & may have seen a recent letter in Nature wherein the writer corrects an obvious blunder in the text.—⁴

The case as put assumes that within a given area the fixed number of individuals of the given species is 10,000 & that each (on an average) produces 100 descendants of which 99 must be destroyed if the species simply holds its ground without increase or decrease. The reviewer then inquires what would be the chance of survival of a modification appearing in a single individual of such a nature as to make the chance of growth & reproduction for that individual as compared with the unmodified members of the species as 2 to 1.—

The answer I make is that in the cases where natural selection can be conceived to be an efficient agent the chance of the modified individual as compared with the others will be very much more favorable than 2 to 1, but I fear that I have not developed the argument sufficiently to make its force fully apparent, nor could I do so in writing for the public without exceeding the limits of a letter. Allow me to indicate a little more fully the way in which I would apply it to a concrete case— For illustration I will take a non-diœcious plant— mutatis mutandis it may be applied to other plants or animals—

In the first place it is clear that unless the modified individual—which I shall call the new variety—arrives at maturity & reproduces offspring like itself the chance of survival is nil— we must assume therefore the appearance of 100 individuals of the new variety in the second generation— Let us suppose that the growth of the species is mainly restrained by two adverse influences— The first—e.g. a hot dry climate—operating so that only $\frac{1}{10}$^th of the young plants (ie. those whose seeds have fallen in shady or moist spots) are able to survive— On an average then 90 out of every 100 young plants are destroyed by this cause. But if in the new variety (A) the vegetative organs are modified so as to resist better than the others heat and drought it may easily happen that 50 out the 100 young individuals will survive   Let the second danger to which the given species is exposed be the larva of some common insect that feeds on the plant so that on an average nine out of ten individuals found growing at the period of activity of the supposed larva are consumed. let the modification of the new variety (B) be the earlier or later germination of the seed or such a modification of the root as will enable the plant to send up new stems after the enemy has ceased to be dangerous— such a change may enormously increase the chance of survival so that five six or eight out of every ten individuals may escape the danger.

In the first case then we should have five individuals—in the second say eight that would reach the stage of reproduction and in the third generation we should have at least 500—or 800 descendants of the new variety— But inasmuch as variations that tend to adapt an organism to external physical conditions usually promote & increase the reproductive process it is more likely that the new variety A would on the average produce more numerous offspring e.g. 1000 instead of 500— But confining myself to the smaller supposition I find that by the seventh generation 312500 descendants of the new variety would make their appearance & that if one in twenty of these were to reach maturity we sh^d have 15625 individuals—i.e. a larger number than the original species counted at the outset.

No doubt this result would be modified by the fact that the new variety would often be crossed with pollen from the unmodified form & that a portion of its descendants would be intermediate varieties but the conclusion is I think certain that a modification that tends to give a real advantage in the struggle for existence would generally be preserved, and indeed if any correct application of mathematics were to lead to an opposite result most people would say ‘so much the worse for mathematics.’

Of course a complete inquiry into any concrete case would involve the question whether the new variety w^d not gain ground at the expense of other species as well as its unmodified ancestor & at the same time increase the severity of the struggle for existence on the part of the latter. Thus if two varieties were growing together of which one was unfitted or less well fitted to serve as food to a common insect the probability is that a larger proportion of the descendants of the edible variety would be consumed than before the appearance of the new non-edible or less edible variety.

But modifications affecting the reproductive organs probably enjoy a still greater advantage in respect to their chance of survival & ultimate preservation. I have followed the reviewer in his assumptions because to a certain extent they correspond with facts & are required to allow the application of figures to the argument. But it is far from true that the population within a given area of most species is at a nearly fixed limit. In ordinary seasons the ground is pretty nearly fully stocked & one main limiting cause that keeps down population is the fact that there is no room for more   the young are simply choked off as they attempt to grow. But external agencies—climate organic foes—&c—do not act uniformly in an unfavorable season but a comparatively small number of individuals survive to produce offspring and at such times the chance of survival of a favorable modification better fitted to produce healthy offspring becomes very great— In the case of annuals nearly as if a gardener went about destroying one variety and preserving the seeds of another.

Perhaps you will allow me to say that speaking as a botanist I have always thought that in the ‘Origin of Species’ you rather overstated the argument for the suppression of intermediate varieties & species—owing to the great advantage in the struggle for existence which you attribute to large groups over small ones—⁵ It must be allowed that in the long run the larger group has a slight additional chance in its favour, but this it seems to me is trivial when compared with the advantage enjoyed by any form in any degree better adapted to contend against adverse external conditions.

In truth one answer to the objection that we ought to have (if your theory be true) a series of closely connected forms rather than well marked species—is in my humble opinion, that we have such series of closely connected forms to a much greater extent than is commonly supposed. As gaps in our knowledge are getting filled up the number of such groups known to us (botanists) is constantly increasing and speaking of a moderately well known region—such as the European & Mediterranean—it is surprising to an old fashioned botanist to find so small a number of thoroughly well defined species.

However inconvenient & even mischievous may be the multiplication of specific names the work done by such men as Jordan so far as it rests on real observations seems to me very important. When he makes 52 species out of so apparently well defined & isolated a specific form as Draba verna of Linnæus & shows that among these there are several such that if the links were removed most botanists would admit them as distinct species—while all maintain themselves at least for a limited time in cultivation he helps very much the argument against admitting well defined species as the rule and groups of nearly allied forms as the exception.⁶

I am at present at work upon the collections which Hooker & I brought back from Morocco—moving slowly because I try to examine carefully.⁷ It is quite surprising to see how small the number of well marked species is & how many of the plants which must be reckoned as new—are merely well marked but very near allied subspecies or varieties that fall into their places as links in the chain of vegetable forms characteristic of the Mediterranean region—

Pray excuse the length of this letter— It has been interrupted & is posted only after the publication of the letter to which I referred at the outset

believe me dear Sir | very faithfully yours | John Ball