_APPENDICES_

APPENDIX A.

MR. GULICK'S CRITICISM OF MR. WALLACE'S VIEWS ON PHYSIOLOGICAL SELECTION.

I have received from Mr. Gulick the results of his consideration of Mr.

Wallace's criticism. As these results closely resemble those which I have myself reached, and as they were independently worked out on the other side of the globe, I deem it desirable to publish them here for the sake of comparison.

In his covering letter Mr. Gulick writes:--

Mr. Wallace has most certainly adopted the fundamental principles of our theory, and in an arbitrary way attempted to claim the results produced by these principles as the effects of natural selection. He takes our principles, which in the previous chapter he has combated; but he makes such disjointed use of them that I am not willing to recognize his statement as an intelligible exposition of our theory.... I have endeavoured to indicate at what points Mr. Wallace has deserted his own principles, and at what points he has failed to make the best use of ours. To bring out these points distinctly has been no easy task; but if you regard this paper on _The Preservation and Acc.u.mulation of Cross-infertility_ as giving any help in elucidating the true principles, and in showing Mr. Wallace's position in regard to them, I shall be satisfied. Please make any use of it that may seem desirable, and then forward it to Professor Dana.

The following is a general summary of Mr. Gulick's results:--

Mr. Wallace's criticism of the theory of Physiological Selection is unsatisfactory; (l) because he has accepted the fundamental principle of that theory on pages 173-9, in that he maintains that without the cross-infertility the incipient species there considered would be swamped; (2) because he a.s.sumes that physiological selection pertains simply to the infertility of first crosses, and has nothing to do with the infertility of mongrels and hybrids; (3) because he a.s.sumes that infertility between first crosses is of rare occurrence between species of the same genus, ignoring the fact that in many species of plants the pollen of the species is pre-potent on the stigma of the same species when it has to compete with the pollen of other species of the same genus; (4) because he not only ignores Mr. Romanes' statement that cross-infertility often affects "a whole race or strain," but he gratuitously a.s.sumes that the theory of Physiological Selection excludes this "racial incompatibility" (which Mr. Romanes maintains is the more probable form), and bases his computation on the a.s.sumption that the cross-infertility is not a.s.sociated with any other form of segregation; (5) because he claims to show that "all infertility not correlated with some _useful_ variation has a constant tendency to effect its own elimination," while his computation only shows that, if the cross-infertility is not a.s.sociated with some form of _positive_ segregation, it will disappear[60]; and (6) because he does not observe that the positive segregation may be secured by the very form of the physiological incompatibility.... Without here entering into any computation, it is evident that, e.g. the prepotency of pollen of each kind with its own kind, if only very slight, will prevent cross-fertilization as effectually as a moderate degree of instinctive preference in the case of an animal.

[60] "Positive segregation" is Mr. Gulick's term for forms of h.o.m.ogamy other than that which is due to selective fertility. Of these other, or "positive" forms, natural selection is one; but as it is far from being the _only_ one, the criticism points out that utility is not the _only_ conserving principle with which selective fertility may be a.s.sociated.

The paper likewise indicates a point which, in studying Mr. Wallace's theory, I have missed. It will be remembered that the only apparent difference between his theory and mine has been shown to consist in this--that while I was satisfied to state, in a general way, that natural selection is probably able to increase a selective fertility which has already been begun by other causes, Mr. Wallace has sought to exhibit more in detail the precise conditions under which it can do so.

Now, Mr. Gulick shows that the particular conditions which Mr. Wallace describes, even if they do serve to promote an increase of cross-infertility, are conditions which preclude the possibility of natural selection coming into play at all. So that if, under these particular conditions, a further increase of cross-infertility does take place, it does not take place in virtue of natural selection. To me it appears that this criticism is sound; and, if so, it disposes of even the one very subordinate addition to our theory which Mr. Wallace "claims" as the most "distinctive" part of his.

The following is the criticism in question:--

On pages 173-186 Mr. Wallace maintains that "Natural selection is, in some probable cases at all events, able to acc.u.mulate variations in infertility between incipient species" (p. 174); but his reasoning does not seem to me conclusive. Even if we grant that the increase of this character [cross-infertility] occurs by the steps which he describes, _it is not a process of acc.u.mulation by natural selection_. In order to be a means of c.u.mulative modification of varieties, races, or species, selection, whether artificial or adaptational [i.e. natural], must preserve certain forms of an intergenerating stock, to the exclusion of other forms of the same stock. Progressive change in the size of the occupants of a poultry-yard may be secured by raising only bantams the first, only common fowls the second, and only Shanghai fowls the third year; but this is not the form of selection that has produced the different races of fowls. So in nature, rats may drive out and supplant mice; but this kind of selection modifies neither rats nor mice. On the other hand, if certain variations of mice prevail over others, through their superior success in escaping their pursuers, then modification begins. Now, turning to page 175, we find that, in the ill.u.s.trative case introduced by Mr. Wallace, the commencement of infertility between the incipient species is in the relations to each other of two portions of a species that are locally segregated from the rest of the species, and partially segregated from each other by different modes of life. These two local varieties, being by the terms of his supposition better adapted to the environment than the freely interbreeding forms in other parts of the general area, increase till they supplant these original forms. Then, in some limited portion of the general area, there arise two still more divergent forms, with greater mutual infertility, and with increased adaptation to the environment, enabling them to prevail throughout the whole area. The process here described, if it takes place, is not modification by natural selection.

On the other hand, it _is_ modification by physiological selection. For, among the several other forms of isolation which are called into requisition, the physiological (i.e. ever acc.u.mulating cross-infertility) is supposed to play an important part. That the modification is not modification by natural selection may perhaps be rendered more apparent by observing, that in as far as _any_ other mode of isolation is involved or supposed, so far is the _possible_ agency of natural selection eliminated _as between the two or more otherwise isolated sections of a species_; and yet it is modes of isolation other than that furnished by natural selection (i.e. perishing of the less fit), that Mr. Wallace here supposes to have been concerned--including, as I have before shown, the physiological form, to which, indeed, he really a.s.signs most importance of all. Or, as Mr. Gulick states the matter in his independent criticism:--

In the supposed case pictured by Mr. Wallace, the principle by which the two segregating forms are kept from crossing, and so are eventually preserved as permanently distinct forms, is no other than that which Mr. Romanes and myself have discussed under the terms Physiological Selection and Segregate Fecundity. Not only is Mr. Wallace's exposition of the divergence and the continuance of the same in accord with these principles which he has elsewhere rejected, but his whole exposition is at variance with his own principle, which, in the previous chapter, he vigorously maintains in opposition to my statement that many varieties and species of Sandwich Island land molluscs have arisen, while exposed to the same environment, in the isolated groves of the successive valleys of the same mountain range. If he adhered to his own theory, "the greater infertility between the two forms in one portion of the area" would be attributed to a difference between the _environment_ presented in that portion and that presented in the other portions; and the difficulty would be to consistently show how this greater infertility could continue unabated when the varieties thus characterized spread beyond the environment on which the character depends. But, without power to continue, the process which he describes would not take place. Therefore, in order to solve the problem of the _origin_ and _increase_ of infertility between species, he tacitly gives up his own theory, and adopts not only the theory of Physiological Selection but that of Intensive Segregation[61] through Isolation, though he still insists on calling the process natural selection; for on page 183 he says, "No form of infertility or sterility between the individuals of a species can be increased by natural selection unless correlated with some useful variation, while all infertility not so correlated has a constant tendency to effect its own elimination." Even this claim he seems to unwittingly abandon when on page 184 he says: "The moment it [a species] becomes separated either by geographical or selective isolation, or by diversity of station or of habits, then, while each portion must be kept fertile _inter se_, there is nothing to prevent infertility arising between the two separated portions."

[61] By Intensive Segregation Mr. Gulick means what I have called Independent Variability.

The criticism proceeds to show yet further inconsistencies and self-contradictions in Mr. Wallace's treatment of this subject; but it now seems needless to continue. Nor, indeed, should I have quoted this much but for the sake of so fully justifying my own criticism by showing the endors.e.m.e.nt which it has received from a completely independent examination.

APPENDIX B.

AN EXAMINATION BY MR. FLETCHER MOULTON OF MR. WALLACE'S CALCULATION TOUCHING THE POSSIBILITY OF PHYSIOLOGICAL SELECTION EVER ACTING ALONE.

We have seen that the only important point of difference between Mr.

Wallace's more recent views and my own on the problem of inter-specific sterility, has reference to the question whether variations in the way of cross-infertility can _ever_ arise and act "alone, in an otherwise undifferentiated species," or whether they can _never_ so arise and act.

It is Mr. Wallace's opinion that, even if they ever do arise alone, at all events they can never act in differentiating a specific type, seeing that the chances against their suitable mating must be so great: only if they be from the first a.s.sociated with some other form of h.o.m.ogamy, which will have the effect of determining their suitable mating, does he think that they can act in the way supposed by our theory of "selective fertility"[62]. On the other hand, as previously and frequently stated, I have so strong a belief in the segregating power of physiological selection, or selective fertility, that I do not think it is necessary for this principle to be _always___ a.s.sociated with some other form of h.o.m.ogamy. From the first, indeed, I have laid great stress (as, also, has Mr. Gulick) on the re-enforcing influence which a.s.sociation with any other form of h.o.m.ogamy must exercise upon the physiological form, and vice versa; but I have also said that, in my opinion, the physiological form may in many cases be able to act entirely alone, or without a.s.sistance derived from any other source. The question here is, as we have already so fully seen, a question of but secondary importance; since, whether or not the physiological form of h.o.m.ogamy ever acts alone, even Mr. Wallace now allows, or rather argues, that it acts in combination--and this so habitually, as well as with so much effect, that it const.i.tutes a usual condition to the origination of species.

Nevertheless, although the only relevancy of his numerical computation of chances--whereby he thinks that he overturns my theory _in toto_--is such relevancy as it bears to this question of secondary importance, I have thought it desirable to refer the question, together with Mr.

Wallace's views upon it, to the consideration of a trained mathematician.

[62] His sentence, "all fertility not correlated with some _useful_ variation has a constant tendency to effect its own elimination,"

still further restricts the possible action of physiological selection to cases where at least one of the other forms of h.o.m.ogamy with which it is a.s.sociated is natural selection. Or, in other words, it is represented that physiological selection must always be a.s.sociated with natural selection, even if it be likewise a.s.sociated with any other form of exclusive breeding. But as this further limitation appears to me self-evidently unjustifiable (seeing that utility is not the only possible means of securing effective isolation) I here neglect it, and take the wider ground marked out above. It is needless to say that this is giving Mr. Wallace every possible advantage, by not holding him to his still narrower ground.

As this "subordinate question" depends entirely on numerical computations involving the doctrine of chances, I should first of all like to remark, that in reference to biological problems of the kind now before us, I do not myself attach much importance to a merely mathematical a.n.a.lysis. The conditions which such problems involve are so varied and complex, that it is impossible to be sure about the validity of the _data_ upon which a mathematical a.n.a.lysis is founded.

Nevertheless, for the sake of meeting these criticisms upon their own ground, I will endeavour to show that, even as mathematical calculations, they are quite untrustworthy. And, in order to do this effectually, I will quote the results of a much more competent, as well as a much more thorough, inquiry. I applied to Mr. Moulton for this purpose, not only because he is one of the ablest mathematicians of my acquaintance; but also because his interest in biology, and his knowledge of Darwinian literature, render him well fitted to appreciate exactly, and in all their bearings, the questions which were submitted to his consideration. I need only add that his examination was completely independent, and in no way influenced by me. Having previously read my paper on _Physiological Selection_, Mr. Gulick's paper on _Divergent Evolution_, and Mr. Wallace's book on _Darwinism_, he was in possession of all the materials; and I merely requested the favour of his opinion upon the whole case from a mathematical point of view. The following is his reply; and I give it _in extenso_, because it serves to place in another light some of the general considerations which it has already been my endeavour to present[63].

[63] In our _Nature_ correspondence of 1890-1891, Mr. Wallace remarked: "If Dr. Romanes will carefully work out numerically (as I have attempted to do) a few cases showing the preservative and acc.u.mulative agency of pure physiological selection within an otherwise undifferentiated species, he will do more for his theory than volumes of general disquisition or any number of a.s.sertions that it _does_ possess this power." Several months before this was written I had already in my hands Mr. Moulton's letter, with its accompanying calculations.

After some introductory remarks on Mr. Wallace's "adoption of the theory of physiological selection pure and simple," and "the pure caricature of it which he puts forward as" mine, the letter proceeds thus:--

The reason why it is so easy to attack your theory is that it is so easy to confuse the survival of an _individual_ with the survival of a _peculiarity_ of _type_. No one has ever said that an _individual_ is _a.s.sisted_ by the possession of selective fertility: that is a matter which cannot affect his chance of _life_. Nor has any one said that the possession of selective fertility in an _individual_ will _of itself_ increase the chance of his having _progeny_ that will survive, and in turn become the progenitors of others that will survive. Taken by itself, the fact that an _individual_ is capable of fertility with some only of the opposite s.e.x lessens the chance of his having progeny. Whether or not he is more or less favourably situated than his _confreres_ for the battle of life must be decided by the _total sum_ of his peculiarities; and the question whether or not this selective fertility will be a hindrance must be decided by considerations depending on the other peculiarities a.s.sociated with it.

But when we come to consider the survival or permanence of a _type_ or _peculiarity_, the case is quite different. It then becomes not only a favourable circ.u.mstance, but, in my opinion, almost a necessary condition, that the peculiarity should be a.s.sociated with selective fertility[64].

[64] As, for example, in the case of s.e.xuality in general. It is not to the advantage of such individual male Arthropoda as perish after the performance of the s.e.xual act that they should perform it; but its performance is necessary for the perpetuation of their species.--G. J. R.

Take the case of the Jews. I don't think that intermarriage with other nations would lessen their fertility, or diminish the number of their progeny; nor is there any reason to think that this progeny would be unequal to the struggle for existence. But no one doubts that the abandonment of their voluntary isolation (which operates so far as this is concerned as a selective fertility), would lead to the disappearance of the familiar Jewish type. All the world would get some of it; but as a whole it would be "swamped."

Now although no doubt Wallace would admit all this, he fails to give it the weight it ought to have. In discussing the question of its operation he considers too exclusively the case of the individual.

Of course, a type can only be perpetuated through the medium of individuals, and all that his argument amounts to is, that selective fertility would be so fatal to individuals that _no_ type which presents it could be formed or perpetuated--a conclusion which is not only absurd in itself, but contradicted by his own subsequent adoption of your theory. Besides, apart from calculations (with which I will deal when I write next), such reasoning brings its own refutation. Selective fertility is not in the same category as some of the other influences to which an important share has been ascribed in the formation of the existing types. _It exists as a recognized phenomenon._ Hence all these numerical proofs that it would lead to extinction, because it is so disadvantageous to the possessor, prove too much. They would show that the degree of selective fertility which so frequently characterizes species is a most onerous gift; and that, were it not present, there would be a vastly increased chance of fertility, which would render the races fitter and lead to their increased survival. Why then has it not been got rid of?

The two answers which no doubt would be given seem to me to support rather than to make against your theory. In the first place, Wallace might say that this infertility is an advantage because it keeps pure a type which is specially fitted to its surroundings, as shown by its continued existence. But if this be so, and it is necessary to protect the _developed_ type, how much more necessary to protect the _incipient_ type! In the second place, he might say that this selective fertility is not so disadvantageous when the species has been formed, because the individual can choose his mate from his like; whereas, when it is beginning to be formed, he must mate blindly, or without what you call "psychological selection."

But this seems to me to be wholly inapplicable to at least half the animal, and to all the vegetable kingdom. Moreover, with regard to the other half of the animal kingdom, it merely raises the question,--How soon will such an incipient type recognize itself?

Seeing it is probable that many families [broods] will belong to the same [incipient] type, I should not be surprised if it were found that this s.e.xual recognition and preference sets in very early.

But this leads me to the question of your letter. I understand you to want me to examine and criticize the attempted numerical arguments against or for your theory. Now it seems to me that it will be best to take, in the first instance, the vegetable kingdom, and with regard to it I cannot see how there can be any numerical argument against the theory. For we often have species side by side with others nearly allied, but much more numerous. The condition of these is precisely a.n.a.logous to that of your incipient species.

They are exposed to fertilization from, say, ten times as numerous individuals of the allied species. They reject this in favour of that from the relatively few individuals of their own. Yet the two species are in compet.i.tion. I could go through the numerical arguments of your a.s.sailant word for word, applying them to such a case as this, and they would triumphantly show that the specific fertility of the rarer kind would lead to its certain extinction.

Yet we know that this is not so.

Indeed, the too triumphant character of the logic used against you seems to me to be capable of being turned to your use. If cross-infertility is so intensely disadvantageous to the individuals presenting it, it cannot have been _that_ which made these individuals and their progeny survive. It is therefore a burden which they have carried. But we find that it is more or less present in all the closely allied types that occur on common areas: therefore it must be a necessary feature in the formation of such types; for it cannot be an accident that it is present in so many.

In other words, it must be the price which the individual and his progeny pay for their formation into a type. And this is your theory pure and simple.

The more I consider the matter, the more I feel that it is impossible to decide as to the sufficiency of selective fertility to explain the formation of species, if we consider merely the effect it would have on the number of individuals, as contrasted with what it would be if no such peculiarity had developed itself.

Indeed, I may say that on pondering over the matter I have come to the conclusion, that mere fertility is probably a comparatively unimportant factor in the preservation of the species, after a certain sufficient degree of fertility is attained. I do not wish to be misunderstood. To a certain point fertility is not only advantageous but necessary, in order to secure survival of the type; but I feel that little reliance can be placed on calculations based on the numerical co-efficient of fertility (i. e. the ratio of the number of offspring to the number of parents) in determining the relative chance of type-survival.

Take, for instance, the oak tree. It produces thousands of acorns, almost the whole of which die without producing any progeny. Have we any reason to believe that if the number of acorns borne by oak trees were diminished, even so much as to one-tenth, the race of oaks would perish? It may of course be said that, if all other things are equal, the probabilities of survival must be increased by increased fertility of this kind; but I feel convinced that when numerical fertility has attained to a high point in circ.u.mstances in which actual increase of the race cannot take place to any substantial extent, the numerical value of this fertility sinks down into a factor of the second or third order of importance--that is to say, into the position of a factor whose effects are only to be considered when we have duly allowed for the full effects of all the main factors. Until we have done that, we gain little or nothing in the way of accuracy of conclusion by taking into consideration the minor factors. It may be very well to neglect the effect of the attraction of Jupiter in our early researches on the motion of the Moon; and our doing so will not prevent the results being approximate and having considerable value, because we are retaining the two main factors that establish the motion, viz. the effects of the Earth and the Sun. But if we exclude the effect of one of these main factors, our results would be worthless; and it would not be rendered substantially less so by the fact that we had taken Jupiter into account in arriving at them.

You must not imagine, however, that I think it wholly profitless to see whether there would be any substantial effect on numerical fertility were _selective_ fertility to manifest itself. But if we want to derive any a.s.sistance from calculation, it must be by applying it with a good deal more precision and definiteness than anything that Wallace shows. And, in the first place, it is useless to confuse the vegetable and animal kingdoms. In the former you have union unaffected by choice; in the latter, so far at all events as the higher animals are concerned, you have "psychological selection." In order to give you a specimen of what can safely be done by calculation if you take a problem of sufficient definiteness, I have chosen the case of a flowering plant in which a certain proportion of the race have developed the peculiarity of being sterile with the remainder, while retaining the normal fertility of the race in unions among themselves. In order to give the greatest advantage to your critics, I have a.s.sumed that such flowers as possess the peculiarity are not self-fertilizable; for it is clear that if we suppose that they are self-fertilizable, the fertility need be very slightly affected.

As I have excluded self-fertilization, it is necessary, if we are to get any trustworthy results, that one should consider the mode in which fertilization will be produced. I have taken the case of fertilization by insects, and have a.s.sumed that each flower is visited a certain number of times by insects during the period when fertilization is possible; and, further, that the insects which visit it have on the average visited a certain number of flowers of the same species before they came there. Of course nothing but observation can fix these latter numbers; but I should not be surprised at finding that they are of considerable magnitude[65]. In order to make the results a little more intelligible, I have grouped them under the numbers which represent the average number of flowers that an insect visits in a journey. This is a little more than twice as great as the number which represents the number of flowers he has on the average visited before coming to the individual whose fertility we are considering.

[65] In this antic.i.p.ation Mr. Moulton is right. The well-known botanist, Mr. Bennett, read a most interesting paper on the subject before the British a.s.sociation in 1881. His results have since been corroborated by other observers. In particular, Mr. R. M. Christy has recorded the movements of 76 insects while visiting at least 2,400 flowers. (_Entomologist_, July 1883, and _Zool. Journal Lin.

Soc._, August 1883.) The following is an a.n.a.lysis of his results. In the case of b.u.t.terflies, in twelve observations on nearly as many species, there are recorded altogether 99 visits to fifteen species of flowers; and of these 99 visits 94 were constant to the same species, leaving only 5 visits to any other, or second species. In the case of the hive-bee, there were 8 individuals observed: these visited altogether 258 flowers, and all the visits paid by the same individual were paid to the same species in each of the eight cases.

Lastly, as regards b.u.mble-bees, there were altogether observed 55 individuals belonging to four species. These paid altogether 1751 visits to 94 species of flowers. Of these 1751 visits, 1605 were paid to one species, 131 to two species, 16 to three, 6 to four, and 1 to five. Adding all these results together, we find that 75 insects (b.u.t.terflies and bees) visited 117 species of flowers: of these visits, 1957 were constant to one species of flower; 136 were paid also to a second species, 16 also to a third, 6 also to a fourth, and 1 also to a fifth. Or, otherwise stated, while 1957 were absolutely constant, from such absolute constancy there were only 159 deviations. Moreover, if we eliminate three individual humble bees, which paid nearly an equal number of visits to two species (and, therefore, would have ministered to the work of physiological selection almost as well as the others), the 159 deviations become reduced to 72, or about four per cent. of the whole.--G. J. R.