Feb. 28, 1884] 



NA TURE 



405 



Instinct 



Were it merely for the sil<e of reiterating my views, I should 

 not feel ju-itified in commenting upon Mr. Romanes' letter on 

 instinct in last week's Nature (p. 379). He seems, however, 

 10 have UTiderstood my "subjective verification" in a sense 

 somewhat different to that which I intended to convey by that 

 expression. I venture, therefore, to beg a little space in these 

 columns for explanation. 



There is but one method in human psychology — that of intro- 

 spection. By this method I obtain certain results. These results 

 I communicate to my neighbour, and he by introspection verifier; 

 them for himself. This I call "submitting the results to the 

 test of subjective verification." In this way and in no other can 

 a science of human psychology be constituted. 



I remember once seeing a schoolfellow caned. He did not 

 flinch, but grew deadly pale. " Did it hurt much ? " I asked 

 afterwards, in schoolboy fashion. "Hurt! Who cares for 

 pain ? I was caned for a lie that I never told." I can remem- 

 ber to this day the indignation that his words roused within me. 

 I could verify to some extent the true nature of his feelings. 

 How can I verify the feelings of my dog? The feeling that I 

 infer may be as wide of the mark as the mere pain I fancied my 

 schoolfellow smarted under. Without myself becoming a dog, 

 I can never know the true nature of my dog's feelings. 



Mr. Romanes contends that "the involuntary groan of pain, 

 the pallor of fear, and a thousand other unintended expressions 

 of emotions, as well as a thousand other unintended expressions 

 of thought, are, as it is proverbially said, ' more eloquent than 

 words.' " In this I cannot agree. The groan, the pallor, tell 

 plainly of some intense feeling ; of its nature they can tell us 

 little. So do the actions of animals testify to some correspond- 

 ing mental states ; of their nature we can form but a dim con- 

 ception. Out of .such dim conceptions no science of compara- 

 tive psychology can, as it seems to me, be constituted. 



Whether this is common sense (for which, by the way, in 

 these matters I have not quite so much reverence as Mr. Romanes) 

 or "an ingeniously constructed argument of scepticism," I must 

 leave others to judge. 



In conclusion let me thank Mr. Romanes for his letter, and 

 assure him that I shall give to his objections to my physiological 

 theory of instinct that weight which I feel to be due to the 

 opinions of one from whose writings I have learnt much and 

 hope to learn more. C. Lloyd Morgan 



University College, Bristol, February 25 



Protection by Mimicry-A Problem in Mathematical 

 Zoology 



Under the above heading in the jfapan JVai'ly Mail of 

 February 3, 1883, we drew attention to what appeared to us an 

 error made by Mr. Alfred R. Wallace in a letter to Nature 

 regarding the protection gained by two distinct species of insects 

 of distasteful nature assimilaiing in appear.ance when subject to 

 the attacks of young and inexperienced birds. The article was 

 sent to Mr. Wallace, who by letter, and in an article in Nature, 

 vol. xxvii. p. 481, without hesitation, acknowltdged the correc- 

 tion, saying that he had misstated Dr. MiiUer's proposition. He 

 then gives Dr. MiiUer's own words, which are : — " If both species 

 are equally common, then both will derive the same benefit from 

 their resemblance — each will save half the number of victims 

 which it has to furnish to the inexperience of its foes. But if 

 one species is commoner than the other, then the benefit is un- 

 equally divided, and the proportional advantage for each of the 

 two species which arises from their resemblance is us Ihe square 

 of their relative numbers." This alters the question altogether. 

 Mr. Wallace had stated it, through an oversight, quile otherwi-e. 

 He said: — "The number of individuals sacrificed is divided 

 between them in the proportion of the square of their respective 

 numbers." Such was what we took objection to; and we showed 

 that it was not according to the squares, but to the simple 

 numbers. 



Mr. Wallace carries out his article, which is accompanied by 

 one by Mr. Meldola (p. 482), to show by examples how it is 

 that, notwithstanding the toss is in direct ratio to the numbers of 

 each species, the proportional saving through resemblance is in- 

 versely as the squares; and he further says : — "The advantage 

 w ill be measured solely by the fraction of its own numbers saved 

 from destruction, not by the proportion this saving bears to that 

 of the other species." On this Mr. Meldola remarks : — " The 



fact that these numbers stand to one another in the ratio of" the 

 squares, "is a mathematical necessity from which I do not see 

 how we can escape." Now even if this latter statement were 

 strictly correct, we fail to see how it affects Mr. Wallace's state- 

 ment. We shall show, however, that it is not correct but only 

 an approximation when the number eaten by the birds is a small 

 percentage, for as this becomes greater the ratio of proportional 

 advantages increases considerably above that of the squares. 



The proportional advantage that either species has alter imita- 

 tion over its former state (before imitation), appears to be accord- 

 ing to the fraction of its original number remaining. Because 

 while in its former state, should it lose one half its number, it 

 would have one-half left, while if it after imitation lost only one- 

 fourth, it would have three-fourths remaining ; a clear advantage 

 of one-fourth over one-half, or 50 per cent. This, however, is 

 not a simple case for an example when we come to consider the 

 relative numbers of the two species ; we will therefore put it 

 thus : — A has double the number of B. Supposing that when 

 dissimilar A loses 30 per cent, then B loses 60 per cent. But 

 after assimilation both lose in the same proportion, namely, 20 

 per cent. A has consequently an advantage, over its former 

 state, of 10, and similarly B of 40. But in the former state the 

 remainder of A not lost h as 70 per cent., while that of B was 

 40 per cent., so that A's real advantage is 10 on 70 or I4'2S57 

 per cent., and B's 40 on 40, or 100 per cent. These two numbers 

 do not bear Dr. MiiUer's ratio of 1 to 4 (the squares of the num- 

 bers) but a greater, namely, i to 7 = 1° x 40 to 2- x 70. 



The following examples will illustrate the increasing ratio : — 



1. A to B as 2 to I. 



If when dissimilar A loses 20 per cent, then B loses 40 per 

 cent., the remains being for A, So per cent. ; for B, 60 per cent. 

 When similar e.ich loses 133 per cent., leaving remains of 86| 

 per cent. 



The advantage to A therefore is the excess of 863 over 80 on 

 80 = 8'33 per cent., and the advantage to B is the excess of S6§ 

 over 60 on 60 = 44'44 per cent. These advantages compared 

 to each other are as i to 533 (according to Dr. Miiller i to 4). 



2. A to B as 3 to I. 



Dissimilar A loses 20 per cent. ; B, 60 per cent. Remains 

 80 — 40. 



SimiLir A loses 15 per cent. ; B, 15 per cent. Remains 

 85-85. 



Advantage to A excess of 85 over 80 on 80 = 6'25 per cent. 



Advantage to B excess of 85 over 40 on 40 = II2"5 per cent. 



Ratio I to 18 (Midler I to 9). 



3. A to B as 4 to I. 



Dissimilar A loses 20 per cent. ; B, 80 per cent. Remains 

 So — 20. 



Similar A loses 16 per cent. ; B, 16 per rent. Remains 

 84—84. 



Advantage to A excess of 84 over 80 on 80 = J per cent. 



Advantage to B excess of 84 over 20 on 20 = 320 per cent. 



Ratio I to 64 (Muller i to i6). 



Dr. Midler's squares require to be multiplied by the remains 

 per cent, (taken also inversely) of the two species when dissimilar, 

 to bring out the proper ratios. Thus : I to 4 (the squares) in 

 the first example, multiplied by 60 and 80 respectively, give 60 

 to 320 or I to 5 '33. In the second i x 40 to 9 x 80 = 40 to 

 720 or I to 18. And in the third, I x 20 to 16 x 80 = 20 to 

 1280 or I to 64. 



It will be understood therefore that, whether we reckon the 

 proportionate advantage that each species obtains over its 

 previous state of existence by the mimic, or calculate the ratio of 

 proportionate advantage of mimicry between the two, the com- 

 parison has to be made with the state each would have been in 

 had not mimicry taken place, indicated by the proportion of sur- 

 vivors each would then have had. If we ignore this, the com-- 

 parison is untrue. What we want is the advantage a species 

 which adopts mimicry has over one which fails to do so. So 

 that if we speak of one numerous species A, and two equal non- 

 numerous species B and B' ; if B mimics A, while B' mimics no 

 species, B receives protection, and thus has an advantage over 

 B', which in particular cases may amount to so much that, while 

 B survives, B' may become exterminated. This is perhaps the 

 simplest way of putting it. 



It must be remembered, however, that B does no harm to A 

 by mimicking it ; on the contrary, the act of mimicry is of ad- 

 vantage to A over its former state of existence as w-ell as to B ; 

 but A being the more numerous the advantage is less. Still 

 after the assimilation neither has an advantage over the other. 



