that such a change should appear suddenly, complete from the start. And if so there is no difficulty in supposing that it might be of some advantage to its possessor through the resemblance to an unpalatable form. Even were the advantage but a slight one it is clear from previous discussion (p. [96]) that the new variety would more or less rapidly replace the form from which it had sprung. With the continued operation of natural selection the new form would entirely supplant the original one, but it is not impossible that in some cases the selecting agent may be removed before this result has been achieved. In this event the proportions of the new and the old form would fall into a condition of equilibrium as in P. polytes in Ceylon, until some other selective agent arose to disturb the balance. On this view natural selection is a real factor in connection with mimicry, but its function is to conserve and render preponderant an already existing likeness, not to build up that likeness through the accumulation of small variations, as is so generally assumed. Recent researches in heredity and variation all point to this restriction of the scope of natural selection. Hitherto an argument in favour of the older view has been that derived from the study of adaptation—of an apparent purpose, which, at first sight, appears to be behind the manner in which animals fit into their surroundings. For many the explanation of this apparent purpose has been found in the process of natural selection operating gradually upon small variations, accumulating some and rejecting

others, working as it were upon a plastic organism, moulding it little by little to a more and more perfect adaptation to its surroundings. On this view adaptation is easy to understand. The simplicity of the explanation is in itself attractive. But when the facts come to be examined critically it is evident that there are grave, if not insuperable, difficulties in the way of its acceptance. To outline some of these has been the object of the present essay. Though suggestions have been made as to the lines along which an explanation may eventually be sought it is not pretended that the evidence is yet strong enough to justify more than suggestions. Few cases of mimicry have as yet been studied in any detail, and until this has been done many of the points at issue must remain undecided. Nevertheless, the facts, so far as we at present know them, tell definitely against the views generally held as to the part played by natural selection in the process of evolution.

APPENDIX I

For the table on p. [155] I am indebted to the kindness of Mr H. T. J. Norton of Trinity College, Cambridge. It affords an easy means of estimating the change brought about through selection with regard to a given hereditary factor in a population of mixed nature mating at random. It must be supposed that the character depending upon the given factor shews complete dominance, so that there is no visible distinction between the homozygous and the heterozygous forms. The three sets of figures in the left-hand column indicate different positions of equilibrium in a population consisting of homozygous dominants, heterozygous dominants, and recessives. The remaining columns indicate the number of generations in which a population will pass from one position of equilibrium to another, under a given intensity of selection. The intensity of selection is indicated by the fractions 100⁄50, 100⁄75, etc. Thus 100⁄75 means that where the chances of the favoured new variety of surviving to produce offspring are 100, those of the older variety against which selection is operating are as 75; there is a 25% selection rate in favour of the new form.

The working of the table may perhaps be best explained by a couple of simple examples.

In a population in equilibrium consisting of homozygous dominants, heterozygous dominants and recessives the last named class comprises 2.8% of the total: assuming that a 10% selection rate now operates in its favour as opposed to the two classes of dominants—in how many generations will the recessive come to constitute one-quarter of the population? The answer is to be looked for in column B (since the favoured variety is recessive) under the fraction 100⁄90. The recessive passes from 2.8% to 11.1% of the population in 36 generations, and from 11.1% to 25% in a further 16 generations—i.e. under a 10% selection rate in its favour the proportion of the recessive rises from 2.8% to 25% in 52 generations.

Percentage of total population formed by old varietyPercentage of total population formed by the hybridsPercentage of total population formed by the new varietyNumber of generations taken to pass from one position to another as indicated in the percentages of different individuals in left-hand column.
A: Where the new variety is dominantB: Where the new variety is recessive
100⁄50 100⁄75 100⁄90 100⁄99 100⁄50 100⁄75 100⁄90 100⁄99
99.900 .09 .000
98.000 1.96 .008 4 10 28 300 1920 5740 17,200 189,092
90.700 9.00 .030 2 5 15 165 85 250 744 8,160
69.000 27.70 2.800 2 4 14 153 18 51 149 1,615
44.400 44.40 11.100 2 4 12 121 5 13 36 389
25.000 50.00 25.000 2 4 12 119 2 6 16 169
11.100 44.40 44.400 4 8 18 171 2 4 11 118
2.800 27.70 69.000 10 17 40 393 2 4 11 120
.030 9.00 90.700 36 68 166 1632 2 6 14 152
.008 1.96 98.000 170 333 827 8243 2 6 16 165
.000 .09 99.900 3840 7653 19,111 191,002 4 10 28 299