I. Four main points are dealt with :--

(a) The widespread existence of fluctuations in the numbers of animals.

(b) The existence, in many birds and mammals, of periodic fluctuations (p.f.).

(c) The cause of the latter, which must be some periodic climatic change acting over wide areas.

(d) The effects of fluctuations in general, and in particular of the p.f., on the method of evolution and other biological phenomena.

2. A short sketch is given of what is known about short- period climatic cycles (2 to 20 years), and their causes.

3. P.f. of lemmings have an average period of about 3½ years. The maxima in numbers occur synchronously in North America and Europe, and probably all round the arctic regions.

The varying hare in Canada has a period of 10 to 11 years.

5. The only regular periods shown by the animals dealt with are the short one of 3½ years and the longer one of 10 to 11 years. The former is probably more marked in the arctic and the other further south.

6. The sandgrouse p.f. point to the existence of an 11-year climatic cycle in the deserts of Central Asia.

7. The effects of these p.f. on evolution must be very great, although at present problematical; but the following suggestions are made :--

(a) Natural selection of some characters must be periodic.

(b) There will be different types of natural selection at the maxima and minima of numbers.

(c) The struggle for existence, and therefore natural selection, tend to cease temporarily during the rapid expansion in numbers from a minimum, and new mutations have then a chance to get established and spread, i.e. without the aid of natural selection. This might happen only rarely.

(d) This would explain the origin and survival of non adaptive characters in a species.

(e) On the other hand periodic reduction in numbers will act as an important factor causing uniformity in the species.

(f) The opposing factors (c) and (e) will vary much in different species, and the problem will require the combined attentions of mathematicians, and of ecologists working on the methods of regulation of the numbers of animals.

(g) This mechanical uniformity factor, since it acts independently of natural selection, explains how a particular structure or habit may evolve, when it only has a general adaptive significance.

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