H. J. Muller

The relation of recombination to mutational advance

Abstract The method of calculation is shown wherebt a formula has been derived that approximately the ratio of the rate of accumulation of advantageous mutant genes in a population that undergoes recombination to the rate in an otherwise non-recombining one. A table is given showing the ratios thus found for different frequencies of advantageous mutations and different degrees of their advantage. It is shown that this calculation does not apply for mutant genes that act advantageously only when in some special combinations with one or more other mutant genes, and that as far as these cases of special synergism are concerned recombining lines have no evolutionary advantage over non-recombining ones. Other limitations of the formula are pointed out and assessed. It is explained that most factors that retard the rate of recombination—for expample, linkage, rarity of outbreeding, intercalation of sexual reproduction between more frequent cycles of sexual propagation, and partial isolation between subpopulations—must usually cause little long-term retardation of the speed of advance that is fostered by recombination. Moreover, even where long-term evolutions has virtually ceased, recombination of mutant genes still confers upon a population the means of adopting short-term genetic “dodges”, that adjust it to ecological and “physical” changes in its circumstances, much more rapidly than would be possible for a comparable asexual population. Under conditions where only stability of type is needed, a non-recombining does not actually degenerate as a result of an excess of mutation over selection, after the usual equilibrium between these pressures is reached. However, a irreversible ratchet mechanism exists in the non-recombining species (unlike the recombining ones) that prevents selection, even if intensified, from reducing the mutational loads below the lightest that were in existence when the intensified selection started, whereas, contrariwise, “drift”, and what might be called “selective noise” must allow occasional slips of the lightest loads in the direction of increased weight.

Why Polyploidy is Rarer in Animals Than in Plants

A CONSIDERABLE number of cases of tetraploidy and also higher forms of polyploidy have been found amongst plants, some having been observed to arise in cultures that were under observation, others being found already established as varieties or species having twice (thrice, etc.) the amount and number of chromosomes present in related types. Evidence also exists that forms of plants thus established may give rise to larger subdivisions (genera, etc.) inheriting all this chromatin, or even more, since the doubling process may be repeated. On the other hand, amongst animals, cases are very rare where there is critical evidence for the occurrence of this evolutionary process.2 Apparently this is not because doubling of chromosome number does not occur in cell division-for cases of tetraploid cells in diploid animals have been observed not infrequently. Neither is it likely that polyploid individuals, would fail to live. For chromosome conditions in the Hymenoptera show that at least two chromosome numbers are equally viable there-haploid and diploid-and polyploid Drosophilae have been found by Bridges to be very vigorous. What, then, is the reason for the rare occurrence of polyploidy in animals, as compared with plants? It is, in essence, very simple-animals usually have two sexes which are differentiated by means of a process involving the diploid mechanism of segregation and combination,

Pilgrim Trust Lecture: The Gene

The gene has sometimes been described as a purely idealistic concept, divorced from real things, and again it has been denounced as wishful thinking on the part of those too mechanically minded. And some critics go so far as to assert that there is not even such a thing as genetic material at all, as distinct from other constituents of living matter.

The rate of change of hereditary factors in Drosophila

A knowledge of the rate at which hereditary changes of various sorts occur is the necessary groundwork for an adequate understanding of evolution. The wide recognition given to this fact is attested to by the vast amount of literature on the subject of “variation,” but, with our new exact knowledge of the Mendelian and chromosomal method of inheritance of the so-called “variations,” it is evident that this literature has very little bearing on the real question of how often changes in the hereditary factors, i.e., mutations, actually occur: for the breeding procedures used in the experiments there considered were not of the type necessary for ferretting out the new mutant factors as they arise, and for distinguishing between them and the apparent variations caused by the sorting out of old mutant factors into new combinations. There is, to be sure, enough work to show that the real mutations are “rare”—whatever that term may mean; but, so far as an approximate quantitative determination of the rate of factor change is concerned, it is not possible, from the published work, to determine even its general order of magnitude. Some special scheme of crossing is required for this purpose. In the present series of experiments with Drosophila, the X chromosome was chosen as the most convenient one for the detection of mutation, since every hereditary factor in either of the X chromosomes of the female fly stand revealed in the characters of one half of her male offspring, no matter what their father was. Thus, if the female has a new mutated factor in one of her X chromosomes, even though she does not usually show that factor herself, and even though her mate does not contain it, nevertheless one half of her sons are bound to show it and the mutation will thus be recognized.

Two Kinds of Stamens with Different Functions in the same Flower

IT may be worth mentioning that cases strongly analogous to those described in NATURE (vol. xxiv. p. 307, and vol. xxvi. p. 386, are also to be observed among the Monocotyledons in the family of Commelynaceæ, and that these cases offer some graduations.

The Fertilisers of Alpine Flowers

A FEW years ago I stated my belief in this journal that lepidoptera are far more frequent visitors and fertilisers of flowers, and that from this cause by far more flowers are adapted to cross-fertilisation by lepidoptera, in the Alps than in the lowland. But it was then impossible for me to give a sufficient number of facts. Now, therefore, having continued my observations in the Alps during six summers, and being about to prepare a detailed work on “Alpine Flowers, their Fertilisation by Insects, and their Adaptations to them,” I will here give a statistical statement of all visits of insects on flowers which I have observed (1) in the lowland, (2) in the Alps generally, (3) above the boundary of trees; the numbers under 1 being extracted from my work, “Die Befruchtung der Blumen durch Insekten, &c.” (Leipzig, 1873).A FEW years ago I stated my belief in this journal that lepidoptera are far more frequent visitors and fertilisers of flowers, and that from this cause by far more flowers are adapted to cross-fertilisation by lepidoptera, in the Alps than in the lowland. But it was then impossible for me to give a sufficient number of facts. Now, therefore, having continued my observations in the Alps during six summers, and being about to prepare a detailed work on “Alpine Flowers, their Fertilisation by Insects, and their Adaptations to them”, I will here give a statistical statement of all visits of insects on flowers which I have observed (1) in the lowland, (2) in the Alps generally, (3) above the boundary of trees; the numbers under 1 being extracted from my work, “Die Befruchtung der Blumen durch Insekten, &c”. (Leipzig, 1873).

The Effect of the Change of Colour in the Flowers of “Pulmonaria offcinalis” upon its Fertilisers

YESTERDAY I had an opportunity of convincing myself by direct observation that the change of colour in the flowers of Pulmonaria officinalis is of the same significance as in Ribes aureum and Lantana, according to Delpino and Fritz Müller (Compare NATURE, vol. xvii. p. 79).

A Simple Formula Giving the Number of Individuals Required for Obtaining One of a Given Frequency

A short approximation formula (see (2)) has been found for estimating the probability of a given expected ratio having been correct, when no individuals of the minority type have appeared. In using the formula for this purpose, it will in some cases be necessary to look up one logarithm, but no other tables and very little calculation are required. The same formula may also be used (in form (1)) to determine the number of individuals that must be raised and classified (by inspection or testing) in order to be sure of finding one of a theoretically given frequency. The calculation for the latter purpose ordinarily consists of only a simple multiplication, without the use of any tables.

On the Fertilisation of Flowers by Insects and on the Reciprocal Adaptations of Both

DURING the last ten years, since, by his wonderful work on Orchids,* Darwin anew turned the attention of naturalists to the remarkable connection between the sructurc of flowers and the insects visiting and fertilising them, many essays on the contrivances of flowers as apparently affording facilities for intercrossing distinct individuals have been published; but there is no doubt that by far the greatest part of the work on this subject is still to be done. The most conspicuous flowers attracted, of course, in the first place, the attention of inquirers, and much greater pains was taken to show the possibility of their cross-fertilisation by insects than to observe whether self-fertilisation may possibly take place if not visited by insects. Another very obvious deficiency of observations indispensable to be made on the subject in question resulted,—the fertilisation of flowers by insects being studied by botanists but little acquainted with insects. From this cause, for the most part, when flowers were examined as to their intercrossing by insects, no complete observations were made as to the insects themselves which were supposed to visit and fertilise the flowers, and in many eases the agency of insects was over-estimated in consequence of not observing them directly.

Flowering of the Hazel

IT was with great interest that I read the communication from F. D. Wetterhan, in NATURE, vol. xi. p. 507. But I cannot help expressing quite a different opinion as to the bearing of the interesting fact that proterandrous and proterogynous individuals are to be found in the same locality. From the structure of the flowers and from insects never visiting the stigmas, I am convinced that the hazel is a strictly anemophilous plant; that the red colour of its stigmas is solely an effect of chemical processes connected with the development of the female flowers to maturity, just in the same manner as in the female flowers of the larch-tree and some other Coniferæ ; and that likewise the coexistence of proterandrous and proterogynous individuals in the hazel relates solely to the influence of the wind, and not at all to the agency of insects.