Mendelian Genes and Rates of Development in Gammarus Chevreuxi

Owing to the brilliant work of the Morgan school, which has placed the chromosome theory of inheritance on a secure foundation, it has become possible at the present time to apply exact quantitative methods to the study of Genetics. So far, however, the genes are known only as the heritable basis whose ultimate effect is the production of one or more visible characters in the adult organism, while the developmental stages by which these are attained are still for the most part obscure. However, some workers, notably Goldschmidt (1923, 1927), have begun to throw light on this part of the problem. It is therefore the object of the present study to investigate genetically-controlled rates of development, in an endeavour to obtain further information on the mode of action of genes.

For this purpose the Amphipod Gammarus chevreuxi has been chosen, and various characters examined, principally relating to the eye-colour. It had already been demonstrated (Sexton and Wing, 1916; Allen and Sexton, 1917) that among the factors influencing this are a recessive mutation “red” (r) which produces red facets, the normal allelomorph resulting in black facets ; and a recessive mutation “no-white” (w) which inhibits the appearance of the normal white interfacetary pigment. Animals pure for “no-white” (WW) have been used in these experiments, as the exact colour of the facets can be judged more accurately when they are not separated by white pigment. (For other eye-colour genes in this species see Sexton and Clark, 1926; Sexton and Pantin, 1927.)

The investigations described in the present paper have been made possible by a grant from the Department of Scientific and Industrial Research, for which we are most grateful. The work has been carried out in the Department of Zoology and Comparative Anatomy, Oxford, and we wish to express our best thanks to Prof. E. S. Goodrich, F.R.S. for the facilities which he has afforded us.

In addition we would like to thank Mrs Sexton of the Marine Biological Laboratory, Plymouth, for kindly providing strains of Gammarus chevreuxi, and for much information concerning this species.

Mrs Sexton (l.c.) had already found that the eyes of many red-eyed specimens darken with age. It was this observation which formed the starting-point of our investigation.

The normal (dominant) black-eyed individuals were examined in order to throw light on this fact. At 23° C. the young of Gammarus chevreuxi are extruded approximately 10 days after fertilisation, and become sexually mature in about 6 weeks. The eggs are laid in a brood-pouch where they develop and hatch, the young being extruded shortly afterwards. Eggs were removed from females and developed artificially in brackish water, which was kept constantly aerated. The eye could thus be examined throughout development. By this means it was seen that the first pigment laid down in the normal black-eyed form is pure scarlet (the facets previously being colourless and transparent). It appears 2 or 3 days before hatching, and 4 or 5 days before the normal time for extrusion. The red pigment then darkens through shades of brown and chocolate to dense black, which stage is normally reached just before hatching, so that these forms are born, and always remain, black-eyed.

It has not yet been possible to determine the chemical nature of these pigments, owing to the excessively minute quantities available. The black, however, appears to be a melanin, and resists the action of such solvents as alcohol, chloroform, and ether, in which the red pigment is readily soluble. That solution in this case does take place, and not the formation of a colourless compound, has been demonstrated. By sacrificing 200 specimens a few c.c. of alcohol tinged a light pink were obtained. This was examined spectroscopically, but no absorption bands were visible ; it was slightly fluorescent in ultra-violet light. It may be taken as probable that the red pigment is a lipochrome.

In the red-eyed form also the darkening is due to the deposition of black pigment. When the red pigment is dissolved in alcohol, an insoluble black residue is left in the eye, which varies in amount according to the stage of darkening reached. (On Plate I will be found microphotographs of various Gammarus eyes with the red pigment extracted. These are, No. 7 pure red, Nos. 6-2 five stages in the deposition of black pigment, No. 1 pure black.) The process of darkening in the red eye is, therefore, similar to that occurring in the wild type, only it takes place very much more slowly. Also it starts later, not for some time after extrusion, and reaches a stable phase before the full black colour is attained.

The difference, therefore, between the black and red-eyed mutation in Gammarus depends upon a time reaction. It is in fact dependent upon a single genetic factor controlling the rate of production of black pigment; this rate in its turn appears to be correlated with the time of onset of deposition, and the final density obtained.

It was observed that some red-eyed Gammarus darken more rapidly than others. This difference has, in certain cases, been shown to depend on a single genetic factor, and must therefore be regarded as a clear-cut example of a genetically controlled developmental rate (Huxley and Ford, 1925).

Rapid- and slow-darkening individuals were kept at a constant temperature of 20° C. (it has since been found more convenient to work at 23 °C., and all subsequent experiments have been conducted at this temperature). made between these types, and the F₁, in all cases but one, showed definite but incomplete dominance of rapidity. In the one exceptional case the brood could be divided into “rapids” and “slows” in a 1 :1 proportion (15 :17), gating the “rapid” parent had been heterozygous. From the remaining F₁’s the F₂’s were bred; the results indicated definite segregation, the numbers being rapid, 8o : slow 31.

Since that time hundreds of individuals, both R₂(i.e. from a back-cross between F₁ and the recessive parental stock) and F₂, have been raised. The resulting broods may be divided into two lots : (A) those where clear-cut monohybrid segregation is obscured by accessory factors : these will be considered in Section 4. (B) Those with simple monohybrid segregation, between a pair of allelomorphs which we may call s (slow-darkening) and S (rapid-darkening). The families obtained of this latter type are summarised in a table at the end of this Section (pp. 118-19).

The accompanying diagrams illustrate a typical segregating family. The actual data are plotted in Fig. 1 a, and the means of the two classes in Fig. 1 b. (Only the individuals kept at 23° C. are utilized here, those at a lower temperature illustrate a point to be brought out later; see Section 6 A.) The abcissae represent time in days, the ordinates 15 stages in the deposition of black pigment, the eyes being matched against a colour chart in which the stages are made as nearly as possible equivalent. This is done by adding, between each stage, a given quantity of black pigment (in drops) to a fixed amount of the red pigment, calculated so that the last stage is not distinguishable from pure black. The limits of accuracy may be taken to lie within one colour-stage in either direction. Figs. 2 a−2 g illustrate frequency polygons calculated from the above segregating family at seven different dates. The eye-colour in some of the earlier experiments was determined every day or every other day. Once the type of pigment change had been established, determinations were made every 4 days. That is to say, for each individual mentioned in the tables, 11 or more determinations have been made.

The phenotypic differences between the segregating types are peculiar in that they alter during development. All the young hatch alike. At 23° C. black pigment begins to be deposited in the eyes of the rapid-darkening specimens (SS and Ss) on the 4th to the 6th day after extrusion, and they quickly become blackish and reach a stable phase. At this time the family is easily separable into two distinct classes. The eyes of the rapid-darkeners remain practically in this condition, though they may become slightly paler as the animal grows up (see Section 6 B). At the same time, or slightly later, the “slow” individuals (ss) begin to darken, but the black pigment appears much more slowly; when they too reach a stable phase, their eyes are nearly, but not quite, as dark as those of the “rapid “type. Visible segregation is thus once more obscured. The phenotypic divergence between the two types reaches a maximum between $212$ to 3 weeks from extrusion at 23° C.

In our preliminary note (1925) we stated that some individuals remained pure red throughout life or until after maturity. This we now find to have been an error, due to our not having discovered that melanin deposition is almost inhibited below 15°C. (seep. 124). All strains so far investigated show some deposition of melanin when kept at 23° C.

In the following tables the various broods from any single pair are added together. Families in which the total amounted to less than 20 have not been included. Those marked ^* were used in temperature experiments, and in these the total recorded here represents only the number kept at 23 ° C., as darkening is almost inhibited at a low temperature—see Section 6 A.

The following table illustrates the frequencies of the various classes (of eye-colours) in the F₂ and R₂ families on the 18th day from extrusion, which may be regarded as the time of maximum phenotypic divergence at 23° C. The numbers do not represent the total individuals obtained (which, for the families above 20, are given in the previous tabulations), since it was not possible to examine the broods on the 18th day in every case.

Fig. 3 is a graphic presentation of these results. It will be noticed that in the F₂ both the slows and rapids are on the average a little darker than in the back-cross. This would presumably indicate that the strains used differed in regard to the modifying factors present.

Certain strains of rapid- and slow-darkening Gammarus fail to give a clear segregation. When crossed, the range of darkening in F₂ is slightly greater than that encountered during normal segregation, owing to the appearance of an un-usually slow type, but no increase in maximum rapidity of darkening is found. All intermediate rates occur, however, and the families are never at any time divisible into two distinct and non-overlapping classes as is the case where one pair of factors is involved, as in Figs. 1 a, 2 b-d. This is illustrated by the frequency polygon, Fig. 4 a.

Such cases as these have given the following results. The offspring of the intermediates exhibit various degrees of darkening without segregation, producing a range similar to, or slightly less than, that of the original F₂. The extreme “rapid” and “slow” individuals, however, breed true. When crossed they recombine, to produce in F₂ the complete series in rates of darkening, once more without sharp segregation. The extreme true-breeding “slow “type (a) when crossed with the intermediates produces an pranging from intermediate to slow; (b) when crossed with normal slow darkeners from a segregating family, it gives an F₂ which appears to represent the two parental “slow” types and the intermediates between them. (It is, however, difficult to speak with any certainty on this point, as the difference between the two kinds of “slows” is not sufficiently marked.)

These results are consistent with the supposition that in the strains which fail to give an obvious segregation, the operation of the factor for the rapid and slow production of black pigment is complicated by the presence of an accessory factor, whose allelomorphs we may call M and m. (It is unlikely that two main accessory factors exist, though minor modifiers doubtless occur.) The interaction of the primary pair of factors with even one supplementary pair, having a similar but less marked effect, would give rise to a number of phenotypes which it would be impossible to distinguish within the limits of accuracy of this work. The F₂ would thus appear to give a complete range in rates of darkening, the frequencies distorted by the partial dominance of rapidity. The extremes, however, would be homozygous dominants and récessives respectively, and would thus breed true.

On this hypothesis the original rapid stock was SSMM, and the slow was ssMM. The presence of mm diminishes the rate of pigment production in a similar way to that of the ss factors, but to a smaller extent; the difference between the normal rapid (SSMM) and slow (ssMM) being considerably greater than between the latter and the extreme slow type (ssmm). The asymmetrical nature of the frequency curves shows that the genes for more rapid darkening are more or less dominant.

The fact that the range of eye-colour of the families from two intermediates mated inter se may be less than that of the original F₂ (Fig. 4 b as against Fig. 4,a) may indicate that an additional (2nd) modifier is to be assumed. This is also rendered probable by the fact that the ranges of Figs. 4 a, b  and especially c extended unusually high, and of Figs. 4 d−f unusually low. In the absence of linkage tests, however, it would appear very difficult to make certain of this point. It is to be noted that in many cases the whole F₂ range was recovered (no family of this type is figured in Fig. 4).

This has been condensed to a mere statement of the numbers obtained in each type of mating, in order to avoid excessive tabulation. It is hoped, however, that the frequency polygons (Figs. 4 a−4f), calculated in each case for the mating giving the largest number of individuals, will make the results intelligible.

• (1) F₂ families in which a series in rates of darkening occurred instead of segregation. See Fig. 4 a.

  9 matings (31 to 107 individuals per mating). Total: 553.

• (2) Intermediates from the above F₂ families mated together, and giving a range similar to, or less than, that of the F₂ itself. See Fig. 4 b.

  8 matings (23 to 86 individuals per mating). Total: 426.

• (3) Extreme types from the above F₂ mated and found to breed true. See Figs. 4 c and 4 d.

  • (a) Rapid × Rapid. 5 matings (12 to 38 individuals per mating). Total: 108.

  • (b) Slow × Slow. 4 matings (8 to 32 individuals per mating). Total: 99.

• (4) Extreme true-breeding “Slow” × Intermediates, giving an R₂ ranging from intermediate to extreme slow. See Fig. 4 e.

  2. matings (33 and 46 individuals). Total: 79.

• (5) Extreme true-breeding “Slow” × Normal “Slow,” giving an F₂ which appears to represent the two F₁ types and the intermediates between them. See Fig. 4f.

The ranges of various crosses involving one or more pairs of melanin rate-factors are presented in Fig. 5. It will be seen that wherever mm is present it extends the range of the slow down to stage 1 instead of stage 2. Further, the fact that normal slow and (extreme slow × normal slow) range up to 6 instead of to 5 indicates that without at least one M factor the range extends no farther up than to 5. The greater range of normal rapid (which is supposed not to include mm types) as against (extreme rapid × extreme rapid), however, would indicate that additional modifying factors are at work. The same conclusion is to be drawn from the range of (extreme slow × intermediate).

A recessive factor has been detected in one of the stocks which retards the rapid development of the black pigment until the appearance of the secondary sexual characters. When this factor is present, therefore, in a family segregating for rapid and slow pigment deposition, all darken very slowly up to sexual maturity, at which point the “rapids” darken almost to black in a few days. The “slows” continue at their previous rate, or, more frequently, rather faster. Slight divergence of the types is nearly always evident before the rapid development of pigment (Fig. 6). This factor may be called “d.”

This mutation appears to be semi-lethal, as the animals homozygous for it are delicate and difficult to rear. For this reason the numbers which have reached sexual maturity are, unfortunately, small. Four appeared in a family of 20, their parents coming from a pot containing “rapid” stock. A pairing was secured between two of these, and from it eleven offspring were obtained which reached maturity; they all showed the “delayed” character.

These “delayed “rapids (rrSSdd) were used in the following experiments. Five were mated to normal “rapids” (rrSSDD), but broods were obtained from only two of them. The F₁’s thus produced were all normal. Some of them were back-crossed to the “delayed” parental type. The total number of R₂’s thus obtained (from several families and broods) was 48, of which 30 were normal and 18 “delayed.” The remaining F₁’s were interbred to produce F₂’s. These, in all, gave 56 normal and 10 “delayed.” The divergence here exhibited from the expected 1 :1 and 3 :1 ratios respectively is almost certainly due to differential mortality, the “delayed” type being, as previously pointed out, considerably the more delicate, for it will be noticed that, in the above ratios, the divergence from the expectation is in favour of the normal animals¹.

This coincidence of melanin production with sexual maturity suggests a number of interesting possibilities. Since, however, they rest at present merely on un-substantiated assumptions, they will not be considered here.

The above experiments have all been conducted in constant temperature in-cubators at 23° C., for it has been found that temperature has a profound influence on the formation of black pigment in the eye. This is most simply demonstrated by the following procedure. Families segregating for rapid and slow pigment deposition, and others homozygous for these two types, have been divided at extrusion into two parts, half being kept at 23° C. and half at 13°-14° C. Those at the higher temperature develop black pigment in a normal manner, those at the lower temperature hardly darken at all. Only slight melanin formation occurs, its onset being delayed for about four months.

At the higher temperature the eye-colour never remains pure red; in all cases it gradually darkens, and it is merely the rate of the darkening process which varies. At the lower temperature, on the other hand, there is but little black pigment in the eyes of even the oldest SS specimens. Eighty rapid-darkeners have been kept at 13°−14° C. for 3 months after sexual maturity. At the end of this time the eyes were all pure bright red, as at hatching, though with a somewhat greater depth of colour. In such specimens, no trace of melanin is visible even after all red pigment has been extracted by alcohol. No visible segregation can occur therefore at low temperatures, while at 23 ° C. it is obvious during development. Fig. 1 a and 6 illustrate this point.

Individuals kept at 13°−14° C. until after sexual maturity darken when placed in the incubators. This process differs, however, in some respects from the darkening which occurs in the young, when these have been kept at 23° C. from extrusion. The rate of melanin deposition is slower, and the eye never becomes quite so black. These differences will be discussed in the next section. Conversely, by putting the darkening specimens into a low temperature, melanin production can be arrested at any stage, for practically no further development of black pigment then takes place.

It is to be noted, however, that the melanin of the normal wild-type eye, which is black from birth (see Sections 1 and 2), and from which the red-eyed forms discussed in this paper are a recessive mutation, does develop at a low temperature. However, its appearance is then somewhat delayed, so that at extrusion the eye is still distinctly red at the edge.

In Gammarus the area of the eye increases (1) by the addition of new facets and (2) by an increase in their size. Each facet behaves as a discrete unit in pigment formation, for, in the rapid-darkeners, the facets present at extrusion darken quickly and become blackish (see Plate I, fig. 8). Later, however, as new facets are developed, these too appear red first, and they pass through a similar colour-series. In a growing animal, therefore, the eye is red at extrusion and then darkens to blackish ; the area first formed remains practically in this condition, and later appears as a dark patch in the middle of newly formed red or brown facets. These darken in their turn until, in the adult animals, the whole eye becomes uniform. The original facets present at extrusion are therefore taken as a standard for darkening, and it is these which are plotted in the curves. That part of the eye which has darkened very early usually becomes slightly lighter as the animal grows up, though never lighter than any later developed facets. This is presumably due to an increase in facet size : we may suppose that pigment formation in each facet reaches a” saturation “point and then ceases ; after this the same quantity of melanin must be shared out over a larger area, since the facets themselves continue to increase in size. On the other hand, this effect is not to be noticed in black (RR) individuals. Presumably whether or not lightening of the central facets occurs depends upon the relative rates of pigment deposition (and therefore the final degree of saturation) and facet-size increase.

These effects are not perceptible in the eyes of old individuals which have been kept at a low temperature until after maturity and then transferred to 23° C. Practically all the facets having been formed by this time, the eye darkens evenly, but more slowly than in the young, as the area over which the pigment has to be distributed is greater. The larger size of the individual facets in such specimens is probably responsible for the fact that no intense temporary darkening occurs in them, such as usually takes place in the rapid-darkening young.

Body-growth, and therefore eye-area, varies greatly, but stocks can be obtained in which it is fairly constant. It is proposed to deal with this question in a sub-sequent paper.

A number of factors have been described which control developmental rates, that is physiological processes in the body. Their action^ as might be expected, is greatly influenced by environmental conditions such as temperature. The question at once raised is, how great a part do factors of this kind play in normal inheritance?

To start with, it may be pointed out that all or almost all the heritable varieties in colour of eye (as opposed to total absences of black and red pigment, as in albino and colourless eyes) so far recorded in Gammarus depend on factors affecting rate of deposition of pigment or else time of onset of deposition.

The factors R—r, S—s, M—m all affect the rate of deposition of melanin. The factor D-d affects the time of onset of deposition of melanin. In addition, Sexton and Clark (1926) refer to a new red mutation which is dark red when extruded, but lighter later : this may be called l. In addition, some individuals lighten completely, others only at the periphery: probably this will be found to depend on more and less rapid darkening. It is not yet known whether melanin is concerned in this eye-type at all. The cases of pure white, flushed-white, and purple-white eyes among the white-bodied forms have not yet been analysed, but will very likely be found to be connected with different rates of red pigment formation.

We have also other rate-factors affecting body-growth, which will in turn affect the amount of melanin relative to the eye. One of these (not discussed in this paper), which may be called g, very markedly affects final eye-colour.

We thus have six pairs of rate-factors certainly concerned with eye-colour, and probably three or four others.

We now come to other forms. The only animal on which anything approaching a thorough genetic analysis has been carried out is Drosophila. This is a holometa-bolous insect in which the adult characters appear only at the imaginai phase, and practically no growth or differentiation occurs afterwards. Any genetically controlled rates of development are therefore obscured in a species such as this, for we see only a “cross-section” through the curves of pigment production and other developmental possesses. If, for example, Gammarus were a holometabolous insect, which reached the imaginai phase during the period of maximum divergence of the curves for rapid and slow pigment formation (at the point illustrated in Fig. 2 c), the result would be an animal with two shades of eye-colour depending on a single Mendelian factor (and, in this case, inhibited at low temperatures). There are many such characters in Drosophila, and it is reasonable to consider at least the multiple allelomorphs for eye-colour, which form a complete series, as primarily influencing the rate of development of the eye-pigments.

It is perhaps not without significance to notice that in some few cases a slight change can still take place after maturity, giving results not unlike those described in Gammarus (see Crew, 1925, p. 140). In a young fly the pink-eyed condition can easily be distinguished from the purple-eyed but, as the individuals age, both become a dark purple shade, and the two are no longer separable. Newly hatched black-bodied flies are indistinguishable from the wild type, and the pigment is not laid down until later. In the great majority of cases, however, further development is cut short when the insect hatches from the pupa. Those factors, therefore, which in Gammarus continue to operate after maturity are normally not to be detected in an insect like Drosophila.

It is reasonable to suppose that in the higher animals, where specific hormone activity plays a greater part in development, genes controlling developmental rates are an equally important factor in inheritance. Thus a number of cases are known in the Mammalia where the characters separating species and geographical races are absent at birth, and only appear during growth. Mr C. S. Elton has kindly drawn our attention to the following examples among African Mammals.

Abel Chapman (1921) points out that in Africa there are two forms of the reed-buck (Cervicapra sudanensis) which differ in the shape of their horns. These are straight and simply bent over at the tips in all the immature animals. In the “Bohor “type, occurring in the equatorial region, they remain at this stage through-out life, but in the Sudan they acquire a characteristic sigmoid curve when the animals are adult. The horns are therefore of the same shape in the immature Sudanese and the adult equatorial types, but in the former their development proceeds a stage further than in the latter. The same author describes an interesting dimorphism in a species of buck known as the “White-eared Cob “(Adenota leucotis). The males may be either dark (blackish) or light (tawny), but the females are always light. At the extremities of its range, which is somewhat restricted, only the light form of the male is to be found, but elsewhere, and especially in the country between the River Sobat and Lake No, blackish males occur, but never to the exclusion of the tawny animals. Both males and females are alike at birth, and the darkening observed in certain of the males takes place only as the animals grow up.

Somewhat similar cases are recorded by Percival (1924) in an account chiefly devoted to the Kenya Game Reserves. He reports that the amount of spotting in the adult lion (Felis mosaica) distinguishes the East African from the other forms. The cubs are spotted, and the adults vary for the length of time that they carry the spots.

Perhaps the African buffaloes described by Christy (1924) are among the most interesting examples of this kind. There are two species distinguished by colour, size, and the shape of their horns ; they neither mix with one another nor interbreed. For the present purpose their most important characteristics are as follows :

Bubalus ciffer. This species has a wide range in Africa, including the Upper Nile, and is found in the bush and grass-lands. The animals are large and have spreading horns. They may be either black or tawny at birth, but all the latter type turn black subsequently, and the majority do so in a short time. In all cases, however, the foetus is at first red. The mature males keep the red coat longest in N.E. Congo.

Black pigment is thus always developed rapidly, but the speed at which it appears is a racial character.

B. nanus. A small species with up-turned horns, found principally in thè forests. All are tawny red at birth and until maturity ; none become black except aged bulls and, very rarely, females.

Black pigment is therefore developed slowly, but the rate varies within the species. It appears to be correlated with the habitat, being slowest in the forms inhabiting dense forest, intermediate in the forest margins, and of maximum rapidity in the open country. But in the most rapidly darkening B. nanus the deposition is slower than in the slowest darkening B. caff er.

We have here two allied species differing in rate of melanin production. Christy believes this to be environmental, and attributes the rapid production of black pigment to the effect of sunlight. Considering the close correlation between colour and environment in these species, it seems probable that this suggestion is in part correct. That other factors are, however, at work seems to be demonstrated by the intra-uterine darkening of B. caffer.

It seems probable, therefore, that the darkening in these species is genetically controlled, and is further modified by environmental conditions (possibly sunlight acting on the skin) in a manner analogous to that described in the eye pigments of Gammarus chevreuxi.

Apart from the racial and specific differences cited above, several other cases are known in which genetic factors control rates of development. Of these human eye-colour is an example. In man the eyes may be either brown or blue, depending upon a single factor pair, brown being dominant. AH babies are, however, bom with blue eyes, which (according to the factorial composition) may either remain in this condition or gradually darken, owing to the deposition of brown pigment. In addition the final stable phase (equilibrium position) appears to be attained at different ages. As in Gammarus, the more rapid the deposition, in general, the higher the final degree of pigmentation, and the earlier is this equilibrium position attained. (See R. M. Fleming, 1927, Anthropological Studies of Children.) For increase in skin pigmentation in negroes, reaching a stable phase at about puberty, see accurate measurements by Herskovits, 1926.

Goldschmidt (1927) has recently published an important general work on the relation of genes to development, in which he attempts to reduce all differences between the action of factors to differences in the rates at which they affect various processes in the developing organism. In its present form, his attempt, though of great value, would appear to have been over-simplified. For one thing, he has not taken into account the differences in final equilibrium position which are probably a general phenomenon, and in Gammarus certainly, and probably elsewhere, are probably closely correlated with rate-differences ; and for another, he has not taken account of factors acting at the same rate but with different times of onset.

For instance, in discussing his own results with the larval coloration of Lymantria dispar, he gives theoretical curves (Figs. 17 and 18) which indicate clearly that he ascribes all differences in dègree of pigmentation between the different larval races solely to differences in rate of melanin deposition. On the other hand, his own figures (Fig. 16) show that in some races (e.g. Hokkaido, Gifu) it is the time of onset of melanin formation and not its rate which is altered; and further, the different shape of the curves would be much better explained by different final equilibrium levels than by the theoretical curves given by him in his Fig. 18, which all converge to the same final level in a way which is theoretically, from the chemical standpoint, very unlikely.

It is here evident what advantages accrue from the employment of an animal like Gammarus in which phenotypic effects of genes can be traced from before hatching to long after maturity.

One or two other cases in which similar relations of hereditary factors to developmental processes are certainly or probably at work may also be mentioned. In the first place there are the cases of so-called “change of dominance.” In Gammarus it at first sight appears that normal black is a dominant, permanently pure red, if such existed, a recessive, while darkening reds show a change of dominance. Our analysis has shown, however, that all coloured eyes, including wild type, begin as pure red. The character with reference to which dominance must be considered is not colour itself, but the rate of change of colour. More rapid melanin formation is always dominant, more or less completely, over less rapid.

It is probable that all other cases of change of dominance will be reducible to the same terms (see discussion in Goldschmidt, 1927). In general the “characters” determined by genes must, whenever possible, be thought of as developmental processes with characteristic rates. We are accustomed to think of characters in static terms, as having fixed values. But such fixed characters, such as definite relative or absolute size, particular colour or pattern, will in general best be considered as end results of the primary gene-effects upon rates of developmental processes. Sometimes the characters appear relatively fixed and stable, because of determinate growth, and because, observed from the static point of view, we neglect the earlier stages and arbitrarily fix upon the conditions in the adult stage as representing our “characters.” Sometimes the earlier steps in the process are not visible, and the phenotypic effects only become visible at the close of determinate growth, or, when growth is indeterminate, after the equilibrium position has been attained. The relative size of the limb affords a good example of the first point. The hind limbs of a grasshopper (adult) have a relative size which is well defined within the limits of variability. The chelae of mature male lobsters or fiddler-crabs, or the abdomens of mature female shore-crabs, on the other hand, have no such fixed relative size. The difference is due entirely to the fact that in the one case growth is determinate, in the other indeterminate. Both, however, are similar in that the relative size of the part in question changes in an orderly way during development—i.e. in both cases the rate of change is the essential character which is inherited. This point has been discussed by one of us in previous communications (Huxley, 1924, 1927).

Further complications are introduced when the earlier stages of the process are invisible, as in holometabolous insects. There can, however, be little doubt that organs like the mandibles of Lucanidae, forceps of male Forfícula, or cephalic horns of various Coleóptera, which show a hétérogonie relation to general body-size, are determined by essentially the same processes (see Huxley, 1927). We thus have a constant differential growth ratio of a part, obviously determined by heredity, as the fundamental character. This may continue visibly throughout life, postmature as well as juvenile (Crustacea) ; or be cut short at maturity by cessation of growth (a and hemi-metabolous insects); or be cut short at maturity and also invisible in juvenile stages (holometabolous insects). But in all cases the essential character is the rate of a developmental process.

In this connection reference may be made to a recent paper by A. Schultz (1926) in which he points out that in the Anthropoidea and Hominidae, in every case investigated, the characteristic relative proportions of parts in the adult, is also found in the foetus, but, while tending towards the characteristic, always in less extreme form. This is at once intelligible on the supposition that what is inherited is (a) a defined rate of relative growth of the limb, (b) a defined adult absolute size.

Analysis of data presented by Davenport (1926—see especially Figs. 11 and 12) shows that the human secondary sexual character of relatively greater sitting height in female than male is due almost wholly to the fact (") that the limbs are growing in relative length through the juvenile period, at approximately the same rate in both sexes, but (b) that growth ceases earlier in the female. Here again a time-relation is the determining factor. Many similar problems of growth in relation both to individual and phyletic development may be found in D’Arcy Thompson (1917), notably in Chap, xv11 and Chap. 11. Finally, the fact that the proportions of certain parts of the body have no constant value even in adults in certain voles (Hinton, 1926) is due to the facts (1) that these voles show indeterminate growth, (2) that the rate of growth of certain parts, notably the jaw regions of the skull, is throughout life greater than the rate of growth of the body as a whole.

In a similar way the character, absence of a particular pigment band on the shell of Helix nemoralis, can be shown with high degree of probability (Diver, unpublished) to depend in reality upon (1) a later onset of pigmentation in this band, (2) the fact of definitive growth in snails. All stages of delay of onset can be found from slight delay confined to the first whorl to great delay with only a trace of the band just before the lip of the shell. Total absence would then merely represent a slightly greater delay.

The fact elicited by W. Schultz (1915-1922) and further analysed by Iljin (1926), that the white areas of Himalayan and even pure albino rabbits can be made to produce pigment by exposure to cold indicates that the allelomorphic genes for Himalayan and albino determine slower rates of the processes leading to melanin formation, which in the white areas normally do not reach the threshold value for actual melanin formation (just as the threshold for actual melanin is only reached later in Gammarus in the “rapid “red than in the wild type eye, later in the “slow” than in the “rapid” red).

Miss Durham (1926) finds that the eye of the cinnamon breed of canary is pink at hatching, but darkens to a shade almost indistinguishable from the normal black, although the pigment is chocolate melanin, not black melanin. Miss J. Procter (1926) states that the green snake Chondropython viridis was almost white at hatching, and only acquires the green markings later. Further, at the meeting of the Zoological Society she stated that the rate of acquiring green is subject to great variation. Berndt (1925), working with goldfish races, found a very close parallel to our case. Some strains are permanently grey. All so-called red strains have grey as their juvenile colour, changing later to red. The change may be effected at any time from $112$ to 17 months of age, and the time of the change—i.e. the relative rate of red pigment formation—is inherited. In some cases the fish changing from grey to red pass through a yellow phase. In a similar way, the white or silver condition almost always succeeds a previous red stage.

It is highly probable that relative rate of thyroid development determines the time of metamorphosis in Anura (Huxley, 1923). The colour- and pattern-changes of spiders during growth (cf. M^cCook, 11,327 seq.) might also be profitably analysed from the point of view we are upholding¹. We have already referred to the classical work of Goldschmidt who has conclusively demonstrated rate-factors for sex determination in moths, and for melanin formation in moth larvae. Many other cases might be cited, but we are here only concerned to point out, with the aid of a few illustrative examples, how fruitfully the factorial theory of heredity can be extended by thinking of the genes, at least in a large number of cases, as influencing not merely the character but also the rate of developmental processes.

Photographs (with standard illumination and other photographie treatment) of eyes of Gammarus chevreuxi (× 80). In all the red pigment has been extracted with alcohol.