## ABSTRACT

Cell number, determined by counting the nuclei, has been studied in preimplantation haploid, diploid, triploid, tetrapioid and hexapioid eggs of

*Mus musculus*, recovered usually days after fertilization. Most of the data concern triploid and tetrapioid eggs, from the early morula to late blastula stages.The mean number of cells in polyploid eggs (and perhaps in haploids), relative to the number in diploids of the same age, is approximately in inverse proportion to the number of chromosome sets present. Thus, the ratio of cell number in polyploid eggs to cell number in diploid eggs decreases with an increase in the number of chromosome sets.

There was no evidence for any one type of heteroploidy that the différences in ratios encountered from mouse to mouse were due to anything other than sampling error, i.e. the ratios remained fairly constant from the early morula to the late blastula. This suggests that the lesser number of cells in polyploids is already apparent in early cleavage.

These findings are compared with the parallel situation in Amphibia.

The counting of nuclei can play a role, but only a limited one, in the identification of polyploid eggs.

## I. INTRODUCTION

In previous papers we have been concerned chiefly with identifying heteroploidy in early embryonic stages of the mouse, determining the type of heteroploidy, and measuring the frequency of occurrence either after experimental treatments, or in silver-stock mice, some of whose embryos are spontaneously heteroploid (Beatty & Fischberg, 1949, 1951*a*, *b*; Fischberg & Beatty, 1950a, *b*, 1951*a*). To avoid laborious routine, the eggs of each mouse were mounted as a squash preparation on one slide. This meant that particular eggs observed under the binocular microscope could not usually be recognized in the preparations, and little could be said about the exact stages of development. One observation could, however, be made safely on squash preparations—the numbers of nuclei could be counted. Nuclear numbers listed in previous papers, together with a roughly equal body of new data, have been brought together in the present paper, and a detailed comparison has been made of nuclear number (and therefore cell number) in haploid, diploid and polyploid mouse eggs from the early cleavage to the late blastula stage. In some plants and invertebrates, cell number in polyploids and diploids is about equal, but the polyploid cells are larger than diploid, and the organism is consequently of giant size. In Amphibia, also, the polyploid cells are larger, but body size does not differ, because the polyploid organism contains fewer cells than the diploid. The present results, with the early mouse embryo, contribute to an understanding of the relative cell number in haploid, diploid and polyploid mammal embryos.

## II. MATERIAL AND METHODS

Mice *(Mus musculus)* of varying genetic constitution were used. In some eggs, heteroploidy occurred spontaneously. In others, it was induced experimentally. Sources of data are listed in the legend to Table 1. The spontaneous and experimental series have been pooled for all purposes, the results from each series being similar. In most mice, eggs were recovered days after copulation. A few were recovered after and days. The procedure for obtaining eggs and for making squash preparations has already been described (Beatty & Fischberg, 1951a), and the nomenclature reviewed in the same paper is used here. Attention has been confined to polyploid eggs (which in our material means triploids, tetrapioids and hexapioids) and to haploids. In accordance with common usage, the pre-implantation mouse embryo is sometimes referred to as an egg.

In considering differences in nuclear number between eggs of the same chromosome number, we find much variation even in eggs from the same mouse, due, for instance, to different rates of development of individual eggs. There is also a variation between different mice, due to differences in the average times of ovulation, in the average rate of development, and to observational uncertainty in that the time of fertilization, as judged by the time of formation of a vaginal plug, was subject to an (absolute) error of ± of a day. It was thought that the best procedure would be to obtain for each mouse an *xn/2n* ratio, which is defined as the ratio of the mean number of nuclei in any given type of heteroploid eggs of the mouse divided by the mean number of nuclei in the diploid eggs of the same mouse. Thus, a 3*n*/2*n* ratio is obtained for triploid eggs, a *4n/2n* ratio for tetrapioids, and so on. The diploid eggs serve, in fact, as an internal control in each mouse, against which the nuclear number of heteroploid eggs can be compared. (In the detailed analysis, as shown on pp. 545–7, the raw data were first transformed into natural logarithms, for the reasons stated, and the final estimate of the *xn/2n* ratio was obtained by taking anti-logarithms. This may be termed the geometric *xn/2n* ratio.).

Table 1 is a protocol of all data available up to 1 September 1950 in which there was at least one diploid and one polyploid (or one haploid) egg per mouse.

An attempt has been made to present the main body of the paper, so that it can be perused independently of the formal statistical treatment on pages 545–7.

## III. RESULTS

### (a) Haploid egg

The single haploid egg (in mouse SiL/107) had 32 nuclei, and was accompanied by two diploid eggs with 25 and 26 nuclei. The 1*n*/2*n* ratio is therefore 1·25. Little reliance can be placed on a ratio derived from only three observations, but the ratio is higher than any of the eight ratios for tetraploidy and hexaploidy, and (with four exceptions) is higher than any of the 47 ratios for triploidy.

### (b) Triploid eggs

The number of nuclei in triploid eggs, relative to the number in diploid eggs of the same age, may be expressed in several ways. In Table 1 there are forty-seven mice each with at least one diploid and at least one triploid egg. In each mouse, the *3n/2n* ratio (the mean number of nuclei in the triploid eggs divided by the mean number in the diploid eggs) may be calculated. The result is summarized in Table 2, from which it may be seen that there is considerable variation, but the most frequent ratios (nearly half of them) lie in the groups 0·6–0·8. The average of the forty-seven ratios is 0·83. When the ratios are arranged in order of magnitude, the median ratio (the 24th from either end of the series) is 0·74. The sum of the forty-seven means for triploid eggs is 2033·7, the corresponding figure for diploids being 2567·7; the ratio of these two numbers is 0·79. Thus, however expressed, the number of nuclei in triploid eggs is about 0·7–0·8 the number in diploid eggs; i.e. there are fewer nuclei in triploid than in diploid eggs. Is this difference in nuclear number significant? If there were no real difference, the expectation would be ratios above a value of 1·0 and below 1·0. The actual figures were 9 ratios above 1·0 and 38 below 1·0. The chance of the observed distribution differing from the expected solely through sampling error is less than one in a thousand. We conclude that the smaller mean number of nuclei in the triploid eggs is a genuine phenomenon, not due solely to sampling error.

The best estimate of the value of the 3*n*/2*n* ratio, as shown in the detailed analysis on p. 547, is 0·78, and lying between 0·72 and 0·85, with a one in twenty probability of these not being the outside limits, or between 0·69 and 0·87, with a one in a hundred probability of error. The same analysis shows also that there is no evidence that the different ratios encountered from mouse to mouse are attributable to any factor other than sampling error.

### (c) Tetr apioid eggs

The data for tetraploid eggs may be examined in the same way as for triploids. In Table 1 there are six mice containing both diploid and tetraploid eggs. The six 4*n*/2*n* ratios are all below a value of 1·0, their average being 0 ·55. The ratio of the total of the six tetraploid means to the total of the six diploid means is 0 ·58. As shown on p. 547, the relatively smaller mean number of nuclei in tetrapioids as compared with diploids seems to represent a genuine difference, with a chance of less than one in a thousand of being due solely to sampling error. The best estimate of the 4*n*/2*n* ratio is 0·52, lying between 0·41 and 0 ·67, with a chance of one in twenty of these not being the outside limits; a more stringent estimate of the limits is 0·38 and 0·73, with a one in a hundred chance of error. The detailed analysis also shows that there is no evidence that the differences in the ratios from mouse to mouse are due to any factor other than sampling error.

### (d) Hexapioid eggs

As shown in Table 1, the two mice SiL/75 and V/94·3 each contained one hexa-ploid egg (nuclear numbers respectively 4 and 12), as well as several diploid eggs. The hexapioid with 4 nuclei contained fewer nuclei than the 6 diploid eggs in the same mouse, and was the least developed egg of all the 222 -day diploid, triploid and tetraploid eggs described in this paper. The hexapioid with 12 nuclei contained fewer nuclei than the 3 diploid eggs in the same mouse; it also contained fewer nuclei than any of the 165 diploid eggs, fewer (with one tie) than in the 49 triploid eggs, and fewer (with one tie and one exception) than in the 8 tetrapioids. It seems reasonable to conclude that hexaploid eggs in general contain fewer nuclei than diploids, triploids and (probably) tetrapioids of the same age, and that exceptions are due to sampling error. The small number of observations, the low absolute value of the cell number in the hexaploids, and an evident disparity in the *6n/2n* ratios of the two mice, seem to render an elaborate mathematical analysis undesirable for the present. The geometric mean 6*n*/2*n* ratio (0·19), with no standard error attached, will be taken as our best estimate of the true 6*n*/2*n* ratio.

### (e) Detailed analyses of the sources of variation in the number of nuclei of triploid and tetraploid eggs

These analyses were performed for two reasons : *(a)* to obtain a clearer picture of the various sources of variation in nuclear number and, in particular, to assess the not easily visualized interaction term, and (*b*) to provide, with fiducial limits of probability, a best estimate of the 3*n/*2*n* and 4*n*/2*n* ratios.

Nuclear number in the developing mouse egg does not increase steadily, but tends to remain at 8, 16, 32 and so on, between successive cleavage waves. As a result, the variance would be expected to rise in proportion to the absolute magnitude of the observations. A logarithmic transformation was therefore carried out with the intention of equalizing the intervals between 8, 16, 32 and so on, and of rendering variance independent of absolute magnitude. A further advantage of the transformation is that the mean difference between logarithmic mean nuclear number in diploid and polyploid eggs, together with the standard error of the mean difference, can very simply be transformed back into a *ratio* of the means, together with a fiducial limit of probability. In addition, the transformation lessens the undue weight which the few - and -day eggs, with their numerous nuclei, would otherwise exert on means.

Since disproportionate numbers were present in the subclasses of the analyses of variance, and it was not evident from inspection whether interaction was present, the method of weighted squares of means was used, assuming interaction (Snedecor, 1948, p. 299).

In the triploidy analysis (Table 3), data were taken from forty-seven mice, which contained altogether 148 diploid and 55 triploid eggs. Differences between mice (46 degrees of freedom) were highly significant at the 0·1 *% P* level. This presumably reflects, among other possible factors, that the times of copulation and fertilization were known only approximately, and that there was a consequent variation between mice in the general level of development of the eggs. The difference between the diploid and triploid means (D.F. I) was highly significant at the 0·1% *P* level; this confirms the result of the simpler analysis (p. 544) in which it was shown that the distribution of the 47 *3n/2n* ratios differed significantly from a chance distribution around unity. The interaction term (D.F. 46) was not significant; hence there is no evidence that the differences between the 47 ratios are due to anything other than sampling error. The constitution of the error term is threefold: (*a*) a large and probably irreducible natural variation in nuclear number between eggs of the same chromosome number in the same mouse, quite evident in the fresh material ; (*b*) an unknown variation due to accidental loss of nuclei during preparation ; and (*c*) error in the counting of nuclei, believed to be negligible, for damaged or weakly stained eggs were excluded from the data. None of these three elements of the error term seems likely to affect diploid eggs more than triploids, or triploids more than diploids, and it is concluded that the error term is a valid and, in fact, necessary basis, on which to judge the significance of the main factors and their interaction. In any case, the differences between mice, or between types of ploidy, remain significant at the 0·1 *% P* level even when the interaction itself is used as error term.

In obtaining our best estimate of the true *3n/2n* ratio, the mean logarithmic 2*n*–3*n* difference in each mouse was weighted by (*n*_{1}*+ n*_{2}*)/n*_{1}*n*_{2}, where *n*_{1} and *n*_{2} are the numbers of diploid and triploid eggs respectively. The weighted mean so obtained was 0·2502. Its standard error, for 109 D.F., was 0·0428 (obtained by dividing the error mean square by 35·371, the latter being the sum of the weighting coefficients). Taking anti-logarithms, the mean *3n/2n* ratio is found to be 0·78, with fiducial limits of 0·72–0·85 (to two places of decimals) at the 5 *% P* level, or 0·69–0·87 at the 1 *% P* level.

A similar analysis was performed with the six mice that contained diploid and tetraploid eggs, and similar results obtained (Table 3). Differences between mice, and between types of ploidy, were highly significant at the 0·1 *% P* level, in comparison with the error term, and significant at the 5 % *P* level in comparison with the interaction. The interaction was not significant in comparison with the error term. The best estimate of the mean logarithmic *2n*–*4n* difference, for 18 D.F., was 0·6495 ± 0·1150. Taking anti-logarithms, this means that the best estimate of the 4*n*/2*n* ratio is 0·522, with fiducial limits of 0·41–0·67 (to two places of decimals) at the 5 *% P* level, or 0·38–0·73 at the 1 % *P* level.

The mean squares in the tetraploidy analysis are slightly higher than in the triploidy analysis, as might be expected from the smaller number of degrees of freedom available in the tetraploidy analysis. Apart from this, the mean squares in the two analyses are of the same order of magnitude for any particular source of variation.

### (f) Combination of results

In Fig. i, the best estimates of the *1n/2n*, 3*n*/2*n, 4n/2n* and *6n/2n* ratios (as derived in the previous sections) are plotted against the number of chromosome sets. There is evidently a decrease in the ratio with increased number of chromosome sets. We have seen that the mean *3n/2n* and 4*n*/2*n* ratios differ significantly from unity. They also differ significantly from one another, the mean difference in logarithmic units being 0·399 ± 0·123, and therefore highly significant (*P* = 0·01–0·001). (It should be noted that the diploid eggs of one mouse—serial number 269—were used in obtaining both the 3*n* and 4*n* estimates; this means, however, only that the true level of significance of the 3*n*/2*n*–4*n*/2*n* difference is likely to be even greater than calculated.) The plots for the *1n/2n* and *6n/2n* ratios, based on few observations, are necessarily approximate, but follow the same trend as those for the better known 3*n*/2*n* and 4*n*/2*n* ratios. We conclude that *the mean number of nuclei in polyploid eggs of the same age is approximately in inverse proportion to the number of chromosome sets present*. This may be appreciated visually in Fig. 1, where the curve derived from observations is seen to be rather close to the theoretical curve expressing an exact inverse proportion. Interpolation between the *1n/2n* and 3*n*/2*n* plots from observations gives a value very close to 1·0, which must necessarily express the ‘2*n*/2*n*’ ratio.

The word ‘approximately’ was used in the above conclusion for two reasons: (*a*) only three of the fifty-six mice contributed to estimates of the 1*n*/2*n* and 6*n*/2*n* ratios, the results being principally those obtained from the 3*n*/2*n* and 4*n*/2*n* ratios; and (*b*) the 3*n*/2*n* ratio (0·78), although of the same order as the theoretical value of 0·67, nevertheless differs significantly from it; the 4*n*/2*n* ratio (0·52), however, does not differ significantly from a theoretical 0·50 ratio.

## IV. DISCUSSION

The results have been expressed so far in terms of the objects actually observed, i.e. nuclei. It is known that polynucleate cells are rare or unknown at the stages of development examined. The number of nuclei counted in a preparation will therefore be equated in this discussion with the number of cells present.

The conclusion that the mean number of cells in polyploid mouse eggs, relative to diploids of the same age, is approximately in inverse proportion to the number of chromosome sets present, parallels closely the situation in amphibian larvae (Fankhauser, 1945; Fischberg, 1944, 1948; Briggs, 1947). In mice the 3*n*/2*n* ratio is rather greater than the theoretical expectation (0·78 instead of 0·67) at the early stages examined by us. Only one haploid mouse egg was found, and, in view of the great variation found between mouse eggs even of the same type of ploidy and in the same mouse, we cannot state whether haploid mouse eggs in general follow an inverse proportion law; for triploid, tetraploid and hexaploid eggs, however, the inverse relation seems quite clear.

The polyploid eggs were of normal cytological appearance, and we have observed in other work (Fischberg & Beatty, 1951 *b*) that triploid mouse eggs can survive to at least days after fertilization. It seems unlikely therefore that the lesser number of cells in polyploid eggs can be due to the eggs being moribund or dead.

In the detailed analyses of the 3*n*/2*n* and 4*n*/2*n* ratios, there was no evidence that the different ratios encountered from mouse to mouse were due to anything pther than sampling error. Nor was any correlation evident when the 3*n*/2*n* or 4*n*/2*n* ratios of each mouse were plotted against the average cell number of each mouse (the latter figure being the average of the mean of the diploid and the mean of the triploid or tetraploid eggs in the same mouse). A reasonable number of mice were involved (52), and we may form the provisional conclusion that both the 3*n*/2*n* and 4*n*/2*n* ratios remain fairly constant over the ranges observed (early morula to late blastula). This suggests that the lesser number of cells in triploid and tetraploid eggs, relative to diploid eggs, arises at an early cleavage stage. In Amphibia, the first cleavage mitosis occurs at the same time in diploid and triploid eggs of *Triturus viridescens* (Fankhauser & Godwin, 1948). In triploid *Rana pipiens* (Briggs, 1947), the first three cleavages take place at the same times in diploids as in triploids. Our results with mice do not show the time of origin of the difference, but do indicate that it arises early. The difference in cell number between diploids and tetrapioids is quite evident in Amphibia at an early larval stage (Fankhauser, 1945), but its exact time of origin is not clear. Most of the tetraploid mouse eggs quoted in the present paper were produced by a hot shock intended to suppress the first cleavage division; thus, at least at this early stage of development, tetraploid mouse eggs would be expected to contain half the number of cells of diploids.

We have seen evidence that the lesser number of cells in triploid mouse embryos arises in early cleavage, and in tetrapioids at the first cleavage. We may now consider the interrelationships of cell size, cell number and body size in later embryos. We have observed (Fischberg & Beatty, 1951*b*) that triploid -day mouse embryos are smaller than diploids in the same mouse. They must be assumed therefore to contaim fewer cells than diploids, and particularly so since cells in polyploid organisms of recent origin are larger than in diploids. (In races with increased chromosome number which have passed through many generations, cell size may regulate in time towards the normal, as in mosses (von Wettstein, 1937).) We feel therefore that triploidy in the -day mouse embryo (and perhaps at least up to birth, unless new factors intervene) follows the pattern of the triploid amphibian larva and adult, in which the triploid contains fewer and larger cells, but body size is not greater than in diploids. This contrasts with the pattern of some plants and invertebrates, where the polyploid cells are also larger, but the number of cells in polyploids and diploids is about equal, and the organism is of giant size. The adult triploid rabbits reported by Häggqvist & Bane (1950 *a*), however (see also Haggqvist & Bane, 1950*b, c*, and Melander, 1950; some criticisms have been raised of the interpretation of data made by these authors—see Beatty & Fischberg (1950) and Nachtsheim (1950*a, b))* seem, unexpectedly, to follow the plant rather than the amphibian pattern.

In plants and invertebrates, triploids of recent origin are usually larger than diploids ; in Amphibia they are of the same size ; in our -day mouse embryos they are smaller. Tetraploid plants and invertebrates are usually larger than diploids and triploids; in Amphibia, tetraploids start the same size, are retarded in mid-larval development (possibly for reasons of physiological inefficiency), and do not reach the same size as diploids or triploids. These facts suggest that the size of polyploid organisms, relative to diploids, decreases the higher they are in the systematic scale. Post-implantation tetraploid mammals are unknown at the time of writing ; if they are found, we feel that they are likely to be smaller than diploids.

A possible intra-uterine competition between polyploids and diploids has been envisaged (Beatty & Fischberg, 1951 *b*; Fischberg & Beatty, 1951*a, b*), whereby the implanted polyploids, with their smaller number of cells, would be at a disadvantage in comparison with diploids. However, in nine of the forty-seven mice with triploid eggs shown in Table 1, the mean number of cells in the diploids was less than or equal to the mean number of cells in the triploids. It seems therefore that a certain number of mice exist in which polyploid eggs, by chance, do not have a lesser number of cells than diploids, and these polyploids might therefore be exempt from intra-uterine competition.

We may now examine the use of nuclear counts as a possible aid in identifying polyploid eggs. If we select one egg at random from each mouse in Table 1, we shall obtain fifty-nine eggs among which will be about a quarter of the total polyploid eggs. If, however, we select from each mouse the egg with the smallest number of nuclei, we shall have included about half of the total number of polyploid eggs. The essential method of determining polyploidy lies in the counting of chromosomes, but the counting of nuclei has evidently a definite though limited use as preliminary or confirmatory evidence.

## ACKNOWLEDGMENTS

We wish to thank Prof. C. H. Waddington, F.R.S., for helpful interest in the work. We are indebted to Mr R. M. Mabon for technical assistance. We are particularly indebted to Mr A. Robertson for advice on statistical procedure, and to Mr W. Russell for carrying out most of the computations. One of us (M. F.) acknowledges grants from the Animal Breeding and Genetics Research Organization and the Schweizerische Stiftung für biologisch-medizinische Stipendien, and wishes to thank the former Organization for its hospitality.

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