Studies on Sterility and Prenatal Mortality in Wild Rabbits: Part IV. The Loss of Embryos After Implantation

The material on which this study is based and the technique employed have been described in a previous paper (Allen, Brambell & Mills, 1947). The experimental error in estimates of prenatal mortality, based on counts of corpora lutea and of implantation sites, was investigated in that paper, as was also the amount and effect of polyovuly and of transperitoneal migration of ova. Since estimates of prenatal mortality occurring after implantation, with which this paper is concerned, are based on comparison of the number of implantation sites and of surviving embryos, they are unaffected by errors in counts of corpora lutea, by the production of two viable ova from a single follicle and by transperitoneal migration of ova, but they are affected by errors in counts of implantation sites. It was pointed out, in the paper referred to, that although there is little likelihood of failure to detect implantation sites containing living embryos the possibility remains of the disappearance before full term of sites in which the embryos had died and were reabsorbed soon after implantation or, more probably, that such sites might be overlooked, through becoming less conspicuous, and hence omitted from the counts. Actually, significant changes were observed in the mean number of implantation sites in the uteri, counted at successive stages of pregnancy. In particular, a decline occurred in the mean number towards the end of gestation, such as would result from the disappearance of approximately 9% of the implantation sites. Although the disappearance of sites would appear to be the simplest explanation of this phenomenon it was by no means clear that it was the correct one, and there were grounds for thinking that it might be more complex. Subsequent experimental investigation of this problem (Brambell, Henderson & Mills, 1948) has shown that sites in which the embryos had been killed at 16 days post-coitum by surgical means persist until full term in pregnant uteri and can be identified as such at the time of parturition. They certainly are less obvious when the uterus is completely distended with large foetuses and might then be easily missed from the counts, although they have not disappeared. The significant decline in the mean number of implantation sites towards the end of gestation may be due to an experimental error arising from disappearance of sites, or failures to count them, but there may be some other explanation.

It has been shown that the prenatal mortality suffered after implantation is distributed independently of that occurring before implantation (Allen et al. 1947). The loss before implantation has been analysed in another paper (Brambell & Mills, 1947b). There is, however, a very important and, indeed, fundamental difference between the methods of estimating the two. The loss before implantation in litters that survive is estimated from the number of corpora lutea in the ovaries and of implantation sites in the uteri; that is from animals in which implantation has already taken place, and in which therefore preimplantation loss has terminated. It follows that whereas the loss of whole litters before implantation cannot be detected by this means, since such animals drop out of the sample of pregnancies before implantation sites are formed, the total loss of ova before implantation in litters that survive is displayed. Theoretically, a comparable estimate of postimplantation loss could be obtained from the numbers of new-born young and of placental sites in post-partum animals, but this is impracticable in dealing with a population of wild mammals. Instead the estimate must be based on the sample of pregnant animals obtained at all stages of gestation between implantation and parturition. It must be based on a sample in process of suffering post-implantation loss and in which, therefore, this loss is incomplete. However, a close estimate of the total loss of embryos up to the time of parturition in litters that survive can be derived from animals approaching full term. No information could be obtained regarding the mortality at the time of parturition.

The fact that the post-implantation loss is estimated from a sample of animals taken during the period in which they were actually in process of suffering that loss has another important consequence. Animals which lose a litter entirely through the death of all the embryos must be excluded from the category of pregnancies as soon as the last surviving embryo has died. Only if all the embryos in each such litter died simultaneously would such animals drop out of the category immediately. Actually the embryos die at intervals, and consequently these animals which are in process of losing their litters remain for a time in the category of pregnancies and display a loss of one or more, but not of all, the embryos. Assuming that the successive embryos die at intervals, then in a large sample of such litters the chances of finding 1,2,3, …,x–1 embryos dead, where x = the number of implanted embryos, would be equal, and the mean number of dead embryos per litter affected would tend towards $12$x. The proportion of dead embryos in such litters would be 0·5. It has been pointed out previously (Brambell & Mills, 19476) that when the prenatal mortality falls on the litters as units the regression lines for the proportion of embryos lost and for the proportion of litters lost on the size of litter at implantation will coincide. This is true of the final result but not of the distribution of the mortality in a sample of litters including those in process of being lost. If l=the proportion of litters in process of being lost, and E = the proportion of dead embryos, then

Another difference between pre-and post-implantation loss is to be found in the speed with which the dead embryos are eliminated. Cleaving ova or early blastulae are so small that they disappear rapidly once they are dead. After implantation the embryos are increasingly substantial structures which persist longer, and the placentae, once established, are still more persistent. It follows that litters in which all the embryos have died and are reabsorbing are identifiable for a considerable period thereafter, and the chances of obtaining them are proportionately greater. It has been shown experimentally (Brambell et al. 1948) that when all the embryos are killed by means of stilboestrol at $1112$–12 days post-coitum they remain identifiable and their age at death can be determined for 3–$312$days, and at 16 days post-coitum for 4–$412$ days. The placental remains persist as recognizable reabsorption sites for 9–10 days. The dead embryos persist much longer when some of the embryos in the litter survive and the reabsorption sites then appear to be easily recognizable at full term, as mentioned above. It is important that dead litters in which the age at death of the embryos can be determined should not be included in the category of pregnancies, as was done in the earlier papers (Brambell, 1942, 1944) before the experiments referred to had revealed the implications. A living litter, which is developing, only remains for 24 hr. in any given daily age group, but a dead litter, because it has ceased to develop, remains in the age group to which it belonged when the last embryo died until that embryo has disintegrated, too much for its age to be determined, say 4 days later. Thus if 20 % of the litters died on the 12th day post-coitum we would expect to get in a large sample equal numbers of living and dead litters containing 12-day embryos.

Once dead, embryos become limp and are distorted by the pressure of the uterus. The brain especially collapses and the cervical flexure is lost. The embryo loses its translucent appearance and becomes opaque and whiter in colour, and the embryonic fluids escape from the membranes, which collapse about the embryo. These characteristics remain for a considerable time after the death of the mother and the consequent death of the other embryos, serving to distinguish those embryos which have died before from those which have died after the mother. Only embryos which had quite unmistakably died before the mother were classed as such, those about which there was any doubt being classed as healthy. There was no difficulty in practice in determining which embryos were dead when surviving embryos were present to compare them with, and very little difficulty even when all the embryos were in the same state. Subsequent experience with embryos killed experimentally has convinced us that our criteria were reliable and conservative. The dead embryo, as autolysis proceeds, becomes fragmented and finally unrecognizable. The limb buds remain recognizable as a rule after the rest of the embryo has disintegrated, and it is possible to determine the age of the embryo from these by the use of the figures in the normal-table of Minot & Taylor (1905). The stage at which it ceased to be possible to determine the age of any of the embryos in a pair of uteri thus formed a natural and definable end-point. The placentae and embryonic membranes are much more persistent than the embryos and their remains, projecting from the mesometrial wall into the uterine lumen, forming a swelling on that part of the uterus, can be recognized and readily distinguished from post-partum or post-abortion placental sites. Animals containing these, but without fragments of embryos sufficient to determine their age, were classed as late reabsorption stages.

There is no doubt that reabsorption, that is the gradual removal in situ of the embryos and placentae, mainly by autolysis, is the usual method of disposal. It occurs when only some of the embryos die at any stage of gestation after implantation and when all the embryos die at early stages up to at least the 15th day. It may occur when all the embryos die even at later stages. Experiments have shown (Brambell et al. 1948) that abortion occurs as a rule when the embryonic tissues die after the 19th day. Prior to this, the necessary zone of weakness does not appear to have developed in the placenta, which consequently does not become detached. There is evidence, however, that the placenta may in certain circumstances survive for a time the death of the embryos. Thus, even when the embryos die before the 19th day, the placenta may survive and abortion may follow after an initial period of reabsorption. This was found to occur when the embryos were killed by surgical means at 16 days post-coitum. The possibility of the loss of litters by abortion at later stages in the wild rabbits therefore must be considered.

A total of 1873 pregnant animals was obtained with surviving embryos between 7 and. 32 days of age post-coitum. Of these thirty-nine are excluded from the analysis of mortality because, owing to damage to the uteri during cleaning, either the number of implantation sites or of surviving embryos or both could not be determined. The number in the sample differs from that employed for estimating the loss before implantation (Brambell & Mills, 1947b) because Series 9, although available for pre-implantation loss, is not available for post-implantation loss; it was necessary for embryological purposes to preserve some swellings in each uterus unopened and hence the loss could not be determined. A few animals in the other series which had the ovaries damaged, preventing the counting of corpora lutea, which had to be excluded from the data for pre-implantation loss, were available for post-implantation loss. The distribution of the mortality according to the number of embryos that become implanted, as shown by the number of implantation sites, in the 1834 litters available is shown in Table 1. The proportion of litters containing reabsorbing sites and the proportion of embryos reabsorbing are shown to the right of the table. Straight regression lines have been fitted to the data, that for the proportion of embryos lost being

These regression lines, together with the observed proportions of litters showing loss and of embryos lost for each size of litter at implantation, are shown in Fig. 1. Testing the significance of these regressions presents some difficulty, because the probability of loss varies with the size of litter at the time of implantation and because the number of examples of each size of litter at implantation vary, thus weighting the means. Let x be the size of litter at the time of implantation, Y be the probability of loss as determined from the fitted regression, and y be the observed loss in a count of n specimens. Then the variance^* from the mean of a single specimen (the expected value of n (y–Y)²) will be

Thus the variance in y for the regression will be

and the variance in b, since σ²y is dependent on x, will be

The resulting curve is represented by the broken line in Fig. 1. It can be seen that the observed proportion of litters showing loss was very much less for all values of x than the expectation on this assumption. This indicates that a substantial part of the loss after implantation may be falling on the litters as units. Comparison of this figure with the corresponding one for loss before implantation (Brambell & Mills, 1947bfig. 1) provides an interesting contrast, for litters lost as units are necessarily excluded from the data for loss before implantation.

The evidence from the distribution of the mortality in litters containing at least some surviving embryos is corroborated by the occurrence of many animals in which all the embryos have died and are in various stages of reabsorption. A total of 164 such reabsorbing litters were obtained, of which 101 contained embryos of which the age could be determined and sixty-three were in late stages of reabsorption. As a rule, when the condition of the embryos permitted accurate determination of the age, it was found that all the embryos had died at approximately the same stage of development, and that the least and most advanced embryos did not differ by more than 24 hr. in the stage of development they had attained. Occasionally, a difference of 36 or 48 hr., or even more, was apparent.

The data of the distribution of these reabsorbing litters according to the size of litter at implantation and according to the stage of development attained by the embryos, when this could be determined, are given in Table 2. Combining these with the 1834 living litters given in Table 1 the total numbers of living and dead litters are given in the second column from the right and the second row from the bottom. The proportions of reabsorbing litters presented as a proportion of all living and dead litters, according to age post-coitum and according to the size of litter at implantation, are given in the right-hand column and the bottom row respectively.

The daily proportion of litters with all embryos reabsorbing, represented as a proportion of all living and dead litters shown in the right-hand column of Table 2 and in Fig. 3, rises abruptly on the 11th day, reaches a maximum on the 13th and declines abruptly on the 15th day post-coitum, thereafter remaining at a very low level throughout the remainder of gestation. Since the ages of these dead litters were determined from the least autolysed embryos, the age is the stage at which the last surviving embryo died. It is, therefore, clear that the majority of litters which are reabsorbed in toto are lost between the 11th and 15th days inclusive. Very few litters with all the embryos dead and reabsorbing were encountered which had died after the 15th day. It follows that if many litters die after the 15th day they are not reabsorbed but must be aborted. The possibility of the loss of whole litters on the 7th to 10th days has been discussed previously (Brambell & Mills, 1947a) and presents a special problem. Many litters of this age were experienced in which all the embryos displayed abnormalities. It is possible that these abnormalities preceded the death of the embryos and that the affected litters would have continued to develop until on or after the 11th day, and that the group of litters shown in Table 2 as being lost between the 11th and 15th days inclusive represent a later and final stage of these abnormal litters. It is also possible that the abnormalities observed are post-mortem changes in the embryos which had already died between the 7th and 10th days inclusive. If this were the case it might be assumed that the very small embryos would disintegrate so rapidly that it would speedily be impossible to determine their age macroscopically and so they would come mainly into the group of late reabsorption stages. The first possibility appears the more probable since it is very difficult to believe that a further heavy loss of whole litters occurs before the nth day, not shown in Table 2, which the second possibility involves.

Since it is clear that the majority of litters which are reabsorbed die between the nth and 15th days inclusive, this age group of living litters should include most of those in process of being lost but in which at least one embryo still survives. The proportion of living litters containing reabsorbing embryos for each day of gestation from the time of implantation is represented graphically in Fig. 4. It can be seen that the proportion rises sharply on the 9th, 10th and 11th days to a maximum on the 12th. The rise is thus 1 day in advance of the rise in the proportion of dead litters, as shown in Fig. 3. There is no appreciable decline in the proportion of litters containing reabsorbing embryos until the 15th day, when it is sharp, but thereafter the decline is more gradual until the 23rd day when only 4% of litters show loss and, apart from minor fluctuations, this level is maintained thereafter. The peak at 26 days cannot be regarded as significant since it is isolated and depends on too few animals. Comparison with Fig. 3 shows that the considerable proportion of living litters with some embryos reabsorbing experienced between the 16th and 22nd days inclusive is not accompanied by a corresponding proportion of litters with all embryos reabsorbing. Therefore, these litters cannot all be accounted for by assuming that all the embryos die and are reabsorbed. Yet the apparent loss declines subsequently, as gestation proceeds, until, at the end of gestation only approximately 5 % of the surviving litters appear to have suffered loss. There are three possible explanations : either those litters in excess of 5 % showing loss in the 16–22-day period survive but the reabsorption sites in them disappear, or they are lost by being aborted, not reabsorbed, or both. It has been shown previously (Allen et al. 1947) that the mean number of implantation sites declines significantly as gestation proceeds, from a maximum of 5·419 ± 0·070 in the 16–20-day age group to a minimum of 4·923 ± 0·067 in the 26–32-day age group. This is difficult to understand otherwise than by supposing that some of the sites, presumably those of which the embryos have died and have been reabsorbed relatively soon after implantation, have either actually disappeared or have become so indistinct as to be frequently overlooked in the counts towards the end of gestation. It is more probable that they are overlooked in the counts than that they disappear entirely for it has been shown (Brambell et al. 1948) that when some of the embryos are killed experimentally at 16 days of age the reabsorption sites remain clearly recognizable until full term. It has been shown by Reynolds (1946) that in the rabbit between the 20 and 24 days of gestation, owing to rotation of the embryos, the previously separate and distinct swellings on the uterus merge, the whole uterus becoming equally distended and cylindrical. Inevitably it is much easier to overlook a small reabsorption site, lying between two healthy placentae, in a uterus that has attained this evenly distended cylindrical stage, than at earlier stages when the uterus is constricted between successive placentae, whether healthy or reabsorbing. It appears, therefore, quite probable that some early reabsorption sites might be overlooked, even if they had not disappeared, from counts made after the 20th day of gestation. Abortion is not inherently improbable either, since it was found (Brambell et al. 1948) that it is the usual sequel to the death of the embryos after the 16th day, when experimentally induced. It should be remembered that, whereas only a dead embryo can be reabsorbed, living embryos as well as dead can be aborted and hence it is possible for a litter to be lost in this way at a time when some of the embryos were still surviving. As has been indicated above, if all the embryos died before any were removed, as is the case when the whole litter is reabsorbed, the mean number of dead embryos per litter in process of being lost would approximate to where x is the number of implanted embryos. The mean number of dead embryos in litters in process of being lost by abortion would be less if abortion occurred while any of the embryos were still living. The daily mean numbers of dead embryos per litter suffering loss after implantation given in Table 3 are relevant in this connexion. It is apparent that 0·5 of the embryos in litters suffering loss are dead on the 11th day, so that the value of is actually attained then, and that the proportion remains high for the succeeding 4 days. The subsequent sharp fall is consistent with either a random loss of embryos in litters that survive or with loss of litters by abortion before all the embryos have died, or both, but not with reabsorption of a large proportion of the litters. It should be borne in mind that the proportion of dead embryos in litters in process of being lost by reabsorption will be attained only when the proportions of litters entering and leaving this category are equal. Thus, if more litters are entering on the process of dying than are finishing it the value will be less, and vice versa. Hence, if reabsorption of litters were the dominant factor the proportion of dead embryos per litter suffering loss should rise, not fall, after the peak of the mortality has been passed.

Analysis of the mortality in the 7–32-day age group is complicated by the fact that the loss of whole litters does not proceed at a uniform intensity throughout this period, and that, therefore, it is based on animals killed before, during, and after the period of maximum loss. It is necessary, therefore, to fractionate the data, and to divide them up into as many successive shorter age groups as the numbers warrant. The data have been divided into five age groups, 7–10, 11–15, 16–20, 21–25 and 26–32 days respectively, each of which contains data of upwards of 300 animals, and which have also been selected so that the whole of the period of maximum loss of litters, 11–15 days, is concentrated in one age group. The distributions of the data for these age groups are summarized in Table 4. Theoretical distributions of the kind given by equation (ix) have been fitted to each, in a manner similar to that for the 7–32-day age group, and tested by means of X²-The expected and theoretical values agree well except in the case of the 21–25-day age group, where the value of P is just below 0 ·1. The values of p and of l for each age group are given in Table 5, together with the resulting expectations of number of litters showing loss and of number of dead embryos for samples of the given sizes, and the observed numbers for comparison. Mean values of p = 0·0175 and l=0·1225, for the whole sample can be calculated simply from the. values for each age group and the number of litters in it. These values approximate sufficiently closely to the values p= 0·0164 and l=0·1228 calculated directly from the 7–32-day age group as a whole. The values of p for the successive age groups rise initially to a maximum for the 16–20-day age group and thereafter decline. The initial rise is to be expected and should continue throughout the period during which the random loss of embryos as units is occurring. The subsequent decline can be accounted for only by a disappearance of reabsorption sites in surviving litters, or by the disappearance of many of those litters which have suffered loss, presumably by abortion since sufficient reabsorptions have not been observed to account for it. That it is due to the disappearance from the counts of reabsorption sites appears the more probable, and the decline in the mean number of implantation sites observed in these age groups, previously recorded (Allen et al. 1947) is adequate to account for it. Thus it would appear that the real loss of embryos in litters that survive to full term is considerably in excess of the apparent loss, as shown by the 26–32-day age group, and is not less than 3·5%. A further loss may occur after the 20th day and be masked by the concurrent disappearance of earlier reabsorption sites proceeding at a faster rate.

The proportion of litters in process of being lost reaches a maximum of 0·4545 in the 11–15-day age group and declines thereafter to 0·0094 in the latest age group. The numbers of litters ill process of being lost represented by the values of l for samples of the given sizes are given in the second column from the right of Table 5 and, in the right-hand column, the numbers of dead and reabsorbing litters observed for comparison. It will be seen that, whereas in the 11–15-day period there are approximately twice as many litters dying as dead, in the 16–20-day period, there are almost four times as many. This suggests that some of the litters dying after the 15th day may be lost by abortion, a suggestion which is supported by the fall in the proportion of dead embryos per litter suffering loss, shown in Table 3 and referred to on pp. 253–4, but the numbers of litters involved scarcely warrant a definite conclusion.

The problem of estimating the actual proportion of litters that are lost entirely presents great difficulty, as has been indicated previously (Brambell, 1942, 1944). Several methods have been employed, but all are open to objection for one reason or another. The obvious method of estimating the proportion of litters lost after implantation is from the proportion of living litters that are in process of dying. This is complicated by not knowing how long a litter takes to die, that is, the period elapsing between the deaths of the first and last embryos. Consequently, we do not know how long these litters remain in the sample of pregnancies nor at what rate they are dropping out of the mortality tables. Clearly, in the absence of this knowledge, the best estimate available is provided by the maximum proportion of litters in process of being lost. Since the major part of the loss occurs during so short a time, the estimate for the 11–15-day age group covers too long a period for the purpose, yet the size of the sample does not warrant dividing it further for the purpose of fitting a theoretical distribution. However, the proportion of embryos lost in litters that survive, p, varies comparatively little and justifies the assumption that it is approximately constant for each day within each age group. Then it is possible to estimate l, the proportion of litters in process of being lost, for each day from the values of p in Table 5 and of E, corrected by omitting litters of one. The results are given in Table 6. It will be seen that the proportion of litters in process of being lost exceeds 0·50 on the 11–14 days inclusive and reaches a maximum of 0·56 on the 12th day. The total proportion of litters lost after implantation should exceed the maximum by the proportion lost before the 12th day plus the proportion which begin to die after the 12th day. It must be concluded, from this method of estimation, that not less than 56% of the litters are lost after implantation, unless the development of the still-surviving embryos in the litters in process of being lost is actually retarded, relative to the embryos in the healthy litters, so that they remain at a given stage of development for longer than normal. This would have the effect of raising the apparent proportion of litters in process of being lost and so increasing the estimate.

The third and the most direct method is to determine the relative frequency of animals in early stages of pregnancy and of those in late stages, after the litters have been lost. This method is.open to the objection that the methods used to obtain the material, trapping, shooting, etc. may have been selective in favouring the chances of obtaining animals at certain stages of pregnancy as compared with others, so biasing the results. For example, animals approaching full term may be more sedentary in habit and hence less liable to be trapped or shot, or, conversely, their greater weight may favour the chances of their springing a trap and being caught. Animals in which the uterus was damaged in cleaning and in which the full number of healthy embryos and implantation sites was not known had to be excluded from the mortality tables. Amongst these, animals approaching full term predominated so that it is necessary to include them all for the present purpose. A total of 764 animals was obtained 0–7 days pregnant inclusive, giving a mean number of 95·5 per day for the 8-day period. A total of 775 animals was obtained 21 days pregnant and over. This is an n-day period since the young are born on the 31st or 32nd day and so gives a mean number of 70·45 per day. The difference represents a disappearance of 26·2 % of litters. Since it is the sample of animals approaching full term which is most liable to be biased by selective trapping, etc. it would appear to be preferable to confine the calculation to those 21–25 days pregnant, of which 308 were obtained, a mean number of 61·6 per day. The difference from the 0–7-day group on this basis represents a loss of 35·5 % of litters.

It would appear safe to conclude that not less than 35 % of litters are lost as such after implantation and that the proportion may be as high as 56 % or even slightly more.

Although the duration of the phase of reabsorption from the time of disappearance of the embryos to the time when the reabsorption sites cease to be recognizable as such has been determined experimentally (Brambell et al. 1948), late reabsorption stages have not been used for estimating the proportion of litters lost. This is because many animals appear to become pregnant again before reabsorption is complete, and then soon cease to be recognizable as late reabsorption stages. Several such pregnant animals with still recognizable reabsorption sites dating from a preceding pregnancy were observed and it is probable that many others were overlooked. Although the late phase of reabsorption lasts about twice as long as the phase during which the embryos are ageable in experimental animals, it can be seen from Table 2 that 101 animals in the earlier phase were obtained as compared to only sixty-three in the later phase, clearly indicating substantial wastage from the latter group.

Since the majority of litters in process of being lost are concentrated in the 11–15-day age group the data for this age group have been examined separately and are summarized in the third column of Table 7. They reveal no significant relation’ to body weight.

The body-weight distribution of the litters in which all the embryos are dead and reabsorbing has been examined also, and the data are summarized in the right-hand column of Table 7. The proportions of dead litters, calculated as proportions of all litters surviving and dead, with their standard deviations, are given and are represented graphically in Fig. 5. It is apparent that the proportion of dead litters falls steeply and consistently with increasing body weight and that the relation is clearly significant. It must be remembered that the proportions of dead litters expressed in this way does not provide reliable information as to the actual proportion of litters lost, because the time during which reabsorption sites remain recognizable after the deaths of the embryos is not known accurately, yet this does not affect their relative significance. It must be concluded, therefore, that the proportion of litters lost in toto after implantation declines steeply with increasing body weight of the mothers.

It has been stated already (Allen et al. 1947) that only the presence or absence of milk in the mammary glands was recorded up till and including February 1942 (Series 01, 0 and part of 1). Thereafter, those with milk in the mammary glands were further subdivided into those with milk but not certainly suckling and those certainly suckling, as indicated by copious milk-secretion, large size of the mammary glands and depleted fur around the nipples. The three categories were recorded under the headings of no-milk, milk and lactating respectively. All animals 28 days pregnant and over were excluded since milk appears in the mammary glands at that stage of gestation irrespective of the previous history of the mother. The proportions of embryos lost after implantation, according to whether or not milk is present in the mammary glands for the two periods before and after the end of February 1942, are compared in Table 8. It is clear that there is no significant difference between the proportions of embryos lost in the two periods, nor between the groups with no-milk and those with milk or lactating combined.

The results are different when for the second period the groups with milk and lactating are separated and are compared with each other and with the no-milk group, as is done in Table 9. The difference between the proportions of embryos lost in the sample with no-milk and in each of the samples with milk and lactating respectively is just over twice its standard error and so is significant, though barely so. The difference between the proportions of embryos lost in samples with milk and lactating respectively is nearly seven times its standard error and is very significant. The loss is greatest in the lactating group and least in the milk group. Comparison of the proportions of embryos lost in each age group of each category reveals further differences. The proportion of embryos lost in the 11–15-day age group, in which the litters in process of being lost entirely tend to be concentrated, is obviously much greater in lactating animals, than in either of the other two categories, and this accounts for the heavier mortality in the lactating animals treated as a single sample. There is clearly no significant difference between the proportions of embryos lost in the no-milk and milk categories respectively for this age group. The difference between the proportions of embryos lost in the no-milk and lactating categories in the 7–10-day age group is not significant, but both are significantly less than in the milk category. The proportion of embryos lost in the no-milk category does not differ significantly from that in either of the other categories for the 16–20-day age group, but the proportion of embryos lost in the lactating animals is significantly higher than that in the animals with milk. The proportions of embryos lost in the milk and lactating categories for the 21–27-day age group do not differ significantly, but both are significantly less than in the no-milk category.

Comparison of the incidence of the mortality after implantation in the different series should show (a) whether it varies geographically from one locality to another in Great Britain, and (b) whether it varies, from one year to another in the sarpe locality. The data for all pregnancies in the 7 − 32-day age group for each series are summarized in the second column of Table 10. The proportion of embryos lost in Series 4 is greater than in any other, and differs significantly, though barely so, from the next greatest in Series 2. The best comparison geographically is between Series 3 and 4, from Anglesey and Caernarvonshire respectively, because these two series were taken simultaneously in 1944, the weekly samples of each being dealt with alternately, and hence the personal factor in arbitrary determinations and in technique was at a minimum. Yet the difference between the proportions of embryos lost in these two series is over seven times its standard error and is clearly significant. Comparison of Series 1 and 4, both from South Caernarvonshire, collected in 1942 and 1944 respectively, is the best for analysis of annual variation, the difference between the proportions of embryos lost being five times its standard error. The difference between the proportions of embryos lost in Series 2 and 3, both from Anglesey in 1943 and 1944 respectively, is also significant, being over three times its standard error, but is less satisfactory as an example of annual variation since the two series were obtained from different parts of the country and the variation might be geographical.

Since litters in process of being lost entirely tend to be concentrated in the 11–15-day age group, comparison of the incidence of the loss after implantation in the different series in this age group should throw light on which fraction of the total loss of embryos varies geographically and annually. The data are summarized in the third column of Table 10. Analysis reveals corresponding differences of similar significance, justifying the conclusion that the incidence of loss of whole litters after implantation varies both geographically and annually.

Information on these points can be obtained also from the numbers of reabsorbing litters in which all the embryos were dead, and which, therefore, are not included in the above data. The data are summarized in the right-hand column of Table 10, and are treated in a similar manner to that in the section on the relation of the loss to body weight. Analysis reveals significant geographical variations in the proportion of reabsorbing litters obtained, but the annual variations are not significant. Nevertheless, the results correspond remarkably well as regards the relative incidence of the loss of whole litters in the different series to those derived from the surviving litters. The results of all three analyses are compared graphically in Fig. 6, and it can be seen that in all the incidence of mortality is highest in Series 4 and lowest in Series 7 + 8, 3, and 5 + 6 in descending order.

The data were grouped into 4-week periods and are summarized in Table 11. The results, which are represented graphically in Fig. 7, are not very satisfactory. It appears that the incidence of mortality attains maximal values in the 2nd and 6th 4-week periods, that is, at the beginning and end of the intensive breeding season. Both these peaks are significant for the 11–15-day group, though barely so, the former is significant in the data for the 7–32-day group but not in those for dead litters, and the latter in the data for dead litters but not in those for the 7–32-day group. Probably both maxima are due mainly, if not entirely, to a greater incidence of loss of whole litters at these periods.

It is not possible to determine the total prenatal mortality suffered by surviving litters since no data are available of the number of newborn young. The mortality at parturition therefore is unknown. An estimate of the total mortality prior to parturition in surviving litters can be obtained from the 26-day-and-over age group and the data for the combined loss before and after implantation in this age group are contained in Table 12. It is apparent that 41 % of the litters have suffered some loss and that 11 % of the ova ovulated have been lost, but it is probable, for the reasons given previously (Allen et al. 1947), that this is an underestimate owing to an error arising through the omission of corpora lutea and of very old reabsorption sites from the counts.

The significance of the separation of the data of loss before implantation from those of loss after implantation is worth stressing again. The former can be derived from comparison of the number of corpora lutea in the ovaries with the number of implantation sites in the uterus, so far as litters that have survived implantation are concerned, and the latter from comparison of the number of implantation sites with the number of surviving embryos. This is so obvious, when attention is directed to it, that its importance may easily be overlooked, yet it is a most valuable procedure in the analysis of prenatal mortality. Not only has the prenatal mortality in each of these two fractions been shown to be mutually independent (Allen et al. 1947), but the two fractions are not comparable and are subject to different limitations. The data for loss before implantation are derived entirely from litters which have survived implantation and, therefore, they do not include litters which have been lost in toto before implantation but do include all the loss in litters that survived implantation, because the loss is then complete. The data for loss after implantation, being derived from pregnant uteri at all stages between implantation and full term; concern loss in progress which, therefore, is not complete but which does include litters in process of being lost in toto at the time of autopsy. Loss at parturition is necessarily excluded. Further, the data for loss before implantation, being derived from animals in which this loss has been completed, provide no information regarding the precise stage between ovulation and implantation at which the loss occurred, whereas the data for loss after implantation, since they are derived from animals at known stages of pregnancy in which the loss is in progress, do provide information regarding the incidence of the loss at successive stages after implantation. These are fundamental differences of great significance.

It has been shown that the distribution of the loss will vary according to whether the mortality is falling on the embryos as units or on the litters as units. The relation of the proportion of litters showing loss to the proportion of embryos lost provides a means of distinguishing between these two kinds of mortality. Assuming that the proportion of embryos lost is constant, irrespective of litter size, then the proportion of litters showing loss will increase geometrically with increasing litter size if the loss is falling at random on the embryos as units, whereas it will remain constant if the loss is falling at random on the litters as units. The loss before implantation, which necessarily excludes loss of whole litters, approximates closely to the expectation for a mortality falling at random on the embryos as units (Brambell & Mills, 1947b, fig. 1). A theoretical distribution that provides both for a loss falling at random on litters as units and for a loss falling at random on the embryos as units in the surviving litters has been worked out and provides a good fit for the data of loss after implantation. Comparison of the figure referred to with Fig. 1 illustrates this point clearly. The whole of the increase in the proportion of litters showing loss with increasing litter size observed can be accounted for by that fraction of the mortality which falls on the embryos as units. Therefore there is no evidence that the proportion of litters lost in toto after implantation increases with increasing litter size, and indeed the data of reabsorbing litters in which all the embryos are dead indicate that it declines. One of us in an earlier paper (Brambell, 1944), before the necessity of distinguishing between the loss before and after implantation was appreciated, concluded erroneously that the proportion of litters lost in toto did increase with litter size and deduced therefrom that, in consequence, lifters of 5 and 6 were more productive than larger or smaller litters (Brambell, 1944, text-fig. 14). This we have now shown to be incorrect and to have been due to the methods of analysis then employed not enabling the mortality falling on the embryos as units to be distinguished from that falling on the litters as units.

The problem of estimating the proportion of litters lost after implantation presents great difficulty, chiefly because of uncertainty in the time factors involved. No precise information is available as to the time elapsing between the deaths of the first and last embryos in a litter, and as to whether this varies according to the number of embryos. Differences in the stages of development attained by the embryos seldom exceed the equivalent of 1 day, but this may be an unreliable guide since it is quite possible, indeed probable, that development may be retarded when the litter is dying. These factors affect estimates based on the proportion of litters in process of dying and which are therefore liable to error. Similarly, the time elapsing between the death of the last embryo in a litter and the point at which autolysis has proceeded so far that the stage of development it had attained at death can no longer be determined is not known precisely. Since no information could be obtained from the literature as to the duration of the reabsorptive processes in the rabbit, a separate experimental investigation Of this problem was undertaken by killing all the embryos in tame rabbits at various stages of development, either by direct surgical interference or by injection of massive doses of stilboestrol (Brambell et al. 1948). Since, however, the time was found to vary both with the experimental method employed of killing the embryos and with the stage of development which they had attained, the results are not entirely adequate, since the cause of death of the embryos in the wild rabbits is unknown and may affect the duration of the reabsorptive processes. The estimates, based on the proportion of dead litters obtained, depend on this time factor, and it has been necessary to employ that derived from the experiments. The third method of estimating the proportion of litters lost, based on the relative numbers of animals in early and late stages of pregnancy obtained, is liable to error arising from selective trapping, as has been indicated. Thus all three methods are liable to errors, which may be large. The first method gives an estimated loss of 56 % of the litters, the other two methods agree in giving an estimated loss of 35 % of the litters. Probably the actual loss lies between these values.

Another difficulty in estimating the total loss of litters arises from the fact that 5 % more embryos are reabsorbing in the 16–20-day age group than in the 26–32-day age group. This can be accounted for only either by the total loss of some of the litters in the intervening period, which therefore are not represented in the 26–32-day age group, or by the disappearance of some of the old reabsorption sites in surviving litters before the 26th day, thus reducing the apparent mortality in the 26–32-day age group. However, the proportion of dead litters in which all the embryos are reabsorbing obtained after the 16th day is too small to account for the necessary loss of whole litters, hence it must be concluded that if whole litters are lost at this stage they must be aborted, not reabsorbed. This conclusion is supported by the experimental evidence (Brambell et al. 1948) that abortion is a more frequent means of removal of a dead litter after the 19th day in rabbits than reabsorption. On the other hand, it has been shown (Allen et al. 1947) that the mean number of implantation sites in the uteri declines from 5·42 ±0·07 at 16–20 days to 4·92 ±0·07 at 26–32 days, an observation which is difficult to account for otherwise than by assuming that 9 % of the old reabsorption sites escape recognition, and are omitted from the counts, in late stages of pregnancy. If so, this error would be more than sufficient to account for the apparent excess of the mortality in the 16–20-day age group as compared to the 26–32-day age group. Of these alternative explanations, the former would have the effect of increasing the estimated loss of whole litters between the nth and 15th days by the proportion aborted subsequently, whereas the latter-would increase the mortality suffered by surviving litters above that apparent in the 26–32-day age group, as shown in both Tables 4 and 12.

Although, for the reasons set out above, estimates of the absolute proportions of litters lost and of embryos lost in surviving litters after implantation must be treated with caution and are likely to be subject to a wide margin of error, the same considerations do not apply to comparisons of the observed proportions either of embryos lost or of dead litters in the various sub-samples. The relative significance of these values for the various sub-samples remains unaffected, assuming that the times taken for a litter to die and to be reabsorbed tend to be constant. The remarkable consistency of the data justify this assumption. Analysis of the relation of the loss after implantation to body weight of the mother, to the functional condition of her mammary glands, to the locality, to the year and to the season therefore have been confined to such direct comparisons. Thus it has been possible to determine that the proportion of litters lost is inversely related to the body weight of the mother; that is, the loss is heavier in the younger and less well-conditioned animals as compared to the older and better conditioned animals. This is shown very clearly by the proportion of dead litters. The mortality varies also with the functional activity of the mammary glands, being heaviest in animals that were certainly suckling and least in those that had some milk in the glands. There is some indication that the mortality tends to occur rather earlier in gestation in the animals with some milk and later in those with no milk than in the undoubtedly suckling animals. The proportion of litters lost also varies significantly both in different localities in the same year and in different years in the same locality. Finally, the mortality appears to be heavier at the beginning and end than during the height of the breeding season.