Originally posted on the Bulblist  (11 April 2002)

Of Mice and Mendelism

I happened across a classic paper by Castle and Little that may be of interest to anyone who breeds anything. The story involves two sets of data regarding the inheritance of yellow fur in mice.

In 1905, Cuenot reported on his experiments. He crossed yellow x yellow, raised 363 offspring, and counted 263 yellows. That's 72.45 percent, which looks like an approximation to a "proper" Mendelian ratio of 3:1. If all the parents were Yy (Y being yellow), we may expect the progeny to follow the proportions of YY:2Yy:yy. If the heterozygotes (Yy) cannot be distinguished from the homozygous YY, then Y is a simple dominant, and everyone is happy.

Cuenot was not happy, though, because among the 263 yellow mice he could not find even one that was homozygous for yellow (YY). Apparently Y is lethal when it is homozygous, which is not unique, so we need only remove the YY class of possible genotypes. That leaves us with 2Yy:yy. But that's a 2:1 ratio, or 67% yellow and 33% other colors.

The difference between 72.45 and 67% (actually, 66.66) is significant, even for a population of 363 mice.

Castle and Little repeated the breeding trials, and came up with 800 yellows and 435 non-yellows, or 64.77% yellows. That's closer!

Then, C&L added Cuenot's data to their own. Bingo! 66.52% yellows. Happiness prevailed.

But I am not entirely happy. If Cuenot could not get a proper Mendelian ratio with 363 offspring, how did Mendel do so well with similar numbers of pea plants? Furthermore, Mendel dealt with some di-hybrids (2 pairs of segregating traits) which should cause more difficulties than the simpler inheritance of Y and y.

A detail caught my eye in the report. C&L noted that yellow x yellow crosses averaged a smaller litter size than yellow x non-yellow: 4.71 for the former, 5.57 for the latter. If the difference were due entirely to the spontaneous abortion of YY embryos, we should expect a loss of 1 in 4 rather than of 1 in 5 or 6.

Apparently there is competition in the womb, and some fertilized ova do not develop into babies even when there is no lethal gene combination. So, when a YY is lost, its place is sometimes filled by a Yy or yy that would have been lost otherwise.

To what extent is competition in the womb influenced by the genotypes of the competitors? If Yy had some competitive edge in Cuenot's strain, they would displace the aborted YY embryos more often than the yy. The C&L strain, on the other hand, produced fewer replacements, and seems to have provided a very slight advantage to yy relative to Yy.

There is clear evidence in the data that the strains were actually different, or were raised in different conditions. Cuenot reported the litter size of yellow x yellow to be 3.38, and for yellow x non-yellow as 3.74. In this case, the loss of YY homozygotes did not reduce litter size so greatly — less than 10 percent compared with C&L's 15.5% (a 25% reduction would be expected).

Competitive advantage can vary with conditions, of course, so perhaps Cuenot had a weaker strain, or didn't feed his mice so well, and inadvertently gave the Yy heterozygotes a stronger competitive edge over the yy embryos in replacing aborted YYs. The Yy heterozygotes replaced most of the YY embryos that didn't survive — enough to make a Mendelist sit up and take notice.

In practical terms, the condition of the mother — or seed parent — can influence the types and proportions of offspring she produces, even with the same male (pollen) parent. If a female produces more ova than can develop into offspring, there may be competition for space and nourishment in the womb or pod or fruit, which may give one or another genotype a competitive edge. The result will be an excess of the favored type.

Castle and Little combined data collected at different times, under different conditions, with different strains in order to achieve an approximation of "good numbers". This is the method of the Mendelist — to go on adding and averaging until the numbers come out right.

Deviations from idealized Mendelian numbers should not be dismissed as "experimental error". There may be some useful principles hiding in the discrepancies waiting to be discovered and exploited.


Castle, W. E., and C. C. Little. 1910. On a modified ratio among yellow mice. Science, N.S., 32:868-870.

Originally posted on the Bulblist (10/7/2003)

Of Mice and Mendelism part 2

On Apr 11, 2002 I posted a note (Of Mice and Mendelism) regarding the curious inheritance of yellow coat color in mice. Cuenot published his study in 1905, Castle and Little followed up in 1910 with a report on their larger study. The inheritance of yellow coat color in mice is regarded as one of the classic demonstrations of Mendelian inheritance. However, after re-examining the data I concluded that this is really a classic demonstration of data falsification.

According to the standard interpretation, yellow coat color (Y) is dominant over non-yellow (y). Cuenot could not identify any specimens true-breeding for yellow (YY) and concluded that this gene is lethal when homozygous. Castle & Little agreed.

However, the numbers did not work out right. Cuenot mated yellow x yellow — presumably Yy x Yy and raised 263 yellows to 100 non-yellows, which does not agree with the theoretical ratio of 2:1. There were 63 yellows too many.

Castle & Little came up with 800 yellows and 435 non-yellows — a deficiency of yellows.

To make the numbers work out better, Castle & Little combined their data with Cuenot's — 1063 : 535, which works out almost perfectly (1.99 : 1).

I wrote:

"There is clear evidence in the data that the strains were actually different, or were raised in different conditions. Cuenot reported the litter size of yellow x yellow to be 3.38, and for yellow x non-yellow as 3.74. In this case, the loss of YY homozygotes did not reduce litter size so greatly — less than 10 percent compared with C&L's 15.5% (a 25% reduction would be expected)."

There is something very wrong with this "classic" demonstration, but at the time I could not figure out just what was going on. I speculated:

"Competitive advantage can vary with conditions, of course, so perhaps Cuenot had a weaker strain, or didn't feed his mice so well, and inadvertently gave the Yy heterozygotes a stronger competitive edge over the yy embryos in replacing aborted YYs."

Today (Oct 7, 2003) a rosarian friend emailed an article from the New York Times, A Pregnant Mother's Diet May Turn the Genes Around by Sandra Blakeslee, dealing with yellow coat color in mice.

It turns out that the trait originated when a virus (presumably) left a transposon (jumping gene) near the agouti gene, causing it to go into overdrive.

The agouti trait in rodents is the normal or wild type for many species. The hair is mostly black with a subapical band of yellow, which results in a neutral gray-tan. When the gene is overdriven the yellow band becomes the predominant color of the hair. But when the transposon is silenced, the mice are normally colored.

The trait is not always expressed, even when a mouse receives two copies of the transposon, since both may be silenced. Furthermore, if a mouse receives two copies of the transposon — one silenced and the other not — there is a battle of sorts over the silencing. The structure of the gene is not altered in any case, but the state (silenced or not) can change.

"Methylation is nature's way of allowing environmental factors to tweak gene expression without making permanent mutations, Dr. Jirtle said."

In addition, differences in nutrition can influence the states of genes.

"To see if extra methylation would affect the mice, the researchers fed the animals a rich supply of methyl groups in supplements of vitamin B12, folic acid, choline and betaine from sugar beets just before they got pregnant and through the time of weaning their pups. The methyl groups silenced the transposon, Dr. Jirtle said, which in turn affected the adjacent coat color gene. The babies, born a normal brownish color, had an inherited predisposition to obesity, diabetes and cancer negated by maternal diet."

My speculation that differences in diet might have played a role in the different ratios observed by Cuenot and Castle & Little was a good guess, but not quite correct. I was thinking in terms of competition between genotypes. In fact there was competition between gene "states" (silenced or not).

[Note: folic acid deficiency is supposed to be a "cause" of spina bifida in humans, but this research suggests that the condition may have a genetic basis that is negated by folic acid and other nutrients carrying methyl groups.]

We are now on safer ground discussing past observations that the health of parents — among plants as well as animals — can influence the hereditary expressions of traits among their offspring. The differences between related species (and between geographical races) can involve different patterns of gene silencing. If one parent is struggling to survive in the current habitat while the other is flourishing, it is not hard to guess which pattern of gene silencing will predominate among the cells of the hybrid offspring.

We may even speculate that nutritional deficiencies encountered by organisms in difficult habitats may result in the un-silencing of genes previously hidden by methylation, giving the illusion of a sudden increase in the rate of mutation. Actually, any change — for better or for worse — could disrupt the patterns of gene silencing. See the NY Times article for more information.

And because the "struggle" between silencing and non-silencing within a particular segment of DNA can continue until both copies have adopted the same state, segregation of expression can occur within the tissues of plant without segregation of physical genes. (Spontaneous silencing and spontaneous unsilencing also occur and are easily misinterpreted as "mutations".)

In the case of yellow mice it could make a great deal of difference whether the non-yellow parent possesses a silenced transposon or lacks the transposon. The external appearance might be the same, but the pattern of segregation (of expression) could be different.

For example, if Cuenot crossed yellow mice with wild types the absence of silencing in either parental line would give an almost Mendelian segregation of 3:1 (Cuenot got 2.6 : 1). The homozygous YY is not absolutely lethal, so the deficiency (not excess) of yellows was probably the result of spontaneous gene silencing.

And if Castle & Little worked with a more inbred strain — most of the non-yellows actually carrying silenced yellow "genes" — the tendency towards silencing would have been stronger, giving a greater deficiency of yellows (1.8 : 1). Castle later became famous for establishing inbred lines of mice for genetic experimentation.

Nutrition certainly plays a role, but we must also consider the ability of an individual to absorb and utilize the appropriate nutrients, which can have a hereditary basis. In such cases it should be possible to modify the ratio of yellow : non-yellow by selective breeding — pushing a strain towards a greater or lesser ratio. I read a report on an attempt to change the segregation ratio, but unfortunately the researcher died before he completed his study. His "friend" who was asked to continue the experiment found enough excuses for the discrepancies to dismiss the whole business in favor of ordinary Mendelism. Pity!

This also is pretty much what Prof. DeVries demonstrated with his study of Cockscombs (Celosia cristata) and twisted teasels (Dipsacus spp.). I was thinking about this on the way home from work today, and was delighted to find that my copy of DeVries' Species and Varieties: Their Origin by Mutation (1906) had arrived in the mail.

DeVries started with a florists' variety of cockscomb, then selected the worst (least crested) seedlings for a few generations. The strain changed from mostly crested with many beautifully fasciated specimens to mostly non-crested with only a few specimens showing small fasciated branchlets. Then he reversed direction. In a few generations he had restored the strain to its original state. I cannot imagine Mendelian model for this.

I have long suspected that the position of seeds within the clusters might have played a role in the degree of fasciation. DeVries did find that planting density (specimens per square yard) influenced the frequency of twisted specimens among his selected teasels, so (I reasoned) it is not unreasonable to suppose that the nutritional state of seeds would vary within a cluster. With the new information about nutrition and gene-silencing we have fewer reasons to doubt that the position of seeds within clusters — and even within fruit — may influence the expression of hereditary tendencies.

And I must mention that Naudin and his followers observed segregation of parental traits within the tissues of hybrids. Physical segregation does occur (resulting from somatic meiosis before or after spontaneous chromosome doubling), and frequently can be observed as twin sports. Other cases may be due to changes in gene silencing.

Many "mutations" found in hybrids and their offspring are no doubt the results of silenced genes being called into expression when brought together with non-silenced counterparts; or non-silenced genes becoming silenced.

How many other classic demonstrations of Mendelian segregation are also illusory? I can't say. But it is time to drop the old dogma and get back to unprejudiced experimentation.

Originally posted on the Bulblist  (10/11/2003)

Heredity and Nutrition

A few days ago Peter Harris forwarded a New York Times article (A Pregnant Mother's Diet May Turn the Genes Around by Sandra Blakeslee), thinking it would interest me. Boy, howdy! I haven't thought of much else since I read it.

Simply stated, yellow mice carry a transposon — a bit of DNA inserted by a virus (probably) — immediately adjacent to the Agouti gene. Ordinarily the Agouti gene is responsible for a small yellow band just below the tip of each hair. When the hair is black — the normal condition — the overall effect is a neutral gray-tan. But the transposon forces the Agouti gene into overdrive, turning the hairs all yellow. In addition, yellow mice are strongly inclined towards obesity, diabetes and cancer.

However, when the transposon is silenced by methylation, the Agouti gene returns to its normal level of activity and the carrier is brown (in the strain studied), and not susceptible to obesity, diabetes or cancer.

Another oddity of this strain is that most of the offspring of yellow mice are yellow, but a few are brown. The state of the transposon — silenced or not — determines the color of the offspring, but silencing does not necessarily remain attached to the chromosome.

Dr. Randy Jirtle wondered if nutrients rich in methyl groups might influence the state of the transposon. He fed yellow females vitamin B12, folic acid, choline, and betaine before they were impregnated and throughout gestation. Most of the offspring born to these well-fed yellow mice were brown with no tendency towards obesity, etc.

I have a special interest in this case because a year and a half ago I wrote a brief article on the subject, arguing that the 1910 paper by Castle and Little on the inheritance of yellow coat color was flawed. Cuenot (1905) did the first study, but came up with numbers that were far from Mendelian expectation. Castle and Little also came up with bad numbers, but in the opposite direction. By combining Cuenot's data with their own, they got very close to the perfect Mendelian ratio. That looked pretty convincing to anyone who wanted to be convinced, but there was a troubling detail. The average litter size for Cuenot's mice was substantially lower than Castle and Little observed. This convinced me that either different strains were used in the two studies, or the mice were fed differently. In either case, combining the data was a bad idea. And now there is solid proof and a definite mechanism.

The upshot is this: heredity does not always fit Mendel's deterministic model. Alternative traits are not necessarily due to structural differences in genes. They can result from differences in the state of genes. The states can change, but in some cases (probably many) the state is determined immediately following fertilization, or within a few cell divisions.

A well-known example of this can be seen in calico and tortoise shell cats. The females inherit two genes for color — one for orange, the other for black. These genes are located on the X chromosomes, so males receive only one copy. Since only one X chromosome is allowed to function in females, the other must be silenced. But in this case the silencing occurs fairly late in development, and randomly. Thus, some parts of the cat are colored orange or yellow, while others are black or gray. The irregular white pattern of calicos is an unrelated trait.

Yellow coat color, or the alternative brown, must be determined earlier because the mice are uniformly colored. Whether a given mouselet is yellow or brown is greatly influenced by the availability of methyl groups in the mother's diet. If she receives an abundance, most of the offspring will be brown. But a lesser quantity allows a greater degree of randomness — and more yellows. The position of the embryo within the womb probably influences how well nourished it is, and thus whether it will be yellow or brown.

There are many instances of traits with similar behavior in other animals and many plants. Devries wrote about these "ever-sporting varieties" in Species and Varieties (1906). He demonstrated that the seed parent's nutritional status can influence the expression of specific traits in the offspring. Furthermore, the position of seeds within the fruit, the position of fruits within clusters, and the location of clusters on the plant also can influence the degree of expression of certain traits.

Devries found a couple of clover plants in Holland, each bearing a few leaves with extra leaflets. After a few years of selective breeding, the strain routinely bore leaves with 4, 5, 6 and rarely 7 divisions.

"I divided a strong individual into two parts, planted one in rich soil and the other in poor sand, and had both pollinated by bees with the pollen of some normal indviduals of my variety growing between them. [Clover is self-sterile.] The seeds of both were saved and sown separately, and the two lots of offspring cultivated close to each other under the same external conditions. In the beginning no difference was seen, but as soon as the young plants had unfolded three or four leaves, the progeny of the better nourished half of the parent-plant showed a manifest advance. This difference increased rapidly and was easily seen in the beds, even before the flowering period."

Devries also drew attention to differences in nourishment of seeds within an undivided plant. Double-flowered stocks produce two distinct forms, a fertile single and a sterile double, in roughly equal proportions. Selective breeding did not alter the proportions.

"Now if one half of the seeds gives doubles, and the other half singles, the question arises, where are the singles and doubles to be found on the parent-plant?

The answer is partly given by the following experiment. Starting from the general rule of the great influence of nutrition on variability, it may be assumed that those seeds will give most doubles, that are best fed. Now it is manifest that the stem and larger branches are in better condition than the smaller twigs, and that likewise the first fruits have better chances than the ones formed later. Even in the same pod the uppermost seeds will be in a comparatively disadvantageous position. This conception leads to an experiment which is the basis of a practical method much used in France in order to get a higher percentage of seeds of double-flowering plants.

This method consists in cutting off, in the first place the upper parts of all the larger spikes, in the second place, the upper third part of each pod, and lastly all the small and weak twigs. In doing so the percentage is claimed to go up to 67-70%, and in some instances even higher."

In better controled experiments all the pods were allowed to ripen before the above method was applied. The seeds that ordinarily would have been discarded gave only 20-30% doubles.

Another technique for increasing the proportion of doubles was to keep the seeds for 2 or 3 years before planting. Many of the seeds died, but the survivors gave a higher percentage of doubles — again indicating that better fed seeds were more likely to yield double flowers.

One point that concerns me is the assumption that desirable qualities — desirable to gardeners — are necessarily associated with high fertility of the soil, or positions on the plant where nutrients are most readily available.

Ivan Michurin, the great Russian plant breeder, started his work with the assumption that the finest qualities of cultivated fruit could be brought out only by high culture — rich soil and abundant moisture. He crossed the best foreign varieties with locally adapted forms, then raised the seedlings in the best possible soil. Most of the seedlings grew strongly at first, but soon were killed by the rigors of the Russian climate. He promptly packed up and moved his nursery to a site with poor soil, and found that the new crop of seedlings were more resistant to the harsh climate. Some expressed the desirable qualities of the foreign varieties, so he knew he had made the right choice.

The point is that by selecting the best qualities among plants grown in optimal conditions, we are favoring a hereditary connection between desirable qualities and a requirement for optimal conditions. Rosa spinosissima, for example, is reportedly very floriferous when grown on poor sandy soil, but less so on rich soil. This demonstrates that "poor" conditions are not absolutely linked to poor development of desirable qualities.  It strikes me as very counterproductive to breed for hardiness and the ability to bloom well in ordinary gardens, but raise our seedlings in greenhouses or outdoors in rich soil.

Speculation aside, there is clear evidence that how a plant is grown can influence the expression of certain hereditary traits in the offspring. And there is equally clear evidence that the hereditary expression among the progeny can be influenced by the position of seeds within a fruit, of the fruit within a cluster, and of the cluster on the plant. Taking Michurin's research into account, we may expect that other hereditary expressions can be modified during the growth of the seedlings — more or less permanently — particularly when they are hybrids. Experiments are in order!