Regarding ancestry

[matt_lustig]

This post is partly a result of a personal and professional interest in genetics (I’m a math teacher but formerly taught science, including genetics concepts).

We understand that in general, when there are offspring of two parents with equivalent ploidy (i.e. the offspring of 2 diploid parents), then those offspring will generally receive 1/2 of their chromosomes from each parent…exceptions such as canina roses aside. As an extremely simple example, my wife and I are obviously both diploid, and our children received 23 chromosomes from my wife and 23 from me.

So it is easy to say that an offspring is genetically “1/2 from each parent.” However, in my experience plant breeders sometimes make the error of assuming that the descendant of hybrids is genetically 1/4 from each grandparent. For instance, if a rose has 4 diploid grandparents, one of which was R. palustris, then that rose might be said to be 25% palustris.

This is, in point of fact, not necessarily or even generally accurate. In reality, a parent passes on to his/her children a random assortment from each set of chromosomes (i.e. in humans 1 each of each chromosome “pair”), and therefore an offspring may end up being anywhere from 0-50% from any particular grandparent (although the total of course still must = 100%!). Essentially, the father has no way of equally dividing the chromosomes in the sperm cell between those chromosomes from paternal grandfather and paternal grandmother, and the mother has no way of equally dividing the chromosomes in the egg cell between those from maternal grandfather and maternal grandmother. To extend on the earlier rose example, if a rose has 4 diploid grandparents, one of which was R. palustris, then that rose does not necessarily have to be 25% palustris–that rose actually might be anywhere from 0-50% palustris. With crossing over of genetic material, it is unlikely that the actual percentage will be either of those extremes, but there is no factual reason to assume that it will be exactly in the middle either.

I used to be involved with the board of a state chapter of The American Chestnut Foundation, which is involved in producing advanced hybrids similar to the American chestnut species. Anyhow, that foundation is essentially breeding 2 species of chestnuts together in this manner:
Generation 1: Species A x Species B
Generation 2: (Species A x Species B) x Species A
Generation 3: [(Species A x Species B) x Species A] x Species A
and so on.

Sometimes the foundation would accurately describe this process (i.e. https://ecosystems.psu.edu/research/chestnut/information/path-resistance), but sometimes discussions would get a bit factually sloppy–such discussions might accurately state that Generation 1 trees must be 50% genetically Species A, but then inaccurately give the impression that generations 2 and 3 must be 75% and 87.5% genetically Species A. In reality, trees from Generation 2 could be anywhere from 50-100% genetically Species A (75% only being an expected average, assuming no selective pressure) and Generation 3 could again be anywhere from 50-100% (87.5% again only being an expected average). Claims of definite percentages might be a useful fiction in describing such breeding to the general public, but are far from a scientific guarantee in actual genetic terms.

Anyhow, something to consider from both a science and breeding standpoint.

Matt

[Rob_Byrnes]

Great information Matt.

[davidzlesak]

Great point Matt! The range of ancestral contributions as we move forward in generations sure makes the possibilities and what we can find interesting.

[Karl_K]

I have spent too much time reading the early neo-mendelists, and have seen that some of them forgot that “on average” does not mean that every small batch of seedlings must exhibit precise proportions. When we drop four coins on a table, we should not assume that they will come up 2 tails and 2 heads every time. Mendel did not understand that fact. I also remember some foolish teachers (back in the day)__ who assumed that a class of only seven or eight students could be squeezed onto “the curve”.

It is also useful to recall that the appearance of segregating phenotypes does not prove that genes are also segregating. For instance, hybrids of the trifoliate orange with the common orange may be trifoliate, unifoliate, unstably intermediate (one or two or three leaflets, scattered), or may even have pinnate leaves with 5 leaflets. This sort of apparent segregation does not prove that the trifoliate orange is heterozygous for unifoliate-ness. Nor is it evidence that common orange carries special genes for pinnate leaves.

[Thompson and Knott] … report that certain seedling populations of petunia and other plants gave a uniform response with respect to growth and flowering under one temperature and photoperiod but showed “segregation” under other conditions. They ascribe this to genetic differences that are not apparent under one set of conditions but do appear under other conditions. Since varietal differences of this kind are common, there seems to be no > a priori > reason why this explanation might not be accepted. In fact this falls directly in line with other work. The only difficulty in accepting it lies in the fact that similar “segregation” was observed among cuttings obtained from the parent of the seedlings. It may be that differences in the initial size of the cuttings and some lack of uniformity in their handling resulted in variability among the cuttings grown under abnormal conditions of temperature and photoperiod that would simulate differences due to genetic diversity.

http://bulbnrose.x10.mx/Heredity/YarnellPlasticity1942.html

The same principle seems to be at play with Rosa omeiensis and sericea. I have read that plants growing in the native habit may bear flowers with four petals or with five. Each plant specializes in one or the other. Hurst (1928) wrote, “My observations show that pentamerous flowers frequently occur in both sericea and ome_i_ensis, indeed in one instance a tetramerous bush of the former at Cambridge after a severe pruning was almost entirely pentamerous in the following year.”
http://bulbnrose.x10.mx/Roses/Hurst/HURST5.HTM

I have seen flowers of Rosa sericea pteracantha with 4, 5, 6, 7,…10 and more petals some years. In fact, I have seen multiple petal counts open at the same time and on the same cane.
http://bulbnrose.x10.mx/Roses/Rose_Pictures/Rosa/R_pteracantha.html

In some cases this apparent segregation involves differences in gene silencing. In some cases the maternal allele is expressed while the paternal is silenced. Or the pattern may be reversed. Or both alleles may be expressed. Such cases may look Mendelian, but are not.
http://bulbnrose.x10.mx/Heredity/King/Election-Variegation.html

[ldavis]

Karl, I’m not sure I agree with you about Mendel. He studied physics at a very good university in Vienna and had a good grasp of the statistics of his time. But they were Bayesian. If you know a prior probability, you can with some reasonable confidence predict the next outcome. Like the probability that the sun or moon rises tomorrow at a predicted time. So you collect data until you are within the appropriate confidence level. Mendel selected just a few traits, whose behaviors he already knew, to demonstrate a model of independent factors. The demonstration was convincing. It was not unbiased. It did not explain the patterns of seedlings coming from apomixis in hawkweed, Hieracium, which was another plant he tried to study.

Mendel’s purpose and approach was very different from Fisher’s rigid statistics of sampling where everything is presumed to be totally unknown until after the experiment. Fisher’s statistical approach did not exist in Mendel’s day. Some of the probability distributions patterns that he used depended on mathematics that was not worked out yet in Mendel’s day. If you read the works of “Student” (William Sealy Gosset) you will find a very interesting alternative to Fisher. He was a great empiricist and the inventor of process control charts amongst other things. Gosset was a first-rate mathematician who developed the critical test that Fisher, and his acolytes used for testing probabilities. Gosset was strongly influenced by Karl Pearson and the biometricians. His distribution was derived from their quantitative measures of things like finger size. Fisher out-lived him and because he was in an important agricultural experiment station, was able to sell his approach. But for looking at genetic traits rather than populations it is really excessively laborious.

[Karl_K]

Larry,
I refer specifically to Mendel’s guess that 10 seedlings would be enough to determine whether a purple flowered F2 seedling was true-breeding or “hybrid”. On the scale of his experiments, 24 seedlings should have been raised.

Suppose he raised 400 F2 seedlings and every detail worked out perfectly as he imagined. 100 would be white flowered, and of no further interest. The remaining 300 would include 100 homozygous purples (PP) and 200 heterozygous (PW). By raising only 10 seedlings from each purple, he would have misidentified about 5.6% heterozygotes as homozygotes. This would give a ratio of about 111 PP : 189 PW : 100 WW.

By an amusing coincidence, it was Carl von Naegeli who challenged Mendel to work with hawkweeds. Carl Correns later studied under Prof. von Naegeli.

Also, Erich von Tschermak’s grandfather, Eduard Fenzl, taught botany to Mendel.

[ldavis]

Yes, Karl, you are absolutely correct on the likelihood in small samples. But until Gosset, no one knew that, at least in a simple way. And Mendel only looked for regularity of pattern, not quantitative evidence. For the large majority of small samples he would be close enough to convince himself and readers.

Years ago I set up a sampling system that allowed one to draw samples averaging 10 beads from a coffee can of two colors of beads mixed in particular ratios. It takes a very large number of such samples to distinguish 3:1 from 4:1 distributions with high statistical confidence. Both students and their teachers struggled with this reality of statistical sampling. Even 2:1 is not totally obviously different from 3:1. But if the distribution for say 5 samples is somewhere reasonable, it is easy to accept the 3:1 ratio, if the 4:1 is not an option under consideration.

BTW, my plant breeding colleagues still use very small samples to sort homo and hetero seedlings. For a recessive, if even 1 of 4 seeds shows heterogeneity, then the plant is a het. But of course they miss a significant fraction of hets, that way. They have to screen them out in the next generation or do a confirmatory screen on the “homozygous”. If they have time they may run samples of 10. But that’s way more than 2x the work of a double stepwise screen. Mendel had a small garden and limited time.

[Karl_K]

I once found an amusing statement that I foolishly failed to document. It was shortly after Fisher tried to explain how Mendel’s numbers were too good to be quite believable. Some dolt wrote to the journal to “explain” that Mendel’s numbers were good because his theory is TRUE.

The guy really missed the point, but was not alone. Cuenot (1905) studied the inheritance of yellow coat color in mice, but could not get the numbers to work out. Even after assuming that the heterozygous were lethal, he got too many of them. Castle & Little (1910) also failed to get “good” numbers, but they got too few yellows. However, by combining Cuenot’s numbers with their own, they achieved “almost perfect” Mendelian numbers. There was much celebration among the Mendelists of the day.

Alas, this was not a Mendelian phenomenon at all. A transposon is involved, and differences in nutrition (methyl donors) played a major role in the proportions.

There was something of an obsession. Jones (1928) wrote, "… even when deficient or excessive ratios are obtained, they have been obscured by the prevalent practice of compiling data from many individuals of different pedigree and in successive generations in order to obtain as large numbers as possible. This procedure serves its purpose well. The thoroughgoing Mendelianist seldom fails to obtain ‘very good ratios.’ "
http://bulbnrose.x10.mx/Heredity/JonesSelectivePollination/jones3.htm

Fortunately, not everyone was engaged in stalking the wild unit character and massaging their numbers. For instance, Kid and West (1918) introduced the subject of Physiological Predetermination, which is another important aspect of inheritance.
http://bulbnrose.x10.mx/Heredity/KiddWest/KiddWestSeeds1920/KiddWestSeeds1920.html

[Karl_K]

I don’t want to come off as anti-Mendel. He did what he could with what he had. It was not his fault that later people would elevate him beyond his merit. He never claimed to be the father of genetics. He was not the first “scientific” plant breeder. And it was not his fault that he became the virtual patron saint of the eugenicists.

One common mistake was to suppose that Mendel’s paper was completely original because there were no footnotes or citations, the work must have been entirely original. Not so. Mendel published the unedited text of a lecture he had given, describing his experiments … many based on earlier work by other people. In fact, we do know that Mendel kept up with contemporary research, especially that of Naudin. When Correns contacted Nageli’s family, he was allowed to take what he wanted of the late prof’s papers, including Mendel’s correspondence.

Mendel should be understood in its proper historical context. For example, Nageli has been reported to be the first person to have observed the division of a chromosome. That is relevant to heredity, but its relevance was yet to be understood.

And Naudin discussed segregation and reassortment. That’s where Mendel read of it. Of course, Naudin, who worked with species, did not find the magic ratios that made Mendel famous.

Wichura (1866) also made an important observation: “In pure willows the mother cells of the anthers are of equal size, and divide, with almost mathematical precision, into four tetrahedric pockets, in which the contents form yellowish shining pollen-grains of exactly the same size; while in hybrids the course of development is far less regular, and subject to the above-mentioned derangements.”
http://bulbnrose.x10.mx/Heredity/WichuraHybrids/WichuraHybrids1866.html

The relevance of Wichura’s observation, as evidence of reduction division, would not be fully understood for many years.

Going through my notes, I came across something I wrote back in 2000:

In the March-April issue of American Scientist there is an interesting article, Tracking Down a Cheating Gene, by Barry Ganetzky, pp. 128-135.

The article deals with the 1956 discovery of non-Mendelian inheritance in fruitflies. The females were homozygous for white eyes, the males heterozygous red/white. A few of the pairs produced only red-eyed offspring. Subsequently it was estimated that 3-5 percent of wild > Drosophila melanogaster > carry a gene SD (segregation distorter) which gives the chromosome carrying it an advantage.
https://www.americanscientist.org/sites/americanscientist.org/files/200571105641_306.pdf

The author went on to discuss just how common segregation distortion really is, and concluded that what we commonly regard as “normal” (mendelian) segregation is really due to the averaging of numerous plus and minus distortions.

1956! It took that long for the neo-mendelists to recognize the existence of a common phenomenon. But I have older reports. For instance, Dr. W. Van Fleet (1902) wrote an article on gladiolus breeding.

“All growers of Gladioli of the > Gandavensis > type know there is a constant preponderance of the red varieties. The white and light colors tend to degenerate with greater or less rapidity, while the reds increase in number and maintain their vigor. So rapid and complete is the reversion in some instances as to amount to wholesale atavism. Considerable numbers of a choice > Gandavensis > variety have, propagated for generations in the usual manner from cormels, changed in a season so as to closely resemble the typical red and yellow > Gandavensis> . This seems to confirm Mendel’s theory of dominant and recessive factors in all hybridizations. Taking > psittacinus > as the dominant, > oppositiflorus > acts in most instances as the recessive type, and tends rapidly to efface itself in favor of its virile partner during reproduction by seeds, and to a lesser degree during extension of a given hybrid plant by cormel or bud propagation.”

This illustrates some of the confusion regarding terminology, while also showing an aspect of heredity that does not fit the mendelian model.

Bradley (1906) described another case of non-mendelian inheritance in Hippeastrum.
http://bulbnrose.x10.mx/Heredity/BradleyAntipode1906.html

The fact that non-mendelian segregation occurs was apparent to anyone who bothered to look. Too few did.

[RBaxter]

Don’t forget tetraploids. Tetraploidy further complicates even the Mendelian aspects

Crossing two heterozygotes for homozygosity of one trait in diploids gives you a 1 in 4 chance.
Crossing two heterozygotes for homozygosity of one trait in tetraploids gives you a 1 in 16 chance.

Crossing two heterozygotes for homozygosity of two traits in diploids gives you a 1 in 16 chance.
Crossing two heterozygotes for homozygosity of two traits in tetraploids gives you a 1 in 256 chance.

With tetraploids the Mendelian math is like you are always crossing for an extra non-existing trait.

Starting with four parent tetraploid parent roses, the possibility of getting all of your desired traits homogeneously are mind-blowingly slim. This makes the work y’all have done even more impressive to me.

Baxter

[Karl_K]

Baxter,
This can become even more non-mendelian when tetraploids contain homeologous chromosomes … those that can pair up, but prefer not to.

For example, a tetraploid raspberry mated with a tetraploid blackberry will yield tetraploid hybrids that combine the traits of both parents. The F2 generation will be much the same, varying about as much as seedlings from a selfed species, with no tendency to return to with of the parental types. Same with the F3 and so on.

The 14 chromosomes from the raspberry parent usually do not pair off. But when their only options are blackberry chromosomes, the raspberry chromosomes get over their differences. Likewise for the blackberry chromosomes,

Iris pumila, a dwarf bearded species, is a tetraploid (X=9). Most of the tall bearded species (pallida, variegata, germanica, etc.) are diploids (X=11), but tetraploid garden varieties are now common. Crossing Pumila with a tetraploid tall bearded type will give intermediate bearded seedlings. These will breed true to their intermediate bearded character, though varying in other qualities.

Again, there is no reversion to the parental types, because Pumila chromosomes prefer to align with their “own kind”. And as confused as the TB varieties are, being derived from multiple diploid species, their chromosomes still get along together better than they would with Pumila chromosomes.

Most Rosa polyploids are allopolyploids. However, R. macrophylla var. Korolkowii is an autotetraploid. Crossing it with a tetraploid selection of R. multiflora (for example) would give allotetraploids that should breed at least as true as any natural tetraploid species.
Karl