An Alternative Analysis on Nilsson-Ehle’s Hybridization Experiment in Wheat

In this paper, an analysis on Nilsson-Ehle’s hybridization experiment in wheat was done by means of self-fertilization method along with the pericarp inheritance. It showed that because seeds of wheat were coated with 2n tissues of mother’s body, the grain colors were determined by mother’s genotype. The color of the F1 grains in this experiment was old red. The phenotypes of the F2 grains were uniformly medium red and did not segregate. Grains in the F3 generation segregated in the ratio 6 red (varying intensities of red) to 1 white with a definite probability respectively. This is the consequence of additive effect of 3 gene pairs and belongs to discrete distribution rather than continuous distribution. Therefore, the multiple-gene hypothesis based on this experiment cannot solve the continuous variations in inheritance of quantitative characters.


Introduction
In early 1900s Nilsson-Ehle conducted hybridization experiments in red seed variety and white seed variety in wheat.On the basis of this study, the famous multiple-gene hypothesis was founded and used to explain the continuity of quantitative characters by William Bateson, G. Udny Yule and other geneticists [1].This hypothesis has become a classic theory of the inheritance of quantitative character [2] and has been popular so far over the world.In this study, an alter-native analysis was done for this experiment and it pointed out the misjudgments of genetics community in the world and drawbacks of this hypothesis.

Data Sources and Analysis Methods
In 1900 Nilsson-Ehle found a wheat variety with old red seed coat in Northern Sweden and crossed it with a white seed variety later on.He got 78 F 2 plants out of a total of 64 plants of the theoretical expectation.8 segregating the F 3 red plants and white plants in the ratio 3:1, 15 segregating the F 3 red plants and white plants in the ratio 15:1, 5 segregating the F 3 red plants and white plants in the ratio 63:1, the F 3 of 50 plants were all red plants, the F 3 of 0 plants were all white plants [3].
Among them the ratio 63:1 should be identical with the expected ratio of plants producing red grains and white grains in the F 2 generation.This is the symbol of inheritance of 3 gene pairs.Because seeds in wheat are coated with 2n tissues of mother's body-pericarp [4] [5], the grain colors rely on the pericarp inheritance and are determined by mother's genotypes [6].According to inheritance of 3 gene pairs, the above data would be tentatively analyzed by means of self-fertilization method along with the pericarp inheritance.

The F2 Genotypes and Seed Phenotypes in Inheritance of 3 Gene Pairs in Crops
The hereditary manners in wheat and other crops are the same, but segregation timelines of their seed colors are different.

The F2 Genotypes and Their Categories, and Seed Phenotypes in the Inheritance of 3 Gene Pairs in Garden Pea
When red seed variety with 2 gene pairs was crossed with white seed variety in wheat, the variation in grain color was explained with the help of additive effect [7].In additive effect, two kinds of dominant genes exist simultaneously and alone, characteristics controlled by them are similar [8].Different reds in wheat grains are similar characteristics.If additive effect was be expanded to inheritance of 3 gene pairs, for example, the inheritance of 3 gene pairs in garden pea would be studied based on this effect.Regarding the results of Nilsson-Ehle's experiment, according to the additive effect, the F 2 genotypes from the inheritance of 3 gene pairs in garden pea [8] can be classified into the following 5 categories: 1) homozygotes with 3 pairs of recessive genes, 2) heterozygotes with 1 pair of heterozygous genes, 3) heterozygotes with 2 pairs of heterozygous genes, 4) heterozygotes with 3 pairs of heterozygous genes, 5) individuals containing 1 -3 pairs of homozygous dominant genes, by adding one dominant gene at a time (Table 1).
Phenotypes of the F 2 seed colors in garden pea: Dividing generation in crops begins with seeds.The seeds produced by maternal parents used in crossing and Table 1.Categories of the F 2 genotype from inheritance of 3 gene pairs in garden pea.pairs in garden pea is known.The above analysis is only used to describe the classification of genotypes considering the additive effect from 3 gene pairs.In fact, the seed color in garden pea is independent inherited without interaction of genes.And the round yellow and wrinkled green of seeds in garden pea [9] are the traits of 2n tissue of embryo-cotyledon [8] [10].Phenotypes of the F 2 seed colors are determined by the F 2 genotypes and in the second hybrid generation the seed colors segregated 3 yellow and 1 green [9].

The F2 Genotypes, Their Categories and Grain Phenotypes in
Crossing with Red Seed Wheat of 3 Gene Pairs In 1909, Nilsson-Ehle used an old red seed variety as mother parent and crossed it with white seed variety [1] [3] [8] to produce the F 1 old red grains, genotype of which is r 1 R 1 r 2 R 2 r 3 R 3 .These grains were sown, and the F 1 plants grown from them produced medium red grains (F 2 ) by self-fertilization [6] (Figure 1).
As additive effect in garden pea mentioned above, the F 2 genotypes in wheat are classified, so that the classification is consistent with the genotype category in garden pea.Because alleles at 3 loci in wheat have equivalent effect (R 1= R 2= R 3 , r 1= r 2= r 3 ) [8], the dominant genes and the recessive genes in garden pea are replaced by R and r, the results obtained are shown in Table 2.
The actual numbers of the F 2 plants are 0, 8, 15, 5 and 50, which fitted with their expected value in 5 genotype categories in Table 2 [11].This indicates that the old reds of seed coat of the variety are indeed determined by 3 pairs of nuclear genes, effect of which is additive, and nuclear genes are segregated normally.
According to the number of R gene, in the F 2 there are 7 types of genotypes that show the ratio 1:6:(12 + 3):(8 + 12):15:6:1 representing binomial distribution.They would correspond with the phenotypes in grain colors in the subsequent hybrid generation in wheat: 1) white, 2) very light red, 3) light red, 4) medium red, 5) dark red, 6) very dark red, and 7) old red.
The phenotypes of the F 2 grain colors in wheat: 1) In Nilsson-Ehle's hybridization experiment, "the grains (the F 2 ) produced by the F 1 plants were medium Applied Mathematics  red [6]".2) When a parent was red seed variety with a single gene pair, all the seeds produced by the F 1 plants were lighter red 1 .The process may be diagrammed as follows (Figure 2).
So, the color of the grains (F 2 ) produced by the F 1 (rRrRrR) in Nilsson-Ehle's hybridization experiment is uniformly medium red, including the grains with a genotype of rrrrrr, and does not segregate.
Like the old red of the F 1 grains, the medium red of the F 2 grains is also determined by mother's genotype [6].This is due to the pericarp inheritance.Tang Kai-dong, Yang Xue-ming and Yao Jin-bao etc. also found this feature in different cultivars of wheat [12] [13] [14].This is neither maternal inheritance nor maternal effect.
There were two misunderstandings in current research community on the inheritance of grain colors in wheat.Some of them considered the inheritance of grain colors in wheat was the same as that of seed colors in garden pea.They were determined by genotype of 2n tissue of embryo.Like garden peas, the segregation of the grain colors in wheat occurred in the second hybrid generation [8] [9] [15] [16].This is fabricated.The other argued that, the pathway was from Thereby, the grains were moved forward by one generation, and the F 3 grains with different colors were said to be the traits of the F 2 [1].This is also improper.

Phenotypes of the F3 Grain Colors in Wheat Representing Segregation
The grains produced by the F 1 plants above were sown and 78 F 2 plants grew up, which distributed at random.They produced the F 3 grains which represented different colors.For convenience reasons, according to the genotype classification in Table 2, the F 2 plants were divided into 5 categories (Figure 3).In Figure 3, there are the actual number of the F 2 plants, genotypes and their theoretical members, and as described in the previous section, standing for different color of the F 3 grains.
The phenotypes of the F 3 grain colors: 1) "The grains produced by the F 2 plants were various shades of red and white" [6].Nilsson-Ehle did not obtain the F 2 plant producing pure white grains, however, from 5 F 2 plants segregating the  F 3 plants producing red grains and white grains in the ratio 63:1, we knew that there could be such a F 2 plant.2) When a parent was red seed variety with a single gene pair, the F 2 plants producing white grains, lighter red grains and red grains were in ratio 1:2:1, in another word, the ratio of the grains of different colors was 1:2:1 in the third hybrid generation 2 [1].So the segregation in the grain colors in Nilsson-Ehle's hybridization experiment deferred a generation and in the third hybrid generation there were various shades of red grains and white grains.According to data in Table 2, their theoretical ratio should be 1:6:15:20:15:6:1, ranging from white to old red.This is the inheritance of nuclear genes and another type of delayed inheritance which is different from that of silkworm eggs.
According to the relevant information in Figure 3 and the relevant theoretical values of the F 2 plant distribution in plants containing the calculated components were shown in Table 3.
Here the actual numbers of the F 2 plants may differ from the real numbers.
However, according to the theoretical distribution of the F 2 plants corresponding to genotype in Table 2, there should be 7 types of actual plants, and when the number of experimental plants increases, they will approach the expected values and have certain fixed probability.

The Above Analysis Being Verified by the Segregation of the F4 Grain Colors
Mendel verified the Law of Segregation and the Law of Independence by the help of self-fertilization method [8].The above analysis can be also verified by the method.
The F 3 grains produced by 78 F 2 plants were sown in plant-to-row nursery and 78 rows of the F 3 plants grew up and produced the F 4 grains.Like the previous section, according to genotype categories, the F 3 plants would be divided into 5 categories (Figure 4).
Phenotypes of the F 4 grain colors: "The F 4 grains produced by offspring of F 2 plants segregated reds and whites in the ratio 3:1, 15:1 and 63:1" [6].But, these are not complete.From the analysis of plant-to-row nursery of F 3 plants we can obtain the following data: The self-fertilized results are not in contradiction with the data obtained by Nilsson-Ehle.It is just that the latter described the wheat propagation as viviparous process, and the F 4 grains were moved to the F 3 generation.This is due to the limitation of historical conditions.It is the fact that these F 2 plants produced from these seeds are the F 1 .The seeds produced by the F 1 plants have been the starting point of the F 2[6] [8].The inheritance of 3 gene

Figure 4 .
Figure 4. Plant-to-row nursery of the F 3 plants.

Table 2 .
The F 2 genotype categories in crossing with red grain wheat of 3 gene pairs.
plants to make the wheat propagation like viviparous species, which skipped forming of the pericarp originating from 2n tissues of mother's body.

Table 2
, what can be calculated out was 6, 22, 15, 6, 1 plants producing light red, medium red, dark red, very dark red and old red grains out of 50 F 2 plants producing red grains.Numbers of the F 2 actual

Table 3 .
The F 3 grain phenotype and the F 2 plant distribution.