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Mendel's First Law of Genetics (Law of Segregation)
Genetic analysis predates Gregor Mendel, but Mendel's laws form the theoretical basis of our understanding of the genetics of inheritance.
Mendel made two innovations to the science of genetics:
- developed pure lines
- counted his results and kept statistical notes
Pure Line - a population that breeds true for a particular trait [this was an important innovation because any non-pure (segregating) generation would and did confuse the results of genetic experiments]
Results from Mendel's Experiments
Parental Cross F1 Phenotype F2 Phenotypic Ratio F2 Ratio Round x Wrinkled Seed Round 5474 Round:1850 Wrinkled 2.96:1 Yellow x Green Seeds Yellow 6022 Yellow:2001 Green 3.01:1 Red x White Flowers Red 705 Red:224 White 3.15:1 Tall x Dwarf Plants Tall l787 Tall:227 Dwarf 2.84:1 Terms and Results Found in the Table
Phenotype - literally means "the form that is shown"; it is the outward, physical appearance of a particular trait
Mendel's pea plants exhibited the following phenotypes:
- - round or wrinkled seed phenotype
- - yellow or green seed phenotype
- - red or white flower phenotype
- - tall or dwarf plant phenotype
Seed Color: Green and yellow seeds.
Seed Shape: Wrinkled and Round seeds.
What is seen in the F1 generation? We always see only one of the two parental phenotypes in this generation. But the F1 possesses the information needed to produce both parental phenotypes in the following generation. The F2 generation always produced a 3:1 ratio where the dominant trait is present three times as often as the recessive trait. Mendel coined two terms to describe the relationship of the two phenotypes based on the F1 and F2 phenotypes.
Dominant - the allele that expresses itself at the expense of an alternate allele; the phenotype that is expressed in the F1 generation from the cross of two pure lines
Recessive - an allele whose expression is suppressed in the presence of a dominant allele; the phenotype that disappears in the F1 generation from the cross of two pure lines and reappears in the F2 generation
- The hereditary determinants are of a particulate nature. These determinants are called genes.
- Each parent has a gene pair in each cell for each trait studied. The F1 from a cross of two pure lines contains one allele for the dominant phenotype and one for the recessive phenotype. These two alleles comprise the gene pair.
- One member of the gene pair segregates into a gamete, thus each gamete only carries one member of the gene pair.
- Gametes unite at random and irrespective of the other gene pairs involved.
Mendelian Genetics Definitions
- Allele - one alternative form of a given allelic pair; tall and dwarf are the alleles for the height of a pea plant; more than two alleles can exist for any specific gene, but only two of them will be found within any individual
- Allelic pair - the combination of two alleles which comprise the gene pair
- Homozygote - an individual which contains only one allele at the allelic pair; for example DD is homozygous dominant and dd is homozygous recessive; pure lines are homozygous for the gene of interest
- Heterozygote - an individual which contains one of each member of the gene pair; for example the Dd heterozygote
- Genotype - the specific allelic combination for a certain gene or set of genes
Using symbols we can depict the cross of tall and short pea plants in the following manner:
The F2 generation was created by selfing the F1 plants. This can be depicted graphically in a Punnett square. From these results Mendel coined several other terms and formulated his first law. First the Punnett Square is shown.
Union of Gametes
D d Punnett
Square D DD
(Tall) d Dd
(Short) The Punnett Square allows us to determine specific genetic ratios.
Genotypic ratio of F2: 1 DD : 2 Dd : 1 dd (or 3 D_ : 1 dd)
Phenotypic ratio of F2: 3 tall : 1 dwarf
Mendel's First Law - the law of segregation; during gamete formation each member of the allelic pair separates from the other member to form the genetic constitution of the gamete
Confirmation of Mendel's First Law Hypothesis
With these observations, Mendel could form a hypothesis about segregation. To test this hypothesis, Mendel selfed the F2 plants. If his law was correct he could predict what the results would be. And indeed, the results occurred has he expected.
From these results we can now confirm the genotype of the F2 individuals.
Phenotypes Genotypes Genetic Description F2 Tall Plants 1/3 DD
2/3 Dd Pure line homozygote dominant
Heterozygotes F2 Dwarf Plants all dd Pure line homozygote recessive Thus the F2 is genotypically 1/4 Dd : 1/2 Dd : 1/4 dd
This data was also available from the Punnett Square using the gametes from the F1 individual. So although the phenotypic ratio is 3:1 the genotypic ratio is 1:2:1
Mendel performed one other cross to confirm the hypothesis of segregation --- the backcross. Remember, the first cross is between two pure line parents to produce an F1 heterozygote.
At this point instead of selfing the F1, Mendel crossed it to a pure line, homozygote dwarf plant.
Backcross: Dd x dd
Gametes D DD
(Tall) d dd
(Short) Backcross One or (BC1) Phenotypes: 1 Tall : 1 Dwarf
BC1 Genotypes: 1 Dd : 1 dd
Backcross - the cross of an F1 hybrid to one of the homozygous parents; for pea plant height the cross would be Dd x DD or Dd x dd; most often, though a backcross is a cross to a fully recessive parent
Testcross - the cross of any individual to a homozygous recessive parent; used to determine if the individual is homozygous dominant or heterozygous
So far, all the discussion has concentrated on monohybrid crosses.
Monohybrid cross - a cross between parents that differ at a single gene pair (usually AA x aa)
Monohybrid - the offspring of two parents that are homozygous for alternate alleles of a gene pair
Remember --- a monohybrid cross is not the cross of two monohybrids.
Monohybrids are good for describing the relationship between alleles. When an allele is homozygous it will show its phenotype. It is the phenotype of the heterozygote which permits us to determine the relationship of the alleles.
Dominance - the ability of one allele to express its phenotype at the expense of an alternate allele; the major form of interaction between alleles; generally the dominant allele will make a gene product that the recessive can not; therefore the dominant allele will express itself whenever it is present
Variations to Mendel's First Law of Genetics
The true test of any theory of science is its ability to explain results that at first glance appear to be a clear exception to the theory. But, if the exception can be explained by the theory, then the theory is further validated. One such genetic example that challenged Mendel's first law was the relationship between two alleles that do not express a typical dominance/recessive relationship. That is, the F1 does not exhibit the genotype of one of the two pure line parents. This type of allelic relationship was termed codominance.
Codominance - a relationship among alleles where both alleles contribute to the phenotype of the heterozygote
Species: Four o'clock plants
Trait: Flower color
Pure line phenotypes: red or white flower
Parental cross: Red x White
F1: We would expect red or white flowers in this generation, depending upon which allele is dominant. But, the F1 plants produced pink flowers. As with any experiment of this sort, the F1 plants are selfed. The results that were obtained were:
F2 phenotypic ratio: 1/4 Red : 1/2 Pink : 1/4 White
Snapdragon Flower Colors
It appears as if the red and white alleles are interacting in the heterozygote to generate the pink flowers. Another example of codominance can be seen by looking at a biochemical phenotype.
Biochemical phenotype - a phenotype that is revealed by biochemical experimentation; examples are DNA markers (RFLPs); protein-size markers (isozymes); quantity of a metabolite; immunological reaction
As an example, let assume that a gene of interest resides on a DNA fragment that is 3.0 kb in size in parent one and 2.0 kb in size in a second parent. (See figure below.) When we cross the two parents, one chromosome carrying the gene comes from each parent. Since our technique recognizes both copies in the parents, the parental signal will be twice as strong as the F1 signal that contains one chromosome, and thus one copy of the particular DNA size, from each parent. The F2 generation will segregate for the three different genotypes in a 1:2:1 ratio.
Genotypic designations could be given for each of the alleles. For example, if the 3.0 kb fragment is designated as allele A1, the genotype of parent 1 will be A1A1. Allele designation A2 will be used for the 2.0 kb fragment and the genotype of parent 2 will be A2A2. Because the F1 is heterozygous, its genotype will be A1A2. Finally, the genotypes of the F2 generation will segregate 1A1A1:2A1A2:1A2A2.
Often expression levels in an individual can only reach a certain intensity regardless of whether the individual is a homozygote or heterozygote. For example, pea plants heterozygote for the tall/dwarf allelic pair are the same size as the homozygous tall parent. But expression is not considered with DNA markers because we are monitoring the presence or absence of a specific DNA fragment. Therefore, DNA fragments are a true example of codominance where each allele is equally expressed in the F1 individual.
Incomplete dominance - the F1 produces a phenotype quantitatively intermediate between the two homozygous parents; if the product is exactly intermediate between the two homozygous parents the relationship is termed no dominance (although some have tried to substitute the term no dominance for codominance, it has not been widely accepted)
Diagrammatic Representation of Allelic Relationships
All of the conclusions regarding gene action (dominant/recessive; codominant) we have discussed so far have been obtained from analyzing the results of controlled crosses. In some situations, we do not have the opportunity to perform controlled crosses. Rather we need to analysis an existing population. This is always the case when studying human genetics. Scientists have devised another approach, called pedigree analysis, to study the inheritance of genes in humans. Pedigree analysis is also useful when studying any population when progeny data from several generations is limited. Pedigree analysis is also useful when studying species with a long genration time. A series of symbols are used to represent different aspects of a pedigree. Below are the principal symbols used when drawing a pedigree.
Once phenotypic data is collected from several generations and the pedigree is drawn, careful analysis will allow you to determine whether the trait is dominant or recessive. Here are some rules to follow.
For those traits exhibiting dominant gene action:
- affected individuals have at least one affected parent
- the phenotype generally appears every generation
- two unaffected parents only have unaffected offspring
The following is the pedigree of a trait contolled by dominant gene action.
And for those traits exhibiting recessive gene action:
- unaffected parents can have affected offspring
- affected progeny are both male and female
The following is the pedigree of a trait contolled by recessive gene action.
Mendel's Law of Independent Assortment
To this point we have followed the expression of only one gene. Mendel also performed crosses in which he followed the segregation of two genes. These experiments formed the basis of his discovery of his second law, the law of independent assortment. First, a few terms are presented.
Dihybrid cross - a cross between two parents that differ by two pairs of alleles (AABB x aabb)
Dihybrid- an individual heterozygous for two pairs of alleles (AaBb)
Again a dihybrid cross is not a cross between two dihybrids. Now, let's look at a dihybrid cross that Mendel performed.
Parental Cross: Yellow, Round Seed x Green, Wrinkled Seed
F1 Generation: All yellow, round
F2 Generation: 9 Yellow, Round, 3 Yellow, Wrinkled, 3 Green, Round, 1 Green, Wrinkled
At this point, let's diagram the cross using specific gene symbols.
Choose Symbol Seed Color: Yellow = G; Green = g Seed Shape: Round = W; Wrinkled = w The dominance relationship between alleles for each trait was already known to Mendel when he made this cross. The purpose of the dihybrid cross was to determine if any relationship existed between different allelic pairs.
Let's now look at the cross using our gene symbols.
Now set up the Punnett Square for the F2 cross.
GW Gw gW gw
round) Male Gw GGWw
wrinkled) Gametes gW GgWW
wrinkled) The phenotypes and general genotypes from this cross can be represented in the following manner:
Phenotype General Genotype 9 Yellow, Round Seed G_W_ 3 Yellow, Wrinkled Seed G_ww 3 Green, Round Seed ggW_ 1 Green, Wrinkled Seed ggww The results of this experiment led Mendel to formulate his second law.
Mendel's Second Law - the law of independent assortment; during gamete formation the segregation of the alleles of one allelic pair is independent of the segregation of the alleles of another allelic pair
As with the monohybrid crosses, Mendel confirmed the results of his second law by performing a backcross - F1 dihybrid x recessive parent.
Let's use the example of the yellow, round seeded F1.
Punnett Square for the Backcross
Gametes gw GgWw
The phenotypic ratio of the test cross is:
- 1 Yellow, Round Seed
- 1 Yellow, Wrinkled Seed
- 1 Green, Round Seed
- 1 Green, Wrinkled Seed
The Chi-Square Test
An important question to answer in any genetic experiment is how can we decide if our data fits any of the Mendelian ratios we have discussed. A statistical test that can test out ratios is the Chi-Square or Goodness of Fit test.
Degrees of freedom (df) = n-1 where n is the number of classes
Let's test the following data to determine if it fits a 9:3:3:1 ratio.
Observed Values Expected Values 315 Round, Yellow Seed (9/16)(556) = 312.75 Round, Yellow Seed 108 Round, Green Seed (3/16)(556) = 104.25 Round, Green Seed 101 Wrinkled, Yellow Seed (3/16)(556) = 104.25 Wrinkled, Yellow 32 Wrinkled, Green (1/16)(556) = 34.75 Wrinkled, Green 556 Total Seeds 556.00 Total Seeds
Number of classes (n) = 4
df = n-1 + 4-1 = 3
Chi-square value = 0.47
Enter the Chi-Square table at df = 3 and we see the probability of our chi-square value is greater than 0.90. By statistical convention, we use the 0.05 probability level as our critical value. If the calculated chi-square value is less than the 0 .05 value, we accept the hypothesis. If the value is greater than the value, we reject the hypothesis. Threrefore, because the calculated chi-square value is greater than the we accept the hypothesis that the data fits a 9:3:3:1 ratio.
A Chi-Square Table
Probability Degrees of
Freedom 0.9 0.5 0.1 0.05 0.01 1 0.02 0.46 2.71 3.84 6.64 2 0.21 1.39 4.61 5.99 9.21 3 0.58 2.37 6.25 7.82 11.35 4 1.06 3.36 7.78 9.49 13.28 5 1.61 4.35 9.24 11.07 15.09
Pleiotropic Effects and Lethal Genes
During the first years after the rediscovery of Mendel's laws, a number of experiments were performed that gave results that at first glance did not coincide with the laws. In 1904, a cross was made between a yellow-coated mouse and a mouse with a gray coat. The gray- coated mouse was extensively inbred and therefore was considered to be pure bred.
What allelic relationship do we have here? We know that the gray mouse is homozygous (because it is a pure line). If gray coat was dominant then we would see all gray mouse. Since we obtain both yellow and gray mice, yellow must be dominant to gray. So what are the genotypes of the two mice populations? First, let's provide gene symbols.
Gene Symbols: gray = y
yellow = Y From the above discussion, the genotype of the gray mouse must be yy. What is the genotype of the yellow mouse? If the mouse was homozygous we would not see any gray mice from the cross, therefore the genotype must be heterozygous or Yy.
Next a cross was made between two yellow mice. What genetic ratio would we expect to see? Yy x Yy should give a ratio of 3 yellow:1 gray. The result, though, was a ratio of 2 yellow to 1 gray mice. How can this result be explained? Let's first set up a Punnett Square.
Expected Punnett Square
Gametes Y YY
As we can see, we should get a 3:1 ratio of yellow to gray mice. Could some genotype be absent from the progeny. How can we test the genotypes of the yellow mice, since we already know the genotypes of the gray mice are yy. Testcross!! All testcross data with the yellow mice give a 1:1 ratio. This ratio is typical of what is seen with heterozygous individuals. Therefore, all of the yellow mice from the cross of two heterozygous yellow mice are genotypically Yy. Somehow the YY genotype is lethal. The 2:1 ratio is the typical ratio for a lethal gene.
Coat Color in Mice
Lethal Gene - a gene that leads to the death of an individual; these can be either dominant or recessive in nature
An important question is how can a gene controlling coat color cause death in an organism? Possibly in a single dose the allele causes a yellowing of the coat, but when expressed in two doses, the gene product kills the animal. Thus, this gene actually has an effect on two phenotypes.
Pleiotropic gene - a gene that affects more than one phenotype
In this example the gene that causes yellowing of the coat also affects viability and is termed a pleiotropic gene.
Instead of masking the effects of another gene, a gene can modify the expression of a second gene. In mice, coat color is controlled by the B gene. The B allele conditions black coat color and is dominant to the b allele that produces a brown coat. The intensity of the color, either black or brown is controlled by another gene, the D gene. At this gene, the dominant D allele controls full color whereas the recessive d allele conditions a dilute or faded expression of the color expression at the B gene. Therefore, if a cross is made among mice that are BdDd, the following phenotypic distribution will be seen:
- 9 B_D_ (black)
- 3 B_dd (dilute black)
- 3 bbD_ (brown)
- 1 bbdd (dilute brown)
The D gene does not mask the effect of the B gene, rather it modifies its expression.
Modifier genes - genes that have small quantitative effects on the level of expression of another gene
Variation in Gene Expression
Not all traits are expressed 100% of the time even though the allele is present. For example the dominant allele P produces polydactyly in humans, a trait that is characterized by extra toes and/or fingers. Two normal appearing adults have been known to mate and produce offspring that express polydactyly. Thus one parent must carry at least one dominant allele (P allele) and its genotype is probably Pp. This parent with the Pp genotype exhibits reduced penetrance for the P allele.
The hand of blues guitar player Hound Dog Taylor exhibiting polydactyly.
Penetrance - the frequency of expression of an allele when it is present in the genotype of the organism (if 9/10 of individuals carrying an allele express the trait, the trait is said to be 90% penetrant)
Not all phenotypes that are expressed are manifested to the same degree. For polydactyly, an extra digit may occur on one or more appendages, and the digit can be full size or just a stub. Therefore, when the P allele is present it expresses variable expressivity.
Expressivity - variation in allelic expression when the allele is penetrant.
Is it possable that the chem dog strain has a modifying gene for thc production? The reason I ask this is the offspring from chem dog and others seem to have a greater thc content than either parent. I have wondered for a long time if this was the case. Chem dog seems to be in the genitics of a large number of high thc strains. Great thread! Always a treat to learn from a master.
Not a fucking clue if this is right, but could explain all the differences....
Originally Posted by Urban Dictionary
Great thread think I gotta read it a few more times though...