Experiments in Plant Hybridization Experiments in Plant Hybridization (Mendel 1865)(Mendel 1865)

Mendel is great science, great statistics and a good puzzle. Mendel is great science, great statistics and a good puzzle. There are many intriguing features of his work, and it is There are many intriguing features of his work, and it is instructive and enjoyable attempting to come to terms with instructive and enjoyable attempting to come to terms with them. them.

What was his aim? What was special about peas? What was What was his aim? What was special about peas? What was special about Mendel? special about Mendel?

Mendel was not the first to experiment in the way he did with Mendel was not the first to experiment in the way he did with peas. He was probably not the first to get the results he got, peas. He was probably not the first to get the results he got, but he seems to have been the first to have noticed this but he seems to have been the first to have noticed this regularity, to have theorized concerning it, to have tested his regularity, to have theorized concerning it, to have tested his theory, and to have gone on to do more. theory, and to have gone on to do more.

There are many readily available English translations of There are many readily available English translations of Mendel's paper: Stern and Sherwood's book includes a Mendel's paper: Stern and Sherwood's book includes a number of related documents ; Fisher's has a few marginal number of related documents ; Fisher's has a few marginal comments, which supplement and update his famous 1936 comments, which supplement and update his famous 1936 paper; while the most recent by Corcos and Monaghan has paper; while the most recent by Corcos and Monaghan has many useful botanical remarks. many useful botanical remarks.

Next few slides courtesy of Terry Speed, Statistics in Genetics Course, UC Berkeley

Cliff’s Notes to MendelCliff’s Notes to Mendel Introductory remarks (1).Introductory remarks (1). Literature review. The Literature review. The

nature of the experiments referred to at the very nature of the experiments referred to at the very beginning is unclear; they are the first Mendelian beginning is unclear; they are the first Mendelian puzzle. He more or less states his aim as seeking puzzle. He more or less states his aim as seeking the laws governing the formation of hybrids. the laws governing the formation of hybrids.

Selection of experimental plants (2).Selection of experimental plants (2). Here Here Mendel rather clearly answers the question: Why Mendel rather clearly answers the question: Why peas? It is important to be clear - and Mendel was peas? It is important to be clear - and Mendel was not always - on the distinction between a trait and not always - on the distinction between a trait and variant forms of a trait, e.g. seed shape, and the variant forms of a trait, e.g. seed shape, and the smooth and wrinkled (angular) forms.smooth and wrinkled (angular) forms.

So, why the sweet pea and not something else?So, why the sweet pea and not something else?

Genus Pisum

Cliff’s Notes (continued)Cliff’s Notes (continued) Arrangement and sequence of experiments (3).Arrangement and sequence of experiments (3). Much has Much has

been written concerning the precise set of varieties Mendel been written concerning the precise set of varieties Mendel used. For example did he have seven pairs of varieties, each used. For example did he have seven pairs of varieties, each differing in the way described, or did he have fewer? (In other differing in the way described, or did he have fewer? (In other words, is the sentence opening section 8 literally true?) If he words, is the sentence opening section 8 literally true?) If he had fewer than seven pairs, did he ignore data on segregating had fewer than seven pairs, did he ignore data on segregating factors other than that under discussion? Despite referring to factors other than that under discussion? Despite referring to the seed, coat color is in fact a character of the maternal plant. the seed, coat color is in fact a character of the maternal plant. Mendel certainly knew this, and it has significant implications Mendel certainly knew this, and it has significant implications for the design and analysis of his experiments.for the design and analysis of his experiments.

Form of the hybrids (4). Form of the hybrids (4). Here we get the first results: the Here we get the first results: the appearance of what we now call dominance, what Mendel called appearance of what we now call dominance, what Mendel called dominating and recessive. Note that he got the same thing dominating and recessive. Note that he got the same thing when he switched seed and pollen parents, i.e. carried out what when he switched seed and pollen parents, i.e. carried out what is known as the reciprocal cross. He also notes some differences is known as the reciprocal cross. He also notes some differences beween the hybrids and the corresponding dominant parents. beween the hybrids and the corresponding dominant parents.

Cliff’s Notes (continued)Cliff’s Notes (continued) The first generation from hybrids (5).The first generation from hybrids (5).

In this section Mendel reports his famous 3:1 In this section Mendel reports his famous 3:1 segregation ratios, and emphasizes the need for segregation ratios, and emphasizes the need for further experimentation to ascertain the composition further experimentation to ascertain the composition of his plants.of his plants.

The second generation from hybrids (6).The second generation from hybrids (6).Now Mendel has determined that his 3:1 is in fact Now Mendel has determined that his 3:1 is in fact 1:2:1. To do so with one seed and all plant 1:2:1. To do so with one seed and all plant characters, he had to sample his first generation characters, he had to sample his first generation (from hybrid) dominant plants, and take only a (from hybrid) dominant plants, and take only a limited number of seeds from each. Why? He also limited number of seeds from each. Why? He also repeated one experiment because the initial result repeated one experiment because the initial result deviated too greatly from what he was expecting. deviated too greatly from what he was expecting.

First generation raw dataFirst generation raw data Expt. 1. Form of seed. -- From 253 hybrids 7324 seeds were obtained in the Expt. 1. Form of seed. -- From 253 hybrids 7324 seeds were obtained in the

second trial year. Among them were 5474 round or roundish ones and 1850 second trial year. Among them were 5474 round or roundish ones and 1850 angular wrinkled ones. Therefrom the ratio 2.96:1 is deduced.angular wrinkled ones. Therefrom the ratio 2.96:1 is deduced.

Expt. 2. Color of albumen. -- 258 plants yielded 8023 seeds, 6022 yellow, and Expt. 2. Color of albumen. -- 258 plants yielded 8023 seeds, 6022 yellow, and 2001 green; their ratio, therefore, is as 3.01:1. 2001 green; their ratio, therefore, is as 3.01:1.

Experiment 1 Experiment 2 Form of Seed Color of Albumen

Plants Round Angular Yellow Green1 45 12 25 112 27 8 32 73 24 7 14 54 19 10 70 275 32 11 24 136 26 6 20 67 88 24 32 138 22 10 44 99 28 6 50 14

10 25 7 44 18

Cliff’s Notes (continued)Cliff’s Notes (continued) The subsequent generations from hybrids (7).The subsequent generations from hybrids (7).

The pattern held up. An explanation for the phenomenon of The pattern held up. An explanation for the phenomenon of reversion was offerred. Mendel's argument shows how reversion was offerred. Mendel's argument shows how repeated selfing leads to homozygosity.repeated selfing leads to homozygosity.

Ratios Generation A Aa a A : Aa : a ---------------------------------------------------- 1 1 2 1 1 : 2 : 1 2 6 4 6 3 : 2 : 3 3 28 8 28 7 : 2 : 7 4 120 16 120 15 : 2 : 15 5 496 32 496 31 : 2 : 31 . .......... ........ n n n 2 - 1 : 2 : 2 - 1

Cliff’s Notes (continued)Cliff’s Notes (continued) The offspring of hybrids in which several differing traits are The offspring of hybrids in which several differing traits are

associated (8).associated (8). In this rather long section, Mendel reported the In this rather long section, Mendel reported the results of his dihybrid and trihybrid experiments. He also makes results of his dihybrid and trihybrid experiments. He also makes greater use of the algebraic notation introduced at the end of section greater use of the algebraic notation introduced at the end of section 7. His proportions 9:3:3:1, and the trihybrid analogue confirmed the 7. His proportions 9:3:3:1, and the trihybrid analogue confirmed the independent segregation of these three traits. Note that once he adds independent segregation of these three traits. Note that once he adds seed-coat color to the other two seed characters, the logistic problems seed-coat color to the other two seed characters, the logistic problems associated with this trihybrid experiment become truly formidable. associated with this trihybrid experiment become truly formidable. Generalization to more than 3 segregating traits is discussed briefly. Generalization to more than 3 segregating traits is discussed briefly.

The reproductive cells of hybrids (9).The reproductive cells of hybrids (9). This is undoubtedly the This is undoubtedly the most interesting (and longest) section of the paper, and perhaps the most interesting (and longest) section of the paper, and perhaps the most difficult to read. In it Mendel formulates his theory, and tells us most difficult to read. In it Mendel formulates his theory, and tells us that it explains his results to date. He then describes new experiments that it explains his results to date. He then describes new experiments which test his theory. A cross between a hybrid and one of the true-which test his theory. A cross between a hybrid and one of the true-breeding lines that gave rise to the hybrid is called a backcross. In breeding lines that gave rise to the hybrid is called a backcross. In every case, the resulting plants were permitted to self, to confirm every case, the resulting plants were permitted to self, to confirm their composition. Further confirmation of his theory was obtained by their composition. Further confirmation of his theory was obtained by carrying out similar crosses with plant traits. In the last part of this carrying out similar crosses with plant traits. In the last part of this section, he restated his theory in algebraic terms, and showed how it section, he restated his theory in algebraic terms, and showed how it also accounted for his observations on the independent segregation of also accounted for his observations on the independent segregation of two or three traits. two or three traits.

Cliff’s Notes (continued)Cliff’s Notes (continued) Experiments on hybrids of other plant species (10).Experiments on hybrids of other plant species (10).

Now Mendel considers the extent to which his findings Now Mendel considers the extent to which his findings generalize. For some bean traits, what he found held true, generalize. For some bean traits, what he found held true, but for color it did not. However, his numbers were small, but for color it did not. However, his numbers were small, and is results did not rule out the possibility that the color and is results did not rule out the possibility that the color trait could be explained by two or more independently trait could be explained by two or more independently segregating factors. He displays algebra foreshadowing the segregating factors. He displays algebra foreshadowing the discovery 40 years later of a Mendelian explanation of discovery 40 years later of a Mendelian explanation of continuously varying traits. continuously varying traits.

Concluding remarks (11).Concluding remarks (11). This is a rather difficult section This is a rather difficult section for us, requiring a knowledge of research of Mendel's day. for us, requiring a knowledge of research of Mendel's day. He discusses a number of segregating traits, true breeding He discusses a number of segregating traits, true breeding hybrids, and what was termed transformation: the hybrids, and what was termed transformation: the conversion of one variety into another by repeated conversion of one variety into another by repeated backcrossing. In each case, his concern was with explaining backcrossing. In each case, his concern was with explaining known phenomena from the viewpoint of his new theory. known phenomena from the viewpoint of his new theory.

Mendel’s Algebraic FormMendel’s Algebraic FormA self-cross of the hybrid AaBb :A self-cross of the hybrid AaBb :

(A + 2Aa + a) * (B + 2Bb + b) =(A + 2Aa + a) * (B + 2Bb + b) =

1 AB1 AB

1 Ab1 Ab

1 aB1 aB

1 ab1 ab

2 ABb2 ABb

2 aBb2 aBb

2 AaB2 AaB

2 Aab2 Aab

4 AaBb4 AaBb

Genetic phaseGenetic phase Haplotype = alleles received by an individual from one parentHaplotype = alleles received by an individual from one parent Phase = For a doubly heterozygous individual A/a B/b, whether the Phase = For a doubly heterozygous individual A/a B/b, whether the

A allele was received in the same haplotype as the B or b allele.A allele was received in the same haplotype as the B or b allele.

A

B

a

b

A

B

A

B

a

b

a

b

A

B

a

borCould be

A

B

a

b

A

B

a

b

A

B

a

b

A

B

a

b

PHASE KNOWN PHASE UNKNOWN

An example:An example:Morgan’s Fly ExperimentsMorgan’s Fly Experiments

One gene affects eye colorOne gene affects eye color((prpr, purple, and , purple, and prpr+, red)+, red)

The other affects wing lengthThe other affects wing length((vgvg, vestigial, and , vestigial, and vgvg+, normal).+, normal).

Morgan crossed Morgan crossed prpr//prpr · · vgvg//vgvg flies with flies with prpr+/+/prpr+ · + · vgvg+/+/vgvg+ and then testcrossed the doubly + and then testcrossed the doubly heterozygous F1 females:heterozygous F1 females:prpr+/+/prpr · · vgvg+/+/vgvg ♀ × ♀ × prpr//prpr · · vgvg//vgvg ♂. ♂.

Because one parent (tester) contributes gametes Because one parent (tester) contributes gametes carrying only recessive alleles, the phenotypes of the carrying only recessive alleles, the phenotypes of the offspring reveal the gametic contribution of the other, offspring reveal the gametic contribution of the other, doubly heterozygous parent. doubly heterozygous parent.

The test cross formatThe test cross format

P pr+/pr+ vg+/vg+ × pr/pr vg/vg

F1 pr+/pr vg+/vg

“Tester” pr+/pr vg+/vg × pr/pr vg/vg

Reverse phase experimentReverse phase experiment

P pr+/pr+ vg/vg × pr/pr vg+/vg+

F1 pr+/pr vg+/vg

“Tester” pr+/pr vg+/vg × pr/pr vg/vg

Another example showing the Another example showing the importance of phase informationimportance of phase information

1 2 3 4 5 6

No Disease

H—C—hc/YHc/YHC/Yhc/Yhc/YHC/Y

1 2HC/YHC/hc

1 2HC/YHC/hc?

Colorblind

Colorblind +Hemophilia

Could this computation be done without the grandparents?

What is the genetic distance between these genes?

SNPs and PharmacogenomicsSNPs and Pharmacogenomics Refers to the complete list of genes that determine Refers to the complete list of genes that determine

the overall efficacy and toxicity of a drugthe overall efficacy and toxicity of a drug Tries to account for all genes that influence:Tries to account for all genes that influence:

– Drug metabolismDrug metabolism

– Drug transport/exportDrug transport/export

– ReceptorsReceptors

– Signaling pathways, etc.Signaling pathways, etc.

Your genotype would allow a physician to Your genotype would allow a physician to determine the optimal dose and medication for determine the optimal dose and medication for optimal therapyoptimal therapy

Pharmas are spending a lot of money to discover Pharmas are spending a lot of money to discover clinically relevant SNPsclinically relevant SNPs

Population Genetics 101:Population Genetics 101:Measuring Genetic VariationMeasuring Genetic Variation

Hardy-Weinberg equilibrium (HWE)Hardy-Weinberg equilibrium (HWE)

Genotype frequencies depend only on gene frequenciesGenotype frequencies depend only on gene frequencies

ppAA = frequency of allele A = frequency of allele A

ppBB = frequency of allele B = frequency of allele B

P(A/A) = P(A/A) = ppAA22 ; P(A/B) = ; P(A/B) = ppBB

2 2 ; P(A/B) = 2; P(A/B) = 2ppAAppBB

ppA A + p+ pB B = 1= 1

ppAA22 + 2 + 2ppAAppB B + + ppBB

22 = 1 = 1

Population Genetics 101:Population Genetics 101:Measuring Genetic VariationMeasuring Genetic Variation

Observed vs. expected heterozygosityObserved vs. expected heterozygosity

HHoo = Observed fraction of heterozygous individuals = Observed fraction of heterozygous individuals

HHee = Expected fraction based on allele frequencies = Expected fraction based on allele frequencies

The frequency f(X) of allele X is the fraction of times The frequency f(X) of allele X is the fraction of times it occurs over all loci (2 per individual)it occurs over all loci (2 per individual)

HHee = 1 – the probability of homozygosity = 1 – the probability of homozygosity

= 1 – [f= 1 – [f22(X) + f(X) + f22(Y) + … ] for all alleles (X,Y,…)(Y) + … ] for all alleles (X,Y,…)

Example: 10 Unique GenotypesExample: 10 Unique Genotypes(in bp lengths of microsatellite)(in bp lengths of microsatellite)

Allele AAllele A Allele BAllele B # # individualsindividuals

243243 243243 11

255255 259259 11

257257 257257 11

257257 259259 11

259259 259259 11

261261 261261 99

261261 263263 33

261261 267267 11

263263 263263 44

263263 271271 11

Ho ≈ 0.30

He ≈ 0.69

H = 1: high diversity

H = 0: asexual mitoticreproduction

Ho << He indicates selective pressure or non-random mating

Components of the genetic modelComponents of the genetic model Components of the genetic model include inheritance pattern (dominant Components of the genetic model include inheritance pattern (dominant

vs. recessive, sex-linked vs. autosomal), trait allele frequency (a common vs. recessive, sex-linked vs. autosomal), trait allele frequency (a common or rare disease?), and the frequency of new mutation at the trait locus.or rare disease?), and the frequency of new mutation at the trait locus.

Another important component of the genetic model is the Another important component of the genetic model is the penetrancepenetrance of of the trait allele. Knowing the the trait allele. Knowing the penetrance penetrance of the disease allele is crucial of the disease allele is crucial because it specifies the probability that an unaffected individual is because it specifies the probability that an unaffected individual is unaffected because he's a non-gene carrier or because he's a non-unaffected because he's a non-gene carrier or because he's a non-penetrant gene carrier. The frequency of penetrant gene carrier. The frequency of phenocopies phenocopies is an important is an important component, too. component, too.

Rough estimates of the Rough estimates of the disease allele frequencydisease allele frequency and and penetrance penetrance can can often be obtained from the literature or from computer databases, such as often be obtained from the literature or from computer databases, such as Online Mendelian Inheritance in Man (Online Mendelian Inheritance in Man (http://www3.ncbi.nlm.nih.gov/Omimhttp://www3.ncbi.nlm.nih.gov/Omim/). Estimates of the rate of /). Estimates of the rate of phenocopies phenocopies and new mutation are frequently and new mutation are frequently guesses, included as a nuisance parameter in some cases to allow for the guesses, included as a nuisance parameter in some cases to allow for the fact that these can exist.fact that these can exist.

Linkage analysis is relatively robust to modest misspecification of the Linkage analysis is relatively robust to modest misspecification of the disease allele frequency and penetrance, but misspecification of whether disease allele frequency and penetrance, but misspecification of whether the disease is dominant or recessive can lead to incorrect conclusions of the disease is dominant or recessive can lead to incorrect conclusions of linkage or non-linkage.linkage or non-linkage.

Steps to linkage analysisSteps to linkage analysis In pedigrees in which the genetic model is known, In pedigrees in which the genetic model is known,

linkage analysis can be broken down into five linkage analysis can be broken down into five steps: steps: – State the components of the genetic model. State the components of the genetic model.

– Assign underlying disease genotypes given information Assign underlying disease genotypes given information in the genetic model. in the genetic model.

– Determine putative linkage phase. Determine putative linkage phase.

– Score the meiotic events as recombinant or non-Score the meiotic events as recombinant or non-recombinant. recombinant.

– Calculate and interpret LOD scores.Calculate and interpret LOD scores.

Let's take a look at each of these steps in detail.Let's take a look at each of these steps in detail.

State the components of the modelState the components of the model

In this example, the In this example, the disease allele will be disease allele will be assumed to be rare and assumed to be rare and to function in an to function in an autosomal dominantautosomal dominant fashion with fashion with complete complete penetrancepenetrance, and the , and the disease locus will be disease locus will be assumed to have two assumed to have two alleles:alleles:

N (for normal or wild-type)N (for normal or wild-type)

A (for affected or disease) A (for affected or disease)

Assign underlying disease genotypesAssign underlying disease genotypes

The assumption of The assumption of complete penetrance of complete penetrance of the disease allele allows the disease allele allows all unaffected all unaffected individuals in the individuals in the pedigree to be assigned pedigree to be assigned a disease genotype of a disease genotype of NN. Since the disease NN. Since the disease allele is assumed rare, allele is assumed rare, the disease genotype the disease genotype for affected individuals for affected individuals can be assigned as AN. can be assigned as AN.

Determine putative phaseDetermine putative phase

Individual II-1 has inherited Individual II-1 has inherited the disease trait together the disease trait together with marker allele 2 from his with marker allele 2 from his affected father. Thus, the A affected father. Thus, the A allele at the disease locus allele at the disease locus and the 2 allele at the and the 2 allele at the marker locus were inherited marker locus were inherited in the gamete transmitted to in the gamete transmitted to II-1. II-1.

Once the putative linkage Once the putative linkage phase (the disease allele phase (the disease allele "segregates" with marker "segregates" with marker allele 2) has been allele 2) has been established, this phase can established, this phase can be tested in subsequent be tested in subsequent generations. generations.

Score the meiotic events asScore the meiotic events asrecombinant (R) or non-recombinant (NR)recombinant (R) or non-recombinant (NR)

There are four There are four possible gametes possible gametes from the affected from the affected parent II-1: N1, N2, parent II-1: N1, N2, A1, and A2. Based on A1, and A2. Based on the putative linkage the putative linkage phase assigned in phase assigned in step 3, gametes A2 step 3, gametes A2 and N1 are non-and N1 are non-recombinant. recombinant.

Calculate LOD scoresCalculate LOD scores

In this example, the In this example, the highest LOD score is highest LOD score is 0.09 at 0.09 at = 0.40. At = 0.40. At no value of no value of is the is the lod score positive, let lod score positive, let alone alone >>3.0, so this 3.0, so this pedigree has no pedigree has no evidence in favor of evidence in favor of linkage between the linkage between the disease and marker disease and marker loci. loci.