What Type of Variation Cause the Diversity We Breed for in ...maizeandgenetics.tamu.edu/SethCMurray/Teaching/Lectures/S2010... · What Type of Variation Cause the Diversity We Breed

What Type of Variation Cause the Diversity We Breed for in Crops?

….Quantitative Variation!

http://www.ars.usda.gov/images/docs/6652_6836/tomato%20colors.jpg

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http://www.sciencedaily.com/images/2009/07/090723113512.jpg

Qualitative variation (mutants) are rarely useful

Presenter

Presentation Notes

Mostly from Ott, R.L. and Longnecker M. 2001. Statistical Methods and Data Analysis

Agro 643 - Review: statistics concepts

Quantitative Genetics = (Genetics + Phenotype + Statistics) for a population

Molecular Quantitative Genetics = (Genetics + Phenotype + Genotype + Statistics) for a population

Basic Probability and Statistics Concepts Review Terms Binary ~ two state distribution [1,0]; [black, white], etc. Qualitative random variable ~ finite and small number of possible outcomes (usually binary) Quantitative random variable ~ any number of possible outcomes

Discrete distribution ~ observations on a quantitative random variable can only assume countable (whole) number values. Continuous distribution ~ observations on a quantitative random variable can assume any of the uncountable number values in a line interval.

Mean (arithmetic) ~ the sum of measurements divided by the total number of measurementsVariance ~ ~ the spread of observations around the mean

where there are n measurements y1, y1, … yn with arithmetic mean1

)(−−Σ

nyyi

y

Presenter

Presentation Notes


Genetic Models Additive model for height

Mean Base Height = 50cm Mean Allele a value = 0cm Mean Allele A value = 5cm

Individual AdditiveHeight

aa 50cmaA or Aa 55cmAA 60cm

Agro 643 - Review: genetics and statistics concepts

AA = 60cmAa = 55cmAa = 50cm

Quantitative Genetic Models for Means and Variances

What is a genetic model? Concrete, mathematical way to discuss the variation in a population

Why do we use these mathematical genetic models? Teaching tools, understanding is needed for later concepts Calculate gain from selection Useful for people who are designing new breeding methods and analyses “Glossy Papers” (Hallaur, 2006 – Cornell University)

Even though we talk about “allele frequencies” it is abstract and based on phenotypic information not molecular markers … though it can and is applied to markers too!

Agro 643 - Genetic Models for Means


If only it were so simple…

Presenter

Presentation Notes



Normal DistributionFirst introduced by French mathematician A. DeMoivre in 1733 who called it the ‘exponential bell shaped curve’. German mathematician K.F. Gauss made it famous so it is called a ‘Gaussian distribution’. Because we believe (often incorrectly to simplify things) that it is found everywhere (thanks Central Limit Theorem) we now call it a normal distribution.

),(~ 2σµNX

60cm55cm50cm

Could be caused by:Other genesEnvironmental effectsGenetic by environmental

interaction (G x E)Random error

- disease- drought- soil differences- other biotic / abiotic- random chance

Num

ber o

f ind

ivid

uals

Presenter

Presentation Notes

Mostly from Ott, R.L. and Longnecker M. 2001. Statistical Methods and Data Analysis And Ross, S. 2002. A first course in probability. Sixth edition


Basic Probability and Statistics Concepts Review

Central Limit Theorem ~

1.

2.

3. When n is large, the sampling distribution of Y will be approximately normal, with approximation becoming more precise as n increases.

4. When the population distribution is normal, the sampling distribution of Y is exactly normal for any sample size n

Where Y can equal either the mean: or the sum of all y1, y1, … yn observations: Σi yn

And μy is the mean of the sample And σy is the standard deviation of the sample (the standard error)

uy=µ

ny /σσ =

y

Presenter

Presentation Notes



Basic Genetics and Statistics Concepts Review

Genetic Models – 100 F2 individuals measured for height. m genes at 50% frequency have value of 40cm/ m ... our expectation

One Additive Gene Two Additive Genes Three Additive Genes

Four Additive Genes Five Additive Genes Six Additive Genes

Height

Freq

uenc

y

50 60 70 80 90

050

000

1000

0015

0000

2000

00

Height

Freq

uenc

y

50 60 70 80 90

050

000

1000

0015

0000

2000

002

Height

Freq

uenc

y

50 60 70 80 90

0e+0

01e

+05

2e+0

53e

+05

4e+0

55e

Height

Freq

uenc

y

50 60 70 80 90

0e+0

01e

+05

2e+0

53e

+05

Height

Freq

uenc

y

50 60 70 80 90

050

000

1000

0015

0000

2000

0025

0000

300

Height

Freq

uenc

y

50 60 70 80 90

050

000

1000

0015

0000

2000

0025

0000

1 1

2

1 1

6

4 4

1 1

1 11 1 1 1

7056 56

29 29

201515

6 6

8 810 10

45 45

120 120

210 210252

924792 792

495 495

220220

66 6612 12

R: #Genetic Ratios Based on Calculation

Presenter

Presentation Notes

From R code developed for class

Basic Genetics and Statistics Concepts Review

Central Limit Therom – As the number of independent random variables (genes involved in a phenotype) approaches infinity, the sum of these approaches normality

Height

Den

sity

55 60 65 70 75 80 85

0.00

0.02

0.04

0.06

0.08

Ten Additive Genes


Presenter

Presentation Notes


Height

Freq

uenc

y

60 65 70 75 80

05

1015

2025

Genetic Models – 100 individuals (n) measured for height. m genes at 50% frequency have value of 40cm/ m ... Reality...

(one simulated draw of 100 individuals for each scenario)

One Additive Gene Two Additive Genes Three Additive Genes

Four Additive Genes Five Additive Genes Six Additive Genes

Height

Freq

uenc

y

50 55 60 65 70 75 80

05

1015

2025

11

3

58

13

2123

25

Height

Freq

uenc

y

50 60 70 80 90

05

1015

2025

1 114

13

2125

13

21

Height

Freq

uenc

y

50 60 70 80 90

05

1015

2025

30

1 17

14

3125

21

Height

Freq

uenc

y

50 60 70 80 90

05

1015

2025

3035

5 6

25

3529

Height

Freq

uenc

y

50 60 70 80 90

010

2030

4050

27

52

21

2145

1112

2225

18

Agro 643 - Review: genetics and statistics concepts R: #Based on probability - Possible Sample Observations

Presenter

Presentation Notes


Genetic Models – Something similar can also be observed if using limited draws using a normal distribution function.


Presenter

Presentation Notes


Agro 643 - Phenotypic Quantitative Genetics - Review: statistics concepts

Basic Genetics Models

Individual AdditiveHeight

DominanceHeight

OverdominanceHeight

aa 50cm 50cm 50cm

aA or Aa 55cm 55cm 55cm

AA 60cm 55cm 50cm

Quantitative Genetic Models for Means and Variances

ASSUMPTIONSHardy Weinberg Equilibrium (Hartl and Clark, 1997)

- The organism is diploid.- Reproduction is sexual.- Generations are non-overlapping.- The gene under consideration has two alleles.- The allele frequencies are identical in males and females.- Mating is random.- Population size is very large (in theory, infinite – no genetic drift).- Migration is negligible.- Mutation can be ignored.- Natural selection does not affect the alleles under consideration.

Additionally:No selection (e.g. human based, or flowering time difference to pollen competition)Single Locus

- No Epistasis- No Linkage

Genetic Effects ONLY- No E or G*E


Genetic models for means

Simple model ( one locus, two alleles)

Genotype

Frequency

Numberof ‘B’

Genotypic Value

Coded Gen. Value

BB p2 2 z + 2a aBb 2pq 1 z + a + d dbb q2 0 z -a

BB

bb

Bb

110 bu/a

105 bu/a

100 bu/a

Gene action ValueAdditive (no dominance)

d = 0

Complete dominance d = aPartial dominance a > d > 0Overdominance d > a

a

-a

Additive Model




Genotype

Frequency

Numberof ‘B’

Genotypic Value

Coded Gen. Value


BB

bb

Bb

110 bu/a

100 bu/a


d = 0


a

-a

Complete Dominance Model




Genotype

Frequency

Numberof ‘B’

Genotypic Value

Coded Gen. Value


BB

bb

Bb

110 bu/a

107.5 bu/a

100 bu/a


d = 0


d = ½ aa

-a

Partial Dominance Model




Genotype

Frequency

Numberof ‘B’

Genotypic Value

Coded Gen. Value


BB

bb

Bb

110 bu/a

115 bu/a

100 bu/a


d = 0


d = 2a

a

-a

Overdominance Model


Genotype

Frequency

Numberof ‘B’

Genotypic Value

Coded Gen. Value


Extended to a population the mean of the population reflects the proportional value of its individuals. Thus, it depends on both allele frequency and level of dominance.

aqpqdapX 22 2 −+=Population

Mean =

p (B) q (b) a d0.5 0.5 2 2 10.5 0.5 2 1 0.50.7 0.3 2 2 1.640.7 0.3 2 1 1.220.3 0.7 2 2 0.440.3 0.7 2 1 -0.38

X

pqdq)a(pX 2+−=

Which reduces to:pqd)aq(pX 222 +−=

Which reduces to:

Population Genetic Mean


R: #C

alculate population means

An alleles average effect is dependent on population allele frequency and allele effect.

Additive (no dominance) - d=0, a=2Complete dominance - d=2, a=2Partial dominance - d=1, a=2Overdominance - d=2, a=1(*Note ‘a’ value is shown lower to fit the same scale)

Genetic Models for Means


Breeding value uses the mean value of progeny to calculate an individuals value. Unlike average effect it can be measured directly in a diploid population. Breeding value is additive genetic variation

Theoretically, breeding value is the sum of the average effects of the individuals gametes.

The reason to go through average effects to determine breeding value is so that you can see that the breeding value of an individual is directly connected to frequency and effects of the alleles in the population.

Genotype Breeding Value from average effects

BB q[a+d(q-p)] + q[a+d(q-p)] =2(qa+q2d-pdq)

Bb q[a+d(q-p)] - p[a+d(q-p)]=qa+q2d-pdq - pa-pdq+dp2

=q2d+dp2-2dpq +qa -pabb -p[a+d(q-p)] - p[a+d(q-p)]

=2(- pa-pdq+dp2 )

Breeding value is additive genetic variation


Alternative explanation:Basically this shows mathematically that if all the individuals are very good then the difference between the best individual and the population is small. However if the population mostly poor with a few very good individuals then the breeding value will be very high on the elite individuals.

Dominance deviation is the difference between the genotypic value (what we observe) and the breeding value (which we must calculate)

Dominance deviation = Genotypic value – Breeding Valued = G – a

Or G = a + dGenotypic value = Breeding Value + Dominance deviation

Genotype Genotypic (G) value

G - population mean

G - population mean ( insert α = a + d (q-p)

BB a = a - a(p-q) +2dpq= 2q(a-pd)

= 2q(a-pd)= 2q(α-qd)

Bb d = d - a(p-q) +2dpq= a(q-p) + d(1-2pq)

= a(q-p) + d(1-2pq)= α (q-p) + 2pqd

bb -a = -a - a(p-q) +2dpq= 2p(a+qd)

= 2p(a+qd)= 2p(α+pd)

The Dominance Deviation is Caused by Dominance Effects


Has Dominance Heterosis Increased in Maize?Few studies have looked at if heterosis has increased in maize over time.

The one study I am aware of:DUVICK, D. N., 1999 Heterosis: feeding people and protecting natural resources, pp. 19–29 in The Genetics and Exploitation of Heterosis in Crops, edited by J. G. COORS and S. PANDEY. ASA-CSSA-SSSA Societies, Madison, WIShows:

Agro 643 – Heterosis in maize

Single Cross Yield

Mid Parent Value

Genetic Models for Means Summary- Dominance causes differences between genotypic values and breeding values

When intermating in a diverse HWE population:- Recessive homozygotes (-/-) give progenies that appear much better than themselves with most progeny (+/-)

- Heterozygotes (+/-) look better than their progeny as they produce (-/-)

-Dominant homozygotes (+/+) give progenies that can appear slightly better than themselves with (+/+) progeny and (+/-).

- Slope of the regression line is the average effect of a gene substitution α = α1 –α2

- Breeding values and population mean are on the regression line

- Regression depends on gene frequency and effects


For Inbreeding, A Way to Think About Genetic Means Across Different Generations

P1 = m + aP2 = m – aF1 = m + dF2 = m + ½dFn = m +(½)n-1dBC11 = m + ½a + ½dBCn1 = m + [1-(1/2) n]a +(½)n dBC12 = m - ½a + ½dBCn2 = m - [1-(1/2) n]a +(½)n d

P1

P2

d

-a

a

m

d/2

d/4d/8

F1

F2

F3F4

Agro 643 - Genetic Models for Variances


Genetic Models for VariancesThe expected population mean of the next generation indicates how much variance is in the population for breeding improvement through selection.

While the red and the blue populations below have the same mean and are the same size, they have different variances for height.

If we select the top 10% of plants to produce a new generation (assuming additive effects only).

σ= 5, σ = 10

R: Population Mean and Variance Normal Distribution


Genetic Models for VariancesThe expected population variance indicates how much variance is in the population for breeding improvement (selection) . This is a function of allele frequency as well as additive and dominant effects.

2222222 ]2)[(2 pqdaqpaqpqdap +−−−+=σPopulation Variance =

])21()(2[2 222 dpqadpqapq −+−+=σ

Thus, when p=q= ½ then our expected σ2 = ½ a2 + ¼ d2

]))5.0)(5.0(21()5.05.0(2)[5.0)(5.0(2 222 dada −+−+=σ

])5.1()[5.0( 222 da −+=σ

The total genetic variance can be broken down into additive and dominance deviation 222

DAG σσσ +=

22222 4])([2 dqpdpqapqG +−+=σ

The Genetic Variance for All Models is a Function of Allele Frequency The expected population mean indicates how much variance is in the population for breeding improvement (selection) .

σG2

σd2 = σa

2 = 2

Com

plet

e do

min

ance

σG2

σd2 = 0

σa2 = 2

Add

itive

(no

dom

inan

ce)

Extr

eme

Ove

rdom

inan

ceσG

2

σd2 = 1000

σa2 = 1

Ove

rdom

inan

ce

σG2

σd2 = 2

σa2 = 1


Sources of Genetic Variance in Different Inbred Generations

σa2 Total

σa2 Between

σa2 Within

σd2 Total

σd2 Between

σd2 Within

F - inbreeding Coefficient

*Genetic variance between inbred families increase and within families decreases with inbreeding

*Total genetic variance doubles from F=0 to F=1

*When F=1 all variance is additive


NOTE: Should be discrete (points) not a continuous line graph…only shown for clarity

Genetic Models for Variances

Back to Reality … Why does this not work for your population?- Random Mating ( Impossible)

- Epitasis effect ( Gets very complex )

- Genes Independent / no linkage ( Impossible)

- No selection ( Near impossible - no matter how hard you try)

- Environmental effects

- Population size


Population Genetics: Genetic DriftThis is much easier to observe using simulations…

N = 10 N = 100

N = 1000

Ten simulations each with p=.5

Agro 643 - Review: population genetics

Presenter

Presentation Notes

See R code for Class for simulation


What Do You Need to Perform Quantitative Genetic Analysis?

1. A Controlled Population ( or at least one you understand)2. Genetic Diversity3. Lots and Lots of Phenotypic Observations ( data points)4. A Genetic Model5. Good Statistical Analysis

Correlation ~ measures strength of the linear relationship of X and YUsually reported as ‘r’ = In writing people prefer ‘ Pearson correlation coefficient ’

Presenter

Presentation Notes

Mostly from Ott, R.L. and Longnecker M. 2001. Statistical Methods and Data Analysis And Ross, S. 2002 A first course in probability. Sixth edition


Heritability - Parent Offspring Regression

Correlation ~ measures strength of the linear relationship of X and YUsually reported as ‘r’ = In writing people prefer ‘ Pearson correlation coefficient ’

http://www.biology.duke.edu/rausher/heritability.JPGHeritability ~ The amount of phenotypic variation attributable to genetics

Presenter

Presentation Notes

Mostly from Ott, R.L. and Longnecker M. 2001. Statistical Methods and Data Analysis And Ross, S. 2002 A first course in probability. Sixth edition

“Citing the well-known correlation between obese dogs and their owners, Marc kept his

New-Year’s resolution to get fit”

Causation can not be deduced from correlation!

Agro 643 - Review: probability theory and statistics

What is Random?What is Significant?Meeting an acquaintance in the backstreets of Venice?

iPod shuffle playing three Jay-Z songs in a row?

Height and flowering time being correlated?

Winning at slots?

Presenter

Presentation Notes


Agro 643 - Phenotypic Quantitative Genetics - Review: statistics concepts

Hypothesis Testing

Null hypothesis is True

Null hypothesis is False

Reject the Null Hypothesis

Type 1 Error!α

Fail to Reject the Null Hypothesis

Type 2 Error!β

Type III error: provides the right answer to the wrong question (discrepancy between the research focus and the research question )

All Breeders Need Genetic Diversity…

…What Does Genetic Diversity Mean to You?


Domestication and the “Domestication Bottleneck”


From: Doebley JF, Gaut BS, Smith BD (2006) The molecular genetics of crop domestication. Cell 127: 1309–1321

From: Tanksley, S.D., and S.R. McCouch. 1997. Seed banks and molecular maps: Unlocking genetic potential from the wild. Science 277:1063–1066.

From: Doebley et al. 2006

From: Doebley et al. 2006

Genetic Diversity – What does it mean?

Diversity is a relative term:In this class we will use genetic diversity when referring to many diversity levels. Similarly geneticists and breeders mean different things when talking about diversity. Make sure it is clear at what level we are interested in!

Genetic diversity (GD) of all wild and cultivated wheat

GD of all cultivated wheat

GD in Elite TAMU material

GD in KSU program

GD in TAMU program

GD in MSU program

GD in a specific bi-parental derived population


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What Type of Variation Cause the Diversity We Breed for in ...maizeandgenetics.tamu.edu/SethCMurray/Teaching/Lectures/S2010... · What Type of Variation Cause the Diversity We Breed