statistical tools in genetics

8/9/2019 Statistical Tools in Genetics

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Mrs. OFELIA SOLANO SALUDARDepartment of Natural Sciences

University of St. La Salle



POPULATION- consists of the entire groupof individuals measured for some variablequantitative character. Since it is rarelysufficiently finite for all individuals to bemeasured, descriptions of populations

must be drawn from its SAMPLES .STATISTICS- measurements derived froma sample.PARAMETERS - attributes of thepopulation from which the sample wasdrawn. The larger the sample size, themore accurately the statistic estimates theparameter.



MEAN - average phenotypic value for a normallydistributed trait. It is equal to the sum of individual measurements divided by thenumber of individuals measured.

VARIANCE - measures variability of the sampleor population. The larger the variance, the

greater the spread of measurements in adistribution about its mean.



STANDARD DEVIATION- reflects the extent towhich the mean represents the entirepopulation.

If a large number of sample means wereplotted, the distribution will be in the form of a normal curve.

A range is arrived at which there is 68.28%,95.44%, or 99.74% confidence that the rangeof sample means lies within the populationmean.



Calculate themean, variance,

and standarddeviation of annual milkproduction

(hundreds of pounds) for this

sample of 10cows.

60 74 5861 56 5554 57 65

42



STANDARD ERROR OF THE SAMPLE MEANS -represents an estimate of the means of the many

samples that might be taken, and is a measure of thecloseness with which the sample meanrepresents the population mean.

Example: Which of the following seeds should

be used by a farmer for planting? Mean of hybrid corn seed 7.95 in 7.88

Standard deviation 0.52 0.23Standard error of sample mean 0.05 0.02

Sample 1: 7.95 in. +/- 1s = 8.47 - 7.43 in.7.95 in. +/- 2s = 8.07 - 6.93 in.

Sample 2: 7.88 in. +/- 1s = 8.11- 7.65 in.7.88 in. +/- 2s = 8.34- 7.42 in.



STANDARD ERROR OFTHE DIFFERENCE IN

MEANS- determinesthe likelihood that 2

sample meansrepresent genetically

different populations.

Days

55 1

56 6

57 9 1

58 40 1

59 28 2

60 14 3

61 2 3 4

62 6 9

63 20 10

64 31 12

65 19 14

66 10 20

67 8 7

68 1 4

69 3

70 3

71 1

72 2

73 1

74 1

75 4 1

76 12 1

77 20

78 35

79 15

80 10

81 3

82 1

x 58.38 77.92 64.22 65.14

s 1.14 1.43 1.49 3.43

s x 0.114 0.143 0.149 0.343

S d 0.183 0.374

Parental and progenystrains of tomato based

on days required toreach maturity



If the difference in sample means is greaterthan 2x the standard error of the difference of sample means, the difference in sample meansis considered significant.

S d = square root of: (s x1 )2 + (s x2 )2

x1- x2 77.92 - 58.38 = 108 xS d 0.183

NUMBER OF POLYGENE PAIRS

n = R 2

8 (s 2F2 ² s 2 F1)



The CORRELATION COEFFICIENT (r) , measures thestrength of association of 2 characteristics. To

determine how these characteristics are correlated,the covariance (cov) of x and y is first obtained:

The correlation coefficient (r) is thenobtained by:

A correlation coefficient can theoretically range from-1 to +1. A positive value indicates that there is a direct association between the variables; as one variableincreases, the other variable also tends to increase. Anegative correlation coefficient indicates that there is

an inverse relation between the two variables.



Regression is used to predict the value of one variable on thebasis of the value of a correlated variable. This technique plays animportant role in quantitative genetics because it allows us topredict characteristics of offspring from a given mating, evenwithout knowledge of the genotypes that encode thecharacteristic.A regression line defines the relation between twovariables. The regression coefficient and y

intercept can be obtained mathematically. Theregression coefficient (b) can be computed fromthe covariance of x and y (cov xy) and the varianceof x (sx 2 ) by :

After the regression coefficient has been

calculated, the y intercept can be calculated bysubstituting the regression coefficient and themean values of x and y into the following equation:

The regression equation (y = a-bx) can then be usedto predict the value of any y given the value of x.



A regression line of the weights of fathers against theweights of sons. Each father²offspring pair is

represented by a point on the graph: the x value of apoint is the father·s weight and the y value of the point

is the offspring·s weight.



HERITABILITY is the total phenotypic variation that isdue to genetic differences.

Phenotypic variance (V P ) in a characteristic can bedivided into components that are due to additive geneticvariance (V G), dominance genetic variance (V D), genicinteraction variance (V 1), environmental variance (V E),and genetic²environmental interaction variance (V GE ).

This model deals strictly with the observablephenotypic variance among individual members of apopulation; it says nothing about the absolute value of the characteristic or about the underlying genotypes

that produce the differences.

Since genetic variance includesadditive genetic variance (VA),Hence, phenotypic variance =



Broad-sense heritability is the proportion of thephenotypic variance that is due to genetic variance.

It can be estimated by eliminating the environmentalvariance component.It is useful in predicting the outcome of artificialselection among clones, inbred lines, or varieties.Broad-sense heritability can potentially range from 0

to 1. A value of 0 indicates that none of the phenotypicvariance results from differences in genotype and allof the differences in phenotype result fromenvironmental variation.A value of 1 indicates that all of the phenotypic

variance results from differences in genotype.A heritability value between 0 and 1 indicates that both genetic and environmental factorsinfluence the phenotypic variance.



Example: Sewall Wright determined that for whitespotting in a genetically variable population of guinea

pigs, V P = 573. Inbreeding them for many generationsobtained V P = 340. Because V G = 0 in this group, V P =VE. Assuming this value of environmental variance forthe original population, their genetic variance can beestimated:

Estimating the broad-senseheritability (H 2), 41% of the variationin spotting of guinea pigs in was dueto differences in genotype.



Narrow-sense heritability is the proportion of the phenotypicvariance due to additive genetic variance. V A determines theresemblance between parents and offspring.

h 2 is used for prediction when artificial selection is carriedout in a randomly mating populationIt can be estimated by comparing the phenotypes of parents and offspring or by comparing phenotypes of individuals with different degrees of relatedness, such asidentical twins and nonidentical twins.



Recurrence risks of common abnormalities. Diagonal linesare the theoretical risks for threshold traits with theindicated values of the narrow-sense heritability of

liability. Horizontal lines are the theoretical risks for simpledominant or recessive traits.



Heritability provides information only about thedegree to which variation in a characteristic results

from genetic differences.It does not indicate the degree to which acharacteristic is genetically determined.

Heritability is based on the variances present within agroup of individuals, and an individual does not haveheritability.Heritability of a characteristic varies amongpopulations and among environments.

Even if heritability for a characteristic is high, thecharacteristic may still be altered by changes in theenvironment.Heritabilities provide no information about the natureof population differences in a characteristic.

LIMITATIONS OF HERITABILITY



Covariance and correlation are important in quantitativegenetics, because the correlation coefficient of a trait between individuals with various degrees of genetic

relationship is related fairly simply to the narrow-senseor broad-sense heritability.



INBREEDING means mating between relatives, suchas first cousins. The most widely used measure of

inbreeding is called the inbreeding coefficient,symbolized F. The inbreeding coefficient of anindividual is the probability that the individual carriesalleles that are identical by descent.

(A) Aninbreedingpedigree in

whichindividual I

results from amating

between half siblings.



(C)Calculation

of theprobability

that the alleles

indicated areidentical by

descent.



(B) The samepedigree redrawn

to show gametesin the closed loopleading to

individual I. Thecolored dots

represent alleles of a particular gene.



Q UANTITATIVE TRAIT LOCI ( Q TL) are genesthat control polygenic characteristics.

Q TLs can be mapped by examining theassociation between the inheritance of aquantitative characteristic and theinheritance of genetic markers.The mapping of numerous genetic markerswith molecular techniques has made Q TLmapping feasible for many organisms.Locating Q TLs in the genome is important tothe manipulation of genes in breedingprograms and to the cloning and study of genes in order to identify their functions



Location of Q TLs for several

quantitative traitsin the tomato

genome. Thegenetic markers

are shown foreach of the12

chromosomes. Theregions in which

the Q TLs arelocated are

indicated by thebars: green for

fruit weight; blue for content of

soluble solids; anddark red bars foracidity (pH). The

data are fromcrosses between

Lycopersiconesculentum and

Lycopersiconchmielewskii.

statistical tools in genetics

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