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Traits or Characters that are affected by one or few genes, and follow a discontinuous variation. 


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discontinuous traits quantitative traits 


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distribution of genotypes is affected by... 

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the number of genes involved 


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what happens as the number of genes affecting a trait increases? 

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the transition between each genotypic class becomes less distinct, such that it resembles a bell curve, known as normal distriibution 


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Traits that are affected by many genes, and exhibit continuous variation 


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some examples of quantitative traits 

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growth egg weight breast meat yield 


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Quantitative traits are... 

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traits affected by many genes 


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other than each other, what do alleles interact with to produce traits? 

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The analysis of a quantitative trait starts by... 

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describing the phenotype of a given trait in a population 


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the distribution most quantitative traits follow 

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the statistical parameters that govern normal distribution 

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standard normal distribution 

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A normal distribution with a mean of zero and a variance of 1 


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amount of population within 1 standard deviation of the mean in a standard normal distribution (μ – 1σ and μ + 1σ) 

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amount of population within 2 standard deviation of the mean in a standard normal distribution (μ – 2σ and μ + 2σ) 

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amount of population within 3 standard deviation of the mean in a standard normal distribution (μ – 3σ and μ + 3σ) 

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how to calculate proportions of a normal distribution 

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Z = (X_{i}  μ) / σ
then find probability of it on the Z score table 


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symbols for mean, variance, and standard deviation for population and sample 

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population standard deviation 


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sample standard deviation 


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Mean = x̄ = (ΣX) / n
x̄ = mean phenotypic value of the sample
X_{i} = the i^{th} phenotypic value
Σ = the summation sign 


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in the breeding context, this refers to differences among individuals in a population 


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Variation is the source of... 

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the raw material for geneticists 

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The most commonly used measures for variation 

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variance standard deviation 


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Variation is measured by... 

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variance or standard deviation 


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how to calculate variance 

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σ^{2} = Σ(X_{i}  μ)^{2} / N
N = number of individuals in that population 


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the best estimate of population variance 

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how to calculate sample variance 

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S^{2} = Σ(X_{i}  x̄)^{2} / (n  1)
or
S^{2} = (ΣX_{i}^{2}  ((ΣX_{i})^{2} / n)) / (n  1) 


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how to calculate standard deviation 

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Y increases as X increases 


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Y decreases as X increases 


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Y stays the same as X increases or decreases 


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3 basic concepts of covariation 

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1.The direction or sign of the relationship, i.e. whether the relationship is positive, negative or nonexistence. 2.The strength of the relationship. 3.The amount of change in one variable that can be expected for a given amount of change in another variable. 


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1. Covariance 2. Correlation 3. Regression 


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the average product of deviation from the means of two variables 


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how to calculate covariance 

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Cov(X,Y) = (Σ(X_{i}Y_{i}  n *X̄*Ȳ)) / (n1) 


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a measure of the degree of the relationship between two variables; indicates relationship and strength of it 


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how to calculate linear corelation 

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r_{xy} = (Cov(x,y)) / (s_{x} * s_{y})
r_{xy} = r_{yx} 


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The simplest functional relationship of one variable to another 

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the simple linear regression 


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the quantitative change in one variable that can be expected for a unit change in another variable 


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the variables involved in linear correlation 

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dependent variable independent variable 


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relationship between dependent and independent variable 

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the magnitude of the dependent variable is determined by the magnitude of the independent variable 


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the relationship between dependent and independent variables if they're linearly related 

Definition
Y = a + b_{yx}X
this is Y on X, i.e. b_{yx} ≠ b_{xy}
Y = the dependent variable
X = the independent variable
b = regression coefficient
a = point of intersection (the value of Y when X =0) 


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linear regression on a graph 

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how to calculate regression variable 

Definition
b_{yx} = (Cov(X,Y)) / (Var(X))
b_{xy} = (Cov(X,Y)) / (Var(Y))
b_{yx} ≠ b_{xy} 


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The most important question about quantitative traits 

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whether or not genes influence the observed variation in the trait 


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comprises of the individual’s genetic value and influences from the environment 


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all nongenetic influences (diet, housing, disease, management) 


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some types of environmental factors 

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diet housing disease management 


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how to calculate phenotype value (P)
equation for phenotype (P), genotype (G), and environment (E) 

Definition
Phenotype (P) = Genotype (G) + Environment (E)
phenotype (P) = Allele value (A) + Dominance (D) + Epistasis (I) + environment (E) 


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the basis for genetic improvement 

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differences in genetic values 


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why the genetic worth of an individual cannot be judged from the phenotypic value 

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because phenotypic and genotypic ranking could be different 


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variation is expressed as... 

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Variance
phenotype (P) = genotype (G) + environment (E) 


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how to calculate genotypic value 

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Genotype (G) = Allele value (A) + Dominance (D) + Epistasis (I) 


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variance components and their symbols 

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Phenotypic variance, V_{P} 

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The total variance is the variation in the performance for a trait between individuals in a population. 


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Genotypic variance, V_{G} 

Definition
The variance in the genotypic values for a trait. The genotypic value is the combined effect of... (1) all the alleles at all loci (2) intraloci interactions (3) inter loci interactions that affect a trait. 


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Additive Genetic variance, V_{A} 

Definition
The variation among alleles transmitted from parents to offspring that affect a trait. The sum of the effect of alleles transmitted from a parent to its offspring for a trait is the Breeding Value (BV) of the parent for that particular trait. 


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Definition
The sum of the effect of alleles transmitted from a parent to its offspring for a trait 


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Dominance Genetic Variance, V_{D} 

Definition
Genetic variation that occurs as a result of interaction among alleles at a locus. This effect is not accounted for by the effect of two alleles taken singly. For example, assuming the value of A_{1} is 2, and value of A_{2} is 3, however the value of the two alleles combined, A_{1}A_{2} is 7. The dominance deviation in this case is 7  (2+3) = 2. The combined effect of the two alleles is not additive. The dominance genetic variance measures the nonadditive effect between alleles at a locus. 


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Epistasis Genetic Variance, V_{I} 

Definition
Genetic variation that occurs as a result of interaction among alleles at different loci. This is also the nonadditive effect between genes at different loci. 


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“Nonadditive genetic variance” 

Definition
dominance and epistasis genetic variations.
nonadditive = V_{D} + V_{I} 


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Environmental Variation, V_{E} 

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Variation in a trait among animals in a population caused by nongenetic factors, e.g... housing feed temperature disease activity etc. 


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The source of variation in a phenotypic value of a trait can be due to... 

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1: genotypic variation 2: environmental variation 


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some types of genotypic variation 

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1: additive genetic variation 2: nonadditive genetic variation 


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types of nonadditive genetic variation 

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heritability in the broad sense 

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the extent to which an individual’s phenotype is due to its genotype 


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how to calculate heritability in the broad sense (H^{2}) 

Definition
H^{2} = V_{G} / V_{P}
or
H^{2} = (V_{A} + V_{D} + V_{I}) / (V_{A} + V_{D} + V_{I} + V_{E}) 


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Definition
heritability in the broad sense 


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heritability in the broad sense reflects the importance of heredity due to... 

Definition
(1) transmission of alleles from parents (2) dominance deviations created at all loci during the formation of zygotes (3) Epistasis deviations created across all loci in the formation of zygotes, in determining phenotypic values 


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when Dominance and Epistasis deviations are reconstituted 

Definition
any time a zygote (an individual) is formed and therefore create noise in determining the direct influence of allele values in determining phenotypic values 


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heritability in the narrow sense (h^{2}), or just heritability 

Definition
the extent to which phenotype is determined by alleles transmitted from parents to offspring 


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how to calculate heritability in the broad sense (h^{2}) 

Definition
h^{2} = V_{A} / V_{P}
or
h^{2} = V_{A} / (V_{A} + V_{D} + V_{I} + V_{E}) 


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Definition
heritability in the narrow sense 


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why heritability is important in breeding programs 

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because it determines the degree of resemblance between relatives 


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how to calculate Genotypic variance, V_{G} 

Definition
V_{G} = V_{A} + V_{D} + V_{I} 


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how to calculate Phenotypic variance, V_{P} 

Definition
V_{P} = V_{A} + V_{D} + V_{I} + V_{E} 


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An alternative meaning of heritability 

Definition
the regression of allelic value on phenotypic value 


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how to calculate linear regression (b_{OP}) on 1 parent 

Definition


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how to calculate heritability (h^{2}) on 1 parent 

Definition
h^{2} = 2 b_{OP}
h^{2} = b_{AP} = ((Cov(A,P)) / V_{P}) 


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how to calculate Additive Genetic variance (V_{A}) on 1 parent 

Definition


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how to calculate covariance (Cov (O,P)) on 1 parent 

Definition


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relationship between heritability (h^{2}), linear regression (b_{OP}), and covariance (Cov (O,P)) 

Definition
h^{2} = 2 b_{OP} = ((Cov(O,P)) / V_{P}) = ((1/2 * V_{A}) / V_{P})
V_{A} = 2 (Cov, OP) 


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the genetic merit of an animal for a given trait. BV is expressed as a deviation from the mean genetic merit of the trait within a defined population 


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The genotype of an individual consists of... 

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(1) allelic values (2) dominance values (3) epistastic values 


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how to calculate an animal's transmitting ability (TA) 

Definition
TA = 1/2 * EBV
EBV = expected breeding value 


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how to calculate breeding value (BV) 

Definition
BV = h^{2}p
BV = 2 * (P  [Pbar]) 


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how to calculate expected breeding value (EBV) 

Definition
EBV = h^{2} * (P  [Pbar])
EBV = ((nh^{2}) / (1 + (n  1)r_{e})) * (P  [Pbar])
EBV = ((ngh^{2}) / (1 + (n  1)_{t})) * (P  [Pbar])
g = genetic relationship (1/2 for full siblings and 1/4 for half siblings) 


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how to calculate accuracy (ACC) of EBV 

Definition
Acc = √(h^{2} * g)
Acc = √((((nh^{2}) / (1 + (n  1)r_{e}))) * g)
Acc = √((((ngh^{2}) / (1 + (n  1)_{t}))) * g)
g = genetic relationship (1/2 for full siblings and 1/4 for half siblings) 


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a measure of the reliability or strength of the relationship between repeated measurements on an individual 


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b_{AP} = ((Cov(A,P)) / V_{P})
b_{AP} = (nh^{2}) / (1 + (n  1)r_{e}) 


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genetic relationship between full siblings (FS) 

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genetic relationship between half siblings (HS) 

Definition


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similarity among full siblings (t) 

Definition
t_{FS} = (1/2 * h^{2}) + c^{2}_{FS}
c^{2} = environmental correlation among siblings 


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similarity among half siblings (t) 

Definition
t_{HS} = (1/4 * h^{2}) + c^{2}_{HS}
c^{2} = environmental correlation among siblings 

