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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 = (Xi - 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
Xi = the ith 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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σ2 = Σ(Xi - 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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S2 = Σ(Xi - x̄)2 / (n - 1)
or
S2 = (ΣXi2 - ((ΣXi)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 non-existence. 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(XiYi - n *X̄*Ȳ)) / (n-1) |
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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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rxy = (Cov(x,y)) / (sx * sy)
rxy = ryx |
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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 |
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Definition
Y = a + byxX
this is Y on X, i.e. byx ≠ bxy
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 |
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Definition
byx = (Cov(X,Y)) / (Var(X))
bxy = (Cov(X,Y)) / (Var(Y))
byx ≠ bxy |
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