Midterm Flashcards
A measure of the central tendency of a set of random variables
Mean
Measures how widely the values of a variable in a set vary
Variance
Measures how much a set of two variables vary together
Covariance
It is the expectation of the squared deviation of a variable from its mean
Variance
It is their average or expected value
Mean
It is the expectation of the product of the deviations of two variables from their respective means
Covariance
Measures the degree and direction of the relationship between two variables
Correlation
Measures the expected change in one variable per unit change in another variable
Regression
Expected value of a constant =
Constant
Expected value of a random variable =
Sum of all values of random variable/ n
What can you do so that the sum of (xi - mean of x) does not equal zero
Square the deviation
Variance equation
= sum (X^2 - 2X(mean X) + (meanX)^2)
Sample variance equation V(X)
(1/(n-1)) * sum(Xi^2 - 2Xi(meanX) + (meanX)^2)
Sample variance V(aX)
= a^2V(X)
Correlation equation
Cov(X,Y)/ (sqrt V(X)*V(Y))
Doesn’t matter order
Not causative
Unitless
0 = unrelated
Correlation
Order matters
Y on X = X is causing Y
Denominator is always variance of the variable that’s causing the other variable (the second variable)
Regression
Regression equation
= Cov(X,Y) / V(X)
ANOVA means
Analysis of variance
Sums of squares equation
SST=SSR+SSE
SST is the
Total sums of squares
SSR is the
Regression sums of squares
SSE is the
Error sum of squares
Mean Yi is the
Mean of observations for the ith individual
The proportion of the alleles in a population at a locus that are of a particular type
Allele frequency
Proportion of individuals in a population with a particular genotype at a particular locus
Genotyped frequency
f(B) = p =
2 * (no. of BB individuals) + 1 * (no. of Bb individuals) / 2 * (total no. individuals)
f(b) = q =
2 * (no. of bb individuals) + 1 * (no. of Bb individuals) / 2 * (total no. individuals)
q =
1-p
f(B) and f(b) are
Allele frequencies
f(BB) and f(Bb) and f(bb) are
Genotypic frequencies
f(BB) = P =
No. of BB individuals / total no. individuals
f(Bb) = H =
No. of Bb individuals / total no. individuals
f (bb) = Q =
No. of bb individuals / total no. individuals
Even though alleles occur in a ____ state in individuals, they are transmitted ____ from parent to progeny
Paired
Singly
How can the allele frequency be the same in sires and dams
If there is random mating and no selection in a large population
OR
If selection occurs at the same rate in males and females
Hardy Weinberg equilibrium assumes
Allele frequencies in progeny = those in their parents
Used to describe computations
Summation and dot notation
Rule 1: sum involving a constant
Ec = c+c+c+c …. +c = nc
Rule 2: sum of sequential positive integers
Ej = 1+2+3+ …. +n = n(n+1) / 2
Rule 3: sums of the squares of sequential positive integers
Ek^2 = 1^2+2^2+3^2+ …. n^2 = n(n+1) * (2n+1) / 6
An equation where any x plugged into an equation will yield exactly one value of y
Function
Use a dot to signify a summation over a subscript
Dot notation
Dot notation single subscript
Exi = x1+x2+x3+ …. xn = x.
What equation does dot notation not work
Exi^2 = x1^2+x2^2+x3^2+ ….. xn^2
Dot notation square of sum of xis
(Exi)^2 = (x1+x2+x3+ ….. xn)^2 = (x.)^2
Useful to introduce concepts of quantitative variation
Single locus model
Inter locus gene action
Different locus
Epistasis
Intra locus gene action
Within a locus
Dominance
Non-additive gene actions
Dominance
Epistasis
Does not pass parent to offspring
Stick with animal throughout lofetime
Our observation of the measurement of a trait
Continuous trait
Phenotypic value (P)
Examples of phenotypic value
Milk yield
Fiver diameter
Birth weight
Back fat thickness
P =
G+E
G is the
Genotypic value
E is the
Environmental value
Represents the effects of the combination of alleles across loci that an animal inherited
Genotypic value
Captures all non-genetic factors that impact the phenotypic value
Environmental value
d = 0 means
There is no dominance
Strictly additive gene action
d = a or d = -a means
There is complete dominance
d>a or d<-a means
There is overdominance
d lies between 0 and +a means
Incomplete or partial dominance
Mean equation
M = a(p-q) + 2pqd
a(p-q) is attributable to
Homozygotes
2pqd is attributable to
Heterozygotes
The vale of ___ reflects both the mean phenotypic and genotypic value of the population
M
Positive mean means that we anticipate
The (blank) rate to be increased on average by _____ if the allele had been introduced into a population at this frequency
With no dominance the mean only is a function of the difference in
Allele frequencies
If we assume that each loci acts independently (ignore epistaxis) then their joint contribution is simple the
Some of their individual effects
Parents only transmit or pass their _____ and not their ______ to their progeny
Alleles
Genotypes
The mean deviation from the population mean of individuals that allele from one parent, while the allele received from the other parent came at random from the population
Average effect of an allele
Increasing the frequency of allele increases the _____
Mean
Because the average effect of the allele becomes less
As the extent or degree of dominance increases, an _____ in the frequency of the allele, f(B), has a _____ impact on the population mean and on its average affect
Increase
Greater
The average effect of the allele is simply a function of changes in f(B) and the genotyped value a with
No dominance
Re-express the average effect as the difference between the average effects of the pair of alleles
Average effect of an allele substitution
What determines the mean genotyping value of their progeny?
The average effects of a parent’s alleles
The breeding value of an individual is equal to
Sum of the pair of alleles it carries across all loci
The average breeding value of its parents
Expected breeding value
The genotyping value can be represented as
G= A+D
D means
Dominance deviation
A means
Breeding value
Mean breeding value and mean dominance deviation value equals
Zero
Because they are expressed as deviations from their respective means
Depends on allele frequencies and the additive effect of allele substitution
Variance (additive genetic variance)
Depends on allele frequencies and the degree of dominance
Dominance deviation variances
Variances are usually maximized at
Intermediary allele frequencies
What typically makes up most of the genotypes variance except in the unusual cases of overdominance or extreme allele frequencies
Breeding value
IAB is the
Epistatic deviation
Multiple loci means our genetic model is
G = A+D+I
What are commonly important sources of environmental effects on performance?
Nutritional and climatic factors
Environmental effects that remain with an animal throughout its lifetime
Ex. Chronic injuries, diseases, training
Permanent environmental effects
Temporary environmental effects examples
Illness that passes
Temporary nutritional deficiency
Phenotypic model
P - mean = A+D+I+EP+ET
If the phenotypic variance is large, observations lie ______ ___ the mean, and the mean provides ____ information about the population
Farther from
Less
V(G) =
V(A) + V(D) + V(I)
Correlation between repeated records on an individual
Repeatability
Repeatability equation
V(G) + V(EP) / V(P)
Heritability broad sense equation
V(G) / V(P)
Heritability in narrow sense equation
V(A) / V(P)
Indicates that repeated performance records an on animal are very much alike
High repeatability
A method for separating total variation between observations into its component parts
ANOVA
A measure of the size of the differences of the repeated observations within an individual group
Within-group variation
A measure of the size of the differences between groups
Between-group variation
The number of independent pieces of information on which the estimate is based
Degrees of freedom
The value of repeated records is that they can
Reduce the variance of a mean
Smaller variances = more exact measurements
When r>0, repeated records will influence the
Variance of a mean
With a high repeatability, repeated measures do _____ to reduce the variance of the mean
Little
A low repeatability has a _____ impact on reducing the variance of the mean
Large
The percentage of phenotypic difference in the parent observed in the offspring
The proportion of the parents’ superiority or inferiority that is passed onto their offspring
Heritability
Can be used for prediction
The regression of adduce or breeding value on phenotype
Heritability
Heritability is the _____ limit of repeatability
Lower
