Time to Pay Off Debt. Victor owes $20,000 on his credit card. The annual interest rate is 17%. a. Approximately how many years will it take him to pay off this credit card if he makes a monthly payment of $300? b. Approximately how many years will it take him to pay off this credit card if he makes a monthly payment of $400?

ANEQ 328 Foundations In Animal Genetics Week 13 Class Notes (4/12/16-4/14/16) Must Know Statistics: Especially To Understand Quantitative Genetics Important Background Information o Population A breeding population of animals. o Value A numeric value applied to an individual as opposed to a population. Phenotypic Trait o Trait A genetically determined characteristics. Trait doesn’t always equal phenotype. o Simple Trait When a gene is controlled by 1 or a few loci. Can be qualitative or categorical. Ex. The coat color of a horse is only controlled by a few loci. o Complex Trait When a gene is controlled by many loci. Can be quantitative or polygenic. Ex. Milk production in cows in controlled by many loci. o Mean The average of a set of numbers. To calculate: Just add up all the numbers, then divide by how many numbers there are. Normal Distribution (Bell Curve) o The statistical distribution that appears graphically as a symmetric, bell- shaped curve. Frequency Category ANEQ 328 Foundations In Animal Genetics Week 13 Class Notes (4/12/16-4/14/16) About 66% of the animal population will fall within the Standard Deviation of the mean. About 95% of the animal population will fall with 2 Standard Deviations of the mean. 99% of the animal population will fall within 3 Standard Deviations of the mean. Mean () o The average of a set of numbers. To calculate: Just add up all the numbers, then divide by how many numbers there are. Units: o Using the following data to calculate the mean of the weaning and yearling weights. Calf ID Weaning Weight (lbs; X) Yearling Weight (lbs; Y) CSU 2001 500 1100 CSU 2002 475 1050 CSU 2003 525 1150 Weaning Weight Mean Calculation (500 + 475 + 425) 1400 = = 466.67 3 3 Yearling Weight Mean Calculation (1100 + 1050 + 1150) 3300 = = 1100 3 3 Variance ( ) o Differences among individuals within a population. 2 ∑(− ) 2 (1 − ) +2 ) 3(− ) …… Equation: = −1 or = −1 o Using the following data to calculate the variance of the weaning and yearling weights. Calf ID Weaning Weight (lbs; X) Yearling Weight (lbs; Y) CSU 2001 500 1100 CSU 2002 475 1050 CSU 2003 525 1150 o We know that the number in our population is 3 calves, so n=3. ANEQ 328 Foundations In Animal Genetics Week 13 Class Notes (4/12/16-4/14/16) Weaning Weight Variance Calculation (500 − 500) + (475 − 500) + (525 − 500) ()2 + −25 )2+ 25 ) 0 + 625 + 625 1250 = = = = 625 = 2 3 − 1 2 2 2 Yearling Weight Variance Calculation (1100 − 1100) + (1050 − 1100) + (1150 − 110)+ −50)2+ 50)2 0 + 2500 + 25005000 2 2 3 − 1 = 2 = 2 = 2 = 2500= Standard Deviation () o The average deviation from the mean. The square root of the variance. Equation: √ 2 o Using the following data to calculate the standard variation of the weaning and yearling weights. Calf ID Weaning Weight (lbs; X) Yearling Weight (lbs; Y) CSU 2001 500 1100 CSU 2002 475 1050 CSU 2003 525 1150 o Based on previous calculations we know that 2 = 625 and 2= 2500 .2 Weaning Weight Standard Deviation Calculation 2 = 625 = 62√ = 25= Yearling Weight Standard Deviation Calculation 2 2 = 2500 = √2500 = 50 = Standard Error (SE) o Equation: or √ √ o Using the following data to calculate the standard error of the weaning and yearling weights. ANEQ 328 Foundations In Animal Genetics Week 13 Class Notes (4/12/16-4/14/16) Calf ID Weaning Weight (lbs; X) Yearling Weight (lbs; Y) CSU 2001 500 1100 CSU 2002 475 1050 CSU 2003 525 1150 o Based on previous calculations we know that = 25 and = 50 and the number in our population is 3 calves, so n=3. Weaning Weight Standard Error Calculation 25 25 = = 15 = .500 ± 15 √ 3 Yearling Weight Standard Error Calculation 50 50 = 3 = 30 = .1100 ± 30 √ Covariance (Cov(x,y)) o How two traits or values vary together in a population. Equation: (1−)(1−)+ 2 −(2−)+ 3−(3−). −1 Has no units, just a positive or negative number. o Using the following data to calculate the covariance of the weaning and yearling weights. Calf ID Weaning Weight (lbs; X) Yearling Weight (lbs; Y) CSU 2001 500 1100 CSU 2002 475 1050 CSU 2003 525 1150 o We know that the number in our population is 3 calves, so n=3. Weaning Weight and Yearling Weight Covariance Calculation (500 − 500 1100 − 1100 + 475 − 500 1050 − 1100 + 525 − 500 1150 − 1100 ) 2500 = = 1250 3 − 1 2 o Covariation 1.) Positive or Negative Number 2.) Correlation shows the strength of a relationship. 3.) Regression show how much (amount). ANEQ 328 Foundations In Animal Genetics Week 13 Class Notes (4/12/16-4/14/16) Correlation (r) o A measure of strength of the relationship between two variables. (Cov(x,y)) Equation: = If the correlation is between 0 and 1 it demonstrates a strong relationship. If the correlation is between 0 and -1 it demonstrates a weak relationship. o Using the following data to calculate the correlation of the weaning and yearling weights. Calf ID Weaning Weight (lbs; X) Yearling Weight (lbs; Y) CSU 2001 500 1100 CSU 2002 475 1050 CSU 2003 525 1150 o Based on previous calculations we know that Cov(x,y( ))= 1250lbs and = 25 and 50. Weaning Weight and Yearling Weight Standard Correlation Calculation (Cov x,y ) = 1250lbs 1250 = = 1 (= 25)(= 50) (25)(50) Regression (b) o The expected or average change in one variable (y) per unit change in another (x). (Cov x,y ) Equation: ∗= 2 o Using the following data to calculate the regression of the weaning and yearling weights. Calf ID Weaning Weight (lbs; X) Yearling Weight (lbs; Y) CSU 2001 500 1100 CSU 2002 475 1050 CSU 2003 525 1150 o Based on previous calculations we know that Cov(x,y( ))= 1250lbs and 2 = 625. Weaning Weight and Yearling Weight Standard Regression Calculation (Cov x,y))= 1250lbs = 1250 = 2 2= 625 625 For every 1lb increase in weaning weight, yearling weight increases an average of 2 lbs. ANEQ 328 Foundations In Animal Genetics Week 13 Class Notes (4/12/16-4/14/16) Introduction to the Genetic Model for Quantitative Traits Important Background Information o Population A breeding population of animals. o Value A numeric value applied to an individual as opposed to a population. Phenotypic Trait o Trait A genetically determined characteristics. Trait doesn’t always equal phenotype. o Simple Trait When a gene is controlled by 1 or a few loci. Can be qualitative or categorical. Ex. The coat color of a horse is only controlled by a few loci. o Complex Trait When a gene is controlled by many loci. Can be quantitative or polygenic. Ex. Milk production in cows in controlled by many loci. Genetic Model for Quantitative Traits o Equation: P=+G+E P= Phenotypic Value The performance of an individual animal for a specific trait. = Population mean The average phenotypic value for the specific trait for all animals in the population. G= Genotypic value The genotypic values of the individual for the specific trait. E= Environmental Effect The environmental effects on the individual’s performance for the trait. Genetic Model for Quantitative Traits Including Breeding Value and Gene Combination Value o Equation: P=+BV+GCV+E P= Phenotypic Value The performance of an individual animal for a specific trait. = Population mean The average phenotypic value for the specific trait for all animals in the population. BV= Breeding Value The value of the individual as a parent, (the sum of the independent genotypes). ANEQ 328 Foundations In Animal Genetics Week 13 Class Notes (4/12/16-4/14/16) Ex. A= +5, a= -5 AA= Value of 10 aa= Value of -10 Aa= Value of 0 GCV= Gene Combination Value An individual’s genotypic value of gene interaction. E= Environmental Effect The environmental effects on the individual’s performance for the trait. Progeny Difference (PD) o The expected difference between the mean performance of the individual’s progeny and the mean performance of all progeny. Equation: PD= ½BV BV= Breeding Value The value of the individual as a parent, (the sum of the independent genotypes). Genetic Prediction and Its Data o The bigger the data the more accurate the EPD’s are. EPD’s get better as time goes on. By adding multiple traits, animal models, and pedigree’s to an EPD it makes it more accurate the younger the animal is. Genetic Model For Repeated Quantitative Traits o Producing Ability (PA) The performance potential of an individual for a repeated trait. Equation: PA= +BV+GCV+E +E p t = Population mean The average phenotypic value for the specific trait for all animals in the population. BV= Breeding Value The value of the individual as a parent, (the sum of the independent genotypes). Ex. A= +5, a= -5 o AA= Value of 10 ANEQ 328 Foundations In Animal Genetics Week 13 Class Notes (4/12/16-4/14/16) o aa= Value of -10 o Aa= Value of 0 GCV= Gene Combination Value An individual’s genotypic value of gene interaction. E = Permanent Environmental Effect p An environmental effect that permanently influences an individual’s performance for a repeated trait. Ex. Increase or decrease in performance. E t Temporary Environmental Effect An environmental effect that influences a single performance record of an individual but does not permanently affect an individual’s performance potential for a repeated trait. Ex. Dry summer results in low numbers being collected for the particular trait.