Animal science
Study-unit Code
In all curricula
Camillo Pieramati
  • Camillo Pieramati
  • 54 ore - Camillo Pieramati
Course Regulation
Coorte 2022
Learning activities
Discipline biologiche
Academic discipline
Type of study-unit
Obbligatorio (Required)
Type of learning activities
Attività formativa monodisciplinare
Language of instruction
Descriptive statistics: central tendency measures, variability measures, the normal distribution.
Qualitative traits: population genetics, frequency estimation, inference on frequencies.
Quantitative traits: additive model, heritability and repeatability, relationship and inbreeding, genetic index.
Reference texts
- R. Bourdon "Understanding Animal Breeding", Prentice Hall ed.
- A. Petrie & P. Watson "Statistics for Veterinary and Animal Science", Wiley-Blackwell ed.
Teaching stuff by the lecturer is available from UniStudium website.
Educational objectives
The module provides the basis to:
- collect and analise data from breeding farm or from trials in an scientific way and by means of information technology;
understand the key role of genetics in animal production.
The required abilities are:
- calculating descriptive statistics;
- using the normal distribution;
- analysis of Mendelian ratios;
- estimates of genetic frequencies and analysis of the Hardy-Weinberg equilibrium;
- calculating relationships and inbreeding.
The main goal of the module is to prepare the student to use the aforementioned knowledge and skills in a competent way, first it in the following disciplines of the degree course, and then in the professional activity.
It is compulsory to have passed the "Biology and genetics" exam; for some biometrics topics, it is useful to have passed the exam of "Mathematics and Physics".
Teaching methods
The lectures will cover all the main topics of the program. About 30% of the time is spent in solving small problems by means of a spreadsheet or "R" software, in order to apply the theorical and methodological knowledge.
Other information
Attendance is not mandatory, but it is strongly advised.
Learning verification modality
Written exam (15 single choice questions and 3 simple exercises) to verify the knowledge and the abilities, then an oral exam to verify competence. During the course there are two optional exams (each one with 10 questions + 2 exercises): the first one on descriptive statistics and the other on population genetics.
Extended program
- Introduction: the contents and the goal; the teaching aids; reference books; the exam; tutorship.
- What is "Animal biometrics"? Why do we need "stats" in Animal Science? Quantitative and qualitative traits. Population and sample; randomness; pseudo random numbers; random numbers table. Sampling techniques. Random error and sistematic error.
- Measuring the central tendency: the arithmetic mean; the average in the discrete distribution case and in the continuous distribution case. Geometric mean, harmonic mean, quadratic mean: calculation and main applications. The mean of "t" order. Position averages: median (single data samples, discrete data samples or interval data samples), mode, central value, quartiles (boxplot), percentile. Properties of the means.
- Measuring the variability: the sum of the residuals in a population or in a sample; the median and the sum of the residual modules; the sum of squared residuals. Population and sampling: the degrees of freedom, the mean square of the residuals (variance) and the standard deviation. The variability coefficient. Skewness and kurtosis. Eterogeneity of qualitative traits. Concentration in transferable traits. The central limit theorem and the standard error.
- The normal distribution; z, the standard deviate; the table of areas under the normal curve. Solving problems: one point direct problem (area of a tail) and two points direct problem (area of an interval); the inverse problem with one or two tails. Calculating the average value of a tail: use of the normal density table; the average value of an interval; the variance of a tail and the variance of an interval.
- Population genetics. The Hardy-Weinberg law. The genetic equilibrium: the proof starting from allelic frequencies and starting from genotipic frequencies. Reaching the genetic equilibrium: after selection; after the crossing of two populations; the X-linked loci. The heterozigosity in 1st and in 2nd generation after crossing: complementary traits and heterosis. One-time mutation and repeated mutations; the loss of the "one-time" mutations; dominant or recessive mutations, and positive or negative mutations; the equilibrium between direct and reversed mutations; the equilibrium between mutation and selection. The test matings; genotyping carriers. Migration: the frequency trend; a zootechnical classification of crossings. Selection: definition; the frequency trend of a lethal recessive gene in natural selection; the selective advantage of the heterozygote and the equilibrium frequencies; calculating the fitness. Genetic drift: the binomial distribution and the population size.
- Statistical inference on frequencies: the "chi" squared distribution; the degrees of freedom. Testing the Mendelian ratios in a single locus by means of the "chi" squared; testing the linkage between two loci; the decomposition of the degrees of freedom. Contingency tables: calculating the expected values and the degrees of freedom. The "chi" squared test and the H-W equilibrium; degrees of freedom: estimating frequencies from samples or using a priori values; the X-linked allele case.
- The difference between qualitative and quantitative traits: an introduction to the additive infinitesimal model; the additive (independent) effect and the dominance or interaction-epistatic (combination) effects; the meaning of "interaction": the genotype-environment interaction; temporary or permanent environment; common (contemporary) or individual environment. The composition of phenotypic variance. The meaning of covariance: the genotype-environment covariance, preferential treatment, covariance between mates, linkage disequilibrium, correlation between traits. Heritability in the broad-sense (degree of genetic determinism), heritability in the narrow-sense and repeatability of quantitative traits. Performance test and progeny test. The flaws of the additive model. Population mean, mean effect of a gene and substitution effect in a biallelic locus. Semi-quantitative genetics: threshold traits and major genes.
- Similarity between genomes. Alike in state genes and identical by descent genes. Jacquard's identity coefficients. Direct relationship and correlated relationship. The relationship according to Sewall Wright. Additive relationship and IBD probability (kinship). Inbreeding and self-relationship. Dominance relationship and interaction-epistatic relationships: the combination within a locus and between loci. Additive relationship and dominance relationship: a comparison between half-sibs and full-sibs. The tabular method of Emik & Terrill to calculate additive relationship in a whole population. Covariance between individual genetic values and higher order relationships. The relationship according to both pedigree data and molecular data: gametic relationship and the "pedigree of genes"; from probabilistic gametic relationship to true gametic relationship; from gametic relationship to effective additive or dominance relationships. The relationship according to molecular data: alike in state and average relationship in a population; the "Z" matrix (residual from expected frequencies) and the genomic relationship; from alike in state to IBD: phasing alleles and haplotype reconstruction. Wright's formula for inbreeding calculation. Inbreeding and recessive abnormalities; inbreeding depression of quantitative traits. The use of relationships: a minimal example of genetic index.
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