Mean and Variance Approach to Equilibrium Under Different Situations | Animal Husbandry & Veterinary Science Optional for UPSC PDF Download

Values and Means

• Value represents the measurable concept in metric units that defines the characteristics of an individual.
• The value observed when measuring an individual's character is known as the phenotypic value.

Genetic Properties Analysis

• To understand the genetic properties of a population, we need to break down the phenotypic value into parts influenced by different factors.
• The initial division involves components attributed to genotype and environment.

Genotypic Value and Environmental Deviation

• The genotypic value is the contribution of the genotype to the individual's overall value.
• The environmental deviation represents the impact of the environment on deviating from the expected value set by the genotype.
• One can envision genotype as setting a baseline value for the individual, while the environment introduces deviations in either direction.

By understanding these concepts, we can delve into the complexities of genetic and environmental influences on phenotypic traits, providing a comprehensive view of how different factors interact to shape the observed characteristics in populations.

Genetic and Environmental Influences on Phenotypic Values

Key Concept: Phenotypic and Genotypic Values:

• In genetics, the relationship between phenotypic (P), genotypic (G), and environmental (E) values is denoted as P = G + E.
• It is assumed that the average environmental deviation in the entire population is zero, making the mean phenotypic value equivalent to the mean genotypic value.
• This implies that in the context of the population, the term 'population mean' is interchangeable with both phenotypic and genotypic values.

Genotypic Values and Frequencies:

• The table provided illustrates three genotypes along with their respective frequencies within a randomly mating population.
• The genotypic values are displayed in the third column of the table.
• To calculate the mean value across the entire population, one multiplies each genotype's value by its frequency, summing over all three genotypes.
• Mathematically, the population mean can be simplified by observing that p² - q² = (p - q)(p + q), where p and q represent allele frequencies.
• The population mean, represented by the sum of the genotypic values column, can be expressed as Ma = (p - q)² + 2pq.

Population Genetics

Average Effect in Population Genetics

In population genetics, we aim to understand the characteristics of a population in relation to its family structure. This involves the transmission of value from parents to offspring. It's important to note that this transmission is not solely based on genotypic values, as parents pass on their genes to their offspring and not their genotypes, which are newly created in each generation.

• Introduction of Breeding Value

  A new measure known as 'breeding value' is introduced to refer to the genes carried by an individual and transmitted to its offspring. This breeding value specifically focuses on the genes and not the genotypes.

• Defining Average Effect

  The 'average effect' can be assigned to a gene in a population. It represents the deviation from the population mean of individuals who received that gene from one parent, while the genes received from the other parent are assumed to be random for the population.

• Understanding Average Effect of Gene Substitution

  An illustrative way to comprehend the concept is by considering the average effect of a gene substitution. If we were to replace a certain gene (e.g., A2) with another gene (e.g., A) randomly in a population and observe the resulting change in value, that change would represent the average effect of the gene substitution.

• Dependence on Gene Frequency

  The average effect of a gene or gene substitution is influenced by the gene frequency within the population. Therefore, the average effect is a property that pertains to both the population and the specific gene in question.

Breeding Value

• Definition: Breeding value refers to the value of an individual as determined by the average value of its offspring. Unlike the concept of 'average effect,' breeding value is quantifiable.
• Calculation: The breeding value of an individual can be expressed as the sum of the average effects of the genes it carries. This summation is conducted across all pairs of alleles at each genetic locus and over all loci.
• Population Equilibrium: In a population under Hardy-Weinberg equilibrium, the mean breeding value is expected to be zero.

When considering breeding value, it's important to understand that it reflects the genetic worth of an individual based on the expected performance of its progeny. This concept plays a crucial role in animal and plant breeding programs, helping breeders make informed decisions to enhance desirable traits in future generations.

• Breeding value is a key metric in genetics and breeding programs.
• It indicates the genetic potential of an individual to pass on favorable traits to its offspring.
• For example, in dairy cattle breeding, a bull with a high breeding value for milk production is preferred to improve the overall productivity of the herd.

In conclusion, breeding value serves as a valuable tool in genetic evaluations, allowing breeders to make strategic selections to achieve desired breeding goals and enhance the overall genetic merit of populations.

Variance and Genetics of Metric Characters

• Variance in genetics refers to the study of variation within a population.
• The fundamental concept in this study involves breaking down variation into components attributed to different causes.
• The relative size of these components plays a crucial role in determining the genetic characteristics of a population.
• It also influences the degree of similarity observed among relatives within the population.