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Introduction


Animal breeding is a branch of animal science that deals with the controlled mating/reproduction of animals in favor of desirable traits within a population. Animal breeding has been practiced for thousands of years, initially to domesticate wild animals and later to improve traits like body size, growth rate, productivity, temperament, and disease resistance in livestock, tolerance to environmental stressors etc.

Selective breeding involves choosing (selecting) individuals with desirable characteristics and allowing them to reproduce, thus passing on those traits to their offspring. Over multiple generations, this process can lead to significant genetic and phenotypic changes in a population.

Animal breeders typically aim to improve various aspects of animals, depending on their purpose. In agriculture, for example, breeders might focus on increasing meat or milk production, improving feed efficiency, or enhancing disease resistance. In the case of companion animals, traits like intelligence, temperament, and appearance are often prioritized.

Modern breeding techniques often involve a combination of traditional selection methods and advanced technologies like genetic engineering and artificial insemination.

Animal breeding and some of the associated technologies raise ethical concerns, particularly when it involves intense selection for specific traits that may compromise animal welfare or genetic diversity within populations.


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CH 1: SELECTION


Lesson 1: Defining Traits


In animal genetics, a trait is an observable characteristic of an animal that are determined by its genetic makeup, or genotype. When a trait can be observed and possibly measured, it is referred to as a Phenotype (P)

Traits (or Phenotypes) are the result of interactions between genes (G) and the environment (E).

P = G + E

G represents the Genotype of the animal, which is the collection of the genes possessed by the animal. E actually represents all the non-genetic conditions that can influence the phenotype.

We can think of the Genotype conferring a particular value on the trait in the individual and the environment causing a deviation from this value in one direction or the other.

Mendelian Traits: Some traits follow Mendelian inheritance patterns, where a single gene controls the phenotype. These traits typically exhibit simple dominant-recessive relationships, such as eye color in humans.

Polygenic Traits: Many traits are influenced by multiple genes and environmental factors. These are called polygenic traits. Examples include height, skin color, and intelligence. Polygenic traits often show a continuous range of variation in a population.

Alleles: Genes exist in different forms called alleles. Alleles can be dominant or recessive, and their combination determines the phenotype. For example, in Mendelian inheritance, a dominant allele will mask the expression of a recessive allele.

Gene Interaction: Sometimes, multiple genes interact to produce a trait. This interaction can be additive, where the effects of each gene add up, or epistatic, where one gene masks the expression of another.

Environmental Influence: Environmental factors, such as nutrition, temperature, and exposure to toxins, can also influence the expression of traits. This is particularly true for traits with a polygenic basis.

Qualitative and Quantitative Traits

Qualitative traits are also known as discontinuous traits. These are traits that exhibit distinct, non-overlapping categories or variations within a population. These traits are typically controlled by one or a few genes and are often influenced less by environmental factors. While the environment can have some impact, the genetic control is more predominant in determining the expression of qualitative traits.

Qualitative traits typically have distinct categories or variations that are easily observable and do not blend into one another. Variation in qualitative traits is discrete, meaning individuals can be clearly categorized into distinct groups based on their phenotypes. Examples include flower color in plants (e.g., purple vs. white), blood type in humans (e.g., A, B, AB, O), and coat color in animals (e.g., black vs. brown).

Mendelian Inheritance: Many qualitative traits follow Mendelian inheritance patterns, with distinct dominant and recessive alleles.

Genetic Disorders: Some genetic disorders are determined by qualitative traits, such as cystic fibrosis and sickle cell anemia. These disorders typically result from mutations in single genes, leading to distinct phenotypic outcomes.

Quantitative traits, also known as continuous traits, are traits that exhibit a range of phenotypic variation within a population. Unlike qualitative traits, which have distinct categories, quantitative traits show a continuum of phenotypes.

Quantitative traits exhibit continuous variation, meaning that individuals within a population vary along a spectrum rather than falling into distinct categories. Examples include height, weight, blood pressure, and yield in crops.

Phenotypic variation in quantitative traits often follows a normal distribution curve, also known as a bell curve.

Quantitative traits are typically influenced by multiple genes, (polygenic) each gene causing small effects on the traits, as well as environmental factors. This polygenic inheritance contributes to the continuous range of variation observed in these traits.

Environmental factors such as nutrition, climate, and stress can significantly impact the expression of quantitative traits. Unlike qualitative traits, which are more genetically determined, environmental factors play a larger role in shaping the phenotype of quantitative traits.

Many complex traits, such as intelligence, disease susceptibility, and behavioral traits, are quantitative in nature. These traits are influenced by a combination of genetic and environmental factors, making them challenging to study and predict.

Selection for quantitative traits often results in gradual changes in the population over multiple generations. Response to selection for quantitative traits is typically slower than for qualitative traits due to the polygenic nature of the traits.

Lesson 2: Genetic Variation


Genetic variation in animals refers to the diversity of genetic material present within a population or species. This variation arises from differences in the DNA sequences of individuals and can manifest as differences in phenotypes such as disease susceptibility, productivity and other performance traits.

Genetic variations can be caused or attributed to several processes such as:

  • Mutation: Mutations are the ultimate source of genetic variation. They can occur spontaneously during DNA replication or in response to environmental factors such as radiation or chemical exposure. Mutations can range from single nucleotide changes to large-scale chromosomal rearrangements.
  • Recombination: Recombination during sexual reproduction shuffles genetic material between homologous chromosomes, leading to new combinations of alleles in offspring. This process increases genetic diversity within populations by generating novel genetic combinations.
  • Gene Flow: Gene flow occurs when individuals migrate between populations, introducing new alleles into the gene pool. It can occur through dispersal of individuals or through movement of gametes (e.g., pollen or sperm). Gene flow can homogenize genetic variation between populations or introduce new variation.
  • Natural Selection: Natural selection acts on genetic variation within populations, favoring individuals with traits that enhance survival and reproduction in a given environment. Over time, natural selection can lead to changes in allele frequencies, resulting in adaptation to specific ecological niches.
  • Genetic Drift: Genetic drift refers to random fluctuations in allele frequencies due to chance events, particularly in small populations. Genetic drift is a significant driver of evolution in small or isolated populations and can lead to loss of genetic variation over time.
  • Balancing Selection: Balancing selection occurs when multiple alleles at a gene locus are maintained in a population over time. This can occur through mechanisms such as heterozygote advantage, where individuals heterozygous for a particular allele have a selective advantage.
  • Artificial Selection: Humans have selectively bred animals for specific traits for thousands of years, leading to the creation of diverse breeds within species. Artificial selection can rapidly change allele frequencies and phenotypic traits within populations.

Genetic diversity is important for the long-term viability and adaptability of populations. Higher levels of genetic diversity can provide a reservoir of adaptive potential in response to environmental changes and reduce the risk of inbreeding depression and genetic diseases. Animal breeders utilize this genetic variation to improve traits of economic or ecological importance within livestock and companion animal populations.

Case Study: The Belgian Blue Cattle Breed

Belgian Blue cattle, also known as BBB or Belgian Blue-White, are a breed of beef cattle originating from Belgium. They are renowned for their distinctive appearance, characterized by their heavily muscled bodies, often referred to as "double-muscling." The double-muscling phenotype is a heritable condition resulting in an increased number of muscle fibres (hyperplasia), instead of the (normal) enlargement of individual muscle fibres (hypertrophy).

The double-muscling phenotype is results from a naturally occurring mutation known as "double-muscling" mutation in the myostatin gene which codes for the protein, myostatin. Myostatin is a protein that inhibits muscle development. This mutation also interferes with fat deposition, resulting in very lean meat. The truncated myostatin gene causes accelerated lean muscle growth mainly due to physiological changes in the animal's muscle cells (fibres) from hypertrophy to a hyperplasia mode of growth. The Belgian Blue's bone structure is the same as normal cattle, albeit holding a greater amount of muscle, which causes them to have a greater meat to bone ratio. These cattle have a muscle yield around 20% more on average than cattle without the genetic myostatin mutation.

The birth weight and width of the calf is usually higher than in animals without the double-muscling gene. Calves are commonly born by Caesarean section. Natural calving is always associated with dystocia.

Belgian Blue cattle require modified diets because of this breed's increased muscle yield. A diet containing higher protein is required to compensate for the altered mode of weight gain. During finishing, this breed requires high-energy (concentrated) feeds, and will not yield the same results if put on a high-fibre diet which reflects the role of the environment in influencing the expression of phenotypes.

Breeding programs for Belgian Blue cattle focus on maintaining and improving desirable traits, such as muscling, while also addressing potential health concerns associated with the double-muscling mutation. Selective breeding and careful genetic management are essential for ensuring the long-term sustainability and welfare of the breed.

Lesson 3: Phenotypic Variation


Phenotypic variation refers to the observable differences in traits or characteristics among individuals within a population. These differences can arise from genetic variation, environmental influences, or interactions between genes and the environment. Phenotypic variation is a fundamental aspect of biological diversity and plays a crucial role in evolution, adaptation, and the functioning of ecosystems.

Phenotypic variation occurs due to the following factors:

Genetics: Genetic variation among individuals is a primary determinant of phenotypic variation. Genes encode the instructions for the development and functioning of organisms, influencing traits such as height, coloration, behavior, and physiological processes. Allelic variation, gene interactions, and gene-environment interactions contribute to the diversity of phenotypes within a population.

Environment: Environmental factors, including temperature, humidity, nutrient availability, and social interactions, can significantly impact phenotypic expression. Environmental conditions during development can shape phenotypic traits and may induce phenotypic plasticity, where individuals with the same genotype exhibit different phenotypes in response to environmental cues.

Interaction between Genes and Environment: Phenotypic variation often results from complex interactions between genetic and environmental factors. Genes provide the potential for trait expression, while environmental conditions determine how genes are expressed. Genotype-environment interactions can result in phenotypic differences among individuals with the same genotype exposed to different environments.

Phenotypic Plasticity: Phenotypic plasticity refers to the ability of a single genotype to produce different phenotypes in response to environmental variation. Phenotypic plasticity allows organisms to adjust their phenotype to optimize fitness in different environments, enhancing their capacity to survive and reproduce in diverse conditions.

Phenotypic variation can be continuous or discontinuous. Continuous variation refers to traits that show a range of values across a population, such as height or weight, and are influenced by multiple genes and environmental factors. Discontinuous variation involves distinct categories or states, such as blood type or flower color, and may be controlled by one or a few genes.

Lesson 4: Genetic Response


Genetic response refers to the changes in the genetic composition of a population in response to selective pressures or environmental factors over time. These changes occur as a result of natural selection, artificial selection, or other evolutionary forces acting on the genetic variation within a population.

A genetic response may arise from the following factors:

Natural Selection: Natural selection is the primary driver of genetic response in natural populations. It occurs when individuals with certain heritable traits have greater reproductive success or survival rates than others, leading to the increased frequency of advantageous alleles in subsequent generations. Over time, natural selection can result in the adaptation of populations to their environments.

Artificial Selection: In artificial selection, humans deliberately choose individuals with desired traits to breed, leading to changes in allele frequencies within populations. Artificial selection has been widely used in agriculture to improve traits such as yield, disease resistance, and quality of agricultural products. It can lead to rapid genetic responses compared to natural selection.

Selective Breeding Programs: Selective breeding programs aim to enhance specific traits in plants and animals through controlled mating. These programs typically involve identifying individuals with desirable traits, such as high productivity or disease resistance, and using them as parents for the next generation. Over successive generations, this process can lead to significant genetic changes in populations. This course focuses on genetic changes arising from selective breeding.

Response to Environmental Changes: Genetic response can occur in response to environmental changes, such as shifts in climate, habitat loss, or the introduction of new predators or pathogens. Populations may evolve traits that confer resistance or tolerance to environmental stressors, allowing them to persist in changing conditions.

Gene Flow: Gene flow, the movement of genes between populations through migration, can influence genetic responses by introducing new genetic variation or altering existing allele frequencies. High rates of gene flow can homogenize populations genetically, while low rates can lead to genetic divergence and local adaptation.

Genetic Drift: Genetic drift, the random fluctuation of allele frequencies in small populations, can also influence genetic responses, particularly in small or isolated populations. Genetic drift can lead to the fixation of alleles or the loss of genetic variation over time, affecting the potential for adaptation to changing conditions.

Genetic change from Selective Breeding

Selective breeding, also known as artificial selection, can elicit specific genetic responses within populations over successive generations.

Selective Breeding involves the following process:

Trait Selection: Selective breeding involves deliberately choosing individuals with desirable traits to serve as parents for the next generation. These traits can vary depending on the breeding goals, such as increased yield, improved disease resistance, enhanced flavor, or altered appearance.

Consider the trait's heritability: The success of selective breeding relies on the heritability of the target traits, which determines the extent to which they are passed from parent to offspring genetically. Traits with high heritability are more responsive to selective breeding, as their phenotypic expression is strongly influenced by genetic factors.

Genetic Variation: Genetic variation within the breeding population provides the raw material for selection to act upon. Initially, the breeding population may exhibit a range of phenotypic variation for the target traits. Selective breeding aims to increase the frequency of alleles associated with desirable traits while decreasing the frequency of alleles associated with undesirable traits.

Breeding Strategies: Selective breeding programs employ various breeding strategies to achieve desired genetic responses. These strategies may include inbreeding, line breeding, crossbreeding, or hybridization, depending on the goals of the breeding program and the genetic characteristics of the target species.

Ability to predict genetic response accurately: Over successive generations of selective breeding, individuals with the desired traits with known heritability and genetic variation lead to predictable changes of favorable alleles in the breeding population.

Lesson 5: Breeding Goals


Animal breeding goals or objectives may vary depending on the specific objectives of the breeding program and the characteristics desired in the animals being bred. These goals can differ widely between different sectors of animal agriculture, and across individual farms. Generally, breeding goals might fall under one or more of the following areas:

Improving Production Efficiency: One of the primary goals of animal breeding is to enhance production efficiency by increasing the quantity and quality of products obtained from animals. This may include improving traits such as growth rate, feed conversion efficiency, milk yield, egg production, and meat quality.

Enhancing disease resistance, resilience and general health: Breeding programs often aim to improve the resistance and/or resilience of animals to diseases and health issues. This can involve selecting for associated traits such as immune response, resistance to specific pathogens, and overall robustness and resilience to environmental stressors.

Optimizing Reproductive Performance: Reproductive traits are critical for the success of animal breeding programs. Breeding goals may include improving fertility, reproductive lifespan, reproductive rate, high conception rates and high offspring survival rates - superior maternal traits.

Enhancing Animal Welfare and Behavior: Breeding programs may prioritize traits related to animal welfare and behavior, such as temperament, docility, stress tolerance, and adaptability to different management systems. Animals with calm temperaments and low stress levels are easier to handle and less prone to behavioral issues.

Improving Environmental Sustainability: Sustainable animal production systems aim to minimize environmental impact while maintaining profitability and productivity. Breeding goals may include selecting for traits that reduce resource inputs (e.g., feed, water) and environmental emissions (e.g., methane from enteric fermentation), as well as promoting traits associated with resilience to climate change and resource scarcity.

Enhancing Product Quality and Marketability: Breeding programs may focus on improving product quality attributes that are valued by consumers, such as flavor, texture, color, and nutritional content. Animals with desirable product quality characteristics can command premium prices in the market.

Preserving Genetic Diversity and Adaptation: In some cases, breeding goals may include preserving genetic diversity within populations and maintaining traits associated with local adaptation and resilience to specific environments. This is particularly important for conserving rare or endangered breeds and for promoting biodiversity in agricultural systems.

Lesson 6: Breeding Programs


An animal breeding program is a systematic and structured approach to improving the genetic characteristics of a population of animals over time. These programs aim to enhance desirable traits.

A breeding program consists of the following components/steps:

Setting breeding goals: The first step in developing an animal breeding program is defining clear and achievable breeding goals. These goals are determined based on the specific objectives of the program, which may vary depending on the industry sector (e.g., dairy, beef, poultry), market demands, and production system.

Selection of Breeding Stock: Once breeding goals are established, suitable breeding stock is selected to serve as parents for the next generation. Selection criteria may include performance records, pedigree information, genetic evaluations, and physical characteristics relevant to the breeding goals.

Develop a Breeding Strategy: Breeding strategies outline how mating decisions will be made to achieve the desired genetic improvements. This may include:

  • Inbreeding and Line Breeding: Used to concentrate desirable traits within a population and fix desired alleles.
  • Outcrossing: Introducing genetic diversity into a population by mating unrelated individuals to reduce the risk of inbreeding depression.
  • Crossbreeding: Mating individuals from different breeds or lines to capitalize on breed complementarity and heterosis (hybrid vigor).

Selection Intensity: Determining the proportion of individuals selected as parents based on their genetic merit.

Genetic Evaluation: Genetic evaluation involves estimating the genetic merit of animals for specific traits of interest using statistical models and performance data. This helps identify superior animals for selection as parents and informs breeding decisions.

Estimating Breeding Value: Breeding values quantify the genetic merit of animals for specific traits, accounting for genetic and environmental factors. Breeding values are used to rank animals and guide mating decisions to maximize genetic progress.

Recording and Data Management: Accurate and comprehensive records of pedigree, performance, and genetic information are essential for the success of an animal breeding program. Data management systems facilitate the collection, storage, analysis, and utilization of breeding data.

Monitor Genetic Progress: Genetic progress is monitored and evaluated over time to assess the effectiveness of the breeding program. Adjustments may be made to breeding strategies, selection criteria, or management practices based on evaluation results to enhance program performance

Introduction


As discussed in the previous chapter, phenotypes can eitherbe qualitative or quantitative. Qualitative traits are categorical and discrete while Quantitative traits are continuous and individual vary in degree with no clear cut distinctions. Quantitative characters and also called Metric Characters because their study depends on measurement instead of counting.

The inheritance of metric characters can be predicted using Population genetics principles, however, it is impossible to track individual genes across different generations, and because in most cases, mating is not random, some modifications to the population genetics principles are necessary.

The branch of genetics focusing on quantitative traits is called Quanititative Genetics or Biometrical Genetics. Animal breding relies on a deep understanding of Quantitative genetic principles because most traits of economic value in plants and animals are quantitative traits.

We understand that the variation present at the genetic level, DNA level, is discrete, with categories of alleles and genotypes. How come this discrete variation in genotypes is translated into continuous variation at the phenotypic level? There are two main reasons for this. Firstly, most quantitative traits are contolled by multiple genes (polygenic) and the combined effect of many discrete variations result in what is observed as less discrete variation in the phenotypes. Secondly, quantitative traits are influenced by the superimposition of non-genetic variation on top of the genetic variation.

Consider an example, where a traits is controlled by 6 unlinked loci each with 2 alleles at frequencies of 0.5. Suppose there is complete dominance of one allele and that the dominant allele adds 1 unit to the measurement of the trait. If these alleles were the only cause of phenotypic variation, we would observe 7 discrete classes in measurement of the character ranging from 0 (where the individual doesnt have even one dominant allele), 1 (where the individual has an dominant allele at one of the 6 loci), 2, 3 (where the individual has 3 dominant alleles and 3 loci), 4, 5, 6 (where the individual has a dominant alele at all the 6 loci). Notice that in this situation, the trait will appear as discrete and we will be able to place any individual in a specific category directly correlated with the number of dominant alleles present. The frequencies of the classes would be according to the binomial expansion of (1/4 + 3/4)6.

The figure shows the distribution expected from the simultaneous segregation of two alleles at each of several loci: 6 loci (a) and 24 loci (b). There is complete dominance of one allele at each locus and the allele frequency is 0.5. Each locus when homozygous for the recessive allele will reduce the measurement by 1 unit in a and by 1/4 unit in b. The horizontal scale shows the number of loci homozygous for the recessive allele and the vertical axis shows the probability or the percentage of individuals expected in each class. Probabilities are derived from the binomial expansion of (1/4 + 3/4)n. Where n is the number of loci. Notice that as the number of genes increases, and each gene contributes only a small effect, it becomes more and more difficult to distinguish the classes.

Variation resulting from non-genetic factors is truly continuous and tends the blur the edges of the phenoptypic discontinuity that might have been present from the influence of genetic factors alone.

A gene whose effect is large enough to result in a detectable phenotypic discontinuity, even in the preence of other genes, or non-genetic factors can be referred to as a Major gene. Minor genes are those that influence a trait but not in a significant way and doesnt cause a discontinuity in the phenotype. Some genes may be major for a certain trait, but minor for another trait. This is called pleitropy.

As previously mentioned, polygenic traits are those that are controlled by multiple genes. The major genes involved in such traits can be called polygenes. Most traits of economic importance in livestock production are polygenic, such as anatomical measurements, lactation, fertility, growth rate etc.

If you plot a histogram with the number of individuals that fall in each class of measurement pltted in the vertical scale and the phenotypic measure or call on the horizontal axis, you will find that the histogram looks like this:

Notice that the frequency distribution of quantitative traits approximate a normal curve especially when the population being meausred is infinitely large.

The degree of resemblance between relatives can be readily observed and is the foundation of quantitative genetics to show how this degree of resembalnce can be used to predict the outcome of selective breeding and to point to the best method of carrying out selective breeding. The practical goal of selective breeding is to find out how we can use the observations made on the population to predict the outcome of any breeding method.

The properties of a population that can be used to understand metric traits are Means, variances and covariances. These form the basis for measuring the degree of resemblance between relatives.

Population Mean


Let us now introduce the concept of values and means. When you measure a character, say for example, body weight, in kilograms, the measure you get is called the Phenotypic Value of that individual. Phenotypic value is expressed in the units used to measure the trait. All other other calculations of means, variances and covariances should be based on measurement of the phenotypic value.

Phenotypic value can be divided into components attributed to the influence of genetics (genotype) and environment. The term 'environment' encompasses all non-genetic factors that can influence a phenotype. These two components are expressed as genotypic value and environmental deviation. We can think of this as the genotype conferring a certain value on the trait and the environment causing a deviation from this value in one direction or the other.

P = G + E --------------------------------(Equation 1)

Because the environment's influence is considered as a deviation, the mean environmental deviation of a population is assumed to be zero, so that the mean phenotypic value is equal to the mean genotypic value. The term population mean refers to mean phenotypic or genotypic values.

When dealing with multiple successive generations, we assume that the environment remains constant from generation to generation and so the population mean only changes if there is a change in genotypes (genotypic value). In principle, the genotypic value is measurable, but in practice it is not. It would have been measurable only under circumstances in which we are dealing with only one locus and the genotypes are phenotypically distinguishable.

Let us assign arbitrary values to the genotypes depending on the behaior of the alleles. Assume a single locus with two alleles A1 and A2. A1 is the allele that increases the value. We can assign the genotypic value of the A1A1 genotype a value of +a, which means the value of the A2A2 will be equal to -a. The value of the heterozygous genotype can be represented as d. We can draw a scale of genotypic values as shown here. The position of the heterozygote genotype on the scale depends on the behavior of the A1 allele. When A1 is not dominant, the value of d = 0 and its positioned exactly in the middle of the scale equidistant from a and -a. When A1 is dominant, then d is positive and is positioned anywhere between 0 and +a.

Please note that the point labeled 0 is the population mean, not an actual 0. It is the mean of the two homozygous genotypes. And a, -a and d are deviations from this population mean. For example, if we study weight of several individual mice in a population with the dwarf gene, represented as pg. Lets assume we record the body weights of pygmy mice with known genotypes and we find the following means. +-+ = 14g +-pg = 12g, and pg-pg = 6 grams. The mean of the heterozygotes is (14+6)/2 = 10. The middle of the scale (population mean) is actually = 10g. This is the zero point. The value of a is 14-10 = 4g. The value of d = 12-10 = 2g. The value of the homozygous recessive genotype - pg-pg, (-a) is -4 g


Genotype Frequency Value Frequency X Value
A1A1 p2 +a p2a
A1A2 2pq d 2pqd
A2A2 q2 -a -q2a
Sum = a(p-q) + 2pqd


The contribution of any locus to the population mean, therefore, has two terms, a(p-q) attributable to the homozygotes and 2dpq attributted to the heterozygotes. If there is no dominance, d = 0, the value of 2dpq = 0 so the population mean is a(p-q). Remember p+q = 1, so p=1-q). Therefore we can also express the population mean as M = a(1-2q) If there is complete dominance, d=a, the population mean is proportional to the square of the gene frequency M = a(1-2q2).

In the absence of overdominance, the total range of values attributable to the locus is 2a. If p is fixed in the population, so that the frequency is 1, the population mean will be a. If q is fixed in the population, so that its frequency is 1, the population mean will be -a.

As shown in the pygmy gene in mice example above, the values of a and d and deviations from the average of the two homozygotes. If you want to express the mean as a deviation from the value of the lower homozygote, M = 2p(a+dq), and if you want to express the mean as a deviation from the value of the higher homozygote, M = 2q(-a+dq).

What happens if there are multiple loci associated with the phenotype. The cumulative effect of these genes will depend on how they interact with each other to result in the trait. In our first case, we will assume that the total effect of the loci is the addition of each locus' effect. For example, if the genotypic effect of A1A1 is aA and the genotypic effect of B1B1 is aB then the genotypic effect of A1A1B1B1 is aA+aB. In additive combination, the population mean resulting from multiple loci is the sum of the contributions from individual loci.

M = ∑a(p-q) + 2∑dpq ---------(Equation 2)

In the absence of dominance, the population mean is 2∑a.

If all alleles that increase the trait were fixed, the mean would be +∑a . If the alleles that reduce the trait were fixed, the population mean would be -∑a.

Average Effect


We have learnt about geoptying value, the value attributed to the individual's genotype. However, parents only pass one allele to their offspring and genotypes reform within the offspring as the alleles of the two parents come together. A new measure that refers to the genes and not the genotypes is therefore important. The Average effect is a measure that depends on the genotypic values, a and d as already described, and the gene frequencies in the population. The average effect is therefore a measure associated with the gene itself and also the properties of the population. The average effect can be defined in many ways, but they are all the same under random mating populations. The average effect of a particular gene is the mean deviation from the population mean of individuals which received that gene from one parent, the gene received from the other parent having come at random from the population. This indicates that the effect of the other gene is already the same as the population mean and any deviation is as a result of the gene that we are studying. For example, assume that gametes carrying A1 unite at random with gametes from the population, then the mean of the genotypes produced will deviate from the population mean by an amount which is the average effect of the A1 gene.

Let us see how the average effect is related to the genotypic values a and d as this will help to make this concept easier to grasp.

Consider a locus with 2 alleles A1 and A2, at frequencies p and q respectively. Lets represent the average effect of the gene A1 as α1 and the average effect of gene A2 as α2. If gametes carrying A1 unite at random with gametes in the population, the frequencies of the genotypes produced will be p of A1A1 and q of A1A2. The genotypic value of A1A1 is +a and that of A1A2 is d. The mean of these, accounting for the allele frequencies is pa + qd. The difference between this mean value and the population mean is the average effect of the gene A1.

α1 = pa + qd - [a(p-q) + 2dpq]
= q [a + d(q - p)]
--------------------Equation 3

The average effect of the gene A2 is:

α2 = -p[a + d (q - p)] ------------- Equation 4

The average effect of a gene can be definedd as the gene substitutiton effect. When A2 genes are taken at random in a population, a proportion p will be found in A1A2 genotypes, and a proportion q will be found in A2A2 genotypes. Changing A1A2 to A1A1 will change the value from d to +a and the effect will therefore be (a - d). Changing A2A2 to A1A2 will change the value from -a to d and the effect will be (d + a). The average change is therefore p(a - d) + q (d + a), which can be rearranged to become a + d(q - p).

α = a + d(q - p)

From equation 3 and 4 above, you can observe that α = α1 - α2

Therefore the average effect of the two alleles expressed in terms of gene substitution are:

α1 = qα
α2 = -pα

Breeding Value


As indicated previously, parents pass on their genes and not their genotypes to their offspring. It is the average effect of the the parent's genes that determine the mean genotypic value of its offspring. The value of an individual, judged by the mean value of its offspring/progeny is called the Breeding value of the individual. The breeding value can be measured. For example, if an individual is mated to individuals taken at random from the population, then its breeding value is twice the mean deviation of the progeny from the population mean. The deviation has to be doubled because the individual contributed only half the genes to the offspring, the other half coming at random from the population. Breeding values can be expressed as absolute values. However, most often, breeding values are expressed as standard deviation units from the population mean. One cannot speak of an individual's breeding value without specifying the population where its mates were randomly drawn from.

Breeding value can also be expressed as the sum of the average effects of the genes it carries. For a single locus with two alleles, the breeding values can be expressed as follows:

A1A1 = 2α1 = 2qα
A1A2 = α12 = (q-p)α
A2A2 = 2α2 = -2pα

If all loci are to be taken into account, the breeding value of a particular genotype is the sum of the breeding values attributable to each of the separate loci. If a population is in Hardy-Weinberg equilibrium, the mean breeding value is 0, and if the breeding value is expressed in absolute units, then the mean breeding value is equal to the mean genotypic value and also equal to the mean phenotypic value.

2p2qα + 2pq(q - p)α - 2q2pα = 2pqα(p + q - p - q) = 0 .

The breeding value of any individual is equal to the average of the breeding values of its two parents. Different offspirng of the same parents will differ in breeding values depending on which of the alleles they received from each parent. So the transmission of value from parents to offspring is expressed by:

o = Āo = 0.5(As + Ad
-----------------Equation 5

Where 'o' represents Offspring, 's' represents Sire and 'd' represents Dam.

Dominance Deviation


The breeding value is a component part of an individuals genotypic value. When we consider a single locus, the difference between the genotypic value G and the Breeding value A of a particular genotype is known as the dominance deviation.

G = A + D ...............................Equation 6

Dominance deviation arises from the iteraction between alleles (within-locus interactions), representing the effect of putting genes together to make genotypes. This is the effect that is not accounted for when we consider just the effect of the two genes separately. Like average effects and breeding values, dominance deviations depend on the gene frequency in the population. Therefore dominance deviation is a property of the population and not simply a measure of the degree of dominance.

In the figure above, the genotypic values are plotted against the number of the A1 genes in the genotype. A straight regression line can be fitted by least squares to these three points, each point being weighted by the frequency of the genotype. The difference between the breeding value and the genotypic value is the dominance deviation.

The average effect α of the gene-substitution is given by the difference in breeding value between A2A2 and A1A2 or between A1A2 and A1A1

If there is no dominance, the value of d is 0 and the dominance deviations are also all 0. So, when there is no dominance, beeding value is equal to genotypic value.

Genes that do not show dominance are also called Additive genes because they act additively.

Interaction Deviation


When several loci are involved in influencing a trait, the genotypic value may contain an additional deviation due to non-additive combination of loci. This can be expressed as:

G = GA + GB + IAB ..... Equation 7

Where GA is the genotypic value of of an individual attributed to one locus, GB is the genotypic value attributed to the second locus and IAB is the deviation from the additive combination of these genotypic values. If IAB is not zero, those genes are said to interact or exhibit Epistasis and is called Interaction deviation or epistatic deviation. Loci may interact in pairs, threes, or even more and the interactions may be of different kinds, some increasing the value of the trait, some reducing the value. For all loci considered together, we can use the formula:

G = A + D + I ............. Equation 8

Where A represents the sum of the breeding values attributable to the separate loci, and D is the sum of the dominance deviations. Because the Interaction deviation is a deviation from the population mean, it has a mean of 0.

The interaction deviation also relies on the gene frequencies of the population, so it is not only a property of an individual.