Chapter 2
Genetics

The ultimate goal of every selective breeding programme is to improve the breeding value of the population. The breeding value is determined by the fish's genes. A farmer hopes that when he improves the breeding value of his population he will also improve its monetary value, which is determined by the fish's phenotypes. To accomplish this goal, a breeder selects (saves) fish that possess certain phenotypes and culls (removes) those that do not, and hopes that his breeding programme will create a genetically improved population (breeding is the applied science of genetics; thus, a farmer who conducts a selective breeding programme is a breeder). If it does, the fish in the next generation will be more valuable because their genes will enable them to grow faster or to exhibit a more desirable colour.

Although the goal of a selective breeding programme is to manipulate a population's genes and thus produce better fish, it is impossible to examine and manipulate the genes directly. Instead, a fish's genes are examined indirectly by examining its phenotypes (also called “traits”), which are the physical expressions of the genes. Because the goal of a selective breeding programme is to manipulate a fish's genes, it is important to understand how the genes are transmitted from a parent to its offspring and how the genes produce the phenotypes. Understanding these processes helps explain how selection works. This is important, because if a farmer understands why he is doing something, he is more likely to do it correctly, and this ensures success. Additionally, an understanding of how the genes produce various phenotypes enables a breeder to choose the breeding programme that will allow him to achieve his goal quickly and efficiently.

This chapter is not an all-encompassing review of basic genetics. Only a few topics are covered: The first section discusses meiosis, which is the process by which a parent's genes are parcelled into its gametes (eggs and sperm). The second section describes the difference between phenotype and genotype. The remaining sections explain how phenotypes are inherited.

The information contained in this chapter is important because many of the terms introduced in this chapter will be used in Chapters 3 and 4 to explain how selective breeding programmes should be conducted and how they work. It is not necessary to become a geneticist in order to conduct a successful selective breeding programme, but a basic understanding of how phenotypes are inherited will make the rest of the manual easier to understand and will also enable a farmer to be a better breeder.

The material in this chapter is intended simply as background information for those who seek a better understanding of how selection alters phenotypes and improves a population. The material in this chapter, especially that dealing with quantitative phenotypes, is intended for extension agents and for highly educated aquaculturists. It is not intended for the vast majority of farmers or for those who are interested only in the nuts and bolts of how to conduct a selective breeding programme and who do not care how it works. It is hoped that extension agents will read this material, because it will provide a better grounding in fish breeding, and an understanding of how selection works genetically may make them more comfortable with the design and implementation of a selective breeding programme.

Those who are not interested in this material or those who already understand basic genetics can skip this chapter and go directly to Chapters 3 or 4 which describe selective breeding programmes.

Meiosis

Genes are located on structures called “chromosomes,” which are located in the nucleus of every cell. Although there are some exceptions, for the most part, chromosomes occur in pairs, which means that a gene is a paired entity. Throughout this manual, we will assume that chromosomes in cultured fishes occur in pairs. One chromosome of each pair comes from a fish's mother, while the other comes from its father. The number of chromosomes varies among species, but it is constant within a species.

Although every cell in a fish contains the entire genome (a fish's genetic make-up--every gene on every chromosome), the genes that exist in the primary gametocytes are those that are ultimately of greatest interest to a breeder. All genes in the various cells of a fish are, of course, important because they produce the various phenotypes that breeders work with and ultimately select. But those in the primary gametocytes are of greater importance because the primary gametocytes are the cells which develop into sperm and eggs-the gametes which carry the genes and which produce the next generation of fish.

Primary gametocytes are the cells that develop into eggs and sperm by a process called “meiosis.” Meiosis is one of the most important of all biological processes, because it greatly increases genetic variability through crossing over and through independent assortment. In addition, mistakes that occur during the replication of chromosomes in meiosis are heritable, and this is how new alleles and genes are created. The end result of meiosis is the creation of haploid sperm and eggs. Were it not for meiosis, life would not have evolved past single-celled organisms.

During the initial part of meiosis, the chromosomes replicate, and the homologues of each pair come together (the homologs are the two chromosomes that form a pair; one homolog comes from the father, and one comes from the mother). The replication of the homologues is usually uneventful, in that they replicate themselves perfectly. Occasionally, however, a mistake is made during replication, and a gene is not replicated perfectly. Such mistakes are called “mutations.” The mutation rate for individual genes is rare and ranges from 1 in 10,000 replications to 1 in 100,000 replications. Although rare, the fact that males are capable of producing several hundred million to over a billion sperm and that females can produce tens of thousands to hundreds of thousands of eggs all but guarantees that each fish will produce dozens of gametes which contain one or more mutations. The production of mutations is a very important biological process, because it increases genetic variability by creating new alleles and new genes which can, in turn, produce new phenotypes.

Because each homolog replicated before they paired, the bundles are composed of four chromosomes and are called “tetrads.” The chromosomes in each tetrad are extremely elongated and drawn out rather than compact, and they twist around each other. As they twist, the chromosomes break, and pieces from different homologues rejoin. The exchange of genes from one homolog to another is called “crossing over,” and it is one of the most important genetic events, because this greatly increases genetic variability by creating new and different gene combinations every generation. These different gene combinations will, in turn, increase phenotypic variability, which helps breeders produce better fish.

The second important process that occurs during meiosis is reduction division. During this process, the chromosome number is reduced from the diploid (paired state) state to the haploid (unpaired) state. When chromosomes are paired, a cell or individual is said to be a diploid (2N). When a cell or individual contains only one chromosome from each pair, it is said to be a haploid (N).

During reduction division, the replicated homologues of each chromosome pair separate, and the primary gametocyte then divides and forms two cells. In males, these cells are the secondary spermatocytes; in females, they are the secondary oocyte and the first polar body. The separation of the replicated homologues of each chromosome pair and the direction in which the replicated homologues go is independent of that which occurs for all other chromosomes. Although each tetrad divides itself along parental lines (the replicated homolog that came from a fish's father separates from the replicated homolog that came from its mother), the division of the homologues of each chromosome pair is random and is independent of that which occurs in all other tetrads. The random division of the maternal and paternal chromosomes is called “independent assortment,” and it is extremely important because it creates new chromosomal and new gene combinations, which greatly increase genetic variability; this ultimately increases phenotypic variability. The secondary spermatocytes and the secondary oocyte are haploid, since each contains only one homolog from each pair.

The final step in meiosis is the equational division, during which the replicated homologues of each chromosome separate and go into one of two sperm cells or into the egg or second polar body. As was the case during reduction division, the direction that a replicated homolog from each chromosome goes is random and independent of that which occurs in all other chromosomes. This final shuffling of the chromosomes and of the genes also increases genetic variability.

The end result of meiosis is the production of haploid sperm and eggs. Each gamete contains a single chromosome from each pair. Even though some fish can produce millions of gametes, few if any are identical because of mutations, crossing over, and the independent assortment of chromosomes that occurs during reduction division.

The reduction of the chromosome number from the diploid state in the primary oocytes and primary spermatocytes to the haploid state in the eggs and sperm is critical. If this did not occur, the number of chromosomes would double each generation. Because gametes are haploid, the normal diploid number for a species is restored when a sperm fertilizes an egg.

Phenotype and genotype

A gene or set of genes contains the blueprints or chemical instructions for the production of a protein. This protein either forms or helps produce various phenotypes, such as body colour, sex, number of rays in the dorsal fin, length of a fin, body length, and weight. When a geneticist talks about this process, he says that a fish's genotype controls or produces its phenotype.

The genotype is the genetic make-up of the fish. It is the gene or genes that controls a particular phenotype. Because chromosomes occur in pairs, genes also occur as pairs (there are some exceptions, but they will not be discussed in this manual), so the genotype is a paired entity.

A gene can occur in more than one form. Alternate forms of a gene are called “alleles.” In a population, a gene may exist in only one form, which means that there is only one allele at a given locus (locus = gene), or there may be up to a dozen alleles at a locus.

Because chromosomes occur in pairs, an individual can possess either one or two alleles at a given locus. Even if there are ten alleles for a specific gene in a population, an individual can possess no more than two (in this manual, we will assume that all fish are diploids). If the pair of alleles at a given locus is identical, the fish is said to be “homozygous” at that locus. If the pair is not identical, the fish is said to be “heterozygous” at that locus. The terms homozygous and heterozygous (the genotype) refer to specific genes, not the fish's entire genome. A fish's genome is composed of tens of thousands of genes, which is a mixture of homozygous and heterozygous loci.

The reason why it is important to make a distinction between individuals that are homozygous or heterozygous, is that different forms of a gene (alleles) produce different forms of that gene's protein. This means that the various alleles at a locus are responsible for the production of various body colours or of different rates of growth. And it is these differences that interest geneticists, because they can be exploited by selection to produce faster-growing or more attractive fish.

The phenotype is the physical expression of what the gene or set of genes produce, and this is what we describe (for example, colour or sex) or measure (for example, length or weight). Breeders divide phenotypes into two major categories: qualitative phenotypes and quantitative phenotypes.

Genetics of qualitative phenotypes

Qualitative phenotypes are the phenotypes that are described, such as colour, sex, or scale pattern. Qualitative phenotypes are those that are the easiest to observe simply because an individual falls either into one discrete, descriptive, non-overlapping category or it falls into another. For example, if there are blue and yellow fish in a population, individual fish fall either into the blue or into the yellow categories.

The genetics of qualitative phenotypes is simple and is often called “Mendelian genetics” in honour of Gregor Mendel who discovered it. These phenotypes are usually controlled by one or two genes. The alternate forms of a phenotype (for example, blue vs yellow) are produced by the alternate forms of a gene (alleles). Often, the normal phenotype is called the “common” or “wild-type” phenotype, while the others are referred to as “mutant” phenotypes.

Qualitative phenotypes are often called “cosmetic” because they primarily affect an individual's appearance. But this does not mean that they are unimportant. These phenotypes can improve health or make the product more acceptable to consumers. For example: dwarf is a desired phenotype in many varieties of wheat because short stalks are stronger than the normal tall stalks, and they do not bend or break while the plant is growing; polled (hornless) is a desired phenotype in many varieties of cattle for safety and health reasons; white feathers is a desired phenotype in poultry because dark feathers leave dark, unattractive spots on the skin when they are removed. Qualitative phenotypes can also greatly increase the value of farmed fish. For example, in the United States, body colour of fathead minnow has a major effect on its market price: normally pigmented (dark) ones are worth $6.05/kg, while rosy red ones are worth $8.25/kg. Fish farmers need only look at the ornamental fish farming industry to see the importance of qualitative phenotypes. The value of an ornamental fish is determined by its colour, colour pattern, fin shape, eye shape, etc.

Qualitative phenotypes can be divided into two major categories: autosomal and sex-linked. Autosomal phenotypes are those that are controlled by genes located on an autosome (a chromosome other than a sex chromosome). Sex-linked phenotypes are controlled by genes located on the pair of chromosomes that determines sex. (There are some exceptions; some fish have more than one pair of sex chromosomes, while other species have an odd number-either one or three sex chromosomes. All important aquacultured food fish have a single pair of sex chromosomes.)

Autosomal genes are inherited and expressed identically in males and females (unless a sex hormone is needed for phenotypic expression). Sex-linked genes are inherited and expressed differently in males and females. To date, all qualitative phenotypes that have been deciphered in food fish are autosomal. Sex-linked genes are known only in ornamental fish, and most information about this type of inheritance comes from the guppy and platyfish. Because all qualitative phenotypes that have been discovered in cultured food fish are autosomal, this section will describe only the genetics of autosomal phenotypes. Sex-linked phenotypes will not be discussed.

For the sake of simplicity, all examples that will be used in this section are genes that have two alleles. In reality, in a population, a gene may have a dozen alleles. Tail spot pattern in the platyfish is an example of a gene that has nine alleles. When there are more than two alleles, the number of qualitative phenotypes that a gene can produce can increase tremendously, depending on the mode of gene action. It is a bit more complicated to work with such phenotypes, and although it only requires an extension of what is discussed in this section, it does require far more effort and record keeping. Fortunately, such genes are rare. The few that are known are in ornamental fish.

Qualitative phenotypes produced by single autosomal genes

Most qualitative phenotypes that have been deciphered genetically in food fish are controlled by single autosomal genes with two alleles per locus. In general, genes express themselves either in an additive or in a non-additive manner. In additive gene action, each allele contributes equally to the production of the phenotypes in a stepwise unidirectional manner, and the heterozygous phenotype is intermediate between the two homozygous phenotypes. In non-additive gene action, one allele (the dominant allele) is expressed more strongly than the other (the recessive allele), and it has a greater influence on the production of the phenotypes (Figure 1).

COMPLETE DOMINANT GENE ACTION

INCOMPLETE DOMINANT GENE ACTION

ADDITIVE GENE ACTION

Figure 1. Schematic diagram of qualitative phenotypes that are controlled by a single autosomal gene with either complete dominant gene action, incomplete dominant gene action, or additive gene action. Genotypes are given below the phenotypes. Gene A produces black and white colours by complete dominance, so there only two phenotypes. Black is the dominant phenotype, and it is produced by both the homozygous dominant (AA) and heterozygous (Aa) genotypes. White is the recessive phenotype, and it is produced by the homozygous recessive (aa) genotype. Gene B produces black and white colours by incomplete dominance. Because the mode of gene action is incomplete dominance, the heterozygous (Bb) genotype produces a unique phenotype (light-black), one that resembles but that is slightly different than the dominant phenotype (black), which is produced by the homozygous dominant (BB) genotype; white is the recessive phenotype, and it is produced by the recessive genotype (bb). Gene C produces black and white colours by additive gene action. Because neither allele is dominant, the heterozygous (CC') genotype produces a unique phenotype (gray) that is intermediate between the phenotypes (black and white) produced by the two homozygous genotypes (CC produces black and and C'C' produces white). When the mode of gene action is additive, there is no dominant or recessive allele or phenotype.

Complete dominant gene action: Complete dominant gene action occurs when the dominant allele is so strong that it produces its phenotype, regardless of the genotype. Only a single dominant allele is needed to produce the dominant phenotype. This means the homozygous dominant and heterozygous genotypes both produce the dominant phenotype; thus, the phenotypes produced by these genotypes are identical. The recessive allele can produce the recessive phenotype only when no dominant allele is present, which means it can produce the recessive phenotype only when a fish is homozygous recessive. Consequently, with this mode of inheritance, there are three genotypes but only two phenotypes (Figure 1):

For example, light-coloured (pink) and normal pigmentation phenotypes in Nile tilapia are controlled by the B gene. The dominant B allele produces the dominant normally pigmented phenotype, while the recessive b allele produces the recessive pink phenotype. Because the B gene exhibits complete dominance, normal pigmentation is produced by both the homozygous dominant genotype (BB) and by the heterozygous genotype (Bb). while pink is produced only by the homozygous recessive genotype (bb) (Figure 2). Table 1 lists some qualitative phenotypes in important cultured food fishes that are produced by single autosomal genes with complete dominance.

Table 1. Examples of phenotypes in cultured food fishes that are controlled by single autosomal genes with complete dominant gene action. All phenotypes in this table are body colours except caudal deformity syndrome, which is a tail deformity.

PHENOTYPE	GENOTYPE
NORMAL PIGMENTATION
NORMAL PIGMENTATION
PINK

Figure 2. Inheritance of normally pigmented and pink body colours in Nile tilapia. These phenotypes are controlled by a single autosomal gene with complete dominant gene action called the B gene: the dominant B allele produces normal pigmentation, while the recessive b allele produces pink. Because the B allele is completely dominant over the b allele, the BB and Bb genotypes both produce the dominant normally pigmented phenotype. The recessive pink phenotype is produced only when a fish is homozygous recessive (bb). The pictorial representations of body colour used in this figure will also be used in Figures 3 and 9.

Figure 3. All possible mating combinations between normally pigmented and pink Nile tilapia, and the phenotypes of the offspring produced by each mating. Pictorial representations of the phenotypes are the same as those used in Figure 2. Genotypes are given below the fish. The arrows represent gametes. Mating combinations a and f are examples of true-breeding populations, the goal of a selective breeding programme.

Figure 3 illustrates all possible mating combinations between pink and normally pigmented Nile tilapia and the phenotypes of the offspring produced by each mating. The mating combinations and the phenotypic ratio of the offspring produced by each mating in Figure 3 (for example, 3 normally pigmented: 1 pink in mating 3d) are typical for all qualitative phenotypes that are controlled by a single autosomal gene with complete dominant gene action (provided no genotype is lethal).

The phenotypic ratios of the offspring that are produced by different mating combinations are used to decipher the genetics that controls the phenotypes. Different modes of gene action produce different phenotypic ratios. In a genetics experiment, mating 3c is one of the first matings made. Offspring from mating 3c are called “F₁ offspring.” When mature, these fish are mated (mating 3d) to produce what are called “F₂ offspring.” The phenotypic ratio of F₂ offspring is the key ratio that is used to decipher most forms of inheritance.

In Figure 3, matings 3a and 3f are examples of true-breeding populations. The goal of all selective breeding programmes is to produce a true-breeding population. Breeding programmes that can be used to produce true-breeding populations are outlined in Chapter 3.

Incomplete dominant gene action: Incomplete dominant gene action occurs when the dominant allele expresses itself more strongly than the recessive allele, but it is not strong enough to completely suppress the recessive allele in the heterozygous genotype. Because of this, the dominant phenotype can be produced only when a fish has two copies of the dominant allele (homozygous dominant). Since the recessive allele is not completely suppressed by the dominant allele, the heterozygous genotype produces a phenotype that resembles, but is not identical to, the dominant phenotype. As was the case with complete dominance, the recessive phenotype is produced only when a fish is homozygous recessive. Because the heterozygous genotype produces a phenotype that is similar to but is different from the dominant phenotype, when the mode of gene action is incomplete dominance, there are three genotypes and three phenotypes, a unique phenotype for each genotype (Figure 1):

For example, black (normal pigmentation), bronze, and gold body colours in Mozambique tilapia are controlled by the G gene. The dominant G allele produces melanistic (dark-coloured) fish, but because the G gene exhibits incomplete dominance, the G allele does not completely suppress the expression of the recessive g. allele in the heterozygous state. The homozygous dominant and heterozygous genotypes produce unique phenotypes: GG fish are black, while Gg. fish are bronze. Gold fish are produced by the homozygous recessive genotype (gg.) (Figure 4). Table 2 provides examples of qualitative phenotypes in important cultured food fishes that are produced by single autosomal genes with incomplete dominance.

Figure 5 illustrates all possible mating combinations among black, bronze, and gold Mozambique tilapia and the phenotypes of the offspring produced by each mating. The mating combinations and the phenotypic ratio of the offspring produced by each mating in Figure 5 (for example, 1 black:2 bronze: 1 gold in mating 5d) are typical for all qualitative phenotypes that are controlled by a single autosomal gene with incomplete dominant gene action (provided no genotype is lethal). In Figure 5, matings 5a and 5f are examples of true-breeding populations, and the phenotypic ratio of the offspring produced by mating 5d is the key that is used to unlock the mode of inheritance.

Additive gene action: With only one exception, all qualitative phenotypes controlled by a single autosomal gene that have been discovered in cultured food fish are controlled either by complete or by incomplete dominance. The lone exception is a gene that controls golden, palomino (the heterozygous phenotype) and normal body colours by additive gene action in rainbow trout. When phenotypes are controlled by additive gene action, there is no dominant or recessive allele. Both alleles contribute equally to the production of the phenotypes, so the heterozygous genotype produces a phenotype that is intermediate between those produced by the two homozygous genotypes. Consequently, when the mode of inheritance is additive gene action, there are three genotypes and three phenotypes, a unique phenotype for each genotype.

The difference between additive gene action and incomplete dominance is that when the mode of gene action is incomplete dominance, the heterozygous phenotype approximates one of the homozygous phenotypes (the dominant one), while it is intermediate between the two homozygous phenotypes when the mode of gene action is additive (Figure 1). Because qualitative phenotypes are descriptive and are not measured, it is possible to mis-classify incomplete dominance and additive gene action. Even if the mode of gene action is mis-classified, it is of no practical importance for a breeding programme. Because both types of gene action have three genotypes and each produces a unique phenotype, the breeding programmes that are used to control phenotypes produced either by incomplete dominance or by additive gene action are identical.

The mating combinations and phenotypic ratio of the offspring produced by the matings that are shown in Figure 5 can also be used to illustrate what occurs for phenotypes that are controlled by a single autosomal gene with additive gene action. The phenotypic ratios for phenotypes controlled by incomplete dominance and by additive gene action are identical. The only difference is the appearance of the heterozygous phenotype-does it resemble the dominant phenotype (incomplete dominance), or is it intermediate between the two homozygous phenotypes (additive)?

PHENOTYPE	GENOTYPE
BLACK
BRONZE
GOLD

Figure 4. Inheritance of black, bronze, and gold body colours in Mozambique tilapia. These phenotypes are controlled by a single autosomal gene with incomplete dominant gene action called the G gene. Because the dominant G allele is not completely dominant over the recessive g. allele, the heterozygous genotype produces a phenotype that is similar to but distinct from that produced by the homozygous dominant genotype. Homozygous dominant fish (GG) are black (the dominant phenotype); heterozygous fish (Gg) are bronze (the heterozygous phenotype); homozygous recessive fish (gg) are gold (the recessive phenotype). Pictorial representations of body colour used in this figure will also be used in Figures 5, 10, 11, 17, and 18.

Figure 5. All possible mating combinations among black, bronze, and gold Mozambique tilapia, and the phenotypes of the offspring produced by each mating. Pictorial representations of the phenotypes are the same as those used in Figure 4. Genotypes are given below the fish. The arrows represent gametes. Mating combinations a and f are examples of true-breeding populations, the goal of a selective breeding programme.

Table 2. Examples of phenotypes in cultured food fishes that are controlled by single autosomal genes with incomplete dominant gene action.

Qualitative phenotypes controlled by two autosomal genes

Some qualitative phenotypes are controlled by two autosomal genes. When two genes control the production of a set of phenotypes, there is usually some sort of interaction, and one gene influences the expression of the other. This means one gene alters the production of the phenotypes that are produced by the second gene. This gene interaction is called “epistasis.”

Most of the examples of epistasis that have been found in fish were discovered in ornamental fish, but several have been found in important cultured food fishes. The two most important are scale pattern in common carp and flesh colour in chinook salmon. Because common carp is one of the most important cultured food fishes in Asia and Europe, it is arguable that scale pattern in common carp is the most important set of qualitative phenotypes that have been found in any aquacultured species. Scale pattern also helps determine colour pattern, and thus the value, of ornamental common carp (koi).

The four scale pattern phenotypes in common carp-scaled (normal scale pattern), mirror, line, and leather-are controlled by two genes (S and N) with what is called “dominant epistasis.” The S gene determines the basic scale pattern via complete dominance. The dominant S allele produces the scaled phenotype (SS and Ss genotypes), while the recessive s allele produces the reduced scale phenotype called “mirror” (ss genotype). The N. gene modifies the phenotypes produced by the S gene. There are two alleles at the N locus. The dominant N allele modifies the phenotypes as follows: in the homozygous state (NN). the N allele kills the embryo; in the heterozygous (Nn) state, the N allele changes the scaled phenotype into the line phenotype and changes the mirror phenotype into the leather phenotype. The recessive n allele has no effect on the phenotypes produced by the S gene. The five phenotypes (one is death) and the underlying genetics are illustrated in Figure 6.

A set of qualitative phenotypes may be controlled by more than two genes. Body colour in the Siamese fighting fish is an example of a set of phenotypes that is controlled by the epistatic interaction among four genes. Working with these phenotypes is far more complicated because of the number of genes involved. Fortunately, in food fish, no qualitative phenotype controlled by more than two genes has been discovered.

Figure 6. Inheritance of scale pattern in common carp. Scale pattern is determined by the epistatic interaction between the S and N genes. The S gene determines whether the fish has the scaled phenotype (SS and Ss genotypes) or the mirror phenotype (ss genotype). The N gene modifies those phenotypes. The NN genotype kills the fish (SS, NN, Ss, NN, and ss, NN genotypes); the Nn genotype changes the scaled phenotype into the line phenotype (SS, Nn and Ss, Nn genotypes) and changes the mirror phenotype into the leather phenotype (ss, Nn). The nn genotype does not alter the phenotypes produced by the S gene, so scaled fish have the SS, nn or Ss, nn genotypes, while mirror fish have the ss, nn genotype.

Genetics of quantitative phenotypes

Quantitative phenotypes are the phenotypes that are measured, such as length, weight, eggs/kg female, or feed conversion. Quantitative phenotypes differ from qualitative phenotypes in that individuals do not fall into discrete, non-overlapping categories. When a geneticist describes a quantitative phenotype, he creates only a single category, such as weight. Fish are not grouped into discrete categories such as “light” or “heavy.” Instead, individuals are arranged along a continuum, and an individual's phenotypic value is determined by the unit of measurement that the farmer uses (millimeters, centimeters, grams, kilograms, etc.).

Because an individual's phenotypic value is determined by measurement (for example, length in millimeters) rather than by descriptive category (for example, colour), the differences between two individuals is a matter of degree (millimeter) rather than of kind (colour). Because the differences among individuals are matters of degree, in a population quantitative phenotypes form what are called continuous distributions, which can be described graphically, as is illustrated in Figure 7.

Figure 7. Distribution exhibited by a quantitative phenotype in a population. Graph a illustrates a perfect distribution, which creates what is called a “bell-shaped curve” with the mean bisecting the curve at its peak. Graph b is the distribution of 7-month length in a population of common carp.

The reason why quantitative phenotypes do not segregate individuals into neat and precise categories, as was the case with qualitative phenotypes, is that they are much more complicated genetically. In general, qualitative phenotypes are controlled by one or two genes. They can be controlled by more, but few are. Quantitative phenotypes are controlled by dozens to hundreds of genes. The exact number is usually never known. Additionally, the genes are shuffled like a deck of cards during meiosis due to crossing over and the independent assortment of chromosomes; the combination of these events ensures that each offspring will receive a slightly different genetic message.

Quantitative phenotypes are also strongly influenced by environmental variables, and this helps produce a continuous distribution. These variables range from the obvious ones, such as stocking density, to ones not often considered, such as size and age of the mother. Some of these variables are felt at the family level (for example, date of birth and age of mother), while others are felt at the individual level (for example, access to food).

The simultaneous actions of these genetic and environmental factors results in the creation of single phenotypic categories where the only way an individual can be described is by measuring it. Because quantitative phenotypes are single categories with continuous distributions, you cannot analyze ratios or determine what percent of the population has a specific phenotype, as is the case with qualitative phenotypes. Instead, you calculate populational values and compare individual or family phenotypic values to the population's values. In a population, quantitative phenotypes are described by the mean, which is the arithmetic average, and by the standard deviation, which is the square root of the variance. The mean describes the central tendency and the standard deviation describes how the values in the population are distributed about the mean.

For practical breeding work on medium-sized fish farms, it is important to know how to calculate the mean, so that a farmer can assess the effect of his selective breeding programme. A farmer really does not need to know how to determine the standard deviation; scientists and researchers, on the other hand, must know how to determine the standard deviation. Table 3 illustrates how the mean is determined.

Because quantitative phenotypes are controlled by dozens to hundreds of genes, the simultaneous and/or sequential expression of these genes makes it impossible to identify individual genes and to decipher their modes of inheritance. Consequently, a different approach is needed to work with and to understand these phenotypes. Because quantitative phenotypes are more complicated genetically, it is more difficult to work with these phenotypes, but quantitative phenotypes are the most important phenotypes in agriculture or aquaculture-weight, fecundity, etc.--so the breeding value of a farmed population of food fish is mainly determined by the genes that control quantitative phenotypes. Their importance is underscored by the fact that quantitative phenotypes are often called “production phenotypes.”

Table 3. How to calculate the mean for a quantitative phenotype. In this example, we will calculate mean length. In general, you determine the mean from a random sample of 30–200 fish.

Step 1.	Obtain individual lengths to the nearest millimeter. Thirty fish are measured.
	98	103	106	111	104	91	87	103	114	107
	101	104	97	105	108	100	110	113	104	105
	95	97	107	108	99	111	112	113	105	103
Step 2.	Determine the sum of the measurements; that is, add the phenotypic values.
	98 + 103 + 106 + 111 + 104 + 91 + 87 + 114 + 103 + 107 + 101 + 104 + 97 + 105 + 108 + 100 + 103 + 113 + 105 + 95 + 97 + 107 + 108 + 99 + 111 + 112 + 105 + 113 + 103 = 3,120
Step 3.	Divide the total value derived in Step 2 by the number of fish that were measured. In this case, 30 fish were measured, so you divide by 30.
	The mean length in this population is 104 mm.

Phenotypic variance

Because quantitative phenotypes exhibit continuous distributions in a population, the only way to work with and to improve these traits is to analyze their variance and to divide it into the heritable and the non-heritable components. Phenotypic variance is the variability that a phenotype exhibits in a population; the mean describes the average phenotypic value, while the variance describes how individuals are distributed around the mean (the standard deviation, which was mentioned earlier, is the square root of the variance). Phenotypic variance (V_P) is the sum of three components: genetic variance (V_G), environmental variance (V_E), and genetic-environmental interaction variance (V_G-E). This can be represented by the following formula:

V_P = V_G + V_E + V_G-E

Genetic variance

Obviously, genetic variance is the component that breeders try to manipulate during a breeding programme. Genetic variance is itself the sum of three components, and different breeding programmes are needed to exploit these sub-components.

Genetic variance (V_G) is the sum of additive genetic variance (V_A), dominance genetic variance (V_D), and epistatic genetic variance (V₁). As before, this can be represented by a formula:

V_G = V_A+ V_D + V_I

The words “additive,” “dominance,” and “epistatic” do not refer to specific types of gene action as they do when discussing the modes of inheritance for qualitative phenotypes. The correct terms are “additive genetic variance,” “dominance genetic variance,” and “epistatic genetic variance” (not gene action), and they refer to specific components of variance that are produced by the entire genome, not by one or two genes.

Additive genetic variance is the genetic component that is due to the additive effects of all the fish's alleles. One way of thinking about this is that additive genetic variance is the sum of the values that each allele makes to the production of the phenotype. Some alleles will make a large contribution; some will make a small contribution; some will make no contribution; and some may even make a negative contribution. The contribution made by every allele is added, and the sum is the additive genetic variance component for each fish.

Dominance genetic variance is the genetic component that is due to the interaction that exists between the pair of alleles at every locus. Because of this, dominance genetic variance cannot be inherited.

The idea that some form of genetics cannot be inherited usually causes confusion, but it is a simple concept. Dominance genetic variance is due to the interaction of the pair of alleles at each locus, which means that dominance genetic variance is a function of the diploid state (2N). The reason that dominance genetic variance is not heritable is that each parent contributes a haploid (N) gamete to the production of each offspring. Gametes do not contain pairs of alleles (2N); the diploid state is reduced to the haploid state during meiosis. During reduction division, all allelic pairs are separated when the chromosomes undergo independent assortment, which means that a parent's dominance genetic effects are destroyed during meiosis. Since an individual's dominance genetic variance is destroyed during reduction division, it cannot be transmitted via a gamete to an offspring-thus, it is not heritable. Dominance genetic variance effects are recreated at fertilization when a haploid sperm fertilizes a haploid egg to produce a diploid zygote. At fertilization, genes once again exist in the paired state, which means that an interaction exists between the pairs of alleles at each locus which, in turn, means that dominance genetic variance exists. Consequently, dominance genetic variance effects are destroyed and then recreated in new and in different combinations each generation.

Epistatic genetic variance is the genetic component that is due to the interaction(s) of alleles between or among loci; in other words, it is the interaction(s) that an allele has with alleles other than its own pair. Epistatic genetic variance is a mixture of heritable and non-heritable variance. The portion of the interaction that is between and among the alleles that were included in a gamete is heritable, but the portion that is between or among alleles that were parcelled to other sperm or to the polar bodies is not heritable. The percentage of epistatic genetic variance that is heritable varies from gamete to gamete because of crossing over and independent assortment. Independent assortment and crossing over tends to disrupt most epistatic genetic variance during meiosis, so only a small random sample is transmitted from a parent to its offspring; consequently, only a small random portion of epistatic genetic variance is heritable.

The differences among additive genetic variance, dominance genetic variance, and epistatic genetic variance and how they are transmitted is important on a practical level because different kinds of breeding programmes are needed to exploit these components of genetic variance. Furthermore, the relative amount of phenotypic variance that can be attributed to these components of genetic variance determines the type of breeding programme that can be used and how effective it will be in improving the phenotype.

The two important genetic components are additive genetic variance and dominance genetic variance. Most breeders assume that epistatic genetic variance is not important. This assumption is made because it is difficult to try and select for combinations of alleles when you do not know what combinations are desirable. Additionally, the improvement that can be gained by selection for epistatic effects is rather small, and it plateaus quickly.

Additive genetic variance and dominance genetic variance are essentially opposites. Additive genetic variance is a function of the alleles, so it is function of the haploid state; dominance genetic variance is a function of allelic pairs, so it is a function of the diploid state. A parent produces haploid gametes, so it can transmit its additive genetic effects to its offspring, but it cannot transmit its dominance effects, which are destroyed during meiosis. Dominance effects are created in each zygote after fertilization. Thus, the additive effects are a function of each parent, while the dominance effects are a function of specific matings. Because the additive effects are transmitted from a parent to its offspring, additive genetic variance is often called the “variance of breeding values.”

Because additive genetic variance is transmitted from a parent to its offspring, selection is the breeding programme that is used to exploit this component of variance and to improve the population. Because dominance genetic variance is not heritable but a function of the mating, hybridization is the breeding programme that is used to exploit this component of variance and to improve the population.

Heritability: Because additive genetic variance is transmitted from a parent to its offspring in a predictable and reliable manner, if the percentage of phenotypic variance that is due to additive genetic variance is known, a farmer can predict the amount of improvement that can be made as a result of selection, and he can even customize selection to achieve a pre-determined amount of improvement per generation.

The proportionate amount of additive genetic variance is called “heritability,” and it can be represented by the following formula:

h² = V_A/V_P

where: h² is the symbol for heritability, V_A is additive genetic variance, and V_P is phenotypic variance. Heritability is expressed as a percentage (0–100% or 0.0–1.0). Thus, heritability quantifies the percentage of phenotypic variance that is inherited in a predictable and reliable manner.

The major reason for determining the heritability of a quantitative phenotype is that it can be used to predict the results of a selective breeding programme by using the following formula:

R = Sh²

where: R is the response to selection (gain per generation), S is the selection differential (the superiority of the select brood fish over that of the population average; to determine this, you simply subtract the population average from the average of the select brood fish), and h² is heritability. Table 4 shows how a heritability can be used to predict response to selection.

Table 4. How to predict the response to selection if the heritability (h²) of the phenotype is known. In this example, we will predict response to selection for increased length and then calculate the predicted mean length of the next generation.

The preceding formula clearly demonstrates that heritability is the factor that determines the percentage of selection differential that can be gained via selection; in other words, how much gain is possible. In general, heritabilities ≥0.25 indicate that selection will produce good gains, while those ≤ 0.15 indicate that selection will be ineffective. Heritabilities > 0.3 are considered to be large.

Although it is advantageous to know the heritability of a quantitative phenotype before conducting a selective breeding programme, it is not necessary. If one exists, it can be used to predict the gains, to customize the selection differential that is needed to achieve a desired response to selection, or to indicate that selection will be so ineffective that the programme should be scrapped. Table 5 shows how a heritability can be used to customize the selection differential in order to achieve a desired response to selection.

It is often unnecessary to determine a heritability, because published information already exists. Several hundred heritabilities have already been determined for phenotypes such as growth rate, food conversion, disease resistance, fecundity, egg size, egg number, dressing percentage, body conformation, and pesticide tolerance in many important aquacultured species of food fish. The heritabilities that are published may not be the same as those in a farmer's population, because heritabilities are specific for the population that was evaluated and for the culture conditions that were used in the experiment, but the published values should be similar to those that exist in most populations. Table 6 lists some of the heritabilities that have been determined in common carp and tilapia.

Table 5. How to use the heritability (h²) of the phenotype to customize the selection differential in order to produce the desired response to selection.

Role of environment in phenotypic expression

Although the genes are the blueprints that are used to produce the phenotypes, they produce these phenotypes in conjunction with the environment. The environment influences the production of all phenotypes, but quantitative phenotypes are more affected by environmental variables than qualitative phenotypes. If a fish cannot eat the necessary nutrients, it will be unable to produce certain proteins, which means the fish will be unable to produce specific phenotypes. This is especially true for qualitative phenotypes which depend on pigments which cannot be synthesized by fish. For example, tropical fish farmers add various plant pigments to fish feed in order to enhance the body colours of ornamental fish, and salmon farmers add pigments to salmon feed so the flesh will be pink rather than white. Environmental factors that influence quantitative phenotypes range from obvious ones, such as stocking density and feed quality, to those which are subtle and usually not considered; these factors include: female age, female size, spawning date, feed particle size, and feeding practices. Even if the environment plays a large role in the production of a quantitative phenotype, the role it plays is not critical to the success of a breeding programme if it is the same for all fish. When conducting a selective breeding programme to improve a quantitative phenotype, it is crucial to be able to control environmental variables and to prevent them from varying among individuals, families, and ponds. If they are not controlled, they will differentially influence phenotypic expression, and a farmer will not know if the select fish are best because they are genetically superior or because they had the better environment. The difference is crucial, because only fish that are superior genetically will be able to transmit this superiority to their offspring, which is the goal of all selective breeding programmes.

Table 6. Heritabilities (h²) for some phenotypes in common carp, Nile tilapia, blue tilapia, and Mozambique tilapia. The existence of different heritability values for a phenotype (for example, 1-year weight in common carp) is because they were determined either by different researchers or in different populations or under different growing conditions. A realized heritability is one that was determined from a selective breeding programme.