genetic structure of the base population used to start the breeding program. Students need to have an appreciation for population and quantitative genetics in order to understand the principles and concepts of practical plant breeding. In fact, there is what some call the breeders' equation, a mathematical presentation of a fundamental concept that all breeders must thoroughly understand. This section will help the student understand this and other basic breeding concepts.
Purpose and expected outcomes
Plant breeders manipulate plants based on the modes of their reproduction (i.e. self‐ or cross‐pollinated). Self‐pollinated plants are pollinated predominantly by pollen grains from their own flowers, whereas cross‐pollinated plants are predominantly pollinated by pollen from other plants. These different reproductive behaviors have implications in the genetic structure of plant populations. In addition to understanding Mendelian genetics, plant breeders need to understand changes in gene frequencies in populations. After all, selection alters the gene frequencies of breeding populations. After studying this chapter, the student should be able to:
1 Define a population.
2 Discuss the concept of a gene pool.
3 Discuss the concept of gene frequency.
4 Discuss the Hardy‐Weinberg law.
5 Discuss the implications of the population concept in breeding.
6 Discuss the concept of inbreeding and its implications in breeding.
7 Discuss the concept of combining ability.
3.1 Concepts of a population and gene pool
Some breeding methods focus on individual plant improvement, whereas others focus on improving plant populations. Plant populations have certain dynamics, which impact their genetic structure. The genetic structure of a population determines its capacity to be changed by selection (i.e. improved by plant breeding). Understanding population structure is key to deciding the plant breeding options and selection strategies to use in a breeding program.
3.1.1 Definitions
A population is a group of sexually interbreeding individuals. The capacity to interbreed implies that every gene within the group is accessible to all members through the sexual process. A gene pool is the total number and variety of genes and alleles in a sexually reproducing population that is available for transmission to the next generation. Rather than the inheritance of traits, population genetics is concerned with how the frequencies of alleles in a gene pool change over time. Understanding population structure is important to breeding by either conventional or unconventional methods. It should be pointed out that the use of recombinant DNA technology, as previously indicated, has the potential to allow gene transfer across all biological boundaries to be made. Breeding of cross‐pollinated species tends to focus on improving populations rather than individual plants, as is the case in breeding self‐pollinated species. To understand population structure and its importance to plant breeding, it is important to understand the type of variability present, and its underlying genetic control, in addition to the mode of selection for changing the genetic structure.
3.1.2 Mathematical model of a gene pool
As previously stated, gene frequency is the basic concept in population genetics. Population genetics is concerned with both the genetic composition of the population as well as the transmission of genetic material to the next generation. The genetic constitution of a population is described by an array of gene frequencies. The genetic properties of a population are influenced in the process of transmission of genes from one generation to the next by four major factors: population size, differences in fertility and viability, migration and mutation, and the mating system. Genetic frequencies are subject to sample variation between successive generations. A plant breeder directs the evolution of the breeding population through the kinds of parents used to start the base population in a breeding program, how the parents are mated, and artificial selection.
The genetic constitution of individuals in a population is reconstituted for each subsequent generation. Whereas the genes carried by the population have continuity from one generation to the next, there is no such continuity in the genotypes in which these genes occur. Plant breeders often work with genetic phenomena in populations that exhibit no apparent Mendelian segregation, even though in actuality, they obey Mendelian laws. Mendel worked with genes whose effects were categorical (kinds) and were readily classifiable (ratios) into kinds in the progeny of crosses. Breeders, on the other hand, are usually concerned about differences in populations measured in degrees rather than kinds. Population genetics uses mathematical models to attempt to describe population phenomena. To accomplish this, it is necessary to make assumptions about the population and its environment.
Calculating gene frequency
To understand the genetic structure of a population, consider a large population in which random mating occurs, with no mutation or gene flow between this population and others, no selective advantage for any genotype, and normal meiosis. Consider also one locus, A, with two alleles, A, and a. The frequency of allele A 1 in the gene pool is p, while the frequency of allele A 2 is q. Also, p + q = 1 (or 100% of the gene pool). Assume a population of N diploids (have two alleles at each locus) in which two alleles (A, a) occur at one locus. Assuming dominance at the locus, three genotypes – AA, Aa, and aa – are possible in an F2 segregating population. Assume the genotypic frequencies are D (for AA), H (for Aa), and Q (for aa). Since the population is diploid, there will be 2N alleles in it. The genotype AA has two A alleles. Hence, the total number of A alleles in the population is calculated as 2D + H. The proportion or frequency of A alleles (designated as p) in the population is obtained as follows:
The same can be done for allele a, and designated q. Further, p + q = 1 and hence p = 1 – q. If N = 80, D = 4, and H = 24,
Since p + q = 1, q = 1 − p, and hence q = 1 – 0.2 = 0.8.
Hardy‐Weinberg equilibrium
Consider a random mating population (each male gamete has an equal chance of mating with any female gamete). Random mating involving the previous locus (A/a) will yield the following genotypes: AA, Aa, and aa, with the corresponding frequencies of p 2 , 2pq, and q 2 , respectively. The gene frequencies must add up to unity. Consequently, p 2 + 2pq + q 2 = 1. This mathematical relationship is called the Hardy‐Weinberg equilibrium. Hardy of England and Weinberg of Germany discovered that equilibrium between genes and genotypes is achieved in large populations. They showed that the frequency of genotypes in a population depends on the frequency of genes in the preceding generation, not on the frequency of the genotypes.
Considering
