Revised November 3, 1999. This lecture is based on part of 1998 Lecture 40.

Lecture 38, MCDB 2150, Fall 1999

Population Genetics II

Textbook Assignment: Chapter 19, pages 591-605 (includes end-of-chapter material for entire chapter). Also, please read the following material on genetic diversity: section 21.3, pages 648-649, and section 27.1, pages 764-769.

Major concepts

Selection: The textbook defines selection as a difference in reproductive successes of different phenotypes. Reproductive success refers not only to how many progeny are produced, but also to the ability of those progeny to survive to maturity and reproduce. Positive selection occurs when a particular phenotype has greater reproductive success than the general population. Negative selection occurs when a particular phenotype has a lower level of reproductive success than the general population.

Directional selection: When selection alters the balance of alleles consistently in one direction, it is called directional selection. This can either be an artificial process in which selective breeding and retention of plants or animals with particular traits are used to alter a genetic balance, or it can be natural selection, which occurs without human intervention. Two examples of directional selection are described in the textbook. The first involves pigmentation of the peppered moth, Biston betularia. As shown in figure 19.7, industrialization darkened the bark of the trees on which they rest on with soot. The moths underwent selection for a more heavily pigmented variant that was better hidden on the dark colored bark. The second example involves rapid selection for insects that are resistant to insecticides when the insecticides are applied indiscriminantly.

Relative fitness: The relative fitness of different genotypes can be defined as the relative ability of each genotype to pass its alleles on to future generations. Relative fitness is designated as w. The phenotype with the highest relative fitness is arbitrarily assigned a fitness of 1.0. The relative fitness of the other phenotypes is expressed in terms of fractions of that value. Thus, if genotype AA has a fitness of w = 1.0, an alternative genotype aa that yields half as many successful progeny per generation would have a relative fitness of w = 0.5. If there is full dominance, the heterozygote Aa would have the same phenotypic fitness as the homozygote AA (see Table 19.3).

Selection coefficient: An alternative expression for the same phenomenon is the selection coefficient, s, which indicates how much selection there is against a particular phenotype. An s value of 1 indicates maximum negative selection (w = 0), with none of the population surviving to reproduce. At the other extreme, an s value of 0 means there is no negative selection relative to the most fit phenotype (w = 1.0).

Relative fitness of heterozygotes: Depending on the pattern of dominance, the relative fitness of a heterozygote can fall anywhere between the most fit and the least fit as shown in table 19.3. If there is full dominance, the heterozygote will experience the same selection as the homozygous dominant genotype. If selection is against the recessive phenotype, the fitness of the heterozygote will be 1. At the other extreme, if the selection is against the dominant phenotype, the fitness of the heterozygote will be 1-s, the same as that of the homozygous dominant genotype. In reading table 19.3, it is important to be aware that selection is always against the allele designated A2, whether it is dominant or recessive.

Selection against the homozygous recessive phenotype: The textbook presents a series of formulas for calculating change in allelic frequency due to selection that is directed only against the homozygous recessive phenotype (one of the most common patterns of selection). Equation 19.12 on page 593 and the other formulas that are subsequently derived from it are widely used in population genetics. Unfortunately, the textbook fails to explain the origins of that equation. The material that follows is derived from an explanation provided on pages 423-424 of Weaver and Hedrick, Basic Genetics, Second edition (available at Norlin reserve). They use the following table to help clarify the steps that are involved (s is the selection coefficient for the homozygous recessive aa)0:

Genotype AA Aa aa total
Relative fitness 1 1 1 - s ----
Frequency before selection p22pqq2 1.0
Weighted contribution
to next generation
p22pqq2(1-s) 1.0 - sq2
Frequency after selection p2 / (1.0 - sq2) 2pq / (1.0 - sq2) [q2(1-s)] / (1.0 - sq2) 1.0

In the formulas in the first column of page 593 of our textbook, q is the allelic frequency of the recessive allele being selected against and s is the selection coefficient. The new allelic frequency for the recessive allele is designated as q1. The value for q1 in equation 19.12 in our textbook is obtained from the total frequency of the recessive allele a after selection has occurred, but some explanation is needed to understand how it is derived. The denominator is the adjusted total allelic population after selection has occurred relative to the previous values. It is necessary to divide by that number to bring the total of all of the genotypes in the progeny back to 1.0 after the losses that occurred due to selection.

Calculation of the numerator requires some juggling, as well as some mental discipline to avoid confusion. The total number of a alleles is twice the number of homozygous aa individuals plus the number of heterozygous Aa individuals. However, since the total number of alleles is twice the number of individuals, we must divide those values by two in order to keep the total frequency of alleles of both types at 1.0 as is required for Hardy-Weinberg calculations. The total frequency of recessive alles after selection is therefore one half of the frequency of the heterozygote Aa plus one half of two times the frequency of the homozygous recessive aa, divided by the total allelic frequency.

q1 = [pq + q2(1-s)] / (1-sq2)
q1 = q(p + q - sq) / (1-sq2)
q1 = q(1 - sq) / (1-sq2)
q1 = (q - sq2) / (1-sq2)   (Equation 19.12)

Inefficient removal of recessive alleles: If selection is only against a homozygous recessive phenotype and not against heterozygotes, complete elimination of the recessive allele from the population is a low and inefficient process (figure 19.8). As the allelic frequency drops, the number of homozygous individuals that can be selected against will become very small and most of the remaining recessive alleles will be in heterozygotes who are not selected against.

Stabilizing and disruptive selection: When selection operates to develop a relatively uniform phenotype (for example, not too large or too small), it is referred to as stabilizing selection. When heterozygotes tend to be selected against, selection will favor two different homozygotes. This is referred to as disruptive selection. In many cases, this may be the first step toward separation of species. For example, in situations where a heterozygote has a reduced fertility because of a pericentric inversion, the two homozygotes may be favored. Comparisons of banded chromosomes from closely related species reveal numerous inversions, which have probably played a major role in speciation. Two inversions between orangutans and other higher primates are illustrated in figure 21.4. Close examination of figure 21.3 reveals numerous inversions (many of them pericentric) among humans, chimpanzees, gorillas, and orangutans.

Changing environmental conditions: It is important to recognize that relative fitness can change sharply with changing environmental conditions (e.g. introduction of new predators, diseases, modification of habitat by natural disaster or manmade effects, etc.). One example illustrated in the book is the relatively recent selective change that now favors darker colors in the English peppered moth, Biston betularia. The environmental change that altered the selective pattern in this case was the darkening of tree bark by industrial soot which provided a selective advantage to moths with darker protective coloration (figure 19.7). See Lecture 25 notes for a brief discussion of the alleles that are involved in these changes.

Heterozygote advantage: If a heterozygous genotype has the highest relative fitness, the population will reach an equilibrium with the heterozygote stabilized. One example of heterozygote advantage that we have touched on before is sickle cell anemia in parts of Africa. Because the electrophoretic patterns of normal beta globin and the sickle-cell mutation are expressed codominantly, it is relatively easy to identify both types of homozygotes, as well as heterozygous individuals. In the absence of modern medical intervention, the sickle cell heterozygote is far more viable in malaria-infested areas than either of the homozygotes. The sickle cell homozygotes die young of sickle cell disease, and the "normal" homozygotes tend to die from malaria. The heterozygotes do not exhibit the recessive sickle cell disease, but are resistant to malaria, and thus form the healthy population that is responsible for most of the reproduction. Despite loss of 1/4 of their children to sickle cell disease and up to 1/4 to malaria, they are able to maintain a viable population of reproducing heterozygotes. (Please note that the above is an exaggeration for clarity, since the loss of normal homozygotes to malaria is not 100%. Nevertheless, the allelic frequency for HbS may be as high as 12.5% in some areas. This corresponds to over 20% heterozygous (2 x .125 x .825) and about 1.6% homozygous for sickle cell anemia (.125 x .125). Calculations based on relative fitness values for the three genetic classes yield similar results. See boxed example 19.7 for an actual example based on data from eastern Senegal.

Balance between mutation and selection: If new recessive alleles with negative selective value are continually arising by mutation, the equilibrium value in the population will reflect a balance between rate of creation of new alleles by mutation and their elimination by selection, and may result in retention of a significant level of the allele in the population, carried primarily by heterozygotes, with homozygous recessives being rare. In addition, other factors, such as heterozygote advantage, may increase the fraction of the alleles retained in the population, even under conditions where the basis for the advantage is not fully understood. The textbook cites cystic fibrosis and Tay-Sachs disease as two examples of recessive diseases that are at higher levels than would be expected based only on balance between mutation and selection.

Polymorphic loci: The material that follows on polymorphic loci and heterozygosity is not presented in our textbook in the same form as in these notes. However, Section 21.3 (pages 648-649) and Section 27.1 (pages 764 - 769) deal with these topics in a slightly different context. In addition, section 19.7 on genetic drift examines some of these topics as they are related to small populations. A genetic locus is considered to be polymorphic if it has two or more known alleles and if the allelic frequency of any one allele does not exceed 0.99. Loci with a single allele at a frequency of 0.99 or greater are considered to be monomorphic. Most species exhibit relatively high frequencies of polymorphic loci (20-40%). However, certain species such as the Northern elephant seal and the cheetah exhibit almost no polymoprhic loci. A low level of polymorphic loci generally is the result of a bottleneck situation (described below) in which a very low surviving population expanded to give rise to the current larger population. Absence of genetic variability makes a species extremely vulnerable to environmental changes (such as new diseases) that could uniformly affect the entire population. There is also a risk that deleterious genes may become fixed in the population due to genetic drift during the bottleneck period (pages 598-602); see also discussion of inbreeding depression and hybrid vigor on pages 615-617).

Heterozygosity: The frequency of occurrence of the heterozygous state at a particular locus is called hererozygosity, (H). In the absence of any distorting forces, H = 2pq, as predicted by the Hardy-Weinberg relationship

(p + q)2 = p2 + 2pq + q2.

However, distorting forces, such as inbreeding and genetic drift often reduce the actual observed heterozygosity (H) to a value that is less that the theoretical prediction of 2pq.

Average heterozygosity is determined by averaging the H values for a number of separate loci, including those that have no heterozygosity. It looks at the extent of heterozygosity in a population, as opposed to the number of different loci that exhibit some degree of heterozygosity due to polymorphism.

Bottlenecks: As indicated above, an evolutionary bottleneck refers to a time when a population was reduced to very small numbers before recovering. In the case of the northern elephant seal, the bottleneck resulted from being hunted almost to extinction before the population recovered after hunting was banned. The cause of the apparent bottleneck in the evolutionary history of the cheetah remains unknown.

Effect of bottlenecks: Two types of distortion of the Hardy-Weinberg equilibrium are likely to result from bottlenecks. The first is increased homozygosity due to increased levels of inbreeding that are almost inevitible when the total population is small. This phenomenon was described in the previous lecture. The second is the so-called founder effect, which results from the chance inclusion of certain alleles in the small founder population, as described below..

Founder effect: One of the potential consequences of a bottleneck is a high frequency of recessive genetic diseases in the population resulting from one of the founders happening to be a carrier of a relatively rare disease whose heterozygote frequency is much higher than its homozygous frequency. The founder effect is based on the fact that a small sample may differ substantially in composition from the larger population it is drawn from, purely by random "sampling errors". You may recall as an example, the very large family group in Venezuela with a high incidence of Huntington disease that could be traced back to a single European immigrant (Lecture 32, Appendix 2). In addition, founder effects can become further established in small populations by genetic drift as described below.

Genetic drift: Another problem that is encountered in small populations is genetic drift. Each new generation is a small sampling of all possible gametes and therefore may not be representative of the overall gene pool, again due to random sampling error. Numerous computer simulations have been done to show that allelic frequencies can drift away from original values as a result of the sampling error. If a population starts with p = q = 0.5, sampling may push the next generation to p = 0.6 and q = 0.4. The next generation may maintain this new ratio, or cause it to move again in either direction. In some cases, several moves in the same direction result in p = 1.0 and q = 0, after which the population is homozygous for p. Because subsets that become fixed as all p or all q cannot drift back, over time more and more of the isolated small populations will become homozygous. Thus, in addition to inbreeding and founder effects, a population that goes through a bottleneck and stays small for a while may become more homozygous through genetic drift (see pages 598-602).

Evolutionary dead ends: Variability provides the basis for natural selection as environmental conditions change. Even if a species is very well adapted to its current environment, it is at risk if it lacks variability (usually expressed as degree of heterozygosity or as fraction of polymorphic loci in the population). Environments do not stay constant. Many variables affect survival in an environment, including the introduction of new competing species, new predators, and new diseases. Disease is probably one of the major driving forces of evolution, although it is not yet as well recognized in that role as it should be. An epidemic that leaves only a few survivors may greatly alter the future gene pool in ways that have nothing directly to do with resistance to the disease (through founder effects, inbreeding of the survivors, and genetic drift). If a species lacks genetic diversity, it is in great danger of not having the resources to survive the next major environmental change and thus of becoming extinct. This is also a serious problem for genetically uniform agricultural crops, as discussed in section 27.1 (pages 764-769).