Evolutionary Genetics

Which again gives you: p²AA+2pqAa+q²aa

After one generation of random mating and in the absence of selection and other forces of evolution (below), a population will be in Hardy-Weinberg frequencies and remain so. Consequently, it is referred also as the Hardy-Weinberg equilibrium equation.

Forces of Evolution

These are the forces that cause gene frequencies to change in a population or species:

• natural selection
• mutations
• migration
• random genetic drift

Natural Selection

Natural selection is the differential survival and reproduction of genotypes. More on this below. It is natural selection that adapts and attunes organisms to their environment.

Mutations

Mutations are changes in the DNA. These can be point mutations of individual DNA bases (A,T,G,C), segments of DNA involving many bases, chromosomal rearrangements, gene duplication (much like the story of alpha, beta, gamma, and fetal hemoglobin genes), or even gene loss. All genetic variants ultimately arise by mutations.

Migration

Migration is the movement of individuals and their genes between populations. These individuals may have different genes and can introduce these new genes to a new populations. Alternatively, if the migrants have alleles in different frequencies than the population they are going to or leaving, this can cause a change in gene frequencies. An excellent example of the this is the invasion of Genghis Khan and his army into Europe in the 13 century. The Mongolian race has a higher frequency of the B allele in the ABO blood gene than the European, Caucasian populations. Even today in the places his army invaded as they swept down through Europe, there is a higher frequency of their B allele in those populations compared to the rest of Europe's populations. Apparently his solders left some of their DNA behind.

Random Genetic Drift

Random genetic drift causes changes in gene frequencies through sampling error in small populations. It is a random process. In small populations there will be sampling error from generation to generation resulting in the loss of genetic variation and variants. The smaller the population, the greater the drift effect, i.e. the more rapid the loss of variation. And, populations want genetic variation.

Genetic  Variation

Genetic variation is good. In general that is. This is the reason we see hybrid vigor--in hybrids between different species (e.g. the mule) or between different strains or, in agriculture, cultivars. Experiments with Drosophila (fruit flies), decades ago took strains of fruit flies that had been made completely homozygous for every gene--that is they had no genetic variation. Geneticists irradiated the treatment group, which caused random mutations. The irradiated treatment group had higher fitness and were healthier than the non-irradiated control group. Similar experiments have been done with a variety of organisms from bacteria to mammals and showed the same affect. Even random genetic variation was better than no genetic variation.

Fitness

Finally, we come to a key concept in evolutionary genetics: fitness. The fitness of a genotype is a measure of how well it survives and reproduces. Let us designate w_ij as the fitness of the ij genotype where i and j are alleles in a population, then
where  v_ij is the viability of the ij genotype and  f_ij is the fertility of that genotype. Viability means how well that genotype survives and fertility is the number of offspring left by that genotype.

Note, fitness is the product of viability and fertility. As either component, v or f, approaches zero, fitness approaches zero. A way to think about this is that if you have some real tough hombre, the meanest and baddest guy on the block, he's top dog, numero uno, the big cheese, but he is sterile. from an evolutionary perspective it does him no good: his fitness (w) is 1 x 0= 0. You have to have both viability and fertility to stay in the evolutionary game.

Fitness is related to selection, w= 1-s, where s is the selection coefficient, a measure of the intensity of selection. Selection acts on individuals or, more accurately, individual genotypes.

Average Fitness of a Population

A related concept is average fitness of a population, designated, W-bar, that is a W with a bar across the top (too hard to do with html), and is is equal to the sum of the various genotypes weighted by their frequencies in the population. This concept will be important when I discusss Adaptive Landscapes as  a prerequisite for talking about psychosocial evolution in relation to spiritual and personal growth.

Fisher's Fundamental Theorem of Natural Selection (1930)

Sir R. A. Fisher, who would lecture and give seminars drinking beer, showed that the rate of change of the average fitness in a population is equal to the variance in fitness between the genotypes. What this means is that if there is a genotype with high fitness, selection will cause rapid changes in the population to increase the population's average fitness.

Types of Selection

I want to mention four types of selection. Most people when they think of natural selection, if they think of it at all, is in terms of what is called directional selection.

Directional Selection

This is selection for or against a specific gene or genotype. In the case of two alleles in a population, say A and B, its end result is fixation (p=10) of one allele (A) and elimination of the other (q=0). A deleterious mutation would be an example here. This type of selection eliminates genetic variation from the population. In contrast to directional selection, we have balancing selection, which is quite common.

Balancing Selection

In balancing selection, selection acts to maintain multiple alleles in a population and results in maintaining or increasing genetic variation. Two mechanisms of balancing selection are overdominance and frequency dependent selection:

Overdominance

In overdominance the heterozygous genotype (A/B) has the highest fitness over both homozygous genotypes, AA or BB. The sickle cell hemoglobin gene in human populations is an example. In a malarial infested environment, the heterozygote that carries one wild-type hemoglobin alpha chain allele and  one sickled allele is resistant to malaria. Unfortunately, the homozygote for the sickle allele is lethal. In a non-malarial environment, the wild-type alpha homozygote has highest fitness.

Frequency Dependent

This is where the frequency of a genotype depends on its frequency in the population. Lets take "blond" genes as a humorous example. Lets assume a population in which most of the individuals have dark hair. Blonds when fairly rare, have a mating advantage because they attract attention. They stand out. However, as their numbers increase in the population and they become common, they loose their mating advantage.