Classification and Evolution

Introduction
Evolution is often defined as change over time, usually in response to a change in the environment. What this means is that the gene pool of a population shifts as time passes.

What is a gene pool? It is simply the collection of all the available alleles of all the genes on all the chromosomes in the population. What’s a population? It is the group of individuals that have geographic and behavioral mating access to each other. Geographic access is obvious; the dandelions in a yard in Virginia are not in the same gene pool as those in a yard in Pennsylvania, even if they are the same species. They could mate if they were brought together, but dandelion pollen doesn’t blow that far, so they are geographically isolated. Behavioral mating access can be less obvious; one example would be a stag that keeps all other males out of his territory and mates with all the does. The other stags are not allowed to mate, so their genes are not in the pool.

A great deal of the time for most species, evolution is not occurring. The gene pool stays the same, because the environmental situation is not changing. In the early days of population genetics, people argued over whether dominant alleles could “take over” a gene pool without any selection. Two mathematicians, Hardy and Weinberg, showed that this would not happen.

The basis of their argument is that the gene pool will not change, and the frequency of the various alleles will stay the same if the following conditions are met:

· The population is large.

· The population is freely interbreeding at random (this excludes the stag and the does).

· No individuals are taking their alleles out of the population (emigrating) or adding their alleles to the population (immigrating), so the percentages of the alleles can’t change because of migration.

· There are no mutations, so no new alleles appear.

· None of the alleles has a selective advantage (in other words, there aren’t any combinations of alleles that give some individuals a better chance of surviving that anyone else).

Here is the mathematical basis of their argument:

Imagine a simple situation in which a gene has only two alleles, A and a, and A is dominant. Let the frequency of A, expressed as a decimal with a value less than one, be p, and let the frequency of a, expressed as a decimal with a value less than one, be q. Because there are only two alleles, every allele must be either A or a, so,

p + q = 1

By definition, p and q are also the frequencies of the alleles in the eggs and sperm produced by this species. These sperm and eggs can come together in four ways when random mating occurs.

1. The chance that a male p sperm will meet a female p egg is p x p, or p2. The children produced by this cross will be genetically AA and express the dominant allele; they will have the A phenotype.

2. The chance that a male p sperm will meet a female q egg is p x q, or pq. The children produced by this cross will be genetically Aa and express the dominant allele; they will also have the A phenotype.

3. The chance that a male q sperm will meet a female p egg is also p x q, or pq. The children produced by this cross will also be genetically Aa and express the dominant allele; they will also have the A phenotype.

4. The chance that a male q sperm will meet a female q egg is q x q, or q2. The children produced by this cross will be genetically aa and express the recessive allele; they will have the a phenotype.

These four situations are the only possibilities, so

p2 + pq + pq + q2 = 1 (1.0 represents 100% of all possible events in a mating)

When we combine the middle two terms, we get

p2 + 2pq + q2 = 1

These two formulas,

p + q = 1

p2 + 2pq + q2 = 1

summarize what is known as the Hardy-Weinberg Law.

However, usually we don’t know the frequency of the alleles in a population; in most cases, we can’t even see the gametes! If we want to know what the frequencies of the alleles are, we have to use these two formulas to figure it out.

The most important things to remember are the two formulas above. In these formulas,

· p = the frequency of the dominant allele

· q = the frequency of the recessive allele

· p2 = the frequency of individuals in the population who are homozygous dominant

· 2pq = the frequency of individuals in the population who are heterozygous

· q2 = the frequency of individuals in the population who are homozygous recessive

Materials

· Three colours of beans (chili, pinto and navy are good, but any three contrasting objects will do – M&Ms, coins, beads, etc).

· Two bowls

· A pocket calculator (MS Windows has one too)