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The Theory of Evolution made it's first "public appearance" in 1859 by Charles Darwin.  It is called a theory because a theory is a hypothesis that is supported by a great deal of evidence.

The Origin of Life 

Scientists studied rates of radioactive decay to determine that the earth was formed about 4.5 billion years ago.  Scientists then learned that life began 3.5 million years ago from fossils found of bacteria, or simple organisms.  Many years ago, the atmosphere of the earth was very rich in Hydrogen.  Now the atmosphere of the earth has changed due to photosynthesis.  

The cell theory states that all living things are made of cells, the cell is functional unit of life, and all cells came from pre-existing cells.  Long ago, there was a big explosion sending gases everywhere, known as the big bang.  Clouds of gases condensed due to gravity.  This is when galaxies and the earth was formed.  Heat from radioactive decay and gravitational compression melt the earth's core.  Gases escape from the interior of the earth producing a reducing atmosphere that consisted mostly of nitrogen, ammonia, carbon dioxide, methane and water vapour.  There was no oxygen.  As the earth cooled, the water vapour condenced and formed the seas.  UV light, radioactive decay, volcanic heat and lightning provide large amounts of energy.  More and more organic molecules formed, and they began to organize themselves.  Eventually, anaerobic photosynthetic bacteria formed.  Life isn't forming from non-life today because it is a different environment, there is less energy, and organic molecules aren't building up.

Charles Darwin

Charles Darwin lived between 1809 and 1882.  He was an english naturalist.  He studied for 30 years before he wrote his famous book: On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life.  This book was published in 1859, and the book created a sensation.  Darwin was the first person to give a logical explanation for evolution.  He went on a five year voyage on The Beagle to study.  This voyage helped him develop many of this ideas.  

Darwin's Theory of Evolution:

Fossils
Extinct species resemble living species
Progressive changes in characteristics of organisms can be seen in different layers of rock
Geographical Distribution
Lands with similar climates have more unrelated plants and animals
Plants and animals of each continent are distinctive
Oceanic Islands
Species are very unique and show relation to other species
Species show similarities to those on nearby mainland

Darwin's observations on his voyage on the Beagle, his readings of Malthus, and his own experiences helped him develop a theory of evolution by natural selection.

At the same time, Wallace, another scientist, also set forth a theory of evolution by natural selection.  Together, Darwin and Wallace developed this theory together.  Although it is usually referred to as Darwin's theory, it correctly should be referred to as the Darwin-Wallace theory of evolution.

Hardy-Weinberg Equilibrium

A mathematician G.H. Hardy and a physician Weinberg individually developed an idea that is now called Hardy-Weinberg Equilibrium.  They said that if a population isn't changing, it is in equilibrium, if it isn't changing, the population will remain constant from generation to generation, and if the genotypic and allele frequency of a population could be calculated it could be determined when a population was changing, and they we would know when evolution is occurring. The equation states:  p² + 2pq +q² = 1 , p is the frequency of one allele and q is the frequency of the other allele.  If a population is to stay in equilibrium, criteria must be met:

population must be large and free from migration
need sexually reproducing diploid individuals
all individuals must survive and reproduce equally well
mutation is at a minimum
mating must be random

Agents of Evolutionary Change

There are five agents of evolutionary change:

Genetic Drift
The changes in allele frequency as a population goes from being very large to being small.
Selection of the alleles in the new population are random.
Gene Flaw
Changes in the allele frequency due to migration
Immigration
Emigration
Mutation
This is the basis of all evolutionary change.  It usually works with another factor to bring about evolutionary change.
Non-Random Mating
Individuals can't take another individual's phenotype into account when they are choosing a mate.
Self fertilization is non-random (in plants)
Natural Selection
This is the strongest agent of evolutionary change.
Individuals that produce the most surviving offspring will pass their alleles onto their children.
Allele frequencies are changed as a result of interactions in the environment.
The environment acts on the phenotype.
Often selection for one trait can result in undesired results in other traits, therefore a balance must be reached.
For natural selection to operate, there must be diversity within a population.

Adaptation

Parallel adaptation is when different geographical areas have plant and animal communities that are very similar, even though they are only very distantly related.  Convergence is where species of animals, even though they are distantly related, come to resemble each other when they live in a similar habitat or environment.  This occurs because the environment is an important shaping force in evolution.