The principle of superposition
Charles Darwin's Theory
The concept of natural selection
Evidence for Evolution
Phyletic Gradualism
Punctuated Equilibrium 

The ideas about evolution arise, in part, on the basis of taxonomy and, in part, on the basis of the principle of superposition. The classification of organisms shows similarities among them, implying an evolutionary relationshipThe principle of superposition is also a basis of evolution. In a vertical outcrop of strata, such as the one shown here, the oldest rocks are at the bottom and the youngest rocks are at the top, according to this principle. In this succession of strata, geologists observe that various types of sedimentary rocks are repeated over and over. This is because particular sedimentary environments, which produced the sedimentary rocks, occurred again and again throughout geologic time.
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But the fossils in the sedimentary rocks do not repeat over and over in successive layers. Rather, the assemblage of fossils changes. Beginning at the bottom of the sequence is a distinct assemblage of fossils within the strata. Proceeding upward, some fossils disappear while new fossils appear. By the top of the sequence, the assemblage of fossils is different from that at the bottom.
Researchers find fossils of primitive flying dinosaur

Why did certain organisms disappear and others appear, causing the assemblages to differ? Certain organisms disappear from the rocks either because they became extinct or because they migrated out of the area. But why do new organisms appear in the assemblage? Biologists and geologists postulate that these new organisms either evolved from earlier forms or were introduced from other areas by migration, Hence geologists can explain why the assemblages differ, and the fossil record shows a trend (from the time it began to the time it ended) --extinction and evolution acting together.
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Evolution is defined simply as change through time. Two types of evolution are recognized based on the extent of the change. Microevolution involves changes within a species-for example, differences both within and between populations of the same species. This term is also sometimes used to describe the changes an organism undergoes in its lifetime (for example, from tadpole to frog and to butterfly). Macroevolution involves large-scale of major lineages -for example, a line of amphibians changing into reptiles.
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Charles Darwin's Theory: Review Was Darwing Wrong? an article in the November, 2004, issue of National Geographic and other related topics

Charles Darwin and Alfred Wallace are credited with independently developing the basic theory of evolution. Both announced their results in 1858.) Darwin's theory of evolution can be summarized by four basic observations.

First, the size of a population of organisms within a  geographic area remains relatively constant over time.
Second, even though the size of the population is constant the number of offspring produced by any one  individual within the population is large. Many more offspring are produced than can survive.
Third, individuals within a population display variation. No two individuals are identical.
Fourth, since relatively few offspring survive, each  individual must experience a "struggle for life," The individuals are under pressure-from the environment, from predators, and from individuals within the same species
The conclusion drawn from these four observations is that  those organisms that have characteristics that best  them to carry on this struggle will survive and reproduce  passing along those traits that are genetically controlled to the next generation.
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The concept of natural selection was Darwin's major contribution to science. In an oversimplified definition, natural selection is the unseen "force" or "forces" (or  process that weed out individuals unable to carry on successfully the struggle for life.

 Darwin's theory was remarkable in explaining how evolution could operate, but Darwin recognized two  problems with it. First, since he maintained that the process was gradual, where were all the supposed transitional forms in the fossil record? Darwin resorted to a long-held notion that the rock record is incomplete-and argued that, if the 3-rock record were more complete, these transitional forms would be seen. Second, Darwin could not explain how variation arose in populations or how the various characteristics were passed on from one generation to the next. This problem was solved by Gregor Mendel and his  study of genetics.
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No theory should  be presented without same evidence. Darwin substantiated his theory of evolution with abundant evidence accumulated during his five-year voyage as naturalist on the HMS Beagle and also from field studies in Britain and much library research.  Since Darwin's time, additional evidence for evolution has been found. Macroevolutionary processes (for example, the change from fish to amphibian), however, may take millions of years. This sort of process is not seen in the laboratory, which further shows that the scientific method as applied to the geosciences must differ somewhat from the classic approach.

Anatomical evidence for evolution includes

1. Embryology. The close resemblance of embryos of  certain organisms.
2. Homology (homologous structures). In some animals,  the bones of the limbs have all been modified for  different functions. The configuration of the bones  arose from a common ancestor, and the modification  through the process of evolution.
3. Vestigial structures. More evidence of evolution is  found in vestigial structures-organs inherited from an  ancestor that now serve no purpose.
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Biological evidence for evolution includes:

I . Selective breeding. Microevolution has been demonstrated in selective breeding, Changes In plants and dogs through this process are common.

2. Ontogenetic changes. Evolutionary changes can occur during an organism's lifetime; for example, the dramatic change from a tadpole to a frog or a caterpillar to a butterfly.

3. Biochemistry. The similar biochemistry of organisms Implies common ancestry.

Paleontological evidence for evolution is clearly documented in the fossil
Evolution is clearly documented in the fossil record. Well-documented examples of several types of evolution are known.

The Speed of Evolution
Evolution at the lowest level begins with speciation the development of a new species. Answering the question, How long does it take for a new species to evolve? is the start of understanding how quickly evolutionary processes generally operate. After Darwin, the process of evolution was thought to be slow and gradual. Then, in 1972, a new model was proposed to explain speciation,
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Phyletic Gradualism

Phyletic gradualism is a model that shows evolution occurring slowly and gradually over many, many generations. This was Darwin's view of how evolution operates.  A population of a certain species (A) at time I. Members of this population display some morphologic trait-for example, size-that clusters around an average value. Over time, the average value of the specified morphologic trait changes. (Perhaps, overall, individuals of the population get bigger.) Eventually, the morphologic change is so great that if the new population (b, at time 2) had been living during the time of the initial population (A), it would have been considered a different species. Species A has now evolved Into species 13. How this situation might appear in the rock record. The geologic literature contains numerous well-documented examples of lineages displaying this type of evolution (for example, Jurassic ammonites and clams). However, most of the time the "transitional forms" occurring between population A and Population B are not found, Darwin stated that the rock record is incomplete. This may be true in some cases but certainly not all, The problem of transitional forms has been both a continuing source of frustration and a point of contention.
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Punctuated Equilibrium

A literal reading of the fossil record shows that new organsisms appear quite suddenly in the strata, stay relatively unchanged throughout their duration, and then disappear just as suddenly. In an attempt to reconcile the ideas of evolution with what is seen in the fossil record, Niles Eldredge and Steven J. Gould in the early 1970s proposed a model they termed punctuated equilibrium. According to their model, within the geographic distribution of a species, the individuals living on the extreme edge of the geographic range are under the most evolutionary pressure, certainly more than that experienced by individuals well within the geographic range. These "peripheral isolates" undergo evolution (change) at an accelerated rate. Speciation. is very rapid and occurs in small regions at the edge of the geographic range  of the main population (figure 19-12B), If the new species, which has evolved very rapidly, migrates back into the geographic range of the old species, in the rock record it will look as if a new species has suddenly appeared, in addition, if the new species is much better adapted to the environment, it could cause the extinction of the old species, for example, by taking all the nesting sites or food. Within this framework, the rock and fossil record is more complete than we thought. The odds of preserving a rapid, geographically limited evolutionary event in the rock record are quite small. No wonder it seems that species appear suddenly. The geologic literature also contains numerous examples of this type of evolution (for example, Cambrian trilobites).

Which model of speciation-phyletic gradualism or punctuated equilibrium-is correct? Like most competing ideas, it is probably not a case of either/or, but rather of both/and. Both processes have operated In particular lineages in the past.

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Follow this link for a more complete Introduction to Evolutionary Biology
Click on this link for some additional thoguhts on evolution

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