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What is Evolution Really?
By D. Jon Scott

Evolution (ev·ô·lü·shun)
1: One of several movements in an ascribed sequence.
2: (a) A process of change in a certain direction; Unfolding.
(b) The event or action of forming and releasing or giving something off; Emission.
(c1) A process of constant or continuous change from a lower to higher, lesser to greater, or worse to better state; Growth.
(c2) A process of gradual, relatively peaceful advance within a society at the social, political, or economic level.
3: The finding, working out, or extraction of a mathematical root.
4: (a) The process of change within all living cells/life forms; Biological Evolution. [Discussed below]
(b1) Morphological change acheived over time: the development of various types of life forms from preexisting life forms, in which the traits of the existing or current life form have been inherited from successive generations; Historical Evolution, Phylogeny.
(b2) The development of all life forms from a single living ancestor; Common Ancestry.
Evolution, Biological
In biology, the term 'evolution' refers to any change in gene frequency of a population over time. Just for the sake of clarification, the word 'population' means, in the context of biological studies, any group of life forms which can and do breed with one another (E.g., a gene pool). 
So what constitutes a change in gene frequency of a population? The answer to that is most simply stated in the form of a syllogism: 
  1. Most (all?) individual life forms have a completely unique DNA sequence.
  2. A population is comprised of several individuals and thus the population as a whole has a unique gene frequency.
  3. Therefor, altering the number of individuals within a population will change the gene frequency of the population.
Evolution below the species level is known as micro-evolution. Evolution at or above the species level is known as macro-evolution. These terms merely have to do with the scope of the degree of change we look at; they are not events. When we look at the evolution of Cro-Magnon people to modern Europeans, we are discussing micro-evolution. On the other hand, if we are looking at the evolution of Homo erectus to Homo sapiens, we are discussing macro-evolution. The terms describe the degree to which a population has evolved within a given scope of time. 
Macro-Evolution and Speciation 
When a new species emerges, it would be generally incorrect to say "macro-evolution has occurred" -- instead, it would be referred to as a "speciation event". Speciation is the best term for describing the appearance of a new species; it literally means a division of one species into a new specific group -- which necessarily means it (the new group) is unable to be reintegrated into the previous group. The definition of a species is somewhat debatable, as inter-specific breeding may occur. Generally, the term 'species' refers to any number of life forms which are genetically isolated from all other life forms, yet can still mate and produce fertile offspring with eachother.  
Exceptions to the rule of speciation? 
One exception might be the species Canis lupus and Canis familiaris, or the grey wolf and domestic dog. They are quite able to breed with one another and produce fertile offspring. However, the two usually do not breed in the wild, and are said to be genetically isolated. 
Horses and donkeys can also breed to produce a mule. However, mules are sterile (infertile). The same is true for tigers and lions, who mate and produce an animal known as a liger - which may (very rarely) be interfertile with either lions or tigers, but never other ligers. 

[pictured left: "Liger" -- Lion/Tiger hybrid] 
This definition of the word 'species' also excludes the possibility of determining whether asexual or parthenogenetic life forms should be deemed different/same species. 
Drawing lines between species is also difficult in prokaryotes such as bacteria and most (all?) basic types of algae (some of whom actually are bacteria in and of themselves). 
So please keep in mind that, although identifying when a speciation event has occurred is relatively easy in most plants and animals, there are many cases in which it can be quite perplexing to decide where to draw the line between species.

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