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I added sections illustrating the mathematical generality of natural selection, what happens when natural selection and random variation combine, and its effects and limitations.
Natural selection is not [[mutation]]. It does not make anything new, alter anything, etc. Natural selection can cause extinction based on survival of the fittest, but the processes of creation and mutation lie outside the scope of natural selection.
Natural selection is not [[mutation]]. It does not make anything new, alter anything, etc. Natural selection can cause extinction based on survival of the fittest, but the processes of creation and mutation lie outside the scope of natural selection.
==See also==
==Generality==
While it is commonly applied to competition between living organisms, natural selection is far more general mathematical model. In general, natural selection applies to any system where a group of different "individuals" (where an "individual" could be anything from a bacterium to a computer program to an architectural design) is evaluated by some metric; each individual is then either discarded or duplicated based on the results of the evaluation (usually with some stochastic weighting of the probabilities of discarding/duplication). The process is then repeated. In most examples, the metric of evaluation is relative--that is, an individual only scores "well" if its score is high compared to the rest of the group.
== Variation and Randomness ==
Natural selection becomes interesting when there is the possibility of random variation in the duplication of individuals--in other words, when an individual is copied, the copy may be slightly different from the original. It is important to note that, as stated above, the ''mechanism'' for this variation is not explained or even taken into account by natural selection. All that matters is that there is ''some'' process that produces variation. Some of the new, slightly different copies of an individual will be evaluated differently from the original, scoring either higher or lower depending on what changed. If this process is iterated many times, individuals which score well on the evaluations will become more and more numerous, and the highest score of an individual will tend to rise. It has been suggested that this process can lead to the appearance of design, as the individuals that are present after many iterations of this process will usually score very well on the evaluation (since those that do not score well are eliminated).
== An Example ==
An engineer starts with 10,000 different sets of plans for a hydroelectric dam. His dam must complete two basic tasks: it must hold back a lake with minimal flooding of the surrounding area, and it must maximize power generation. The intrinsic worth of a dam is determined by how well it completes these tasks; a dam which produces 100 kW of electricity while only raising water levels 2 feet is superior to one which produces 10 kW of electricity while raising water levels 5 feet. In our simplified example, let us assume that the design of a dam is based on just a few numerical parameters: height, width, thickness, concrete mixture, hydroelectric turbine size, curvature, etc. After evaluating all the dams, the engineer picks the 100 best and discards the rest. He then copies each of these dams 100 times. When copying, the engineer randomly introduces minor differences: say he rolls a die each time he copies a design parameter; if he rolls a six, he then changes that parameter by 1%, flipping a coin to determine if he will increase or decrease the parameter. Once he has finished copying, he will have 10,000 more dams, most of them very similar to the original 100 but with some small differences. He then evaluates these 10,000 dams again, picks the best 100, and copies them again, introducing random "errors" in the same way. After completing this process several thousand times, the engineer has 10,000 dams, all of which perform excellently. He picks the best of them and thus has an excellent design, without ever doing any real "design" himself.
== Local and Non-Local Improvement ==
The above section illustrates how natural selection and random variation can combine to create improved individuals. However, it is important to note that there is no long-term planning involved in natural selection. This means that all changes must be locally beneficial in order to survive. Essentially, no improvement can take place if a deterioration must take place first. In order for a change to propagate to future "generations" of individuals, it must not be significantly harmful to ''any'' generation. In the language of the above example, let us say that one of the dams would be much improved if the curvature were increased by 10%, but would be worsened considerably if the curvature was 3 to 7% higher. Since curvature can only change by 1% at a time, and a regime of "bad" curvature lies between the current regime and the regime of "good" curvature, the dam will never reach the "good" regime. Thus, in order for a large change to take place over several generations, it must be beneficial (or at least not significantly harmful) at ''each'' generation.
* [[Theory of evolution through natural selection]]
* [[Theory of evolution through natural selection]]