Natural selection is most closely related to Darwin's theory of evolution.
Individuals suited to the struggle for existence will survive and reproduce better than individuals not so suited. Differential reproductive success is just another name for evolution by natural selection.
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Natural selection.
A simplified explanation. Natural selection is the nonrandom survival and reproductive success of randomly varying organisms who by this reproductive success change the allele frequency over time in populations of organisms, which is evolution.
Natural Selection!
It wasn't! The theory of evolution by natural selection has nothing to do with social Darwinism and to posit such a connection is ill posed. The theory of evolution by natural selection is about individual selection of organisms and has nothing to do with group to group success in economic terms.
All natural selection results in evolution. But natural selection is not necessarily the only mechanism leading to evolution. There are processes at work on a molecular level, such as intragenomic conflict-type processes, that also result in differential reproductive success, but aren't exactly related to the kind of processes Darwin first described.
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Reproductive success. You are not evolving, but your progeny will; if you have any.
Selection acts directly on individuals within a population, favoring certain traits that increase an individual's survival and reproductive success. This process leads to the differential reproductive success of individuals with advantageous traits, ultimately shaping the genetic makeup of the population.
Differential reproductive success of variant replicators.