There are many thousands of papers, even considering only recent publications, that detail examples of contemporary evolution. Some of these are about experimental evolution, others about observations of evolution in the wild.
The following (fairly recent) paper details one of such observations, in this case about the influences of human settlement on the behavioural and morphological development of populations of blackcaps:
Rolshausen et al, 2009, Contemporary evolution of reproductive isolation and phenotypic divergence in sympatry along a migratory divide, Current Biology 19.
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Darwin thought evolution occurred in short periods of rapid change. For example, when he traveled to the Galapagos he observed how different species on each island had various characteristics that helped them adapt to their environment. From this you can infer that Darwin's belief was punctuated equilibrium.
You are an example of human micro-evolution as the population of humans has changed allele frequency over time. Micro-evolution is just evolution; change over time.
The branches of genetics, paleontology, observed natural selection and speciation all support evolution. Examples: (Genetics) Human chromosome 2 resulted from a fusion of two ancestral chromosomes. (Paleontology) Evolution of the horse. (Natural selection) Observed in Peppered moths. (Speciation) The Hawthorn Fly
Insects have evolved resistance to pesticides is one.
Polyploidy in plants leading to new species.
Yes. Evolution is routinely observed in both labs and in nature.
My favourite example of evolution is the development of multicellular organisms (this has also been observed). A kind of eukaryotic cell once started to bind to its fellow cells in order to make it more difficult for predators to kill them. This is an example of evolution as a result of predation, a selective agent.
Evolution is routinely observed both in nature and in the lab. Even several speciation "events" are on record.
Because adaptations are an observed effect of evolution. They could not happen if evolution did not occur.
The theory predicts that evolution will happen and in certain ways. The observed evolution makes this prediction correct. It also defines evolution as happening, and as such is perfect evidence in support of it.
There are thousands of instances of direct evidence of evolution. The most well-known example is that of Darwin's Finches. These finches were observed through fossil records to have changed over time to adapt to their environment.
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Evolution, the change in allele frequency over time in a population of organisms, is an observed and observable fact. That's why.
example of an micro-evolution in an organism?
First of all, evolution is not a science. One of the first rules of science is observation, and no one has observed evolution. We have observed gene mutation, yes. Breeding almost any animal will show you variation and mutation. I suppose, to answer your question, evolution is a theory derivative of genetics and biology. But, evolution is a theory, it has no confirmation. It is just a theory.