Natural selection is the differential survival and reproduction of individuals due to differences in phenotype.
Natural selection, a process that results in the adaptation of an organism to its environment by means of selectively reproducing changes in its genotype or genetic constitution.
Natural selection, then, can be defined as the differential reproduction of alternative hereditary variants, determined by the fact that some variants increase the likelihood that the organisms having them will survive and reproduce more successfully than will organisms carrying alternative variants.
Darwin's definition of natural selection his book "On The Origin Of Species By Means Of Natural Selection or the Preservation Of Favoured Races In The Struggle For Life" is:
The preservation of favorable variations and the rejection of injurious variations
In Evolution 101, natural selection is not defined, but rather the concept "evolution by natural section" is characterized as the outcome of variation, differential reproduction and Heredity, and a clarifying example is provided.
Clearly, the wording in each of the above is different!
I searched Biology StackExchange for any explicit statement of the definition of natural selection, I couldn't manage to find one. There are some discussions about whether it is a tautology or not, but even in those discussions, the definition of natural selection was not quoted.
I tried to search tags "natural selection" and "definitions" of biology StackExchange, and yet I didn't see any particular wording mentioned as the official definition of natural selection.
Actually, the tag [natural selection] mentions this definition in the tag information itself:
Natural Selection is a mechanism of evolution that leads to non-random spread of genes due to the effect that genes have on reproductive success
Natural selection is the process by which heritable traits that make it more likely for an organism to survive and successfully reproduce become more common in a population over successive generations.
Is there an official definition of natural selection that is adopted by biologists nowadays? and what is that definition exactly?
[EDIT] It came to my awareness that this question might be a possible duplicate of the following question: "How is Selection best defined", and indeed in the answers provided to that question the topic of definition of natural selection has been addressed.
I didn't know of this posting. I simply surfed for "natural selection", and not just for "selection", and I didn't notice it. But indeed what's presented in the answers does cover the question present here.
However there is some difference in the question itself from that present here. Here I wanted to know of what I thought would be an official definition, and I was asking in particular about "natural selection", while in the referred question, the question is more general, it's about what qualifies "any" force (apparently he means related to biology and especially evolution) to be labeled as "selection", including artificial selection, sexual selection, etc.., so it's a wider topic, at least as far as terminology is concerned.
Here in this question I've quoted the main results that one would see upon surfing the web for "definition of natural selection", and I wanted to know which one would be the official or as @Remi.b had put it, the most commonly used or referred to in biological research.
I still think, that for precision purposes, exact wordings are important, and such an extremely important concept like "natural selection", it would have been expected that it had an agreeable, kind of, official definition, by some convention or the alike.
Anyhow, I think, whether this question is a duplicate or not, can be better assessed by experts in evolution field present in this website, like those who provided answers, and others.