Can one instance of the mutation of a nucleotide cause a gill to branch inward as opposed to outward. Or would it take a succession of these mutations all beneficial, all passed down from one fish to another until it was pointing inward?
There are several kinds of mutations, one of them called "homeotic." These change the whole pattern of tissue development in embriogenesis, so that indeed just one nucleotide change can cause a very radical change in the way respiratory tube is branching.
And doesn't it take a number of nucleotides to mutate at the same time to actually change a DNA strand in any beneficial type of way.
You see, there is no "policeman" that stands there with a baton and tells nucleotides, "hey, make sure you guys change in a beneficial way!" Mutagens - like UV light, cosmic radiation, some chemicals - just keep acting and changing the sequence of nucleotides in DNA. Whether or not these changes will be "benefitial," will be decided during the interaction of mutants with their particular, peculiar environment. A stream of cosmic particles can hit the DNA in a fruit fly, and the wings of this fruit fly will become dark rather then light-colored. If the progeny of this fly lives in the environment where the fruit on which it feeds is somewhat darker, then it's "beneficial," because these flies will hide from predators who eat them, but if it's lighter, then, on the contrary, this same mutation will be harmful. One nucleotide substitution in your hemoglobin gene that results in the so-called s-allele is harmful for you if you live in the USA or Western Europe, because you will suffer from anemia. This same siutation, however, is beneficial if you live in the Amazon basin jungle, because, even though you will still suffer from anemia, you will be resistant to Plasmodium malariae (the unicellular organism that causes malaria by invading normal red blood cells - but it cannot invade red blood cells filled with s-hemoglobin), so you will less likely die of malaria when you are 20 or 30, and have more children.
And aren't most observed mutations usually harmful, not beneficial?
No, actually, because of the so-called redundancy (or "degeneracy") of the genetic code, most mutations, statistically speaking, are "silent" (not affecting the amino acid sequence at all), and, therefore, indifferent, neither harmful nor helpful. Very many mutations are harmful. A minority turns out to be beneficial; but, given the enormous rate of DNA mutation, even this relatively small number of potentially beneficial mutations cannot be discounted. The rate of DNA mutation is estimated to be 10 (-9) per base per generation in every individual cell, which means that during the lifetime of an organism that consists of many trillion cells, at least several thousand cells (including germ cells) will acquire new mutations. And populations consist of many, many thousands of these mutation-carrying individuals, so even if most are either indifferent or harmful, some will be beneficial to this ever-changing environment. Therefore, evolution keeps going. Besides, random events like earthquakes, forest fires or floods cause the so-called genetic drift, which can cause profound genetic changes in populations even regardless of the natural selection.
What are some examples of current species where a mutation was observed, it was beneficial and new to the species, and was then passed down to the "population."
Peppered moth is one "classical" example.
Thanks for your patience!
You are certainly most welcome, thank you for good questions. Fixed the quotes, nothing else. --YtterbiumAnalyst