Not after one generation, no. But after several hundred million generations, given the right circumstances, then yes, it is slightly possible. If you understood Darwin's Theory at all, then you would see how this is so.
Here, I'll try and summarise the theory here as best I can:
Darwin's Theory of Evolution: A SUMMARY
1 - Every time an organism passes on its genes through reproduction, the female reproductive cell's DNA (The DNA in the ovum / egg) combines with the DNA of the male reproductive cell (the DNA in the sperm) to give a completely different genome - meaning, each generation will have new DNA, and each individual will have different DNA. (With me so far?)
2 - In a rudimentary sense, clustres of DNA called genes code for specific traits in an organism. Because each organism within a species (ie, humans) have slightly different DNA, each human will have slightly different traits.
3 - Throughout human history we have had to compete for limited resources in various harsh environments to keep our race alive, just as we have had to reproduce efficiently in order to keep going. This is the same for all organisms, really.
4 - At the end of the day, the organism with the DNA best suited for survival and reproduction will be the organism most likely to survive and pass on their superior genes. This is termed natural selection. In a simple sense, half of the DNA from the father and half from the mother go into creating an offspring, correct? Well what monitors what genes are passed on where? Nothing. That much is utterly random. What isn't random is natural selection, otherwise known as survival of the fittest. The individual with the inferior genes will die out, just as the individual with the best genes for the environment will live on and cause the continuation of that species.
5 - As generations progress, the genes passed on begin to change because of slightly different genomes (all the DNA in the somatic cell of a species) and karyotypes (the type of DNA in the somatic cell of a species) which arise through repetetive reproduction. This change in the karyotype of a species and generations progress, and as natural selection plays its role -- this is termed evolution.
EVIDENCE LISTED BELOW:
Now. Here are some lines of evidence for evolution:
1 - Humans have grown about a foot or so in the past century or two. There are thousands of different races on Earth which arose as humans were introduced to differing environments. There are hundreds, if not thousands, of different dog breeds - and these all stemmed from just a handful of original breeds and careful breeding. All of this can be explained by evolution.
2 - The sedimentation layers of places like the Grand Canyon have been thoroughly looked at. Older species were found on the bottom of the canyon, while the younger ones were found up near the surface (think about why this may be the case). In the long term, fossil records found in places like the Grand Canyon affirm that a plethora of species slowly changed as time progressed.
3 - By analysing all of the different compartments of our DNA and RNA (RNA is sort of the medium through which DNA does its work), we're able to see just how much our DNA has changed over time. Correct me if I'm wrong, Painted Wolf, but RNA is analysed to discern long-term evolutionary changes because it remains largely conserved over time, while DNA is analysed to discern short-term changes.
4 - In Arica... Or was it Ethiopia...? Anyway, a group of people in that region have developed a trait known as sickle-celled anemia. This occurs when the gene which codes for the protein known as haemoglobin undergoes a substitution mutation, meaning that one of the nucleotide / DNA monomer base in the gene is changed. The result is a haemoglobin protein with a slightly different structure. Now, this new haemoglobin cannot carry oxygen around the body as efficiently -- so why have it? Well, guess what? It helps to protect against malaria. The protein somehow depresses the virulence of the malaria parasite! And considering that catastrophic numbers of people in Africa are dying of malaria, this is a pretty neat change.
Now ask yourself, why would forty percent of all people in the region I'm talking about have Sickle-Celled Anemia? The answer is Natural Selection. The people without the Sickle-Cell trait die off at a faster rate than those with the trait, leaving more Sickle-Celled individuals to pass on their genes.
EVOLUTION IS HAPPENING. It's happening everywhere, every second, of every day. It's just really slow, so if you want to see some significant changes, you will have to stay alive for another few thousand years.
Now then, let me get to a few misconceptions which you might have.
A human cannot breed with a dog or a fish or even a mosquito. This is absolutely correct. But that does not mean that, if for some reason, a human is forced to change into a mosquito over a period of several billion years (through evolution), then this would be possible.
The reason that a dog cannot reproduce with a human (yuck!) is because the genes in their somatic cells are far too different. The egg (oocyte / ovum) gets aborted during embryonic devolopment. Mitosis of the fertalised egg cell just dun' happen, because the body sends the signal that says something ain't right, and the embryo gets aborted.
Anyway, if you have any questions, feel free to ask.
