I'm afraid I laughed a bit when reading that paper for the first time.
Why? Well, here's what they essentially did: They tried to model evolution by implementing an algorithm. They had a population of 10000 individuals, represented by their genetic sequence, and had an algorithm do mutations of those sequences and modeled selection and reproduction to get the next generation. They did that for a long time. Why did that make me laugh? I did both my BSc and MSc theses in the field of Evolutionary Bioinformatics. Almost every student there implements something like that when they first start, to learn to write that kind of program. It's not exactly novel. They even cite several other studies doing this kind of analysis.
Now, their result is basically that human evolution from human-chimpanzee ancestors couldn't have happened because it would have taken way too long. Not only would the whole difference between these two species have taken too long, every single difference of more than two nucleotides would have taken too long to get fixed.
Since this goes against established science, this algorithm better be good... The paper is lengthy and much of it isn't all that interesting or related, in my opinion. But here's the big problems, in my opinion:
When natural selection successfully amplified the target string to the point of fixation (i.e., when the allele frequency reached 99–100 %),
Their target is for their target sequence to reach a frequency of at least 99 percent. That's unnecessarily high, and will of course take a long time, especially as they hold their population constant at 10000 individuals. They don't show a figure with how frequency changed over generations - I'd assume that 90 percent is reached a lot earlier than their threshold.
Holding the population size constant is of course also not a realistic model for human evolution. It wasn't at 10000 individuals for millions of years.
initialization : initialize every individual to the same random or user-specified string (e.g., AAAAA)
Humans didn't start with random sequences and then mutated them to make them do something useful, we started with useful genetic material that then changed. If you start at AAAAA, expect a target of TAGGC, don't confer any benefit to intermediate steps (as they did) at a mutation rate of something like 1 per ten million nucleotides per generation, of course you are going to wait a long time. Mutation rate in genomes also isn't uniform, it varies by region. From what I can see, this was neither taken into account nor discussed.
There is also the problem of them only looking at single nucleotide mutation, not gene duplication, insertions, etc. that also make up a lot of the difference between humans and their ancestors.
Then there's random "mate-choosing", which is a valid simplification to make if you are just looking at some mechanisms of evolution, but not valid if you are going to use your model to estimate time needed for speciation.
They also only allow for one beneficial mutation to arise, then wait for it to be fixed, claiming that anything else would have just resulted in even longer times, without, as far as I can see, just implementing this and then testing that assumption.
At some points, their paper is just going to going for some kind of dramatic effect:
waiting time was 500 million years – which is still extremely prohibitive. This amount of time approximates the estimated time required for the evolution of worm-like creatures into people
500 million years ago, we had the first animals emerging on land and the first chordates. Chordata and the "worm-like" phyla had already diverged.
Basically, in my opinion, they took a very simple model and drew sweeping conclusions from it. This kind of analysis is suited for looking at how evolution might result in speciation, what parameters might play a part, etc. but it is not suitable for estimating the time this takes.
But these are just my first thoughts, I hope there'll a more thorough review of this on the internet somewhere soon.