Actually, one of the strong arguments the Singularity has going for it is that biological evolution has pretty much come to a standstill, especially relative to cultural and technological evolution.
The conviction that humans are special runs extremely deep (see: pretty much all sci-fi), but the reality is that we are a very general purpose platform evolved to shove dead animals and plants into its face whilst not being killed by snakes and tigers. We need to exercise regularly, just to convince our body not to degrade into a terrible mess on the brink of collapse. We're terribly frail and break down easily (modern medicine helps, but there are still many things that can happen to you that do irreversible damage). Space travel is out of the question without 20 layers of protection and even then a lack of gravity destroys our structural integrity. Our prehistoric heuristics (a.o.: self-interest and xenophobia) are pretty much the main reason for every war ever and are a terrible detriment to progress in pretty much all issues all around the world. 80% of all issues our societies face are directly caused by the disconnect between primitive human nature and modern society.
Even though our neural processing capabilities are currently unmatched, it is really the only leg up we have against an AI life form. Considering our processing capabilities don't scale at all and any AI would be able to scale relatively easily (more power, more hardware) we are looking at the short end in the long run.
And that is not even mentioning the terrible amount of redundancy and inefficiency in human neural processing. A human brain runs on about 20 watt. Assuming 7 billion people, we're talking about 140GW of processing power. In 2008, the average world power output was ~2300GW. Considering that a huge amount of the 140GW processing power is dedicated to useless and redundant shit like Instagramming photo's of food, it's not that far out to say that the useful human processing power is maybe 10GW. So 4-5 big coal plants, a shitload of artificial neural processing hardware and there's your potential to match the useful processing capabilities of all humans on this planet.
Don't get me wrong. There are many, many issues in getting all that power and hardware to actually do useful processing and it certainly won't happen in a couple of years. What I am saying is that the physical requirements for a Singularity to occur are very, very modest. Simply because humans are quite shitty(^Hily adapted to modern society).