First we need to know exactly what you mean by increased complexity. Could you give a couple super concrete examples? Try to be very specific.
I think I can sense a reference to eyes, which are a whole lot more complex than mere light-sensitive cells or aggregates of cells in lower forms of life.
Or how about how did we get from single-celled creatures to human beings?
We have a pretty good idea about going from small fish creature with a backbone to human. It's before the little fish that things start getting hazy.
Yeah...something like that. But I'd prefer he give out a super concrete example so it could be explained. The numerous ways eyes developed isn't the same kind of "increased complexity" as say...the emergence of multi-celled organisms. So a specific very detailed example would be helpful
A mantis shrimps eyes are extremely advanced. They can see wavelengths and ranges of colors we can't even get close to....they have 24 photoreceptor types compared to our three for example.
Remember, we are biased, and think of OURSELVES as the highest point in evolution...but, a mantis shrimp has been evolving longer than we have.
The hearing of a cat. The olfactory sense of a wolf. The vision of an hawk. We are a functional combination of senses, but we don't have a single sense that isn't wildly more sensitive in a "lower" animal.
I think broadly speaking it means a genome with more genes versus a genome with fewer genes. But this is not the whole story.
The number of genes is not proportional to the complexity of the organism.
A chimp has 24 chromosomes, we have 23 because our 23rd and 24th fused into one new chromosome....which, when you look at the match points, looks exactly like the chimps 23rd and 24th chromosome's match points.
They have more chromosomes...are they more advanced?
Some of the extra genome used to be considered to be left over junk....but, later studies found that the "junk" did stuff...important stuff.
So, a wee beastie with a lot more chromosomes and a wee beastie with but a few, might have a reversed "advancement" relationship...its not predictive.
The OPTIONS for those with more genetic info can, one day, prove to allow survival when conditions return to/change to, ones that favor the previously dormant "junk".
For example, there's ~ 100 - 350 or so known genes that pretty much all life on earth has.
Some of the deep sea vent critters have ONLY those genes for example, and not even genes that code for making amino acids, etc, as the vents make them for example.
They don't have genes that code for ATP or ADP, because they use the thermal energy to establish the gradients that ATP, etc, is used for in more modern critters.
Some scientist are not even sure some of these vent critters are actually alive, or just really really complicated chemicals.
They ARE, either way, about as early primitive as it gets...and are typically considered to be a last common universal ancestor of all life on earth.
@Anthony – You should reconsider your usage of the term “Darwinism”. It is really only used by Creationists. Scientists today use Modern Evolutionary Theory which is something much more complex. If Darwin was around today he would be amazed at what his idea had evolved into.
It would be like trying to imply that there is something wrong with Alchemy when everyone else has moved on to use Modern Chemistry.
On the other hand, I'm pretty sure I've seen Dawkins refer to himself as a Darwinist, and I don't recall it being in an ironic context.
When a parent DNA is copied to make a child DNA, sometimes like @matt.clerke says, the copying mechanism goes wrong and a section of DNA is copied more than once, or several times. This of course is where the increasd complexity comes from.
Or DECREASED complexity...it depends on the mutation/damage.
Complexity is a red herring in general btw.
A pile of rocks is no more meaningful than one larger one per se.