From what I can see, he said there is no empirical evidence that evolutionary lineages increase in complexity with time. That isn't what you claim he says. I'm not sure who actually wrote the subheading to that article, because the article itself seems to assume the opposite, and goes on to suggest mechanisms and ideas that may explain the major evolutionary transitions - transitions which no evolutionary biologist denies; they're pretty obvious.
what exactly do you think he means when he says "evolutionary lineages"?
this man is basically talking about macro evolution here, he must be.
he cannot be talking about microevolution , because THAT has been observed.
also, he proposes a method by which this can be achieved.
he bases this method on the similarities he has noticed.
in the conclusion he says this is a basis for further research, not a verified process.
also take note that he says this complexity is achieve by a few major transitions, not by accumulating gradual changes.
this seems to confirm PE, and the gaps in the fossil record.
IOW, these gaps are real, they aren't a matter of "missing fossils"
also, these gaps dominate the record.
There are, incidentally, at least two theoretical reasons why complexity of an evolutionary lineage might be expected to increase over time, one of which was not apparent at the time that article was written. One is a statistical reason - when an organism has minimal complexity, there are obviously more ways for it to become more complex than more simple (it can't become simpler). Slightly more complex organisms can be radically more efficient, so one expects a proliferation of simple but not minimally simple organisms. As some organisms become more complex, the balance changes, and they can evolve to become either more complex or simpler. However, with increasing complexity, the ways to become more complex also increase, so the potential for increasing complexity diminishes at a slower rate. The expected result is a large number of organisms of low (but not minimal) complexity, with the numbers of creatures diminishing rapidly with increasing complexity - which is exactly what we see in the world.
smith explains that complexity isn't well defined, and he used examples in lieu of a definition.
apparently, complexity on the genetic scale, is measured by the number of traits a particular gene can code for.
Another reason is also statistical, but at the much lower level of statistical mechanics (thermodynamics); systems with low entropy & high available energy density tend to towards configurations that maximize their energy dissipation and increase in entropy. Complex subsystems dissipate energy, increasing entropy more effectively than simpler ones, so one should expect a tendency in favour of the development of the most complex configurations that can be supported by a given system, which will maximize the rate of dissipation of energy and the increase in entropy.
i don't know, i question statistics for 2 reasons:
1. you pretty well have to know what is being measured to be sure of the data.
2. correlation doesn't imply causation.
let's not forget what twain said:
"there are 3 types of lies, little white lies, damnable lies, and statistics".
yes, statistics can be a valuable tool, but you need to know for certain what you are looking at.