Tuesday, August 28, 2012

Seeing the forest *in* the trees

I previously posted on the human bias toward seeing patterns and causation everywhere, even when the pattern doesn't hold up. There are, however, cases where we fail to really notice a pattern that is all around us. A great example to an evolutionary biologist like me is the hierarchical pattern manifest in all the animals and plants we see in the world around us.

"Get OFF my lawn!"
I often ask my students "Wouldn't it be cool if you found a squirrel with a crab claw?" They usually chuckle at the apparent absurdity of the question - of course you would never find that. Mammals don't come with crustacean parts. They're right, of course - but is it so absurd to ask?

Here is a pattern that we're so accustomed to that we don't often bother to ponder it. The diversity of the natural world is divided up quite distinctly; you have conifers and angiosperms in plants, mammals, birds, lizards, fish, and amphibians among animals with backbones, insects, crustaceans, and arachnids among invertebrate animals, etc. We are so accustomed to this pattern that it would be really surprising to see a pine tree with a dogwood flower or an oak tree with a pine cone, or to find a bird giving birth to live young. In simple terms, birds are birds, fish are fish, and insects are insects - the names correspond to a suite of characteristics that are, quite literally, synonymous with the group.

This pattern gets interesting when you move to more or less-inclusive groups of species. For instance, within mammals, you can find species that give live birth to well-developed offspring (placental mammals - including us humans), species that give birth to live young that must latch on and nurse their mom for a long period of time (marsupials - think kangaroos with their cute pouches) and species that actually lay eggs (monotremes like the duck-billed platypus). In other words, there are subgroups within mammals that are clearly mammals, yet they differ in pretty fundamental ways. Those subgroups are also really distinct; it's tough to confuse a marsupial mammal with a therian mammal if you look carefully. That's why opossums seem so weird to North Americans - it's basically the only marsupial we ever encounter in our backyards.

Going in the other direction, we find that while birds and mammals are not at all hard to tell apart, they have lots of characteristics in common, from the bones in our skeletons to lots of details of our physiology and development. In other words, birds and mammals are distinct, but not nearly as distinct as birds and insects, or birds and flowering plants.

What's so interesting about this pattern is that there is no a priori reason for it. Why should diversity be divided up hierarchically? Why can't we have a squirrel with a crab claw? In the world of human-created things, there is lots of sharing around between designs (think, for example, about how much computer technology has infiltrated your car; I doubt carmakers were thinking about that in the days of ENIAC!).

Carl Linnaeus noticed the hierarchical pattern of characteristics way back in the 18th century and built a system of naming species on it (the one we have all seen that calls us Homo sapiens). What produced the pattern wasn't really worked out until the 19th century, when various theories of evolution from common ancestors suggested that the hierarchical pattern reflected the degree of shared ancestry among groups of species. For the vertebrate animals, the hierarchy looks like this:

image credit: University of California Museum of Paleontology's Understanding Evolution, http://evolution.berkeley.edu

In other words, the hierarchy of characteristics is the product of a hierarchy of ancestry of animal and plant species. The things we think of as "mammalian" are the vestiges of the common ancestor of what we call mammals (and for most people, that's the ancestor of marsupial and placental mammals). The things we think of as defining birds owe their origins to the ancestor of that particular lineage of sauropods. The pattern of diversity is the product of the evolutionary process.

Often when the theory of evolution is attacked, one will see it defended with documented artificial selection among laboratory bacteria, or observed small-scale adaptation in Darwin's finches. Those are fine examples, but they pale compared to the way the whole grand tapestry of species screams out "I'm the product of evolution from common ancestors!" The hierarchical pattern is ubiquitous and incredibly exhaustive (I leave it to the reader to work out the interesting example of whales and dolphins, and the ways in which they are quite distinct from their fishy marine colleagues) because the evolutionary process is likewise ubiquitous.

So the next time someone wonders if evolution really happens, explain to them that there are a lot of bats out there that could really use some feathers. And send me some gills if you can.

Wednesday, August 8, 2012

A Laffer of a statistical gaffe...

We humans are funny creatures. We're so primed to look for patterns that it gets in the way of our judgement about the real world. Examples run the gamut from cryptozoology to astrology. Much of the time, we harden our misinterpretations of reality with confirmation bias, the tendency to see new evidence as confirming what we already think. It takes real mental discipline to be honest about what we really know, versus what we would like to think is true.

You might think that we could improve that discipline with an extensive education, especially in a model-based field like economics. Indeed, a tough educational environment that challenges our beliefs can reduce our tendency to self-deception. But it's not a perfect solution, judging by a recent example from the Opinion page of the Wall Street Journal.

Arthur Laffer, who holds a PhD in economics from Stanford and was tenured at the Chicago Graduate School of Business, included in his piece a figure comparing the rate of change of government spending with the change in gross domestic product for the 34 nations in the OECD. Laffer then points out that several nations that have notably high increases in government spending also have big drops in GDP. In other words, what statisticians call a correlation. Laffer then goes on to claim that
...there's no arguing with the data in the nearby table, and the fact that greater stimulus spending was followed by lower growth rates. Stimulus advocates have a lot of explaining to do. Their massive spending programs have hurt the economy and left us with huge bills to pay.
However, Laffer has made the oldest statistical error in the book in trying to align reality to his views: he has assumed that correlation implies causation. In other words, he is assuming that as two things changed, one clearly caused the other. It starts with the simplest nuance, describing the change in government spending before describing the change in GDP; that reads a lot like a narrative, where one thing happened before the other. The first must have caused the second, right?

Unfortunately, there are lots of other interpretations completely consistent with the table. One could simply reverse the causation - isn't it remarkable how much a drop in GDP caused governments to spend more money on social support! - and still get the same data. Or there could be a third factor that caused the changes in the things measured (perhaps there is some other similarity among the countries with a big drop in GDP that caused both changes). In short, you simply cannot know from a correlation between things how, or even if, one caused the other.

To be sure, someone of Arthur Laffer's background should know better than to draw such unjustified conclusions from these data, and the WSJ should know better than to print it. One might see the invisible hand of supply-side ideology behind that novice's mistake. Nonetheless, the example points out once again how vulnerable we are to confirmation bias - and how much more stringently we must examine our ideas about the world.