Tuesday, July 29, 2014

It’s all about the variance: science and life at N > 2

Variation is the grist for, and the flour from, the evolutionary mill. Without variation, no evolution occurs. With variation, evolution can generate even more variation by causing organisms in different environments to evolve different traits. We all know this, and we proceed accordingly in our research; but perhaps we too often take it for granted. Only sometimes are we smacked in the face by variation in such a way that it makes us pause and re-evaluate the way we view the world. Well, variation smacked me upside the head a few weeks ago during a trip into the field. In so doing, it made me reflect on how we estimate and interpret variance – and how this flavors the way we view our research and our daily experiences.

Threespine stickleback (Gasterosteus aculeatus)
Threespine stickleback could be the world’s most variable vertebrate. In some populations, average size at maturity is less than 30 mm – in others it is greater than 85 mm. In some populations, the pelvis is a huge structure – in others it is completely lacking. In some populations, the side of the fish is almost completely covered with bony plates – in others plates are entirely absent.  In some populations, mature males are almost entirely black – in others they have massive amounts of red – and in others black and red can be minimal. In some populations, the head is huge and the mouth massive – in others they are very small. In some populations, mean egg size (dry mass) is less than 0.047 mg – in others it is greater than 0.089 mg. This is just a small set of examples: stickleback, even just in freshwater, vary dramatically both within and among populations in almost any trait one cares to measure. This is why they are such a spectacular model system for studying adaptation.

A representation of stickleback diversity. The marine ancestor is surrounded by various freshwater forms.
Tom Reimchen, a professor at the University of Victoria, has long maintained that variation in stickleback on Haida Gwaii, a modest-sized archipelago off the coast of northern British Columbia, Canada, are as variable as are stickleback across the rest of their massive range in the northern hemisphere. Ever the skeptic, I have – when reviewing or editing Tom’s papers – pointed out that this assertion isn’t strictly true as (slightly) smaller stickleback are found in North Uist, Scotland. I am sure my nit was annoying to Tom as it was just a technicality and it required him inserting some rather pointless qualifiers into a few of his papers.

Several weeks ago, I had the opportunity to visit Tom in the field to see Haida Gwaii stickleback for myself. The first lake we visited was Drizzle, where Tom lived for 15 years and worked for 40. Drizzle is a modest-sized (112 ha) and heavily-stained (tannic, the color of very strong tea) lake with large and dark stickleback. A highlight here (besides camping and having a breakfast of bannock beside the lake) was walking the shoreline on Tom’s annual survey of loon-induced stickleback mortality. Several species of loon, particularly common and red-throated loons, congregate on Haida Gwaii lakes like Drizzle in numbers I had not thought possible, despite visiting countless lakes in my life. On Drizzle, dozens of loons would cruise nearby checking us out during our survey. And they would capture stickleback as if on cue – probably dozens were dispatched as we watched. Not surprisingly, many of the stickleback we found on the shore had been captured and killed, but not eaten, by loons. (Of course, many others are eaten - but we obviously can't find those on the shore.) Tom has an effective strategy for motivating search efforts. The person in front gets one point for every dead stickleback found. The following person gets two points. The third person gets three points. Tom was first, then Hannah, then me. Although it was like following two vacuum cleaners – I named one Hoover and the other Roomba – I held my own as tail-end Charlie (on points anyway).

Tom's cabin at Drizzle Lake (the lab is the wing at left).
A common loon with a Drizzle Lake stickleback.
The next lake we visited was Mayer, where Ric Moodie had – before I was born – discovered and described what is probably the world’s largest freshwater stickleback. This lake is larger (627 ha) than Drizzle, also quite stained, and even more overrun by loons. I had the good fortune, the day before meeting Tom, to happen by Mayer Lake just as it had stopped raining, in perfect time to cook my breakfast while watching 33 loons swim back and forth in front of me. Our next planned stop was Boulton Lake, in which more than half of the stickleback completely lack a pelvis, but this plan was derailed by happenstance. It seems that some delinquent and potentially dangerous kids had run off into the woods around Boulton Lake, and police parked along the highway nearby strongly discouraged us from going in.

So we instead hiked into Rouge Lake. This lake is a very shallow and small (1.5 ha) lake in the middle of a bog near the northern end of Graham Island (Drizzle and Mayer are on this same island). Rouge Lake stickleback are exceptional in several respects, especially their frequent lack of one of their dorsal spines, their (until recently) extreme red colour, their occasional possession of two dorsal fins, and the complete fixation of an otherwise locally-rare genetic variant (the Japanese clade of mitochondrial DNA). It was on the way back from this lake, tramping my way through bog behind Tom and three students, that variance smacked me upside the head. Just walking to these few lakes and hearing about (and seeing some of) their stickleback had finally brought home Tom’s assertions about the exceptional variation on Haida Gwaii and, more generally, the exceptional variation that organisms can achieve on very small spatial scales.

The Abbey Road of stickleback biology – the Rouge Lake trip. (Note: the picture is inverted for a reason that should be obvious.)
Along with this abrupt realization came a more fundamental epiphany: why had I been really impressed by the variance only after the third lake (not counting our aborted attempt to visit Boulton)? All of a sudden, I was struck by the parallel that, in statistics, we require a minimum sample size of three to get our first proper (albeit still weak) estimate of variance. The reason is that we need at least N = 2 to estimate a mean, and estimating a variance requires first estimating the mean and then needing at least one more data point. This makes sense statistically, of course, but – walking back from Rouge Lake – I began to wonder if our brains work the same way. That is, we really have to experience three things before we begin to get some mental perspective on how much they vary – because we need to consider the possibility of outliers. That is, with N = 3, we can see if any of the points stick out particularly far with respect to the mean – something that is impossible with N = 2 because in that case each point is equally distant from the mean. Stated another way, a sense of how variable things are first requires us to get a sense of the “average” or “typical” value and then a distribution of values around this average, which requires at least N = 3. Perhaps statistical principles match our mental processing machinery.

Now I can hear you saying: “Sheesh, N = 3 is way too low for a proper variance estimate.” You are, of course, correct. My point is simply that an assessment of variation, both statistically and mentally, can only begin at N = 3. Getting this third data point (visiting that third site) is the first moment when one has the potential to be impressed by that variation. Following that, much more data needs to be collected (many more sites experienced) to get a real estimate/understanding of the variance, but N = 3 is the first time you might be inspired by experience to try further. Hmmm, in writing this, I am reminded that I have only two kids. “Sweetheart, I’ve been thinking …”


Some other cool Haida Gwaii experiences:

More Haida Gwaii photos: https://www.flickr.com/photos/andrew_hendry/sets/72157645239128218/

Eagles were everywhere.
Bleeding tooth fungus - how cool is that?
Sandhill crane in the rain.
Drizzle Lake
Native tree frog.
Masset, Haida Gwaii.
River otters in a tiny rainforest stream.
Sandpiper squadron.

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