Katabasis Central: La Rosa de los Vientos

How fine are the shades of the directions in which we turn, along the way? Trying to find this or that, aiming to get there or here. Interesting to realize that bearing is of the utmost importance for long trajectories, but not as important over small distances, within reason.

The 32 point compass, La Ros de los Vientos

I have been working closely with the data for another chapter of the dissertation, wherein I am trying to develop models for the rather narrow habitat "preferences" of Mammillaria halei. The challenge is to work with geospatial data over such a small scale, when the analytical tools that are usually used work best over much larger scales. The issue is mostly a demon called "spatial autocorrelation," which is when locations that are close together, along with their covariate environmental variables, amplify their local signal and bias the overall data. The problem with the taxon I am studying is that it is naturally densely clustered on the landscape, in patchy clumps, with only a few individuals in between clumps. It's also problematic that the species has distinct habitat preferences where the clumps are even more dense, but over very short distances. So the issue is how to capture the habitat suitability but without incorporating too much noise resulting from positive autocorrelation.

I am experimenting with a scaling factor that artificially "stretches" the landscape by some constant proportion, as if the plants lived in a much larger habitat, so that clusters of plants that are in a neighborhood network with adjacent distances of 3 meters or fewer are more randomly dispersed in artificial space, but the disproportionate representations in particular habitat types are still captured. I'm also comparing those results with a much more simple model where I just eliminate all the occurrence points I have that are within 100 m of any other occurrence.

The usual spatial autocorrelation statistic, Moran's I, doesn't really like either approach, but Moran's I is based on two assumptions-- the null is a completely random distribution, which my cactus absolutely does not have, and the basic law of geography, which is that the closer things are to each other, the more they have in common. from Wiki: "The First Law of Geography, according to Waldo Tobler, is "everything is related to everything else, but near things are more related than distant things."^[1] This first law is the foundation of the fundamental concepts of spatial dependence and spatial autocorrelation and is utilized specifically for the inverse distance weighting method for spatial interpolation and to support the regionalized variable theory for kriging." However, in my weird island habitat, the geological regions are highly heterogeneous, the microclimates are dramatically different even over very short distances, and the response of the plant I'm studying is noticeably distinct as a result, within incredibly short distances. So, basically, I am trying to redefine what "near" means in my habitat. Within a few meters, where you might find one sickly looking plant and then three meters away at a slightly higher elevation in a different soil type, find a cluster of 30 plants, three meters is definitely not "near," in Tobler's sense of the word. It might as well be three kilometers. In any attempt to smooth the bias in my spatial data using normal techniques, the two adjacent plots would weigh the same, since they are "near." So the usual approach is to cut 29 occurrence points from the second plot. But the biological reality of my cactus gets completely flattened by that approach.

Some scientists have used a weighted weights matrix, where abrupt jumps in near microhabitats are weighted as if they are far apart, and larger distances between different environmental regimes are weighted as if they are indeed far apart. But this technique requires the creation of weird interpolated artificial surfaces and the potential for error amplification is high. More importantly, the necessary digital elevation model terrain map is not available for my habitat and would cost me $25,000 to generate. haha. Anyway, the approach is ridiculously complex and seems entirely unnecessary, mostly because it is overcalibrated and all I'm trying to do is create a reasonable model.

I think I will just go with an iterative process where I try that 100 m buffer, see what the results are, and adjust if necessary. The fact is that I have 1,200 occurrence records connected to environmental variables that I gathered over four years, so I can always just compare my models to the actual damned occurrence data. You get an idea of how clustered the plant is when I tell you that my 1,200 occurrence points get flatted to 350 points when I apply the 100 meter buffer.

The point of this enterprise is to find some protocols that ecologists could use to do predictive modeling for endangered species that grow within very small (relative) geospatial ranges. As it is, most researchers have bypassed this project, since the small scale spatial autocorrelation effects are potentially intractable. But call me Don Quixote.

Along these lines, one of the things I noticed while surveying on the islands, was that slope aspect, that is, the compass direction of the slope face on which a plant was growing, seemed to be a strong driver of site selection. So I started recording slope aspect down to within about 11.5 degrees, suitable for mapping to a 32 point compass. In searching around for reference images of the 32 point compass, I discovered that, in Spanish, it's called La Rosa de los Vientos. The importance of very fine differences in the heading of the wind must have been high indeed for sailors. Our crude understanding of compass directions these days generally boils down to north, east, south and west (if that!). The four point compass is enough, generally, when wind is more of a nuisance than anything, and we often just need to know we are roughly going in the right direction. But on the 32 point compass, between north and east, for example, there are seven distinct gradations- for some reason I find them highly entertaining to list: north-by-east, north-northeast, northeast-by-north, northeast, northeast-by-east, east-northeast, east-by-north.

So-- which way am I headed? How detailed do I need to be? How heterogeneous is my landscape? What would 11.5 degrees mean, if it were in error? If my assumption is 11.5 degrees off just for today, probably not too terrible. But imagine a lifetime 11.5 degrees off. Or 1 degree. Or 1/1000th of a degree? If my goal is 100 light years away, and I head out 1 picometer in the wrong direction, I'm fucked.

It reminds me of the panchromatic octave I imagined when I learned that even the average human pitch perception can distinguish 12 tones within the span of a semitone, for example, between C and C# (in the octave above middle C). Technically this would mean we could have a 244-pitch octave, just for fun. Just jump up the infinite harmonic series 244 times and fold each resulting pitch within the space of an octave. Or I guess we could more easily do a 244 mean tone equal tempered octave-- simply multiply each pitch by the 244th root of 2, 244 times. I thought we could call it The Panchromaticon. But if you want more than 244 pitches, why not? The compositions created using that palette would only be audible in their details by extreme pitch hearers, but maybe they are a higher class of mammal anyway?

My old friend Harry Partch, who I never met, but with whom I feel an enduring connection, developed a just tuned 43 tone octave, so he captured about 18% of the Panchromaticon. And then he built his own instruments to make the air vibrate along those lines.