Constructing Fiddler Range Maps, part 2: The Problem of Ranges as Data

This is the second of four planned posts about how I constructed the range maps for fiddler crabs. The first part gave the history and background of how these maps were drawn in the first place. This part will discuss where the maps become problematic when we want to use them as input data for analysis. The third  part will present a possible solution to the problem detailed in the second part. The fourth and final part will step back and ask if we’re actually thinking about range maps the wrong way entirely.

In the first post I discussed how the range maps were originally created and have evolved over time. As general tools for the display of information, they work perfectly fine (there are some limitations that will be raised in part 4).

But what if we want to go beyond the display itself and think about the ranges as input data for other analyses. What type of analysis? As an example, a few years ago, Jeff Levinton (my PhD advisor) published a study on the Latitudinal diversity relationships of fiddler crabs. In general, fiddler crab diversity declines as latitude increases (as it does for many other groups of species), and this paper explored potential factors that explain this pattern. In this paper, the species ranges themselves made up a key piece of the raw data.

For the purposes of that sort of study, there’s nothing wrong with the ranges as data. You mostly only need to know the upper and lower latitudes between which a species is found, and while there may be some uncertainty on the precise boundaries (I’ll come back to this in part four), small errors are not likely to make a huge difference in the results. Other aspects of the ranges may become more problematic if looked at too closely, however.

For example, one of the results that can be found in the above paper is a slight northern bias to fiddler crab species diversity: globally, peak diversity is not found at the equator, but rather about 10° north (regionally, the northern bias is strongest in the Americas, but largely absent from the Indo-West Pacific). There are any number of reasons why there may be a slight northern bias, but one hypothesis that could be suggested is that there is more land in the northern hemisphere than the southern and diversity is partially tracking habitat availability. Since land area as a whole is fairly meaningless to fiddler crabs, this hypothesis can only make sense if the increased land mass in the northern hemisphere corresponds to an increased coastline. There are a number of reasons I suspect this hypothesis about fiddler diversity is likely incorrect (the simplest of which is that the greatest species diversity is often found in very small areas), but what if we wanted to test it? We would need a way of measuring the amount of of coastline available. Because fiddlers only live on coastlines, this also leads to the idea of measuring the “size” of a fiddler crab range by the total length of coastline it inhabits. Unlike most other species, fiddler crab ranges can be thought of as one-dimensional lengths measured in km, rather than two-dimensional areas measured in km2 (this 1D argument might fall apart for some of the species which range over large parts of the western Pacific islands, but that is a discussion for another time).

So, whether we are interested in the range of a species of the potential habitat it inhabits, we are looking at measuring the length of the coastline. How do we do this? The coastlines and species ranges on our maps are recorded as a series of connected coordinates, so it’s simple to imagine simply calculating the distances between connected pairs and adding them together. Voilà, species range and/or coastline length! Except, now we need to go back and look at our map data more closely.

The coastlines and countries boundaries in our new cartoon maps (see previous post) came from the Natural Earth data sets. These maps come in three different scales: 1:10 m, 1:50 m, and 1:110 m. Essentially, fine scale to rough scale. For simple display purposes, most of the fiddler crab ranges could use the medium or roughest scale; the finer scale maps are only really needed if we need to zoom in to fairly small regions. For example,  Uca osa is a recently described species of fiddler crab known only from the Gulf of Dulce, in Costa Rica. Below is a zoomed-in look at the Gulf drawn from two of these data sets.

Maps of the Gulf of Dulce, Costa Rica. The top map is from the 1:50 m scale, the bottom map 1:10 m scale.

At this level, the two maps are strikingly different. Because the gulf is so small, it does not even show up in the 1:110 m map data (not shown)! But it is more than just a visual difference. The measurement of coastline will be different in each of these. The finer the scale of the map, the longer the coastline.

This issue has been known for a long time; in fact, coastline length is considered to be a fractal mathematics problem called the coastline paradox. Theoretically (if not practically), if you could keep measuring a coastline at greater and greater accuracy, it’s length would continue to increase…all the way to infinity. One of my favorite oddities of fractal mathematics is the proof that a finite area can contain an infinitely long line (e.g., see the Koch Snowflake). If we want to measure the length of the coastline, we need to be concerned with the scale at which we measure it.

Since our species ranges are also based on coastlines, they have the same issue. But here, a secondary problem arises. The ranges are currently based on yet a different map set (this one extracted from Google Earth). If we draw the coastline data for Uca osa on top of one of our Gulf maps…

we immediately find that it is at yet a different scale than any of our background maps.

This all just highlights how we need to be careful about thinking of these species ranges as data. They’re perfectly good for generally asking about where species are and questions of overlap, but if we want to translate these ranges into measures of distance or area, more thought is needed. Some of those more thoughts in part three…