Plant Species of the Borrego Desert:
Distinguishing Cylindropuntia echinocarpa and C. ganderi
Distinguishing Cylindropuntia echinocarpa and C. ganderi
This page is just a shell right now to hold the following graphs, and to give a very brief explanation of the plots. I'll add lots of pix in the future to illustrate the different characteristics.
Principal Componants Analysis
In all the graphs, B.S. stands for the Borrego Springs area; Cnbrk = Canebrake; Thimble = Parking area for the Villager Peak Trail, across from the beginning of the Thimble Trail; JTNP = Joshua Tree National Park southern entrance area, including upper Box Canyon Road; Culp = Culp Valley.
The PCA plot for data through 18 January 2020, using 30 characteristics measured for 16 specimens. Many of these 30 characteristics are the min - median - max of measurements of a single physical characteristic. There are 13 distinct physical characteristics that were measured.
The species separate extremely well using all the measured characteristics.
This plot does not include one hybrid plant that was measured, which falls exactly between the species in PC1, since the purpose of this page is to show how well the species themselves are separated.
The difference in PCA2 for different populations of the two species is probably environmental, plus perhaps some intrinsic variation to adapt to different environmental conditions. For example, it is well known that the height of golden yarrow plants varies strongly with elevation, but all those plants are the same species. In this case, the Culp plant of C. ganderi is growing in a quite different environment than the Borrego Springs plants, and the Joshua Tree National Park specimens of C. echinocarpa are growing in a quite different environment than the Borrego Springs plants.
The coefficients for PC1 show that 15 of the 30 characteristics strongly separate the two species (coefficients from 0.28 to 0.19). Another 9 characteristics separate the two species about half as strongly as the top 15 (coefficients from 0.16 to 0.12). Six characteristics were not very useful in separating the species (coefficients from 0.08 to 0.00).
From the PCA, the best two characteristics to use to separate the species are the maximum segment length and the maximum branching angle:
The maximum branching angle is by far the best single characteristic to use. This is readily derived in the field by looking at the entire plant from the side, from several different directions, looking for the branch with the maximum angle between its base and the stem from which it branches. Dead or damaged branches don't count. Several different viewpoints are sometimes needed, especially for C. echinocarpa, since the stems are sometimes mostly hidden by the crown of the plant.
The maximum segment length separates the two completely, but there is not a large gap between some specimens of the two species, like there is for the maximum branching angle.
The next best two characteristics are the maximum terminal segment length and the median length to width of the tubercles:
Both characteristics have some individual overlap between the species, but the combination just barely completely separates the species, at least so far.
Two characteristics that I had thought were important in the field were in the top 15 group as well, the percent of the mass of the plant that is above the middle of the plant, and the number of stems near the base (I counted the number of stems at a distance of 15 cm above the ground):
But as you can see, there is more overlap between the species in both of these characteristics than in the four characteristics shown above.
The beauty of a PCA is that it robustly combines all of the measured characteristics to give the optimal separation in a single variable, PC1.
As an illustration of how robust a PCA can be, I accidentally entered the terminal segment length for six measured specimens in mm, instead of cm, making those six specimens way out of bed with the others for that characteristic. PC1 was essentially unaffected! But it made PC2 look a bit funny, which is how I caught it.
The reason PC1 was mostly unaffected is that the best fit line in 30 dimensions for all 16 specimens was mostly influenced by the 29 correctly-entered characteristics. Its total length, and 30 dimensional direction, could not be changed much by having one screwy dimension, especially since the 10 other specimens helped keep the influence of that 30th dimension more "on track".
Using the Maximum Branching Angle in the Field
To see how well using the maximum branching angle worked in the field, I compiled a histogram of the maximum branching angle in the field from two locations on 22 January 2020. I walked a small loop centered on each location, and circled around each mature healthy cholla I came across to estimate its maximum branching angle seen from any angle. It generally took just 15 seconds to make that estimate. The exception was that some plants of C. echinocarpa were so dense at top that it was difficult to see the branches clearly enough to estimate their branching angle. Some of those I was able to finally see some branching angles with further inspection, but a very few were too dense to see, and those specimens were then ignored.
Because I was testing how well the maximum branching angle worked, I was quite strict about including all branches and taking the maximum branching angle even if it was not representative of other stems on a given plant.
I tallied the numbers in the field, and kept taking data until the observed histograms were not dominated by small number statistics. I ended up with 52 measured chollas for the upper end of the road, and 58 measured chollas for the lower end of the road.
The first location was the upper end of the dirt road going to Henderson Canyon, the parking area for hikes into Henderson Canyon. The second location was the lower end of that dirt road at the intersection of the paved Henderson Canyon Road and Borrego Springs Road. The histogram for each location is shown in the following plot:
I've added bars to the plot that show the range of the maximum branching angle from the small number of samples plotted previously used for the PCA, five plants of C. ganderi and nine plants of C. echinocarpa.
The histograms are quite different between the two locations, with the peaks in the histograms corresponding to the range in maximum branching angle found in the small number of specimens analyzed for the PCA.
The histogram for the lower end of the dirt road shows two peaks, corresponding to a small population of C. ganderi and a large population of C. echinocarpa. This corresponds with what I found in a detailed survey of that area where I was visually assessing the species determination of each plant using several characteristics (but without measuring anything). From the histogram, it is quite likely that some C. echinocarpa have maximum branching angles as low as 60°, a small extension of the range of 70 to 90° found in the nine specimens measured for the PCA. It is very reasonable that a sample of 58 plants would show a wider range than a sample of just nine plants.
The histogram for the upper end of the dirt road shows only a single peak, with the strong majority of plants having the maximum branching angle of C. ganderi found in the five samples measured for the PCA. However, a small number of plants have larger branching angles.
In fact, as I was compiling the histogram, I noted that some very clear plants of C. ganderi did in fact have a single branch with a branching angle of 60 to 90 degrees, which I was duty-bound to record, with the next largest branching angle significantly smaller. If I had instead compiled a histogram of the second largest branching angle, most of those specimens would have had a much smaller value.
There are two strong arguments that all of the plants in the histogram for the upper end of the road are C. ganderi: the smooth decline of the histogram from its peak at 40° to the small number of plants at 90°, and because the detailed survey of that area found no C. echinocarpa.
Conclusion: The field study of the larger sample shows, as expected, that the separation in maximum branching angle between the two species is not quite as overwhelmingly good as shown in the sample used for the PCA, but it still highly reliable in separating the species. To improve the use of the maximum branching angle to separate the species simply requires one to note whether the maximum branching angle comes from a single branch that is not representative, or whether most branches have a high branching angle. If there are two branches with a maximum branching angle above 60°, the plant is extremely likely to be C. echinocarpa. If no branch, or only a single branch, has a maximum branching angle above 50°, the plant is extremely likely to be C. ganderi.
And, of course, chollas are rarely found singly, so one can examine a few neighbors to see if they have similar maximum branching angles. Since the overlap zone between the two species is very small, the vast majority of the time you will get good agreement among all the specimens at a given location.