 L. schottii |
|  L. matthewsii |
This page is just a draft, to hold the preliminary work I've done on separating these two species. More work needs to be done on this!.
Loeseliastrum matthewsii and L. schottii are two terribly-cute little species whose flowers are like eye candy.
Unfortunately, these two species are very difficult to separate, and I (and others) have in fact wondered whether these species are distinct. My suspicions were based on the (mostly) lack of separation in geographic range, and on the instability of characters used to separate them.
The geographic range of the two species is curious. The range of L. matthewsii is inside the range of L. schottii in almost every direction. It is as if one took the range map of L. schottii and shrunk the voucher locations to fit inside a smaller area:
 Fig. 1. Plot of voucher locations for L. matthewsii. |  Fig. 2. Plot of voucher locations for L. schottii. |
The plots above were from data provided by the participants of the Consortium of California Herbaria (ucjeps.berkeley.edu/consortium/; Thu Mar 17 12:20:58 2011).
Specifically:
- In many places, the voucher locations for both species fall right on top of each other, with vouchers from the same area, and probably from the same collection event, being determined as two different species (note: I need to check on this and give an example).
- In DMoj, L. schottii is mostly out in the real desert, whereas L. matthewsii has a big concentration next to the mountains, especially on the immediate northern edge of the SnGb, SnBr, and Little SnBr, and the southwest edge of the SN.
- Oddly, though, L. schottii is found in the Central Valley, and densely along the w DSon edge, especially in middle San Diego County.
(Section to be added on how different floras use different characters to separate them, each implying that some of the characters used by other floras are bogus.)
(Section on preliminary analysis done on 3/21/08 showing corolla lobe spacing and tip properties seem to separate them.)
As a result of the preliminary analysis I did, I began photographing a representative sample of the flowers of all plants that I came across, in order to then analyze those pictures to see if there was a separation of the species, or if the flowers were part of a continuum, implying there was just one species here.
On 16 March 2011, I spent one day doing a preliminary analysis of my pictures. This page presents the results of that analysis, so that others can see what I've done and make comments on it. My conclusions may change as I analyze more data!!.
Analysis
Measured quantities.
From pictures, one can easily measure the angles between the corolla lobes, so that was a no-brainer to measure. I had thought that the shape of the corolla lobes tips was important, so I estimated whether the tip was truncate or not, and began to measure the length of the tooth at the tip of the lobes above the truncate portion.
But I was immediately faced with a problem; I couldn't reliably measure where the truncate tip occurred. So I decided to measure the length above and below the widest portion of the corolla, a well-defined point in general, and, if there was a tooth, measure it separately.
That turned out surprisingly well, although a few flowers had oblong corolla lobes without a well-defined widest portion. I need to return to this to decide how to treat such flowers.
The following figures show what quantities I measured.
Loeseliastrum flowers are bilateral and 2-lipped, consisting of a 3 lobed upper lip and a 2 lobed lower lip. Fig. 3 shows my numbering scheme for the corolla lobes and angles, with lobe #1 defined as the leftmost of the 3 upper lobes as they appear in looking at a photograph of the flower from its front. The other lobes are numbered clockwise.
Fig. 4 shows the lengths measured in the pictures. Length 1 is from the base of the lobe to the widest point. Length 2 is from the widest point to the truncate portion of the tip, if one exists; otherwise, to the tip itself. Length 3 is the length of the tooth above the truncate portion of the tip, if one exists. These lengths are normalized by the length of the entire lobe, so that the scale of the photograph doesn't matter.
 Fig. 3. Numbering scheme for corolla lobes and angles. |  Fig. 4. Definition of measured lengths (see text) |
Preliminary Results.
I first tried to analyze Calphotos pictures of the two species, but in general the pictures were not optimal for this analysis, since most pictures were not close-ups of the flowers, and, most surprisingly for pictures from photographers, most pictures did not have a full on frontal view of a single flower.
Since my pictures were optimized for this project, I decided to measure my pictures first. I measured 11 flowers from six different areas spread over a geographic distance of roughly 20 miles east west, from the San Felipe Valley to the Arroyo Salado, and 20 miles north south, from the Arroyo Salado to Pinyon Mountain Road.
Measuring the pictures was straightforward, except for a few of the L. schottii pictures, in which I could not clearly tell which were the upper lobes and which were the lower lobes. Fortunately, it turns out that the flower of L. schottii is so symmetric that it makes no difference which angles are measured for it! I.e., I rotated the angles (making angle 1 be angle 2, etc.) and it made almost no difference at all in the angular quantity computed below (of angles 3 + 4 - 1 - 2 - 5).
Before I put the data into a Principal Component Analysis, I attempted to see if some simple analysis would separate these species.
I defined an angular deviation from regularity by adding the absolute values of the deviation of each angle from 72°, and I plotted how truncate the tip of the leaf was vs. that quantity.
That didn't do a very good job in producing anything that looked like two separate species, so I was a bit skeptical as to whether the traits I had relied upon worked to separate these species.
I then put the 25 individual measurements per picture in a Principal Component Analysis, and was surprised to see that they separated into what looked like two different species in the plot of PCA2 vs. PCA1! Best of all, those two species, as defined in the PCA plot, had different geographic ranges!
There was only a single interloper of one flower from one area being found amidst the points from another area, instead of it being with other flowers from its area. When I looked back at the picture, the flower seemed unusual, so I removed it from the analysis. (I will return to this flower in the future, since apparent exceptions often have something to teach us.)
Fig. 5 shows the PCA with that interloper removed, with the points labeled by their location:
Fig. 5. Principal Component 2 plotted versus Principal Component 1.
I've drawn roughly circular boundaries around the points corresponding to the two species (see plot without circles if you want to stare at the points sans my interpretation).
Drawing the boundaries was pretty straightforward; I simply enclosed areas that contained all the points from a given area, and used the knowledge that points ought to spread over roughly ± two standard deviations from the center of their distribution. For example, the two pink rectangles in Fig. 5 are both from the West Borrego Mountain area, and hence a first draft boundary should include both of those points unless one suspects they were different species found next to each other.
Contrary to my expectations, the PCA plot strongly suggests there are two species here. Note that the points span nine standard deviations in PCA1. A single species would span about four, which is the distance that the points within each of the two circles span.
Furthermore, there is beautiful geographic coherence, with the points corresponding to L. schottii found in the desert transition zone of the San Felipe Valley and the Pinyon Mountains, and the points corresponding to L. matthewsii found in the desert floor.
In fact, I had erroneously determined one of those L. matthewsii pictures as "L. schottii", based on my previous usage of the corolla tip shape and lobe angles to define the species, which also agreed with voucher determinations from that particular area.
I then looked at the components for PCA 1 to try to translate them into quantities more easily understood by a mere human like myself. It was straightforward to see that the components came from two sources:
- an angular asymmetry portion which was roughly angles 3 + 4 minus angles 1 + 2 + 5.
- a simple measure of the location of where the corolla lobe was the widest, which was roughly length1 minus length 2, plus the length of any tooth at the tip, adding the measure for each of the five lobes together.
Surprisingly to me, the truncateness of the corolla tip was totally ignored by PCA1, as being insignificant.
I then made a plot of these quantities, and the species separated almost as well in that plot.
I then measured some Calphotos pix and added them to my plot, making no modifications. Fig. 6 gives the plot including those measurements, where I've now just called all my desert floor points as being from the Borrego Valley:
Fig. 6. Corolla lobe length measurements vs. Angle measurements
See also plot sans interpretation.
I've drawn a line that appears to separate the species, but I reserve the right to change that line when I put all of these into a new PCA.
The separation seems to hold up well, as long as one accepts that one Calphotos pix called L. matthewsii is actually of L. schottii (corresponding to the green diamond amidst the other L. schottii points). Even before I measured that pix I was pretty sure it was misdetermined.
OK, so what do these pictures corresponding to the above data look like?
Fig. 7 gives thumbnails of all the pictures used in this analysis, separated by the two variables I defined above. You can judge for yourself if you believe these represent two species.
Looking at the pictures myself, I wonder about two of the pictures that fall into the L. schottii, the ones with fatter corolla lobes with values of (63, 0.8) and (-34, 1.3). When I next have time, I'll re-analyze those pictures to see if I just screwed up the measurements or not.
Remember, this is an analysis in progress.
I have many more pictures I can measure from many additional locations. I'll reserve final judgment until I analyze them and the outlier I tossed. But for now, I've changed my opinion, and it looks like there are indeed two separate species here.
The numeric values for each picture are given below each one.
Some of the pix below are from Calphotos, and I haven't yet obtained permission from the photographers to use them, but I have written each one of them. I'll delete any photo for which I don't get permission within a week.
Not all squares are populated by pictures. As can be seen from Fig. 6, no points fall into the region of 80-160 for the angle quantity for values of less than 1.0 for the length quantity. I.e., apparently L. schottii never has that irregular a corolla, and L. matthewsii never has corolla lobes with the maximum width that close to the proximal end.
For Lengths 1 + 3 - 2, lobes widest toward the tip have larger values, to the bottom of the figure. The measure in this column is the sum of this quantity for all five lobes. If each lobe was widest at the exact tip, with no tooth, the measure for each lobe would be 1.0 and the sum would be 5. If each lobe was widest in the middle, with no tooth, the measure for each lobe would be 0.0, and the sum would be zero. If each lobe was widest at the base, with no tooth, the measure for each lobe would be -1.0, and the sum would be -5.
Fig. 7. Thumbnail plots of pictures used in this analysis, separated by corolla lobe length measurements and a measure of the uniformity of the angles between lobes.
I thank Aaron Schusteff for stimulating me to use the phrase eye candy, from his notes on his photograph of L. matthewsii in which he said: This is a lovely little plant...foliage and flower-wise. It's like vegetative candy..