Preliminary Analysis of Elevations of the Species in the Flora

Table of Contents

Quality Control for the GPS Points
Geographic Map of Species in the Database
Number of GPS Points Per Species
Elevation Minimum and Maximum Values
Elevation Ranges
Number of Species At Each Elevation
Cumulative Number of Species Versus Elevation


As of 5 February 2014, Kate Harper and I have digitized 6,106 accurate quality-controlled GPS positions that we have taken in the field of 473 confidently-identified taxa. Although this is only about 1/4 to 1/2 of our entire survey so far, and is missing something like 200 to 400 taxa, it is enough to have a little fun analyzing the content of that database. This page gives a very preliminary peek into the elevation records.

In the following, these terms are used interchangeably: GPS positions; GPS points; GPS locations.

Important Caveat: This analysis was done on an incomplete database. The number of species in the database will probably eventually significantly increase, and the elevation ranges for many species will widen as more points are added.

Quality Control for the GPS Points

The GPS positions have been carefully quality-controlled in the following manner. They were taken from GPS units that were on continuously during each survey, eliminating the large start-up error that GPS units often have. The first GPS point was not taken until the unit had converged on a good position fix, and often was not taken until 10-15 minutes later. The GPS-unit-estimated location error was monitored regularly, with times / areas of high error noted.

Each GPS position was plotted on a topographic map, with the positions visually checked to make sure they were taken along the actual path surveyed. This eliminates the occasional crazy jumps that GPS units often produce in terrain with significant exposed rock surfaces that create multipath error, as well as problems due to poor satellite reception due to satellite visibility or satellite configuration. Points that were obviously incorrectly-located were thrown away.

A separate topo-map elevation, in addition to the GPS-estimated elevation was recorded in the GPS point database in the following manner.

An elevation was visually obtained from the topographic map for each GPS position by my interpolation between the elevation contours. It was checked against both the GPS-estimated elevation and the Digital Elevation Model elevation estimate. In nearly all cases, the elevation produced by my interpolation was the one recorded in the Topo map elevation field in the GPS database. In some cases, where points were taken close together in time and space, and/or where I knew that there was significant topographic variability between the topo map contours, the elevation was assigned based on a blend of topo map estimates from surrounding points, and differential elevation recorded by my GPS unit, which has a built-in altimeter independent of the satellite GPS elevation estimate.

The topo-map elevations were given to the precision allowed by the contours on the topo map. With the usual 40 foot elevation contours, in areas where the terrain elevation varied smoothly (e.g., there were no cliffs between the contours), elevations were usually estimated to the nearest 10 feet. When 20 foot contours were available, elevations were usually estimated to the nearest 5 feet. On the desert floor or other flattish places, elevations could sometimes be reliably estimated to the nearest foot.

All of the analysis below was done using the topo-map elevations. However, for most of the analysis below, only the first quality-control step is important, and the plots would all look almost identical if the GPS-estimated elevations were used.

Analysis of the difference between the topo-map elevations and the GPS-estimated elevation finds a mean difference of 5 feet and a standard deviation of typically 15 feet in areas that are not GPS-signal-challenged by multipath error. For comparison, points taken at San Jacinto Mountain, where the contour intervals are typically 80 feet, and there are significant challenges to the GPS signal from multipath error from many exposed large rocks, and signal strength from the forest canopy, the standard deviation is 32 feet.

However, there are a small number of extreme outliers, and occasionally an entire survey area will have a GPS-estimated elevation that is systematically different from the topo-map elevations by 20 to 40 feet. These deviations are generally caused by multipath error similar to the errors at San Jacinto. The 15 foot standard deviation was actually a trimmed standard deviation calculated ignoring those outliers, since the bulk of the differences fit a Gaussian bell-shaped curve extremely well out to three trimmed standard deviations.

The mean difference of 5 feet (with a standard deviation of 0.7 feet in that mean difference) is in the sense that the GPS-estimated elevation is 5 feet higher than the topo-map elevations, and is almost certainly caused by my holding the GPS about 4 feet off the ground surface. I was impressed that this small difference could be deduced from these data!

Geographic Map of Species in the Database

To give the reader an idea of the locations of the digitized surveys, I plotted the locations of the point for each species with its highest elevation and the point for each species with its lowest elevation. These two maps are not very different. You can see points jump from east to west, and vice versa, by opening both maps in separate windows on top of each other and flipping between the images.

For various reasons, most of the digitized surveys have been at higher elevations so far, although a handful of lower-elevation surveys have been digitized as well. For an idea of some locations of not-yet-digitized surveys, see the map showing areas surveyed before 2009, the vast majority of which have not yet been digitized.

Maps showing the distribution of points in the database as of 29 November 2014 (later than the analysis of the rest of this page), using the clustering algorithm of the Consortium of California Herbaria: all points; points at Whale Peak and north.

Number of GPS Points Per Species

Although the average number of GPS positions per species is 13 (=6106 / 473), as always with plants, there are many more species with few locations than with many locations. This follows the general rule that rare species are common; common species are rare, in terms of the number of species that are rare, and the number of species that are common. See How Common Are The Plants Of Southern California? for more information on this surprising fact of biology.

Fig. 1 shows the histogram of the number of GPS positions per species.

Fig. 1. Histogram of the number of GPS positions per species. Most species in the database have a small number of GPS points, even though the average number of GPS points per species is 13. The point plotted in the 60 to 70 bin includes all higher values as well.

80 species have just a single GPS point for them so far, the same number of species as the total number of species with 26 or more GPS points.

The overall shape of this histogram will remain the same as we complete our digitization of our surveys. Although the number of GPS points per species will go up for most species as we add more points, we'll continuously add new species with only a single GPS point. One way to think about this is to note that we have something like 200 to 400 species not yet in the GPS point database, and which thus currently have zero GPS points associated with each. If I plotted that in the histogram, it would produce a large spike at zero! As those species enter the database, they will first create a single GPS point for each species.

However, simply counting points for each species in our GPS point database is not the best way to get relative abundances of species. The following examples show how the number of GPS points can deviate from the true abundances for each species.

Examples of species with just a single GPS point in our database now are:

Species with many GPS points in general are the most abundant and widespread species, but this is not always true. The species with the largest number of GPS points for each in the database now are: Calliandra eriophylla (200 points), Cylindropuntia ganderi (183 points), Ambrosia salsola var. salsola (100 points) and Ericameria brachylepis (80 points). The latter three species are indeed abundant and widespread, but Calliandra eriophylla is one of the rarest species in the Borrego Desert! In each case we did special mapping for those species (see for example the map for Calliandra eriophylla) and took a lot of GPS points for them.

Abundances of species are best determined by combining the information from the numeric floras we produce for each area, with abundance numbers associated with GPS points in the database.

Elevation Minimum and Maximum Values

Fig. 2 plots the maximum vs. minimum elevation of each species.

Fig. 2. Top: Maximum vs. the minimum elevation of each species

The following discussion should help clarify the basic structure of this plot.

Each species is represented by a single point in this plot, although different species can have the same minimum and maximum elevation, and hence fall on the same point.

We have no records below 16 feet elevation in our database, so the lowest elevation in Fig. 2 is 16 feet. Our highest records are at Whale Peak, elevation 5349 feet, accounting for the boundary at the top of the plot.

All the points in Fig. 2 are found above the apparent diagonal line from lower left to upper right, since the maximum elevation has to be greater than or equal to the minimum elevation. Points along the diagonal line are almost always species with just a single GPS point with a single elevation.

Species at the bottom left have a minimum and maximum elevation that are both nearly zero, such as Fagonia pachyacantha, with a minimum elevation of 16 feet and a maximum elevation of 57 feet. This is truly a low elevation species,being found in our surveys and vouchers in this area only up to 1000 feet. Its maximum elevation will eventually be 1000 feet in our database as we digitize more of our surveys.

Species at the upper right have a minimum and maximum elevation that are both at or near the highest limit of our digitized surveys, 5340 feet, such as Lomatium mohavense, with a minimum elevation of 4760 feet and a maximum elevation of 5340 feet. This species has reliable vouchers that go down to 2500 feet in more coastal areas to the west of where we have surveyed, but we have not encountered it below 4760 feet in any of our surveys, including ones not yet digitized.

Species at the upper left in the plot are species that cover nearly the entire range of elevations that we have surveyed, such as Phacelia distans, ranging from 16 to 5349 feet, which is the entire range so far in our database.

With that introduction to Fig. 2, I've taken the same plot and identified some regions in Fig. 3 that correspond to fairly-easily-understood geographic areas. Other areas in the plot do not correspond to such easily-understood areas, and just show species "doing their own thing" and not following a crowd.

Fig. 3. Maximum vs. the minimum elevation of each species, with some regions in the plot labeled.

The delineated areas are described below, with representative species in each given in Table 1:

In Fig. 3, I've used the term Desert Transition Zone to describe the region above the desert floor where the elevation typically rises from 1000 feet to over 5000 feet, but can begin at elevations as low as 200 feet at the base of the Santa Rosa Mountains and the Vallecito / Fish Creek Mountains. Although this clearly appears as a transition zone if one drives from the Laguna Crest at Banner to the desert floor beyond The Narrows, it actually is a very complex region that contains plant species from other habitats as well. Specifically, this Zone contains species that are:

The most interesting category above is the ones unique to this area in San Diego County. That includes:

Table 1 gives three representative species from each of the regions labeled in Fig. 3.

Table 1. Minimum and Maximum Elevations for Selected Species

Species# GPS PointsElevation (feet)
Species Extending Throughout Most of the Elevation Range
Larrea tridentata45164380
Opuntia basilaris501505285
Cylindropuntia ganderi1832605349
Species Confined to Desert Floor
Cylindropuntia ramosissima8361070
Cylindropuntia echinocarpa345201160
Datura discolor5675990
Species Confined to Lower Desert Transition Zone
Ayenia compacta4511103585
Cheilanthes viscida2715203585
Senna covesii1619953360
Species Confined to Upper Desert Transition Zone / Mountain Areas
Quercus cornelius-mulleri1430955349
Pinus monophylla1235905349
Eriogonum wrightii var. membranaceum936355349

As can be seen in Fig. 3, there are many species intermediate to these three categories, that are a mixture of these three categories. Desert species drop out at various elevations above ~1000 feet, and montane species drop out at various elevations below ~5000 feet.

Giving an area a plant community label is therefore problematic in general. Species composition varies in a complex way throughout the entire area, and only in certain areas can one feel comfortable giving an area a single name.

However, Fig. 3 does not show a random distribution of points. There is clearly structure in the plot, but until we analyze the biases in where we have surveyed, we cannot say for sure whether the structure is from the geography in this area; from where we have surveyed; and/or from true ecological preferences by the Borrego Desert species. With that caveat, some of the structure in the plot is:

In the future, I'll compare the minimum and maximum elevations for species found in our surveys to the ones reported in Munz and the Jepson Manual, which will help to unravel some or all of the biases.

Elevation Ranges

Fig. 4 shows a histogram of the elevation ranges for these species.

Fig. 4. Histogram of the elevation range for all species (note that the x-axis is not elevation; it is the difference between the maximum and minimum elevation for each species, the elevation range). The large spike in the bin from 0 to 250 feet due to the 80 species found so far at only a single location, and hence have an elevation range of zero in the database.

Fig. 4 shows an amazingly-uniform distribution of species elevation ranges, ignoring the peak at zero elevation range due to species found so far at just a single elevation. From an elevation range of 1200 feet to one of 4200 feet elevation, a species is just as likely to have any any elevation range within that interval. The interpretation of this has to await further analysis to understand the biases in our survey mentioned above.

There is a larger number of species with elevation ranges of 250 to 1000 feet, which is almost surely due to the bias caused by the geography of the surveyed area for species that live on the desert floor, with the elevation range of the desert floor being about 1000 feet in our survey area. If our survey area also included desert floor areas at higher elevation, such as are found north and east of the Borrego Desert, many of those species would undoubtedly be found to have a larger elevation range.

In the future, I'll compare the elevation ranges found in our surveys to the ones reported in Munz and the Jepson Manual, which will help to unravel some or all of the biases.

Number of Species At Each Elevation

The number of species at each elevation is given in Fig. 5, assuming that each species is present at all elevations between their minimum elevation and their maximum elevation.

Fig. 5. Number of species present at each elevation.

Note that this curve applies only to the areas in our GPS point database. I've plotted only the elevation range from 500 feet to 4200 feet, since the curve outside those elevations is probably dominated by the small number of areas surveyed at those elevations, and not by the true number of species found at those elevations.

The curve is surprisingly flat over a large range of elevation, with about 200 species present at elevations of 1800 feet to 3200 feet, and declining in elevations outside that interval. In that interval, as one changes elevation, approximately as many species drop out as are gained by going to a new elevation. Above 3200 feet, more of the desert species are dropping out than are being added by new higher-elevation species. Below 1800 feet, more of the higher-elevation species are dropping out than are being added by new lower-elevation species.

This flatness appears to be an effect of the true elevation ranges of the species. A simulation cutting the elevation ranges in half, by moving up the lowest elevation by one quarter of the elevation range, and decreasing the highest elevation by the same amount, which cuts the elevation range for each species in half, produces a distinctly-different curve that is no longer flat, but instead has a peak at 2500 to 3000 feet. As expected, there are fewer species at each elevation in that simulation as well.

This simulation might be more representative for some species since the extreme elevations of a species are sometimes outliers. For example, Chamaesyce melanadenia typically is only found above ~2200 feet, but occasionally gets washed down to lower elevations by flooding events, producing waifs that don't survive past one year. Justicia californica is normally found only below 2000 feet, but we've found two outliers at 2600 feet and 3060 feet.

However, the simulation is not representative of species whose maximum elevation is 1000 feet or so. Most of those species are quite abundant at their maximum elevation, and so the simulation erroneously cuts down the number of species at 1000 feet by a large factor. The simulation should just be viewed as one way to understand that it is the species elevation ranges that account for the flatness of the observed curve.

Further work using elevations from Munz and the Jepson Manual is needed to understand the biases in our survey mentioned above.

Note that even though the number of species at each elevation has a maximum value of 200, this doesn't mean one expects to see 200 species in a survey of a given area at constant elevation. To get the 200 species one would have to cover all areas that we have surveyed at that elevation.

It does mean that if one is restricted to a given elevation, and one wants to see as many species as possible, one should pick an elevation in the interval 1800 to 3200 feet.

This result surprised me, since I had always thought that 4000 feet elevation was the magic elevation with the most species. That thought probably came from my first survey at 4000 feet elevation, which was on the Cactus Spring Trail on the north side of the Santa Rosa Mountains. That trail starts at 4000 feet and drops to 3500 feet, and is very rich with species since it includes a large number of habitats, including several different riparian habitats. Having gotten that impression, even though I was always impressed by the number of species found in Culp Valley surveys, it never occurred to me to revise my initial impression that 4000 feet was the magic number. Now I'll remember that the magic number in the Borrego Desert is 1800 to 3200 feet.

Cumulative Number of Species Versus Elevation

Fig. 6 plots the cumulative number of species versus elevation, with one curve starting at the lowest elevation in our surveys and going up in elevation, and the other curve starting at the highest elevation in our surveys and going down in elevation.

Fig. 6. Cumulative number of species versus elevation, separately from the lowest elevation up, and the highest elevation down.

In Fig. 6 both curves start at one species and end at 473 species. Half of these 473 species are found below elevations of ~1100 feet, and half the species are found above elevations of 3500 feet. Those elevations of 1100 and 3500 feet are not the same because most species have a significant elevation range. The non-zero elevation range is also why both curves are steepest near their starting point, and flatten out near their end point. Both curves show an approximately linear increase in the number of species versus elevation near their starting points, and a smaller linear increase in their middle sections. Near their end points, both flatten out since nearly all species have been counted within about 1000 feet of elevation from their end points.

Specifically, starting at zero elevation, the number of species picks up rapidly to about 1000 feet, and then the increase becomes slower up to about 4000 feet, with very few species picked up between 4000 and 5350 feet. Starting at 5350 feet, the number of species picks up rapidly down to about 3200 feet, and then the increase becomes slower down to about 1000 feet, with very few species picked up between 1000 and zero feet.

I have no idea if there is any significance to the point where these two curves cross, at roughly 345 species found below 2100 feet, and 345 species found above 2100 feet. I suspect not; the lines simply have to cross at some point.

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Copyright © 2014 by Tom Chester.
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Updated 9 February 2014 (maps showing all database points added on 29 November 2014).