Analysis of The Flora of the PCT: Sections A1 to A7

Introduction
Major Conclusions
Analysis of the number of taxa found in each segment
Analysis of the number of segments in which each taxon was found, using the flora of all segments
Analysis of the number of segments in which each taxon was found, using the flora of an individual segment
Summary of the Analysis of the Number of Segments in which each Taxon was found
Percent of Taxa in Common vs. Distance Between Segments

Introduction

This page analyzes the native flora of Sections A1 to A7, which contains 334 total taxa. We use the word taxa instead of the word species since taxa includes varieties or subspecies as well as species that don't have varieties or subspecies. For example, in this flora, there are two subspecies of Pentagramma triangularis, ssp. rebmanii and ssp. triangularis, which represents two taxa but only one species.

Non-native species are not included in this analysis, since they are not expected to follow the same distribution behavior as the native species (many are not in distribution equilibrium since they are still spreading), and because we wish to understand how the native species are distributed.

In the following, we use the words section and segment to mean the same thing, one of the seven sections A1 to A7.

Major Conclusions

The analysis given below may not be easy to follow for many people, so we present here the major conclusions of the analysis given below. See below for details on each of these conclusions.

The major conclusions of the analysis present here are:

Analysis of the number of taxa found in each segment

Table 1 gives the length of each segment and the number of taxa found in each segment alone, and Fig. 1 shows the number of taxa found in each segment.

Table 1. Trail Section Length and Number of Taxa Observed

SegmentLength (miles)# Taxa
A12.3126
A217.5166
A36.3121
A43.8113
A512.4176
A610.5118
A76.8119

Fig. 1. The number of taxa found in trail segments A1 to A7. Segments A2 and A5 are the longest segments, and also have the greatest number of taxa found in their surveys. The other segments have virtually-identical observed number of taxa, despite a range in trail segment length from 2.3 to 10.5 miles (see Table 1).

The segments range from 2.3 miles for segment A1 to 17.5 miles for segment A2, with the longest segment almost eight times as long as the shortest segment. However, the number of taxa found on each segment ranges only from 113 taxa on segment A4 to 176 taxa on segment A5, a factor of only 1.6.

The reason why the number of taxa varies so much less than the ratio of the mileage is that many botanical studies have found that the number of species in an area increases much less rapidly than the area increases. This makes sense, since neighboring areas often have similar habitat, with similar taxa in them. Additional taxa appear only when something in the environment changes, such as going from an open location to the shade of a boulder or tree, from a south slope to a west slope, a change in the elevation, a change in the soil type, and other changes that are less easy for a human to observe, such as different night-time temperatures or different winds at different times of year. Every good field botanist has an eye for observing micro-habitats where they expect to see some new species in a given survey.

Fig. 2 plots the number of taxa found in each segment vs. the mileage of each segment, along with a model of the usual increase of the number of taxa with area (in this case, vs. distance).

Fig. 2. The number of taxa found in each of the trail segments A1 to A7 plotted versus the segment length. The red smooth curve is a best-fit power-law model of the expected increase in taxa versus distance. The three segments farthest from the model fit are labeled.

Given the differences in survey coverage for each segment, from the number of times each segment was covered, the dates each segment was covered, and the number of people doing the survey for each segment, the number of taxa found for each segment is fairly close to expectations. Possible reasons why three segments deviate from the model fit are:

Of course, chance also plays a role in the observed differences. One expects a statistical one-standard-deviation variation of the observed numbers equal to the square root of the model predicted number, in this case 10 to 13 taxa. It is not unusual to observe a deviation of two standard deviations, in this case 20 to 26 taxa. Only section A1 deviates more than could be explained by chance.

Analysis of the number of segments in which each taxon was found, using the flora of all segments

In the combined flora from all segments, one can count up how many segments in which each taxon was found. For example, the first taxon in the list, Selaginella bigelovii, was found on three segments, A1, A2 and A5. The second taxon in the list, Azolla filiculoides, was found on two segments, A3 and A4. The third taxon, Dryopteris arguta, was found on only a single segment, A2.

We can take the number of segments for each taxon to count the number of taxa found on only a single trail segment; the number found on two trail segments, up to the number of taxa found on all seven trail segments.

Table 2 gives the number of taxa that were found on 1 to 7 trail segments in which the 334 taxa are found, and Fig. 3 plots those numbers. Table 2 also gives the percent of the 334 taxa found on a given number of trail segments.

Table 2. # of Taxa found on 1 to 7 Trail Segments

# of segments# Taxa% Taxa
110030
28225
36018
4319
5196
6185
7247
 
Total334100

Fig. 3. Histogram of the number of taxa found on 1 to 7 trail segments.

These are quite standard results, which are a direct consequence of the observation that the number of species increases with area. In order to pick up more species with area, there have to be species found in only some areas. The observed usual increase of the number of species directly implies that most species are found in few areas. For more discussion of this fact, with examples from other species lists, see How Common Are The Plants Of Southern California?.

It is worth noting that it is entirely expected that there will be taxa found in only 6 out of the 7 trail segments, and that this is not in general a problem with the completeness of the surveys. Even if future surveys of these sections find some of these taxa in the segment where they were formerly missing, those surveys are equally likely to find an additional occurrence of taxa formerly found in 5 out of the 7 trail segments, promoting them to the 6 out of 7 trail segment list. Hence the shape of this histogram will likely remain the same as more surveys are done in these segments, with the previous list of found taxa moving to higher observed number of trail segments, and being joined by newly-found taxa that occur on only one trail segment.

Table 4 gives the number of taxa unique to a given trail segment, as well as the number of taxa that are not present from that segment, but which are found in the other six segments (these are taxa present in 6 out of 7 segments).

Table 4. # of Taxa Unique to a Trail Segment, and # of 6 out of 7 Taxa Absent in a Trail Segment

Segment# Taxa Unique to Segment# Taxa Absent in Segment
found in all other segments
A1163
A2282
A3125
A432
A5221
A683
A7112
 
Total10018

The total number of taxa unique to each of the segments totals 100, the same number as given in Table 3 for taxa observed on only one segment. The total number of taxa observed on 6 out of 7 segments is 18, again the same number as given in Table 3.

The number of taxa absent from a given segment is very uniform between segments, ranging only from 1 to 5, with most segments have 2 or 3 "absent" taxa.

The variation in the number of unique taxa is much larger, ranging from just 3 taxa in A3 to 28 taxa in A2. The two sections with the largest number of unique taxa are also the two longest sections, which provides more opportunity to find different habitats that might not be present in the other segments. The segment with the smallest number of unique taxa is A4, with just 3 unique taxa. It is the second shortest segment, and was surveyed fewer times, by fewer people, at fewer times of year, than the shortest segment.

Analysis of the number of segments in which each taxon was found, using the flora of an individual segment

The previous analysis was done for the entire list of 334 taxa found from all segments A1 to A7. One can also ask the question: of the taxa found on a single segment, what is the average number of segments in which those taxa are found? I.e., if one considers only the 126 taxa found in segment A1, or only the 166 taxa found in segment A2, what is the histogram of their number of segments?

These taxa will have a higher average number of occurrences, since the large number of taxa found on only a single trail segment in other trail segments are not in the plant list for that single trail segment.

The total number of occurrences for each taxon is simply the number of times it was seen in the seven surveys. A taxon found on all seven segments has seven occurrences in the set of seven trail segment floras; a taxon found on six segments has six occurrences in the set of seven trail segment floras, etc. The number of occurrences for the entire taxon list can be easily computed by taking the numbers in each line of Table 2 for the # Taxa, and multiplying them by the # of segments. For example, the 100 taxa seen on only one segment have a total of 100 occurrences; the 82 taxa found on two segments have a total of 82*2 = 164 occurrences, etc. The 334 taxa have a total of 939 occurrences.

Another way to think of the list being analyzed in this section is to take the checklist for A1, add to that the checklist for A2 repeating taxa seen in both lists, add to that the checklist for A3 in the same way, etc. That list would have 939 entries (= occurrences), with most taxa being repeated at least once in the list.

The number of such occurrences for all taxa found in A1 to A7 is given in Table 5 and Fig. 4.

Table 5. # of Occurrences for taxa found on 1 to 7 Trail Segments

# of segments# Taxa% Taxa
11000.11
21640.17
31800.19
41240.13
5950.10
61080.12
71680.18
 
Total9391.00

Fig. 4. Histogram of the number of the 939 occurrences of the taxa found on 1 to 7 trail segments.

The number of occurrences is much more constant, with a variation of only a factor of 1.8, compared to a factor of 5 in the histogram in Table 2. To a first approximation, a given taxon in the flora of a given segment is as likely to be found only on that segment as it is to be found on all seven segments, or in fact on any number of other segments. The actual average number of segments for the taxa found in the individual floras of A1 through A7 is 4.1, 3.8, 4.2, 4.5, 3.7, 3.9, and 4.2, an average of 4.1, close to the 4.0 it would be if a taxa were exactly equally likely to be found in any number of other segments.

Summary of the Analysis of the Number of Segments in which each Taxon was found

To recap the different numbers present above:

The fundamental reason why these numbers differ is that the number of uncommon taxa accumulate in the combined flora of all segments, whereas the large number of observations for the common taxa increases the number of occurrences for those taxa. For more discussion of why these numbers differ, using a simple example of three segments each with three species, see How Common Are The Plants Of Southern California?.

Percent of Taxa in Common vs. Distance Between Segments

The floras of the individual segments can be compared to see how the number of taxa in common between segments falls off with increasing separation of the segments. Table 6 gives the number of taxa in common between the segments.

Table 6. # of Taxa in Common Between Different Trail Segments

 A1A2A3A4A5A6A7
A1126926872654150
A2921667882874962
A3687812168704958
A4728268113734557
A5658770731769582
A6414949459511869
A7506258578269119

Each entry in Table 6 gives the number of taxa in common between the segment given at the left of the row and the one given at the top of the column. The entries in blue compare a segment with itself, and thus simply give the number of taxa in a given segment (e.g., 166 in segment A2). For example, the entry with row labeled A2 and column labeled A4 is 82, indicating that there are 82 taxa in common between those two segments.

This table is of course symmetric about the diagonal, since the number of taxa in common between A2 and A4 is the same as the number of taxa in common between A4 and A2.

Table 7 gives the fraction of taxa in common comparing one segment with another. This is not a symmetric process since the segments have a different number of taxa. In Table 7, the entries in the upper right of the table give the percent of taxa from the list in the column segment to the one at its left. The entries in the lower left of the table give the percent of taxa from the list in the row segment to the one above it.

An example comparing the flora of segment A1 to A2 will make this clear. A1 has 126 taxa; A2 has 166 taxa; and they have 92 taxa in common. The 92 taxa in common are 73% of the taxa in A1, but only 55% of the taxa in A2. Thus row A1, column A2 has an entry of 0.73, whereas row A2, column A1 has an entry of 0.55.

Table 7. Fraction of Taxa in Common Between Different Trail Segments

 A1A2A3A4A5A6A7
A11.000.730.540.570.520.330.40
A20.551.000.470.490.520.300.37
A30.560.641.000.560.580.400.48
A40.640.730.601.000.650.400.50
A50.370.490.400.411.000.540.47
A60.350.420.420.380.811.000.58
A70.420.520.490.480.690.581.00

As expected, the percent of taxa in common gets smaller as the distance between segments increases. Fig. 5 plots the numbers in Table 7, in the form of the average for a given segment distance, as well as the minimum and maximum for a given segment distance. Fig. 5 shows that on average, neighboring segments share 60% of the number of taxa in one of their lists, but segments separated by 4 to 6 segments share only 40% of their taxa. But there is considerable variation between neighboring segments. Some share 80% of their taxa; some only share 40% of their taxa.

Fig. 5. Plot of the average, minimum and maximum percent of taxa shared between segments separated by a given number of segments. On average, neighboring segments share 60% of the number of taxa in one of their lists, but segments separated by 4 to 6 segments share only 40% of their taxa.


Go to:


Copyright © 2014 by Tom Chester, RT Hawke, and Shaun Hawke.
Permission is freely granted to reproduce any or all of this page as long as credit is given to us at this source:
http://tchester.org/pct/a/a1_to_a7_flora_analysis.html
Comments and feedback: Tom Chester
Updated 31 December 2014.