In Spring of 2019 my Environmental Fieldwork class surveilled the herbaceous plants growing on and around the Tufts campus, recording their identities and locations into a GIS database. For a final project I created a simple Cartesian quadrature algorithm in Python to identify the distinct plant pairs most likely to share the same soil.
Whether due to reporting bias or the natural wind channel on campus known as the hill, Dandelion was most abundant plant overall. Likewise, the pair of plants most likely to be found at the same location turned out to be Dandelion+Chickweed.
plant map quadrature
Begin by drawing a rectangle around the entire surveyed area.
Divide the rectangle into quadrants and count the plant occurrences; repeat.
n := 0; K := .5;
[rect_width,height] := survey_area_width,height
while No. empty rectangles < K * No. rectangles:
[rect_width,height] *= .5
count_plants_in_rectangles()
count_empty_rectangles()K=1/2 is a density coefficient used as a stopping criterion. When half of the resulting grid rectangles contain no plants we stop subdividing.
Plant locations and identities were recorded using our phones. For our final projects, we were to deliver something valuable out of the data we’d collected as a class.
As a math major at the time, and inspired by my Real Analysis lectures on Riemann integration, I chose to produce an algorithm to determine the most frequent plant pairings that were observed on campus following a similar approach. If clover and dandelions were observed close to one another, the algorithm would record their locations as coinciding within a grid square.
Without having to send samples to a lab for testing, we could infer a lot about soil from the plants growing in it, and likewise learn about a plant from its neighbors.
Done using satellite imagery, this is called Remote Sensing and is an active area of research. From the sky we can determine which areas have acidic soil, which areas are sandy, &c, by vegetation coverage.
Results
Equipped with plastic spoons and our phones, our class had a good time discovering, at the least, our collective preference for bright golden petals that can be spotted from meters away.
There were 40 plant species that were catalogued by the class. This provides a maximum number 
of distinct neighboring pairs that could have been observed. Since the map quadrature algorithm returned 130 observed pairs, local soil properties arguably played a hand in the pairings that we observed. And of the observed pairs, 35 combinations 
were counted at most 5 times on the Tufts campus.
Least observed
pairs were not counted at all. The pairs that were counted the least number of times under quadrature included
| Pair | # | Pair | # |
|---|---|---|---|
| Nimblewill, Sowthistle | 1 | Dock, Mint | 1 |
| Common chickweed, Plantain | 1 | Fleabane, Wild garlic | 1 |
| Common chickweed, Yellow wood sorrel | 1 | Wild lettuce, Plantain | 1 |
| Bull thistle, Violet | 1 | Mouse-ear chickweed, Nimblewill | 1 |
| Dock, Mouse-ear chickweed | 1 | Clover, Mouse-ear chickweed | 2 |
Despite the few occurrence of these pairs, some of these plants were rarely observed to begin with. Further investigation would require more sampling of the underrepresented. After all, our results for the urban Tufts campus may tell us mostly about concrete runoff, herbicides, and fertilizers for them.
Most observed
| DND | dandelion | VLT | violet |
| BTR | bittercress | YWS | yellow wood sorrel |
| CHK | common chickweed | GLC | wild garlic |
| BPL | broadleaf plantain | CLO | clover |
| NPL | narrowleaf plantain | MCK | mouse-ear chickweed |
Our class’s survey of the Tufts campus yielded
530 locations (latitude, longitude),
40 plant species, and
130 plant pairings.
