The West Cascades

Park City

The West Cascades

• NaNationwide FForest IImputation SStudy

Gradients in Plant Community Ecology

• Plant species exhibit distributional patterns that are a reflection of changing environmental conditions.

500 1000 1500 2000

01

02

03

0

Douglas-fir

Elevation

Ba

sal A

rea

Hierarchies from landscape ecology

• “… a system of interconnections wherein the higher levels constrain the lower levels to various degrees...” (Turner et al. 2001)

• Broad-scale, factors (e.g., climate) constrain local species pools.• Local topography, disturbance, succession and competition

determine which species from that pool occupy a given site.

Time ------------------------------------->

Sp

atia

l E

xten

t --

----

-- > CLIMATE

Disturbance

Local Topography

Objective

• Explore vegetation-environment relations in the context of imputation mapping.

• Different modeling techniques make different assumptions about the world.

– Euclidean Nearest Neighbor. – Gradient Nearest Neighbor.– Random Forest.

Methods

– Maps built from:

– 784 records from our plot database (FIA annual plots)– and 16 mapped explanatory variables.

Landsat Bands 3,4,5

Climate PRISM: Means, seasonal variability

Topography Elevation, slope, aspect, solar

Location X, Y

studyarea

(2) Place new pixel

withinfeature space

(3) find nearest-neighbor plot within feature

space

(4) impute nearest

neighbor’s value to

pixel

Methods: Euclidean Nearest Neighbor Imputation

feature space geographic space

Elevation

Rainfall

(1)Place plots

within feature space

• Advantages – Simplicity.– Quick to run.– Makes no assumptions about how vegetation

relates to the environment.

• Disadvantages– May not represent species-environment

relations well.

Pros and Cons: Euclidean Imputation

(2) calculate

axis scores of pixel from

mapped data layersstudyarea

(3) find nearest-

neighbor plot in

gradient space

(4) impute nearest

neighbor’s value to

pixel

Methods: Gradient Nearest Neighbor Imputationgradient space geographic space

CCAAxis 2

(e.g., Temperature, Elevation)

CCAAxis 1

(e.g., Rainfall, local

topography)

(1)conductgradient

analysis ofplot data

• Advantages to GNN– Shapes environmental space as it relates to forest

composition. – Model structure is straightforward, reasonably

intuitive.

• Disadvantage to GNN– Assumes that species show a unimodal response to

environmental gradients (Gauch, 1982; ter Braak and Prentice, 1988).

Pros and Cons: Gradient Nearest Neighbor Imputation

500 1000 1500 2000

01

02

03

0

Douglas-fir

Elevation

Ba

sal A

rea

studyarea

Methods: Random Forest Nearest Neighbor Imputation

Random Forest space geographic space

Methods: Random Forest• One Classification Tree:

|Elevation < 1244

August Maximum < 23.24 Temp

August Maximum < 25.60 Temp

Summer Mean < 12.79 Temp

Aug. to Dec. Temperature < 12.79 Differential

Elevation < 1625LANDSAT Band 5 < 24

PSME TSHEPSME THPL

ABAM TSMEPSME PIPO

High Elevation ( > 1244)High August Temp (> 23.24°C)High reflectance in Band 5 (> 24)

Methods: Random Forest

• A “Forest” of classification trees.

• Each tree is built from a random subset of plots and variables.

|ANNHDD < 4271.43

SMRPRE < 5535.09

X < 8808.88ANNHDD < 3950.45

SMRPRE < 5576.65

SMRTP < 2088.19

MR4300 < 166.968

ANNHDD < 4779.98

4215 4222 4224 4224

4228

4267 42154272 4228

|ANNTMP < 665.874

ANNVP < 591.82

ANNHDD < 4710.98X < 7248.68

STRATUS < 3.7435

X < 7762.43 X < 6340.86

ANNHDD < 3901.34215 42284215 4272

4215 4205

4224

4226 4224

|ANNGDD < 2578.11

ANNVP < 591.82

ANNGDD < 2190.48

ANNPRE < 740.947

STRATUS < 40.8768

R5400 < 117.208

ANNGDD < 3028.96

4228 4215

4272

4215 42154224

4224 4224

|ANNFROST < 1693.8

ANNFROST < 1271.82

CONTPRE < 788.967IDSURVEY < 456

ANNFROST < 2051.42

IDSURVEY < 423ADR5700 < 70.8343

4224 4224 4224 4224

4215 4272 4267 4228

|SMRTMP < 1206.3

ANNVP < 608.87

R5400 < 158.673

SMRTMP < 1105.53

ANNVP < 660.51

ANNVP < 610.822

TC200 < 134.347

SMRTMP < 1444.82

CONTPRE < 785.7484228 42154267

4272

4267 42154215

4224

4214 4224

|ANNHDD < 4204.74

DIFTMP < 2847.06

ANNHDD < 3669.42

CVPRE < 8079.84

DIFTMP < 3022.3

DIFTMP < 2854.2

SMRTMP < 1123.01SMRTMP < 1184.12

4226 42144224 4224 4215

4228 4272 4228 4215

|

Methods: Random Forest Imputation

|

157915

23610

81413

11181925

242317

1620

302726

2829

26162028

• Advantages– Models vegetation-environment relations – Free from distributional assumptions– High accuracy

• Disadvantages– Computing time– Interpretation is difficult

Pros and Cons: Random Forest Imputation

Comparisons

• Root Mean Square Difference (RMSD) for species basal area.

• Mapped distribution (presence/absence)– Douglas-fir (Pseudotsuga menziezii)– Sugar Pine (Pinus lambertiana)

Results

Accuracy

(scaled RMSD)

GNN Advantage

Random Forest Advantage

Methods Equally Good

Pacific Dogwood

Sugar Pine

Red Alder

Bigleaf Maple

Englemann Spruce

Grand Fir

Incense Cedar

Ponderosa Pine

California Black Oak

Giant Chinkapin

Shasta Red Fir

Western Red Cedar

Pacific Madrone

Western Hemlock

Lodgepole Pine

Western White Pine

Noble Fir

Mountain Hemlock

Pacific Silver Fir

Oregon White Oak

Douglas-Fir

White Fir

Subalpine Fir

Pacific Yew

0.0

0.5

1.0

1.5

RFGNNEuclidean*

Euclidean model not shown. Results were comparable, but never best.

Douglas-fir

• Often dominant.

• Widespread, early colonizer, long-lived.

• Only disappears at v. high elevations.

Douglas-fir Range

Euclidean78.0%

GNN59.2%

RandomForest74.3%

Estimated Actual Area79.77%

PresentAbsent

Douglas-fir Range

RMSD

0.0

0.2

0.4

0.6

0.8

1.0

Euclidean GNN Random Forest

(scaled)

Sugar Pine

• Spotty distribution, wide elevation range, mostly in the South.

Sugar Pine Range

Euclidean5.4%

GNN3.5%

RandomForest4.3%

Estimated Actual Area4.6%

PresentAbsent

Sugar Pine RangeEuclidean GNN Random Forest

RMSD

0.0

0.2

0.4

0.6

0.8

1.0

1.2

(scaled)

Conclusions

• The answer is...

YES!!

– The world can be seen as a gradient.

– But in some cases, the world is better described by a hierarchy.

Conclusions: Which model?• Broad-scale patterns are consistently predicted

by all 3 model types.• GNN works well most of the time.• If rare, or quirky species are our focus, however,

Random Forest may provide a very useful alternative.

• Both Random Forest and GNN are an improvement over simple euclidean imputation in terms of RMSD, but euclidean was often less biased in the range-maps.

The End.

• Questions?