N-tree-distance sampling in riparian forests of western
Oregon: a simulation study
Z. Haxton, T. Marquardt and H. Temesgen
College of Forestry
Oregon State University
Western Forest Mensurationists’ Meeting
Missoula, Montana
June 21, 2010







Challenges in sampling riparian areas
N-tree distance sampling overview
Objectives
Methods
Results
Conclusions


High within-stand variation.

Alternating conifer-hardwood patches.

Edge effects.

Wensel et al. 1980

USFS crews told to switch prisms to get 7 in-trees every time (Bell
1994).


The same number of trees is measured at every sample point, leading to potential gains in field efficiency.

Can be more efficient for estimating density of rare objects (e.g. snags; Kenning et al. 2005).


Requires accurate horizontal distance measurements.

Determining which trees are the nearest n to a sample point is not necessarily a trivial undertaking.

Practical, universally design-unbiased estimators are currently not available.


Operational forest inventory using n-tree distance sampling is currently being explored in Germany (Nothdurft et al. 2010).

The development and testing of new estimators is currently an area of active research.

Many estimators have been developed in the last 20 years, but not all are necessarily easy to understand and implement.


Compare the statistical performance of selected n-tree-distance sampling estimators for estimating stem density and basal area of headwater riparian forests of western Oregon.

Compare the statistical performance of the estimators to that of fixed plot sampling and variable plot sampling for estimating density and basal area, respectively.

From Cissel et al. (2006)

From Cissel et al. (2006)

From Marquardt (2010)


Monte Carlo simulation programmed in VBA

Procedure:
◦ Randomly locate four sample points.
◦ See what trees would be captured using fixed plot, variable plot and n-tree distance sampling at each point.
◦ Estimate stem density and basal area with each method.
◦ Repeat 2,000 times!

Values of n from 2 to 10 explored
◦ Variable plot BAF and fixed plot radius were scaled to capture an average of n trees per sample point.

Relative bias
RB

2 i
, 000 

1
 
* 100
Y * 2 , 000
Relative RMSE
RRMSE


2 , 000 i

1


Y
ˆ i Y
2

2 , 000
100
Y where
Ŷ i
= estimated value for a given repetition
Y i
= known true value

BL13 KM19
Moore
Prodan
Kleinn-Vilcko
2
KM18
4 6 n
8 10 2
TH75
4 6 n
8 10
2 4 6 n
8 10 2 4 6 n
8 10

BL13 KM19
Moore
Prodan
Kleinn-Vilcko
2
KM18
4 6 n
8 10 2
TH75
4 6 n
8 10
2 4 6 n
8 10 2 4 6 n
8 10

BL13 KM19 fixed plot
Moore
Prodan
Kleinn-Vilcko
2
KM18
4 6 n
8 10 2
TH75
4 6 n
8 10
2 4 6 n
8 10 2 4 6 n
8 10

BL13 KM19 variable plot
Moore
Prodan
Kleinn-Vilcko
2
KM18
4 6 n
8 10 2
TH75
4 6 n
8 10
2 4 6 n
8 10 2 4 6 n
8 10

BL13 KM19 fixed plot
Moore
Prodan
Kleinn-Vilcko
2
KM18
4 6 n
8 10 2
TH75
4 6 n
8 10
2 4 6 n
8 10 2 4 6 n
8 10

BL13 KM19 variable plot
Moore
Prodan
Kleinn-Vilcko
2
KM18
4 6 n
8 10 2
TH75
4 6 n
8 10
2 4 6 n
8 10 2 4 6 n
8 10


Results should be extrapolated with caution.

No statistical advantage to n-tree distance sampling.
Density » fixed plots best.
Basal area » variable plots best.

Moore estimator had lowest overall bias, Kleinn-Vilcko estimator had a less skewed distribution of estimates.

An n of 6 may be most appropriate for n-tree distance sampling.

There may be an application for these estimators as long as the population is not too clumped.

Bell, J. (1994). Is it true that… maintaining a constant tree count in VP gives better answers? Available online at http://www.proaxis.com/~johnbell/newsindex/isittruethat.htm; last accessed June 8, 2010.
Cissel, J., P. Anderson, et al. (2006). BLM Density Management and Riparian Buffer Study: establishment report and study plan, U.S. Geological Survey. Scientific Investigations Report 2006-5087.
Kenning, R. S., M. J. Ducey, J. C. Brissette and J. H. Gove. (2005). Field efficiency and bias of snag inventory methods.
Canadian Journal of Forest Research 35:2900-2910.
Kleinn, C. and F. Vilcko (2006). A new empirical approach for estimation in k-tree sampling. Forest Ecology and
Management. 237(1-3):522-533.
Lessard, V., D. Reed and N. Monkevich (1994). Comparing n-tree distance sampling with point and plot sampling in northern Michigan forest types. Northern Journal of Applied Forestry 11(1): 12-16.
Lynch, T. B. and R. Rusydi (1999). Distance sampling for forest inventory in Indonesian teak plantations. Forest Ecology and Management 113(2-3):215-221.
Marquardt, T., H. Temesgen and P. Anderson (2010). Accuracy and suitability of selected sampling methods within conifer dominated riparian zones. Forest Ecology and Management. 260(3):313-320.
Moore, P. G. (1954). Spacing in plant populations. Ecology 35(2): 222-227.
Nothdurft, A., J. Saborowski, R. Nuske and D. Stoyan (2010). Density estimation based on k-tree sampling and point pattern reconstruction. Canadian Journal of Forest Research 40(5):953-967.
Prodan, M. (1968). Punkstichprobe für die Forsteinrichtung (in German). Forst. und Holzwirt 23(11):225-226 (not directly examined by author, citation via Lynch and Rusydi 1999).
Wensel, L. C., J. Levitan and K. Barber (1980). Selection of basal area factor in point sampling. J. For. 78(2):83-84.
Yamada, I. and P. A. Rogerson (2003). An empirical comparison of edge effect correction methods applied to Kfunction analysis. Geographical Analysis 35(2): 97-109.

Uncorrected
N
U

1 m i m 

1

 n
A i


Prodan
N
P

1 m i m 

1
 
 n
A i
0 .
5


Moore
N
M

1 m n n
1 m  i

1

 n
A i

 where
m = number of sample points r d i
n = number of trees at each sample point
A i
= plot area of the ith plot in ha = π (r
= radius of the ith plot in m d n
= distance to the nth tree n+1
= distance to the n+1th tree i
2 )/10,000
Kleinn-Vilcko
N
K

1 m i m

1

A j


*

 d n


 A d n n j

1




2
40 , 000

From Yamada et al.
(2008)

Conifers
Hardwoods
0 10 20 30 40
Easting (m)
50 60 70

BL13 KM17 KM18 KM19 KM21 OM36 TH46 TH75
N G N G N G N G N G N G N G N G
DF 110 168 49 113 66 101 98 137 54 95 136 147 123 198 171 236
WH 0 0 108 172 146 135 72 67 69 98 6 2 45 62 13 6
WR
GF
RA
0
0
0
0
0
0
0
0
0
34
0
9
0
45
0
0 15 12 15 11 5
13
0
3
13
0
17
4
0
15
2
6
10
0
2
10 0
0
0
0 10 2
0 0 0
0 6 5
BM 17 13 0
Other 5 1 0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
68
0
23
0
Total 132 181 171 297 260 256 221 221 153 212 161 162 167 260 268 271

Species
Douglas-fir western hemlock western redcedar red alder bigleaf maple
All combined
BL13
B CE B
KM17
CE B
KM18
CE B
KM19
CE B
KM21
CE B
OM36
CE B
TH46
CE B
TH75
CE
9.1
1.03
8.5
0.80
10.1
1.05
6.4
0.93
16.2
0.80
8.3
1.22
7.2
1.11
8.4
1.12
8.0
1.08
8.0
0.97
8.8
0.90
14.1
0.75
-
-
-
14.6
3.8
0.36
-
0.81
0.37
12.7
-
0.82
-
16.7
28.9
0.86
0.54
-
-
-
-
12.0
0.84
-
12.6
-
0.48
0.0
0.24
11.
5 0.21
18.3
0.58
8.3
0.99
6.6
1.22
6.5
1.09
4.3
0.96
6.7
0.99
8.3
1.25
7.4
1.14
7.9
1.08