Do stem form differences mask responses to silvicultural treatment?
Doug Maguire Department of Forest Science Oregon State University
Typical responses monitored during silvicultural trials
-Dbh
-Height
-Height to crown base? -Upper stem diameters?? -Branch diameters??
Monitor Dbh and Ht (perhaps crown size), but do regional or subregional volume/taper equations adequately estimate tree volumes?
How would you test statistically for silvicultural treatment effects on stem form?
Lennette thesis – Effects of stand density regime on stem form in larch Garber thesis – Effects of initial spacing and species mix on tree and stand productivity Scott Ketchum, Robin Rose – Does relative stem profile respond to early control of competing vegetation? Mark Gourley et al. – Are Swiss needle cast and/or nutrient amendments changing stem form in Douglas-fir?
Wider spacing (increasing dbh)
(same relative stem profile?)
Wider spacing
Larger crowns
(length and width) Influence on distribution of bole increment Change in relative stem profile?
Are any responses in stem form accounted for by monitoring treatment effects on crown size (length)?
Andy Lennette. 1999. Twenty-five-year
response of Larix occidentalis stem form to five stand density regimes in the
Blue Mountains of eastern Oregon. M.S. Thesis, Oregon State University
Lexen (1943): bole surface area as measure of growing stock (Approximation of cambial surface area on which wood accrues) =>Measurement of bole surface area to regulate stocking
Catherine Creek Levels-of-growingstock study Stocking regulated by bole surface area =>Accomplished with Barr and Stroud optical dendrometer
=>Many upper stem measurements over time
Growing stock levels
1: 2: 3: 4: 5:
5,000 ft2/ac 10,000 ft2/ac 15,000 ft2/ac 20,000 ft2/ac 25,000 ft2/ac
35 yrs old in 1966 at start of study Thinned twice, ages 45 and 65 (last thinning in 1965
Last measurement in 1991 – upper stem diameters retrieved for 25-29 trees per treatment
On average 10 d.o.b.s per tree
GSL I II III IV V
Dbh (in) 16.1 12.2 11.4 10.7 9.5
Ht (ft) 83.6 74.1 73.7 72.6 74.8
Increasing thinning intensity
Height on tree
dob
75
70
65
Crown ratio Crown Ratio(%)
60
55
50
45
40
35 0 1 2 3 4 5 6
GSL
Increasing thinning intensity
Analysis: Kozak variable exponent model
Dob/DBH = XC
where X = [1-(h/H)0.5] / [1-(4.5/H)0.5] C = a1sin-1(h/H) + a2(h/H)2
Fitted to each individual tree, then SUR for
a1 = f( GSL or tree attributes (eD/H) ) a2 = g( GSL or tree attributes (CR) )
Increasing thinning intensity
Height on tree
dob
Light thinning
Heavy thinning
Light thinning
Heavy thinning
Light thinning
Heavy thinning
Conclusions:
Relative stem profile was significantly different between the 2 most intensive thinning treatments, and these 2 were significantly different than the 3 least intensive thinnings There was no marginal effect of treatment beyond its effect on D/H and crown ratio
Production analysis requires development of taper/volume functions (without attempt at explicit test of treatment effects on stem profile) Sean Garber. 2002. Crown structure,
stand dynamics, and production ecology of two species mixtures in the central Oregon Cascades. M.S. Thesis,
Oregon State University
Ponderosa pine/lodgepole pine mixed species spacing trial, planted in 1967 Grand fir/ponderosa pine mixed species spacing trial, planted in 1974
Both sampled in fall 2001 (34 and 27 yrs old, respectively)
Upper stem measurements from trees felled outside of permanent spacing trials Analysis based on Kozak variable exponent model: Dob/DBH = XC where X = [1-(h/H)0.5] / [1-(4.5/H)0.5] C = f(h, H, and D)
Objective was NOT to test for spacing and species effects on stem form, but rather on relative productivity. BUT needed a reliable volume or taper function for the site.
Rather than two-stage approach, can a mixed-effects model be applied ? Is a random tree effect sufficient to eliminate autocorrelation among observations within a tree?
Nonlinear residuals
NLME with two random tree effects
NLME + CAR(1)
Relative height
Subtle spacing effects on relative stem profile
(but estimated adequately from D/H)
Average tree in each spacing
( a)Pinus contorta 1.8 ( 1 1.5, 9.0 ) 3.7 ( 1 7.0, 9.3 ) 5.5 ( 2 0.5, 9.5 ) ( b) Pinus ponderosa 1.8 ( 1 2.8, 6.8 ) 3.7 ( 1 6.8, 7.3 ) 5.5 ( 2 3.5, 9.3 )
0.8
1.0
Lodgepole pine
0.6 0.4
Ponderosa pine
0.0
( c ) Abies grandis 1.8 ( 1 0.3, 6.3 ) 3.7 ( 1 6.2, 8.7 ) 5.5 ( 1 6.7, 8.5 )
0.2
( d) Pinus ponderosa 1.8 ( 1 4.3, 8.6 ) 3.7 ( 2 1.5, 9.7 ) 5.5 ( 2 7.3, 10 .4)
1.0
Grand fir
0.8
Ponderosa pine
0.4 0.0
0.0
0.2
0.6
0.4
0.8
1.2 0.0
0.4
0.8
1.2
Relative diameter
Spacing effect was not tested explicitly in taper model since trees were felled off the plots Instead profiles were plotted for the tree of average dbh and height within each spacing-species combination
Effect of species composition was even more subtle
(a) 1.8-m spacing
Pure PP (12.8, 6.8) Mix PP (10.5, 6.5) Pure LP (11.5, 9.0) Mix LP(13.0, 8.5)
(b) 3.7-m spacing
Pure PP (16.8, 7.3) Mix PP (16.8, 7.5) Pure LP (17.0, 9.3) Mix LP (17.8, 9.0)
(c) 5.5-m spacing
Pure PP (23.5, 9.3) Mix PP (23.0, 9.5) Pure LP (20.5, 9.5) Mix LP (21.0, 9.5)
Relative height
0.0
0.2
0.4
0.6
0.8
1.0
(d) 1.8-m spacing
Pure PP (14.3, 8.6) Mix PP (17.7, 9.4) Pure GF (10.3, 6.3) Mix G (7.7, 6.0) F
(e) 3.7-m spacing
Pure PP (14.3, 8.6) Mix PP (17.7, 9.4) Pure GF (10.3, 6.3) Mix G (7.7, 6.0) F
(f) 5.5-m spacing
Pure PP (27.3, 10.4) Mix PP (28.8, 10.4) Pure GF (16.7, 8.5) Mix G (16.8, 8.3) F
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Relative diameter
Conclusions: Random tree effect dramatically reduced the order of autocorrelation, but did not eliminate it.
A first-order continuous autoregressive error process eliminated the remaining autocorrelation.
Conclusions (continued): The taper functions had <3% bias in almost all cases.
Regional volume equations (Cochran 1985) differed from the taper equation estimates by 20-30% for grand fir, 2060% for lodgpole pine, and 2-10% for ponderosa pine.
Rose, Ketchum, & Hanson. 1999. Threeyear survival and growth of Douglas-fir seedlings under various vegetation-free regimes. Forest Science 45:117-126. 8 treatments, 3 reps/trt @ each of 2 sites Area of herbaceous and woody control (1st two growing seasons): 0, 4, 16, 36, 64, 100 ft2 + 100 ft2 woody only + 100 ft2 herbaceous only
1-ft
2-ft
3-ft
4 ft2 16 ft2 4-ft 36 ft2
5-ft
64 ft2
100 ft2
Planted in February 1993 with 1+1 Douglas-fir
Rose et al. (1999) present 3-yr results:
Maximum growth response under the largest (Summit) or 2 largest (Marcola) areas of treatment (height, D2H, basal diameter) Greater growth under herbaceous only, not under woody only, relative to controls
Winter 2001-2002, stem d.o.b. measurements
Does the intensity of early weed control affect stem profile beyond the effect on diameter and height? Do existing volume equations accurately predict stem volume of weeded plantations?
Difference = observed - predicted
30
25
20
Height (ft)
15
10
Marcola Summit
5
0 -0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Difference (in)
Difference = observed - predicted Summit and Marcola averaged
30
25
20
Height (ft)
15
10
5
4 16 36 64 100 0 herb woody -0.4 -0.3 -0.2 -0.1 0 0.1 0.2
0 -0.5
Difference (in)
Difference = observed - predicted Marcola site only
30
25
20
Height (ft)
15
10
5
4 16 36 64 100 0 herb woody -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6
0 -0.4
Difference (in)
Difference = observed - predicted Summit site only
30
25
20
Height (ft)
15
10
5
4 16 36 64 100 0 herb woody -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2
0 -0.7
Difference (in)
Potential for systematic bias by treatment
To test for treatment effects on stem profile,
mixed-effects linear and non-linear models
finish start
Analysis: Kozak variable exponent model
Dob/DBH = XC
where X = [1-(h/H)0.5] / [1-(4.5/H)0.5] C = b1(h/H) + b2(h/H)2
Fitted to each individual tree, then SUR for
b1 = f( site, treatment, tree attributes ) b2 = g( site, treatment, tree attributes )
Tentative conclusions: No treatment effects, but significant site effects.
Relative stem profiles similar even without accounting for differences in height and diameter.