Estimation and Application of Genetic-Gain Multipliers for Douglas-Fir Height
and Diameter Growth
Peter J. Gould1, David D. Marshall2,
Randy Johnson1 and Greg Johnson2
1USDA Forest Service Pacific Northwest Research Station2Weyerhaeuser Co.
Outline
• Issues, concepts, objectives
• Data and modeling approach
• Results
• Applications for projecting yield
Why Model Genetic Gain?
• Improved Douglas-fir is a reality in the PNW.
• Insight into stand development and return on investment (without waiting 20+ yrs).
• Genetics studies have not focused on stand-level growth and yield.
Genetic-Gain Multipliers
Example: ΔDG = M∙ ΔDWR
• Extrapolates information from genetics studies to existing growth models.
• Other approaches include refitting equations and SI adjustments.
Predicted growth from woods-run
model
Predicted growth with genetic-gain
Genetics Studies: Questions Asked
Geneticist: What is the total height and diameter of a genotype at a given age relative to woods-run?
• Single-tree plots
• Families tested on multiple sites; interested in mean across sites.
• Select best parents for seed orchards / breeding
Genetics Studies: Questions Asked
Modeler: What is the rate of height and diameter growth of an individual tree for a given period based on its pedigree and site, stand, and tree characteristics?
• Interested in growth within a stand.
• Genetics is one of many factors controlling growth.
Concepts from Genetics
• Breeding value: the value of a parent for passing some trait to its progeny (estimated from progeny tests).
• Genetic worth: the expected level of gain for some trait of an improved seedlot.
GW = f(BVorchard, outside pollen)
• Both expressed as percentage difference from population (woods-run) mean in traits such as total height and diameter at a given age.
NWTIC 1st Generation Progeny Tests
• Seed collected from wild, woods-run parents to test half-sib families.
• BV calculated for mother trees at age 10 yrs (genetics perspective).
• We used same data (up to age 20 yrs). Half-sib families treated as individual seedlots where:
2/)(
2/)0(
2/)(
Mother
Mother
FathersMother
BVGW
BVGW
VBBVGW
Study Objectives
• Estimate genetic-gain multipliers for height and diameter growth for improved DF seedlots when GW is known.
M = f (GW, stand age)
• Evaluate multiplier effects in growth models (ORGANON and FVS).
Modeling Strategy1. Estimate growth of individual trees (e.g., ΔDWR) in progeny tests using woods-run models.
2. Calculate seedlot-level multipliers (M) from observed growth and expected growth under the woods-run model.
ΔDG = M∙ ΔDWR
M = ΔDG / ΔDWR
3. Estimate M from seedlot’s GW.
NWTIC 1st Generation Progeny Tests
Breeding zone: area of relatively uniform environment (≈ 50,000 ha)
Site: Geographical location within breeding zone.
Set: Group of families tested together. A more-or-less random sample of woods-run population.
Rep 1 Rep 2
Rep 3 Rep 4
Rep 1 Rep 2
Rep 3 Rep 4
Rep 1 Rep 2
Rep 3 Rep 4
SET 1 SET 2 SET 3
DBH Data: Variation Between Breeding Zones
10-yr DBH (cm)
10 t
o 15
yr
DB
H I
ncre
men
t (c
m)
DBH Data: Variation Between Sites
10-yr DBH (cm)
10 t
o 15
yr
DB
H I
ncre
men
t (c
m)
DBH Data: Variation Between Sets
10-yr DBH (cm)
10 t
o 15
yr
DB
H I
ncre
men
t (c
m)
Challenges of Progeny Test Data
• Limited individual-tree measurements– No crown ratios or crown class
• Single-tree plots– No stand density (e.g., basal area)– No site index
• Mixed genotypes –Superior trees may perform better– Inferior trees may perform worse
Modeling Strategy
• Could not use an existing model– Unmeasured variables– Precision needed to estimate small effects
• Created “custom” woods-run models:
Ex: ∆HT = b1∙HTb2∙b3HT
random effects on b1,b2,b3 at set level
• Separate models fit for 5- 10-, and 15-yr periods.
Mixed Genotypes
GW = 10
GW = -10
GW = 0
Probably not very important:
– much overlap between seedlots in size / competitive position.
– Woods-run models account for differences in initial size.
NWTIC 1st Generation Progeny Tests
Period
(yr)
Height Growth Diameter Growth
BZ Seedlots N BZ Seedlots N
5-10 14 1802 166,870 1 145 7,704
10-15 16 2485 222,818 7 1178 83,072
15-20 1 90 7,571 2 321 20,396
Woods-run Model: Height Growth
0
1
2
3
4
5
5 10 15
Period (yr)
5-yr
Hei
gh
t In
crem
ent
(m)
All Predicted
Top 25 Predicted
Top 25 Observed
Woods-run Model: Height Growth
0
1
2
3
4
5
5 10 15
Period (yr)
5-yr
Hei
gh
t In
crem
ent
(m)
All Predicted
Top 25 Predicted
Top 25 Observed
Woods-run Model: Height Growth
1.8%3.3%
Woods-run Model: Height Growth
0
1
2
3
4
5
5 10 15
Period (yr)
5-yr
Hei
gh
t In
crem
ent
(m)
All Predicted
Top 25 Predicted
Top 25 Observed
1.028
1.013 1.018
Estimating Height-Growth Multipliers
M = α0 + α1 ∙ GW
• OLS, WLS and method-of-moments regression fits (error in GW).
• WLS fits:
Period Equation
5 1 + 0.006277∙GW
10 1 + 0.003112∙GW
15 1 + 0.004474∙GW
Estimating Diameter-Growth Multipliers
WLS fits:
Period Equation
5 1 + 0.010105∙GW
10 1 + 0.003370∙GW
15 1 + 0.002944∙GW
We Have Multipliers; Now What?
• ORGANON (Mark Hanus and David Hann).
• FVS PN and WC (FIXHTG and FIXDG keywords).
• Tested “virtual” seedlot with 10% GW for height and diameter at 10 yrs.
We Have Multipliers; Now What?
• Tree list for 10-yr-old stands generated with FGROW (Flewelling and Marshall).
• Adjusted 10-yr height and diameters by multiplying by 1.10.
• Tested adjusted tree list with and without genetic-gain multipliers.
Projections
Wo
od
s-R
un
V
olu
me
(cu
ft)
Gai
n w
ith
M
ult
ipli
ers
(cu
ft)
Gai
n w
ith
T
reel
ist
(cu
ft)
Wo
od
s-R
un
V
olu
me
(cu
ft)
Gai
n w
ith
M
ult
ipli
ers
(cu
ft)
Gai
n w
ith
T
reel
ist
(cu
ft)
1.1% 5.7%
6.6%12.7%
Projections: 40-yr Rotation
Wo
od
s-R
un
V
olu
me
(cu
ft)
Gai
n w
ith
M
ult
ipli
ers
(cu
ft)
Gai
n w
ith
T
reel
ist
(cu
ft)
0.2%2.2%
4.3% 7.0%
Projections: 60-yr Rotation
Conclusions
• Multipliers can put genetic information in models right now, though many questions remain.
• Genetic effects are relatively small, but significant.
• Modelers need more information and more precise estimates than tree breeding programs.
• Operational and controlled experiments are needed.