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.