Estimation of Genetic Multipliers for Douglas-Fir Height- and Diameter-

Growth Models

Peter J. Gould, David D. Marshall, Randy Johnson and Greg Johnson

1. Estimate growth differences between average (wood’s-run) tree and individual families in terms of genetic-gain multipliers.

2. Relate multipliers to breeding value (BV = percent gain at age 10).

3. Evaluate multipliers effects in model.

Study Objectives

Effect of Multipliers

0

5

10

15

20

25

0 20 40 60 80 100Year

Dia

met

er (i

n)Initial Size Advantage

Gain Multiplier= 0.05

Typical Tree

Coop: breeding zone. Completely independent families.

Sites: Geographical locations within coops.

NWTIC 1st-Generation Progeny Tests

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 Coops

10-YR GROWTH PERIOD

DBH Data: Variation between Sites

10-YR GROWTH PERIOD

DBH Data: Variation between Sets

10-YR GROWTH PERIOD

DBH Data: Breeding Values

BV = Age 10 Gain 1 (percent)

1. Average growth = wood’s run.

2. Multipliers work with any unbiased growth model.

3. Removing sources of variation other than genetics is very important.

Modeling Strategy: Assumptions

Strategy:1. Fit models with random effects at site-set level.

2. Calculate genetic multiplier (m) for each family at coop level.

Obs = m ∙ Pred

3. Estimate m from BV.

m = A0 + A1 ∙ BV

>16 coops

> 109 sites

> 513 site-sets

> 2485 families

> 222 818 observations

10-YR Modeling Dataset: HT Model

∆HT = b1∙HTb2∙b3HT

random effects on b1,b2,b3

Fixed Effects: ∆HT = 231.7∙HT0.94∙0.86HT

HT Model 1

HT Model 1Model R2

Base 37.6

Base + random effect 69.0

Residual Variation (%) 31.0

Between Families (%) 2.4

HT Model Results: Family M

>7 coops

> 45 sites

> 193 site-sets

> 1160 families

> 76 012 observations

Modeling Datasets: DBH Model

∆DBH = b1∙DBHb2∙b3DBH∙b4BA REP

random effects on b1,b2,b3

Fixed Effects: ∆DBH = 3.7∙DBH0.3∙1.01DBH∙0.97BA REP

DBH Model 1

DBH Model 1Model R2

Base 25.5

Base + random effect 61.6

Residual Variation (%) 38.4

Between Families (%) 3.3

DBH Model Results: Family M

10-yr A1 estimates:

Study Ht Diameter

Gould 0.001434 0.001577

Marshall 0.001498 0.001657

--

R. Johnson(BV = 13%)

0.001145 --

G. Johnson(assume BV=13%)

0.001824 0?

Other Periods

• Ht data for 5-yr (167,000 obs) and 15-yr (7600 obs) growth.

• DBH data for 5-yr (7,700 obs) and 15-yr growth (20,000).

• Estimates of m are higher for 5-yr, but about the same for 15-yr growth.

What’s Next?

• Manuscript on multipliers.

• ORGANON interface.

• Test multipliers.