Winter Injury in American chestnut

James Sharpe

Rebecca Stern

April 20, 2015

Stat 231

Main Objective

Examine winter injury in American chestnut trees to see if small and large chestnut trees at two different levels of canopy openness are affected differentially by winter injury.

Main goal is to contribute information about restoration of American chestnuts in Northern Forests.

Sources of Variation

Experimental Units: Individual trees.

Observational Units: Individual trees.

Factor/Type of Effect

Levels Code

Size of treeFixed

Small: 25.0 cm or less 1

Medium: 25.1 cm - 85.0 cm 2

Large: 85.1 cm or larger 3

Light TreatmentFixed

Partially open canopy 1

Fully open canopy 2

Measurements

Percent injury will be measured for each tree. This is amount of dieback a tree experiences after winter.

This will be assessed via visual examination of trees; after leaf-out, any visible dieback will be considered winter injury.

Notice the dead leaves that occurred due to winter injury. Normally, the leaves would be robust and green.Poor sapling.

Experimental Procedure

A planting of American chestnut trees was established in the Green Mountain National Forest in 2009 in two different treatments: open canopy and partially open canopy.

Open canopy treatment Partially open canopy treatment

Anticipated Difficulties

Tree death

Voles and other animals eating tree roots

Measurement error, such as inaccuracies due to subjectivity of measuring percentage of dieback.

Differences in collecting the data: differences in person measuring, specific day and weather conditions.

Natural variability of planting sites: for example, one site may be naturally more wet than another, which could affect ability of tree to recover from winter injury.

A vole. Deadly for American chestnut.

Statistical Model

𝑌 𝑖𝑗𝑘=µ+𝛼 𝑖+𝛽 𝑗+(𝛼𝛽)𝑖𝑗+𝜀𝑖𝑗𝑘i=1,2,3j=1,2K=1,2,…,r

is the fixed effect of the ith treatment of tree size: is the fixed effect of the jth light treatment: is the fixed effect of the interaction between light and size treatments: and is the experimental error term: iid

Analyses

We would perform an ANOVA.

To check assumptions, we would construct a QQ-Plot to make sure the residuals are normally distributed. If the residuals are not normally distributed, then an appropriate transformation would be made.

HOV test and spread-location plot to make sure variances are equal. Since this is a CRD, the assumption of independence is met.

Analyses - Continued

Contrast Small Medium Large Treatment

C1a 0 1 -1 Partial

C1b 0 1 -1 Open

C2a 1 0 -1 Partial

C2b 1 0 -1 Open

C3a -1 1 0 Partial

C3b -1 1 0 Open

To perform multiple comparisons we would use the Tukey Procedure since we are making all pairwise comparisons with respect to tree size.

Power Analysis

Using the effect size method, we found that 8 observations per group were needed to attain 90% power to detect a two standard deviation change. From previous literature, we guesstimated that two standard deviations corresponds to 15.2% change.

We used PROC POWER in SAS to get a range of replications needed for 90% power to detect previously stated changes in variance components. The minimum standard error used was 0.05 and the maximum standard error estimate used was 0.30. This yielded r=3 to r=53.

For this study, we will go with 8 obs. per group, since this was within the range given by SAS.

Reference:Saielli, T.M., Schaberg, P.G., Hawley, G.J., Halman, J.M., & Gurney, K.M. (2014). Genetics and silvicultural treatments influence the growth and shoot winter injury of American chestnut in Vermont. Forest Science, 60, 1-9