Community abundance data
Fig 6. Weed community data
The first analysis I performed was a principal component analysis of my vegetation assessment data with species abundance being averaged across all quadrats, both years, and grouped by site. See Fig 6 for a simplified sample of the data table used to represent the weed community around each tree. Prior to analysis the data underwent a Hellinger transformation to make it amenable to PCA analysis.
Simultaneously recorded with the community data is my response variable of tree growth. Tree growth is defined as the difference between the starting and ending tree stem volumes. Stem volumes were calculated using the formula for a cone which is: 1/3*basal area*height. Stem volume growth will be the response variable for all following analyses.
Simultaneously recorded with the community data is my response variable of tree growth. Tree growth is defined as the difference between the starting and ending tree stem volumes. Stem volumes were calculated using the formula for a cone which is: 1/3*basal area*height. Stem volume growth will be the response variable for all following analyses.
Data for weed community composition grouped by abundance, proximity, and time
Fig 7. Weed community subdivided by form, quadrat, and year
To get a further picture of the relationship between the characteristics of the neighboring weed community and tree growth I performed a multiple regression tree analysis using package Rpart with total stem volume growth as the response with weed cover values as the predictor variable. Also included was site and initial tree volume as a covariate.
For simplicity each weed species was classified into its functional group (perennial forb, annual forb, or perennial grass), which was then further categorized by quadrat and year. The code for each variable is constructed as "functional group.quadrat.year". For example, a variable labeled PFORBS.Q2.2011 represents the percent cover of perennial forbs in the 2nd quadrat averaged out over the year 2011. Labels of "ALL" means either total vegetation cover of all functional groups or average vegetation cover of all quadrats depending on where it appears in the variable code. Similarly a label of "BOTH" in the 'year' spot means the data was averaged over 2011 and 2012. See Fig 7.
For simplicity each weed species was classified into its functional group (perennial forb, annual forb, or perennial grass), which was then further categorized by quadrat and year. The code for each variable is constructed as "functional group.quadrat.year". For example, a variable labeled PFORBS.Q2.2011 represents the percent cover of perennial forbs in the 2nd quadrat averaged out over the year 2011. Labels of "ALL" means either total vegetation cover of all functional groups or average vegetation cover of all quadrats depending on where it appears in the variable code. Similarly a label of "BOTH" in the 'year' spot means the data was averaged over 2011 and 2012. See Fig 7.
Vegetation control data
Fig 8. Tree growth by treatment
My second objective as written in the introduction page is to determine the efficacy of different vegetation control treatments. This involves a simple one-way ANOVA with initial stem volume as a continuous co-variate, site as a random factor, and stem volume growth as a continuous response variable. See Fig 8 for a sample of the data table.
This data was analyzed using Proc Mixed in SAS which can adjust for unequal variances - thus only normality of residual distribution is required. A histogram of the growth residuals for each treatment is presented below in Fig 9. Growth is the total stem volume growth over the two year study period. An approximate normal distribution was obtained for each treatment when the data was square-root transformed. Proc mixed is robust to moderate deviations from normality thus a squareroot transformation I believe is sufficient to continue with this test
This data was analyzed using Proc Mixed in SAS which can adjust for unequal variances - thus only normality of residual distribution is required. A histogram of the growth residuals for each treatment is presented below in Fig 9. Growth is the total stem volume growth over the two year study period. An approximate normal distribution was obtained for each treatment when the data was square-root transformed. Proc mixed is robust to moderate deviations from normality thus a squareroot transformation I believe is sufficient to continue with this test
(Sqrt) growth residuals of stem volume
Fig 9. square-root transformed residuals of tree growth data by treatment