Christian O. Marks
The Nature Conservancy
136 West Street, Suite 5
Northampton, Massachusetts
01060 USA
E-mail: [email protected]

Charles D. Canham
Cary Institute of Ecosystem Studies
Box AB
Millbrook, New York
12545 USA
E-mail: [email protected]

R code:

Density.r (MD5: f71c1a46140489f578396c94f68fe207)

Figure_8.r (MD5: 699b7bc5cbf555b7c083558a4bf7bfee)

Figure_9.r (MD5: c4a5563938c98b82b92495eb67bf32ea)

Growth.r (MD5: 267de400f01ff4e12943fbf41116fbec)

Species_demography.r (MD5: 8d8009f3e1d9a4c917e33c03cda8a429)

Species_trends.r (MD5: 2fb71dca4c5e0fcb891cda993a835039)

Survival.r (MD5: c2090386464c71d1bb5e1e85f50b5f43)

Data files:

BeavMortCoef.csv (MD5: 7978eaecf8967b8c58f78d58f90cb84d)

CT_River.csv (MD5: 09a3c66bf4dca32315e9b7d40aee7e83)

DensCoef.csv (MD5: c187547fcbad357bdfbc76797011c150)

EnvCoeffGrowth.csv (MD5: 4f7e2c875b3a3470057bd02f0dfb4a16)

EnvCoeffMort.csv (MD5: b1503351dcaaab1aef7a284bc1831f7c)

equilibrium.Rda (MD5: 5be113378d6286355e3daa91075911d5)

GrowthCoef.csv (MD5: 3808520fe98e40856380fde8a6301451)

MortCoef.csv (MD5: 4208690ff668d7712afd7f0b394a1bbc)

selfthinning.Rda (MD5: a8aff690c28c4913113dc52f38f78169)

Spplist.csv (MD5: 085ac7db4f98f7cb9f31629d132a1914)

tblSpecies.csv (MD5: 30b86d1a00d4e03dbfc03a02f9a3380c)

R code:

• Survival.r applies maximum likelihood methods to fitting models to survival data taking into account tree size and environmental variables. Models can be for data where survival can be defined as one minus all mortality or as one minus a particular type of mortality such as cutting by beavers. CT_River.csv is an example of input data. Note that maximum likelihood methods find a slightly different estimate of coefficients values each time they are run. This code requires the R package likelihood.
• Growth.r applies maximum likelihood methods to fitting models to growth data taking into account tree size and environmental variables. CT_River.csv is an example of input data. tblSpecies.csv and spplist.csv provide additional input data on individual species. Note that maximumlikelihood methods find a slightly different estimate of coefficients values each time they are run. This code requires the R package likelihood.
• Density.r applies maximum likelihood methods to fitting models to tree density data that has been binned by size (diameter). This r-script includes a function for binning the data by diameter. CT_River.csv is an example of input data. Note that maximum likelihood methods find a slightly different estimate of coefficients values each time they are run. This code requires the R package likelihood.
• Species_trends.r estimates the current population trends for different tree species at a common diameter as a basis for comparison that is not biased by species differences in size distribution. This script requires the fitted coefficients and models from Density.r, Growth.r and Survival.r. An example of inputs for this r-script includes GrowthCoef.csv, MortCoef.csv, and DensCoef.csv. Note that if users change not just the coefficients but also the functions used to model density, growth and mortality, then the functions for population trends will also need to be changed in this R code (see equations 2 in the associated Ecosphere article for needed functions and derivatives).
• Species_demography.r estimates and plots the current population trends and baseline morality rates as a function of tree size. This script requires the fitted coefficients and models from Density.r, Growth.r and Survival.r . An example of inputs for this r-script includes GrowthCoef.csv, MortCoef.csv, BeaverMortCoef.csv, and DensCoef.csv. Note that if users change not just the coefficients but also the functions used to model density, growth and mortality, then the functions for population trend and baseline mortality will also need to be changed in this R code (see equations 2 & 4 in the associated Ecosphere article for needed functions and derivatives).
• Figure_8.r computes and plots mortality and growth rates at a particular diameter for several species using the models fitted with Survival.r and Growth.r. Using the demographic models fitted with the data from all of the species combined, Figure_8.r also computes the estimated relationship between survival and growth that would be expected from stand self-thinning alone. It does so in the following two ways: assuming that tree size distribution changes as observed during the study as an upper bound; and by assuming that tree size distribution is not changing (i.e., structure is at equilibrium) as a lower bound. These equations for these two relationships for the floodplain example data are saved in the files selfthinning.Rda and equilibrium.Rda, respectively. Note that if users change not just the coefficients but also the functions used to model density, growth and mortality, then these equations will also need to be changed in this R code. An example of inputs for this r-script includes GrowthCoef.csv, MortCoef.csv, and DensCoef.csv. Note that if users change not just the coefficients but also the functions used to model density, growth and mortality, then the functions of the self-thinning driven relationship between growth and mortality will also need to be changed in this R code (see equation 3 in the associated Ecosphere article for needed functions and derivatives).
• Figure_9.r computes and plots mortality and growth rates at a particular diameter and particular values in an environmental variable. The coefficients for these model functions are in the data files EnvCoeffMort.csv, and EnvCoeffGrowth.csv and were computed by creating a modified version with Survival.r and Growth.r. Figure_9.r also plots the relationship between mortality and growth due to self-thinning using the relationships selfthinning.Rda and equilibrium.Rda which were computed with Figure_8.r.

Data files:

• BeavMortCoef.csv lists the maximum likelihood estimates for beaver-caused, decay-caused, liana-caused, and storm-caused mortality rates of different tree species followed by low and high support intervals. These estimates were calculated using Survival.r with the floodplain tree example data.
• CT_River.csv is a table of the demographic data collected on Connecticut River floodplain forests (see associated article). These data include columns for tree number, tree species, dates for first and second date tree was measured (i.e., dates to calculate census interval), diameters during these visits (cm), Bins of size classes (to compute tree size distribution), diameter growth rate (cm/year), different types of mortality (where TRUE = tree died, FALSE = tree survived), and four environmental variables associated with the tree’s location. Exceedance is the exceedance probability flow that floods the location (in %), or the percent of time that the location is flooded. PH is the soil pH. GDD0C is the annual total number of growing degree days calculated with a base of 0°C. ANNUALMIN is the annual average of the daily minimum temperatures (°C). Note that mortality includes trees that are still alive but fell to the ground because we were interested in calculating the rates at which trees were destroyed by storms and vines.
• DensCoef.csv lists the type of function used to model the tree density distribution and maximum likelihood estimates for associated coefficients followed by low and high support intervals. These estimates for individual species and for all species combined were calculated using Density.r with the floodplain tree example data.
• EnvCoeffGrowth.csv lists the maximum likelihood estimates for coefficients used to model survival of trees as functions of environmental factors. For each coefficient, the low and high support intervals are also listed. These estimates were calculated using a modified version of Growth.r with the floodplain tree example data.
• EnvCoeffMort.csv lists the maximum likelihood estimates for coefficients used to model survival of trees as exponential functions of environmental factors. For each coefficient, the low and high support intervals are also listed. These estimates were calculated using a modified version of Survival.r with the floodplain tree example data.
• equilibrium.Rda is an R data file that contains the equation for the upper bound estimate of the self-thinning driven relationship between growth and mortality that was computed with Figure_8.r.
• GrowthCoef.csv lists the maximum likelihood estimates for the 2 coefficients in the power function used to model size-dependent growth rate in different tree species and for all tree data combined. For each coefficient, the low and high support intervals are also listed. These estimates were calculated using Growth.r with the floodplain tree example data.
• MortCoef.csv lists the maximum likelihood estimates for the 4 coefficients in the double exponential equation used to model survival in different tree species and for all tree data combined. For each coefficient, the low and high support intervals are also listed. These estimates were calculated using Survival.r with the floodplain tree example data. N is the number of trees used to calculate the estimate.
• selfthinning.Rda is an R data file that contains the equation for the lower bound estimate of the self-thinning driven relationship between growth and mortality that was computed with Figure_8.r.
• spplist.csv lists the maximum diameter and number of individuals in each species in the example floodplain forest data set (CT_River.csv).For most species this is the largest diameter encountered but for a few species this maximum diameter was set manually to avoid the largest diameters where lower replication results in excessively wide support intervals (see methods in associated Ecosphere article).
• tblSpecies.csv is a table of species names and acronyms.