Philippa Kaur

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Forest Inventory dataTree growth, tree survival, and plot-level basal area data were compiled from the Forest Inventory and Analysis (FIA) program database (accessed on January 24, 2017, FIA phase 2 manual version 6.1; http://www.fia.fs.fed.us/). Aboveground tree biomass was estimated from tree diameter measurements44 and then multiplied by 0.5 to estimate aboveground C. Tree growth rates were calculated from the difference in estimated aboveground C between the latest and first live measurement of every tree and divided by the elapsed time between measurements to the day. Tree species that had at least 2000 individual trees after the data filters were applied were retained for further growth and survival evaluation. The probability of tree survival was calculated using the first measurement to the last measurement of a plot. Trees that were alive at both measurements were assigned a value of 1 (survived) and trees alive at the first and dead at the last measurement were assigned a value of 0 (dead). The duration between the first and last measurement was used to determine the annual probability of tree survival. Trees that were recorded as dead at both measurement inventories and trees that were harvested were excluded from the survival analysis.Predictor data: Climate, deposition, size, and competitionThere were six predictors that were related to the response rate of growth or survival for each individual tree: mean annual temperature, mean annual precipitation, mean annual total nitrogen deposition, mean annual total S deposition, tree size, and plot-level competition.To obtain total N and S deposition rates for each tree, we used spatially modeled N and S deposition data from the National Atmospheric Deposition Program’s Total Deposition Science Committee32. Annual N and S deposition rates were then averaged from the first year of measurement to the last year of measurement for every tree so that each tree had an individualized average N deposition based on the remeasurement years, and each species had an individualized range of average N deposition exposure based on its distribution. Monthly mean temperature and precipitation values were obtained in a gridded (4 x 4 km) format from the PRISM Climate Group at Oregon State45 for the contiguous US and averaged between measurement periods for each tree in a similar manner. Tree size was represented by estimated aboveground tree C (previously described). Because the climate and deposition predictors were tailored to each plot, the years assessed varied by plot, but spanned 2000–2016. Thus, the results from the earlier study6 used conditions from the 1980–1990s, whereas the results from this study used more recent environmental and stand conditions. Tree competition was represented by a combination two factors: (1) plot basal area and (2) the basal area of trees larger than the focal tree being modeled. How all six variables were statistically modeled is discussed below.Modeling tree growth and survivalWe developed in ref. 20 multiple models to predict tree growth (G; kg C year−1) and survival (P(s); annual probability of survival). Our growth model (Eq. 1 and 2) assumes that there is a potential maximum growth rate (a) that is modified by up to six predictors in our study (which are multipliers from 0 to 1): temperature (T), precipitation (P), N deposition (N), S deposition (S), tree size (m), and competition. The potential full growth model included all six terms (Eq. 1 for the general form and Eq. 2 for the specific form). The size effect was modeled as a power function (z) based on the aboveground biomass (m). N deposition may affect the allometric relationships between tree diameter and aboveground tree biomass46, but these relationships are not yet accounted for in U.S. inventories44. Competition between trees was modeled as a function of plot basal area (BA) and the basal area of trees larger than that of the tree of interest (BAL) similar to the methods of47. The environmental factors (N deposition, S deposition, temperature, precipitation) were modeled as two-term lognormal functions (e.g., t1 and t2 for temperature effects, n1 and n2 for nitrogen deposition effects). The two-term lognormal functions allowed for flexibility in both the location of the peak (determined by t1 for temperature, for example), and the steepness of the curve (determined by t2 for temperature, for example). Thus, the full growth model is presented in Eq. 2.$$G=potentialgrowthratetimes competitiontimes temperaturetimes precipitationtimes {S}_{dep}times {N}_{dep}$$
(1)
$$G=a* {m}^{z}* {e}^{({c}_{1}* BAL+{c}_{2}* {{{{mathrm{ln}}}}}(BA))}* {e}^{-0.5* {left(frac{ln(T/{t}_{1})}{{t}_{2}}right)}^{2}}* {e}^{-0.5* {left(frac{ln(P/{p}_{1})}{{p}_{2}}right)}^{2}}* {e}^{-0.5* {left(frac{ln(N/{n}_{1})}{{n}_{2}}right)}^{2}}* {e}^{-0.5* {left(frac{ln(S/{s}_{1})}{{s}_{2}}right)}^{2}}$$
(2)
We examined a total of five different growth models: (1) a full model with the size, competition, climate, S deposition, and N deposition terms (Eq. 2); (2) a model with all terms except the N deposition term; (3) a model with all terms except the S deposition term; (4) a model with all terms but without S and N deposition terms; and (5) a null model that estimated a single parameter for the mean growth parameter (a in Eq. 2).The annual probability of survival (P(s)) was estimated similarly as for growth, except that the probability was a function of time and we explored two different representations for competition. The general form of the model is shown in Eq. 3, and the full survival model in Eqs. 4, 5 for the two competition forms.$$P(s)={[acdot {{{{{rm{size}}}}}}times competitiontimes temperaturetimes precipitationtimes {N}_{dep}times {S}_{dep}]}^{time}$$
(3)
$$P(s)= {left[a* [((1-z{c}_{1}{e}^{-z{c}_{2}* m})* {e}^{-z{c}_{3}* {m}^{z{c}_{4}}})({e}^{-b{r}_{1}* B{A}_{ratio}{,}^{br2}* B{A}^{b{r}_{3}}})]vphantom{{left.* {e}^{-0.5* {left(frac{ln(T/{t}_{1})}{{t}_{2}}right)}^{2}}* {e}^{-0.5* {left(frac{ln(P/{p}_{1})}{{p}_{2}}right)}^{2}}* {e}^{-0.5* {left(frac{ln(N/{n}_{1})}{{n}_{2}}right)}^{2}}* {e}^{-0.5* {left(frac{ln(S/{s}_{1})}{{s}_{2}}right)}^{2}}right]}}^{time}right.}\ {left.* {e}^{-0.5* {left(frac{ln(T/{t}_{1})}{{t}_{2}}right)}^{2}}* {e}^{-0.5* {left(frac{ln(P/{p}_{1})}{{p}_{2}}right)}^{2}}* {e}^{-0.5* {left(frac{ln(N/{n}_{1})}{{n}_{2}}right)}^{2}}* {e}^{-0.5* {left(frac{ln(S/{s}_{1})}{{s}_{2}}right)}^{2}}right]}^{time}$$
(4)
$$P(s)= {left[a* left({e}^{-0.5* {left(frac{ln(m/{m}_{1})}{{m}_{2}}right)}^{2}* -0.5* {left(frac{ln(BA/b{a}_{1})}{b{a}_{2}}right)}^{2}* -0.5* {left(frac{ln(BAL+1/b{l}_{1}+1)}{b{l}_{2}}right)}^{2}}right)vphantom{{left.* {e}^{-0.5* {left(frac{ln(T/{t}_{1})}{{t}_{2}}right)}^{2}}* {e}^{-0.5* {left(frac{ln(P/{p}_{1})}{{p}_{2}}right)}^{2}}* {e}^{-0.5* {left(frac{ln(N/{n}_{1})}{{n}_{2}}right)}^{2}}* {e}^{-0.5* {left(frac{ln(S/{s}_{1})}{{s}_{2}}right)}^{2}}right]}^{time}}right.}\ {left.* {e}^{-0.5* {left(frac{ln(T/{t}_{1})}{{t}_{2}}right)}^{2}}* {e}^{-0.5* {left(frac{ln(P/{p}_{1})}{{p}_{2}}right)}^{2}}* {e}^{-0.5* {left(frac{ln(N/{n}_{1})}{{n}_{2}}right)}^{2}}* {e}^{-0.5* {left(frac{ln(S/{s}_{1})}{{s}_{2}}right)}^{2}}right]}^{time}$$
(5)
A total of nine survival models were examined: four using the formulation for size and competition in Eq. 4 (with the same combinations of predictors as above for growth), four using formulation for size and competition in Eq. 5, and a null survival model in which a mean annual estimate of survival (a) was raised to the exponent of the elapsed time.Parameters for each of the growth and survival models above were fit for a given species using maximum likelihood estimates through simulated annealing with 100,000 iterations via the likelihood package (v2.1.1) in Program R. Akaike’s Information Criteria (AIC) was estimated for all models. The best model was the model with the lowest AIC, and statistically indistinguishable models are those with a delta AIC  More

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