The contribution of a given flux (recruitment, growth or mortality) at time \(t\) can be written as:
\[CF_{F,t} = \sum_{i\in F_t}\frac{ba_{i,t} (ft_{i} - CWM_{t-1})}{BA_{t}}-\sum_{i\in F_t}\frac{ba_{i,t-1} (ft_{i} - CWM_{t-1})}{BA_{t-1}}\] where \(F_t\) is the set of trees contributing to a given flux between \(t-1\) and \(t\) (recruitment: trees recruited at \(t\); growth: trees that were measured and alive at \(t\) and \(t-1\); mortality: trees that died between \(t-1\) and \(t\)).
\(ba_{i,t}\) is the basal area of a tree \(i\) at time \(t\); \(ft_{i}\) is the functional trait value of tree \(i\); \(BA_t\) is the basal area of the entire community at \(t\); \(CWM_t\) is the community weighted mean trait value at \(t\).
We subtract \(CWM_{t-1}\) to have negative contributions when the flux decreases the CWM between \(t-1\) and \(t\); and positive contributions that increase the \(CWM\).
As written, the contributions are additive:
\[CWM_t= CWM_{t-1} + CF_{G,t} + CF_{R,t}+CF_{M,t}\]
plot_info <- read.csv("data/raw_data/bioforest-plot-information.csv") |>
select(site, plot, Year_of_harvest, Treatment)
data <- read.csv("data/derived_data/aggregated_data_v9.csv") |>
mutate(plot_new = Plot) |>
separate(Plot, "Plot", "_") |>
left_join(plot_info, by = join_by(Site == site, Plot == plot)) |>
filter(grepl("cwmdiff", variable)) |>
separate(variable, c("trait", NA, "flux"), sep = "_")
