The goal of mappestRisk package is to facilitate the transition from development data of pests obtained in lab-controlled conditions to understandable forecasts assessing risk of pest occurrence in a given region.
For that purpose, mappestRisk is built upon previous efforts such as
devRate (Rebaudo, Struelens, and Dangles 2018), rTPC and
nls.multstart packages (Padfield, O’Sullivan, and Pawar 2021) and a
methodology for predicting climatic suitability based on fundamental
thermal niche as estimated by mechanistic, process-based approaches
suggested in Taylor et al. (2019) . Therefore, mappestRisk has three
different modules: (1) model fitting & selection using a set of the
most widely used equations describing developmental responses to
temperature under the nls.multstart (Padfield and Matheson 2020) and
nlme (Pinheiro, Bates 2022) frameworks, with visualization of model
fitting to help model selection by the user; (2) thermal traits
extraction: including selection of the suitability threshold guiding
the forecast (i.e. obtaining the temperatures at which estimated
performance lies upon a performance higher threshold percentage); and
(3) climatic data extraction & visualization with either exportable
rasters or interactive maps with leaflet (Cheng, Karambelkar, and Xie
2022).
# install.packages("devtools")
# devtools::install_github("EcologyR/mappestRisk")
#or alternatively
# remotes::install_github("EcologyR/mappestRisk")
#and load the package
#library(mappestRisk)
devtools::load_all() #for now, provisionally
#> ℹ Loading mappestRisk
#> The legacy packages maptools, rgdal, and rgeos, underpinning this package
#> will retire shortly. Please refer to R-spatial evolution reports on
#> https://r-spatial.org/r/2023/05/15/evolution4.html for details.
#> This package is now running under evolution status 0
#> Warning: package 'testthat' was built under R version 4.2.2
#> Warning: Objects listed as exports, but not present in namespace:
#> • sim_tpcs_uncertainty
library(ggplot2)
#> Warning: package 'ggplot2' was built under R version 4.2.3
library(dplyr)
#> Warning: package 'dplyr' was built under R version 4.2.3
#>
#> Attaching package: 'dplyr'
#>
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#> filter, lag
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#> intersect, setdiff, setequal, union
library(nls.multstart)
#> Warning: package 'nls.multstart' was built under R version 4.2.3
library(rTPC)
#> Warning: package 'rTPC' was built under R version 4.2.3
library(devRate)
#> Warning: package 'devRate' was built under R version 4.2.3
library(tidyr)
#> Warning: package 'tidyr' was built under R version 4.2.3
#>
#> Attaching package: 'tidyr'
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library(purrr)
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#> Attaching package: 'purrr'
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#> is_nullIf you want to clone or fork the repository or open and read some issues, you can find the code here.
In this example, we’ll show how to fit one to several thermal
performance curves to a data set of development rate variation across
temperatures1. The following code provides an example as given in
fit_devmodels() function documentation, with a data table showing the
output of fitted models.
data("b.schwartzi_satar2002")
fitted_tpcs_aphid <- fit_devmodels(temp = b.schwartzi_satar2002$temperature,
dev_rate = b.schwartzi_satar2002$rate_value,
model_name = "all")
print(fitted_tpcs_aphid)
#> # A tibble: 68 × 8
#> param_name start_vals param_est param_se model_name model_AIC model_BIC
#> <chr> <dbl> <dbl> <dbl> <chr> <dbl> <dbl>
#> 1 a 0.145 0.143 0.00629 beta -43.0 -43.3
#> 2 b 25 26.7 1.10 beta -43.0 -43.3
#> 3 c 25 202. 13601. beta -43.0 -43.3
#> 4 d 2 100 12049. beta -43.0 -43.3
#> 5 e 2 32.6 2283. beta -43.0 -43.3
#> 6 rmax 0.145 0.143 0.00649 boatman -42.4 -42.7
#> 7 tmin 15 0 102. boatman -42.4 -42.7
#> 8 tmax 32.5 43.3 62.7 boatman -42.4 -42.7
#> 9 a 1.1 1.45 1.03 boatman -42.4 -42.7
#> 10 b 0.4 2.35 18.7 boatman -42.4 -42.7
#> # ℹ 58 more rows
#> # ℹ 1 more variable: model_fit <list>To help select which model might be more appropriate, the function
plot_devmodels() draws the predicted TPCs for each
adequately-converged model. This step aims to improve model selection
based not only on statistical criteria (i.e. AIC and number of
parameters) but also on ecological realism, since curves can be
graphically checked to select realistic shapes and thermal traits
–vertical cuts with x-axis such as
plot_devmodels(temp = b.schwartzi_satar2002$temperature,
dev_rate = b.schwartzi_satar2002$rate_value,
fitted_parameters = fitted_tpcs_aphid,
species = "Brachycaudus schwartzi",
life_stage = "Nymphs")
After careful examination of fitted TPCs in plot_devmodels(), the
predictions of the selected models must be allocated in a data.frame
in order to continue the package workflow towards climatic projection
for pest risk analysis. Additionally, we recommend here to propagate
uncertainty in parameter estimation of the fitted and selected TPC
models using bootstrap procedures following vignettes in Padfield,
O’Sullivan, and Pawar (2021). This can be done with the function
predict_curves() by setting the argument propagate_uncertainty to be
TRUE and by providing a number of bootstrap sampling iterations in the
argument n_boots_samples.
This function requires some time to compute bootstraps and predictions
of the multiple TPCs it generates. Hence, it is important to use only
one or few TPC models in the argument model_name_2boot based on visual
examination from plot_devmodels() with reasonable selection. We
discourage to bootstrap all TPC models for computational and time
consuming reasons.
In our example, we choose three models that performed similarly and,
unlike others with similar or even higher AICs, had a markedly higher
left-skewness, e.g., briere2, thomas and lactin2. After a few
minutes, we obtain the data.frame:
library(boot)
library(car)
#> Loading required package: carData
#>
#> Attaching package: 'car'
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#> recode
preds_boots_aphid <-predict_curves(temp = b.schwartzi_satar2002$temperature,
dev_rate = b.schwartzi_satar2002$rate_value,
fitted_parameters = fitted_tpcs_aphid,
model_name_2boot = c("briere2",
"thomas",
"lactin2"),
propagate_uncertainty = TRUE,
n_boots_samples = 100)
#> [1] "Predicting bootstrapped TPCs 0.1 %"
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#> [1] "Predicting bootstrapped TPCs 21.7 %"
#> [1] "Predicting bootstrapped TPCs 21.8 %"
#> [1] "Predicting bootstrapped TPCs 21.8 %"
#> [1] "Predicting bootstrapped TPCs 21.9 %"
#> [1] "Predicting bootstrapped TPCs 22 %"
#> [1] "Predicting bootstrapped TPCs 22.1 %"
#> [1] "Predicting bootstrapped TPCs 22.1 %"
#> [1] "Predicting bootstrapped TPCs 22.2 %"
#> [1] "Predicting bootstrapped TPCs 22.3 %"
#> [1] "Predicting bootstrapped TPCs 22.4 %"
#> [1] "Predicting bootstrapped TPCs 22.4 %"
#> [1] "Predicting bootstrapped TPCs 22.5 %"
#> [1] "Predicting bootstrapped TPCs 22.6 %"
#> [1] "Predicting bootstrapped TPCs 22.7 %"
#> [1] "Predicting bootstrapped TPCs 22.8 %"
#> [1] "Predicting bootstrapped TPCs 22.8 %"
#> [1] "Predicting bootstrapped TPCs 22.9 %"
#> [1] "Predicting bootstrapped TPCs 23 %"
#> [1] "Predicting bootstrapped TPCs 23.1 %"
#> [1] "Predicting bootstrapped TPCs 23.1 %"
#> [1] "Predicting bootstrapped TPCs 23.2 %"
#> [1] "Predicting bootstrapped TPCs 23.3 %"
#> [1] "Predicting bootstrapped TPCs 23.4 %"
#> [1] "Predicting bootstrapped TPCs 23.4 %"
#> [1] "Predicting bootstrapped TPCs 23.5 %"
#> [1] "Predicting bootstrapped TPCs 23.6 %"
#> [1] "Predicting bootstrapped TPCs 23.7 %"
#> [1] "Predicting bootstrapped TPCs 23.7 %"
#> [1] "Predicting bootstrapped TPCs 23.8 %"
#> [1] "Predicting bootstrapped TPCs 23.9 %"
#> [1] "Predicting bootstrapped TPCs 24 %"
#> [1] "Predicting bootstrapped TPCs 24 %"
#> [1] "Predicting bootstrapped TPCs 24.1 %"
#> [1] "Predicting bootstrapped TPCs 24.2 %"
#> [1] "Predicting bootstrapped TPCs 24.3 %"
#> [1] "Predicting bootstrapped TPCs 24.3 %"
#> [1] "Predicting bootstrapped TPCs 24.4 %"
#> [1] "Predicting bootstrapped TPCs 24.5 %"
#> [1] "Predicting bootstrapped TPCs 24.6 %"
#> [1] "Predicting bootstrapped TPCs 24.6 %"
#> [1] "Predicting bootstrapped TPCs 24.7 %"
#> [1] "Predicting bootstrapped TPCs 24.8 %"
#> [1] "Predicting bootstrapped TPCs 24.9 %"
#> [1] "Predicting bootstrapped TPCs 24.9 %"
#> [1] "Predicting bootstrapped TPCs 25 %"
#> [1] "Predicting bootstrapped TPCs 25.1 %"
#> [1] "Predicting bootstrapped TPCs 25.2 %"
#> [1] "Predicting bootstrapped TPCs 25.2 %"
#> [1] "Predicting bootstrapped TPCs 25.3 %"
#> [1] "Predicting bootstrapped TPCs 25.4 %"
#> [1] "Predicting bootstrapped TPCs 25.5 %"
#> [1] "Predicting bootstrapped TPCs 25.5 %"
#> [1] "Predicting bootstrapped TPCs 25.6 %"
#> [1] "Predicting bootstrapped TPCs 25.7 %"
#> [1] "Predicting bootstrapped TPCs 25.8 %"
#> [1] "Predicting bootstrapped TPCs 25.9 %"
#> [1] "Predicting bootstrapped TPCs 25.9 %"
#> [1] "Predicting bootstrapped TPCs 26 %"
#> [1] "Predicting bootstrapped TPCs 26.1 %"
#> [1] "Predicting bootstrapped TPCs 26.2 %"
#> [1] "Predicting bootstrapped TPCs 26.2 %"
#> [1] "Predicting bootstrapped TPCs 26.3 %"
#> [1] "Predicting bootstrapped TPCs 26.4 %"
#> [1] "Predicting bootstrapped TPCs 26.5 %"
#> [1] "Predicting bootstrapped TPCs 26.5 %"
#> [1] "Predicting bootstrapped TPCs 26.6 %"
#> [1] "Predicting bootstrapped TPCs 26.7 %"
#> [1] "Predicting bootstrapped TPCs 26.8 %"
#> [1] "Predicting bootstrapped TPCs 26.8 %"
#> [1] "Predicting bootstrapped TPCs 26.9 %"
#> [1] "Predicting bootstrapped TPCs 27 %"
#> [1] "Predicting bootstrapped TPCs 27.1 %"
#> [1] "Predicting bootstrapped TPCs 27.1 %"
#> [1] "Predicting bootstrapped TPCs 27.2 %"
#> [1] "Predicting bootstrapped TPCs 27.3 %"
#> [1] "Predicting bootstrapped TPCs 27.4 %"
#> [1] "Predicting bootstrapped TPCs 27.4 %"
#> [1] "Predicting bootstrapped TPCs 27.5 %"
#> [1] "Predicting bootstrapped TPCs 27.6 %"
#> [1] "Predicting bootstrapped TPCs 27.7 %"
#> [1] "Predicting bootstrapped TPCs 27.7 %"
#> [1] "Predicting bootstrapped TPCs 27.8 %"
#> [1] "Predicting bootstrapped TPCs 27.9 %"
#> [1] "Predicting bootstrapped TPCs 28 %"
#> [1] "Predicting bootstrapped TPCs 28 %"
#> [1] "Predicting bootstrapped TPCs 28.1 %"
#> [1] "Predicting bootstrapped TPCs 28.2 %"
#> [1] "Predicting bootstrapped TPCs 28.3 %"
#> [1] "Predicting bootstrapped TPCs 28.3 %"
#> [1] "Predicting bootstrapped TPCs 28.4 %"
#> [1] "Predicting bootstrapped TPCs 28.5 %"
#> [1] "Predicting bootstrapped TPCs 28.6 %"
#> [1] "Predicting bootstrapped TPCs 28.6 %"
#> [1] "Predicting bootstrapped TPCs 28.7 %"
#> [1] "Predicting bootstrapped TPCs 28.8 %"
#> [1] "Predicting bootstrapped TPCs 28.9 %"
#> [1] "Predicting bootstrapped TPCs 28.9 %"
#> [1] "Predicting bootstrapped TPCs 29 %"
#> [1] "Predicting bootstrapped TPCs 29.1 %"
#> [1] "Predicting bootstrapped TPCs 29.2 %"
#> [1] "Predicting bootstrapped TPCs 29.3 %"
#> [1] "Predicting bootstrapped TPCs 29.3 %"
#> [1] "Predicting bootstrapped TPCs 29.4 %"
#> [1] "Predicting bootstrapped TPCs 29.5 %"
#> [1] "Predicting bootstrapped TPCs 29.6 %"
#> [1] "Predicting bootstrapped TPCs 29.6 %"
#> [1] "Predicting bootstrapped TPCs 29.7 %"
#> [1] "Predicting bootstrapped TPCs 29.8 %"
#> [1] "Predicting bootstrapped TPCs 29.9 %"
#> [1] "Predicting bootstrapped TPCs 29.9 %"
#> [1] "Predicting bootstrapped TPCs 30 %"
#> [1] "Predicting bootstrapped TPCs 30.1 %"
#> [1] "Predicting bootstrapped TPCs 30.2 %"
#> [1] "Predicting bootstrapped TPCs 30.2 %"
#> [1] "Predicting bootstrapped TPCs 30.3 %"
#> [1] "Predicting bootstrapped TPCs 30.4 %"
#> [1] "Predicting bootstrapped TPCs 30.5 %"
#> [1] "Predicting bootstrapped TPCs 30.5 %"
#> [1] "Predicting bootstrapped TPCs 30.6 %"
#> [1] "Predicting bootstrapped TPCs 30.7 %"
#> [1] "Predicting bootstrapped TPCs 30.8 %"
#> [1] "Predicting bootstrapped TPCs 30.8 %"
#> [1] "Predicting bootstrapped TPCs 30.9 %"
#> [1] "Predicting bootstrapped TPCs 31 %"
#> [1] "Predicting bootstrapped TPCs 31.1 %"
#> [1] "Predicting bootstrapped TPCs 31.1 %"
#> [1] "Predicting bootstrapped TPCs 31.2 %"
#> [1] "Predicting bootstrapped TPCs 31.3 %"
#> [1] "Predicting bootstrapped TPCs 31.4 %"
#> [1] "Predicting bootstrapped TPCs 31.4 %"
#> [1] "Predicting bootstrapped TPCs 31.5 %"
#> [1] "Predicting bootstrapped TPCs 31.6 %"
#> [1] "Predicting bootstrapped TPCs 31.7 %"
#> [1] "Predicting bootstrapped TPCs 31.7 %"
#> [1] "Predicting bootstrapped TPCs 31.8 %"
#> [1] "Predicting bootstrapped TPCs 31.9 %"
#> [1] "Predicting bootstrapped TPCs 32 %"
#> [1] "Predicting bootstrapped TPCs 32 %"
#> [1] "Predicting bootstrapped TPCs 32.1 %"
#> [1] "Predicting bootstrapped TPCs 32.2 %"
#> [1] "Predicting bootstrapped TPCs 32.3 %"
#> [1] "Predicting bootstrapped TPCs 32.4 %"
#> [1] "Predicting bootstrapped TPCs 32.4 %"
#> [1] "Predicting bootstrapped TPCs 32.5 %"
#> [1] "Predicting bootstrapped TPCs 32.6 %"
#> [1] "Predicting bootstrapped TPCs 32.7 %"
#> [1] "Predicting bootstrapped TPCs 32.7 %"
#> [1] "Predicting bootstrapped TPCs 32.8 %"
#> [1] "Predicting bootstrapped TPCs 32.9 %"
#> [1] "Predicting bootstrapped TPCs 33 %"
#> [1] "Predicting bootstrapped TPCs 33 %"
#> [1] "Predicting bootstrapped TPCs 33.1 %"
#> [1] "Predicting bootstrapped TPCs 33.2 %"
#> [1] "Predicting bootstrapped TPCs 33.3 %"
#> [1] "Predicting bootstrapped TPCs 33.3 %"
#> [1] "Predicting bootstrapped TPCs 33.4 %"
#> [1] "Predicting bootstrapped TPCs 33.5 %"
#> [1] "Predicting bootstrapped TPCs 33.6 %"
#> [1] "Predicting bootstrapped TPCs 33.6 %"
#> [1] "Predicting bootstrapped TPCs 33.7 %"
#> [1] "Predicting bootstrapped TPCs 33.8 %"
#> [1] "Predicting bootstrapped TPCs 33.9 %"
#> [1] "Predicting bootstrapped TPCs 33.9 %"
#> [1] "Predicting bootstrapped TPCs 34 %"
#> [1] "Predicting bootstrapped TPCs 34.1 %"
#> [1] "Predicting bootstrapped TPCs 34.2 %"
#> [1] "Predicting bootstrapped TPCs 34.2 %"
#> [1] "Predicting bootstrapped TPCs 34.3 %"
#> [1] "Predicting bootstrapped TPCs 34.4 %"
#> [1] "Predicting bootstrapped TPCs 34.5 %"
#> [1] "Predicting bootstrapped TPCs 34.5 %"
#> [1] "Predicting bootstrapped TPCs 34.6 %"
#> [1] "Predicting bootstrapped TPCs 34.7 %"
#> [1] "Predicting bootstrapped TPCs 34.8 %"
#> [1] "Predicting bootstrapped TPCs 34.8 %"
#> [1] "Predicting bootstrapped TPCs 34.9 %"
#> [1] "Predicting bootstrapped TPCs 35 %"
#> [1] "Predicting bootstrapped TPCs 35.1 %"
#> [1] "Predicting bootstrapped TPCs 35.1 %"
#> [1] "Predicting bootstrapped TPCs 35.2 %"
#> [1] "Predicting bootstrapped TPCs 35.3 %"
#> [1] "Predicting bootstrapped TPCs 35.4 %"
#> [1] "Predicting bootstrapped TPCs 35.4 %"
#> [1] "Predicting bootstrapped TPCs 35.5 %"
#> [1] "Predicting bootstrapped TPCs 35.6 %"
#> [1] "Predicting bootstrapped TPCs 35.7 %"
#> [1] "Predicting bootstrapped TPCs 35.8 %"
#> [1] "Predicting bootstrapped TPCs 35.8 %"
#> [1] "Predicting bootstrapped TPCs 35.9 %"
#> [1] "Predicting bootstrapped TPCs 36 %"
#> [1] "Predicting bootstrapped TPCs 36.1 %"
#> [1] "Predicting bootstrapped TPCs 36.1 %"
#> [1] "Predicting bootstrapped TPCs 36.2 %"
#> [1] "Predicting bootstrapped TPCs 36.3 %"
#> [1] "Predicting bootstrapped TPCs 36.4 %"
#> [1] "Predicting bootstrapped TPCs 36.4 %"
#> [1] "Predicting bootstrapped TPCs 36.5 %"
#> [1] "Predicting bootstrapped TPCs 36.6 %"
#> [1] "Predicting bootstrapped TPCs 36.7 %"
#> [1] "Predicting bootstrapped TPCs 36.7 %"
#> [1] "Predicting bootstrapped TPCs 36.8 %"
#> [1] "Predicting bootstrapped TPCs 36.9 %"
#> [1] "Predicting bootstrapped TPCs 37 %"
#> [1] "Predicting bootstrapped TPCs 37 %"
#> [1] "Predicting bootstrapped TPCs 37.1 %"
#> [1] "Predicting bootstrapped TPCs 37.2 %"
#> [1] "Predicting bootstrapped TPCs 37.3 %"
#> [1] "Predicting bootstrapped TPCs 37.3 %"
#> [1] "Predicting bootstrapped TPCs 37.4 %"
#> [1] "Predicting bootstrapped TPCs 37.5 %"
#> [1] "Predicting bootstrapped TPCs 37.6 %"
#> [1] "Predicting bootstrapped TPCs 37.6 %"
#> [1] "Predicting bootstrapped TPCs 37.7 %"
#> [1] "Predicting bootstrapped TPCs 37.8 %"
#> [1] "Predicting bootstrapped TPCs 37.9 %"
#> [1] "Predicting bootstrapped TPCs 37.9 %"
#> [1] "Predicting bootstrapped TPCs 38 %"
#> [1] "Predicting bootstrapped TPCs 38.1 %"
#> [1] "Predicting bootstrapped TPCs 38.2 %"
#> [1] "Predicting bootstrapped TPCs 38.2 %"
#> [1] "Predicting bootstrapped TPCs 38.3 %"
#> [1] "Predicting bootstrapped TPCs 38.4 %"
#> [1] "Predicting bootstrapped TPCs 38.5 %"
#> [1] "Predicting bootstrapped TPCs 38.5 %"
#> [1] "Predicting bootstrapped TPCs 38.6 %"
#> [1] "Predicting bootstrapped TPCs 38.7 %"
#> [1] "Predicting bootstrapped TPCs 38.8 %"
#> [1] "Predicting bootstrapped TPCs 38.9 %"
#> [1] "Predicting bootstrapped TPCs 38.9 %"
#> [1] "Predicting bootstrapped TPCs 39 %"
#> [1] "Predicting bootstrapped TPCs 39.1 %"
#> [1] "Predicting bootstrapped TPCs 39.2 %"
#> [1] "Predicting bootstrapped TPCs 39.2 %"
#> [1] "Predicting bootstrapped TPCs 39.3 %"
#> [1] "Predicting bootstrapped TPCs 39.4 %"
#> [1] "Predicting bootstrapped TPCs 39.5 %"
#> [1] "Predicting bootstrapped TPCs 39.5 %"
#> [1] "Predicting bootstrapped TPCs 39.6 %"
#> [1] "Predicting bootstrapped TPCs 39.7 %"
#> [1] "Predicting bootstrapped TPCs 39.8 %"
#> [1] "Predicting bootstrapped TPCs 39.8 %"
#> [1] "Predicting bootstrapped TPCs 39.9 %"
#> [1] "Predicting bootstrapped TPCs 40 %"
#> [1] "Predicting bootstrapped TPCs 40.1 %"
#> [1] "Predicting bootstrapped TPCs 40.1 %"
#> [1] "Predicting bootstrapped TPCs 40.2 %"
#> [1] "Predicting bootstrapped TPCs 40.3 %"
#> [1] "Predicting bootstrapped TPCs 40.4 %"
#> [1] "Predicting bootstrapped TPCs 40.4 %"
#> [1] "Predicting bootstrapped TPCs 40.5 %"
#> [1] "Predicting bootstrapped TPCs 40.6 %"
#> [1] "Predicting bootstrapped TPCs 40.7 %"
#> [1] "Predicting bootstrapped TPCs 40.7 %"
#> [1] "Predicting bootstrapped TPCs 40.8 %"
#> [1] "Predicting bootstrapped TPCs 40.9 %"
#> [1] "Predicting bootstrapped TPCs 41 %"
#> [1] "Predicting bootstrapped TPCs 41 %"
#> [1] "Predicting bootstrapped TPCs 41.1 %"
#> [1] "Predicting bootstrapped TPCs 41.2 %"
#> [1] "Predicting bootstrapped TPCs 41.3 %"
#> [1] "Predicting bootstrapped TPCs 41.3 %"
#> [1] "Predicting bootstrapped TPCs 41.4 %"
#> [1] "Predicting bootstrapped TPCs 41.5 %"
#> [1] "Predicting bootstrapped TPCs 41.6 %"
#> [1] "Predicting bootstrapped TPCs 41.6 %"
#> [1] "Predicting bootstrapped TPCs 41.7 %"
#> [1] "Predicting bootstrapped TPCs 41.8 %"
#> [1] "Predicting bootstrapped TPCs 41.9 %"
#> [1] "Predicting bootstrapped TPCs 42 %"
#> [1] "Predicting bootstrapped TPCs 42 %"
#> [1] "Predicting bootstrapped TPCs 42.1 %"
#> [1] "Predicting bootstrapped TPCs 42.2 %"
#> [1] "Predicting bootstrapped TPCs 42.3 %"
#> [1] "Predicting bootstrapped TPCs 42.3 %"
#> [1] "Predicting bootstrapped TPCs 42.4 %"
#> [1] "Predicting bootstrapped TPCs 42.5 %"
#> [1] "Predicting bootstrapped TPCs 42.6 %"
#> [1] "Predicting bootstrapped TPCs 42.6 %"
#> [1] "Predicting bootstrapped TPCs 42.7 %"
#> [1] "Predicting bootstrapped TPCs 42.8 %"
#> [1] "Predicting bootstrapped TPCs 42.9 %"
#> [1] "Predicting bootstrapped TPCs 42.9 %"
#> [1] "Predicting bootstrapped TPCs 43 %"
#> [1] "Predicting bootstrapped TPCs 43.1 %"
#> [1] "Predicting bootstrapped TPCs 43.2 %"
#> [1] "Predicting bootstrapped TPCs 43.2 %"
#> [1] "Predicting bootstrapped TPCs 43.3 %"
#> [1] "Predicting bootstrapped TPCs 43.4 %"
#> [1] "Predicting bootstrapped TPCs 43.5 %"
#> [1] "Predicting bootstrapped TPCs 43.5 %"
#> [1] "Predicting bootstrapped TPCs 43.6 %"
#> [1] "Predicting bootstrapped TPCs 43.7 %"
#> [1] "Predicting bootstrapped TPCs 43.8 %"
#> [1] "Predicting bootstrapped TPCs 43.8 %"
#> [1] "Predicting bootstrapped TPCs 43.9 %"
#> [1] "Predicting bootstrapped TPCs 44 %"
#> [1] "Predicting bootstrapped TPCs 44.1 %"
#> [1] "Predicting bootstrapped TPCs 44.1 %"
#> [1] "Predicting bootstrapped TPCs 44.2 %"
#> [1] "Predicting bootstrapped TPCs 44.3 %"
#> [1] "Predicting bootstrapped TPCs 44.4 %"
#> [1] "Predicting bootstrapped TPCs 44.4 %"
#> [1] "Predicting bootstrapped TPCs 44.5 %"
#> [1] "Predicting bootstrapped TPCs 44.6 %"
#> [1] "Predicting bootstrapped TPCs 44.7 %"
#> [1] "Predicting bootstrapped TPCs 44.7 %"
#> [1] "Predicting bootstrapped TPCs 44.8 %"
#> [1] "Predicting bootstrapped TPCs 44.9 %"
#> [1] "Predicting bootstrapped TPCs 45 %"
#> [1] "Predicting bootstrapped TPCs 45 %"
#> [1] "Predicting bootstrapped TPCs 45.1 %"
#> [1] "Predicting bootstrapped TPCs 45.2 %"
#> [1] "Predicting bootstrapped TPCs 45.3 %"
#> [1] "Predicting bootstrapped TPCs 45.4 %"
#> [1] "Predicting bootstrapped TPCs 45.4 %"
#> [1] "Predicting bootstrapped TPCs 45.5 %"
#> [1] "Predicting bootstrapped TPCs 45.6 %"
#> [1] "Predicting bootstrapped TPCs 45.7 %"
#> [1] "Predicting bootstrapped TPCs 45.7 %"
#> [1] "Predicting bootstrapped TPCs 45.8 %"
#> [1] "Predicting bootstrapped TPCs 45.9 %"
#> [1] "Predicting bootstrapped TPCs 46 %"
#> [1] "Predicting bootstrapped TPCs 46 %"
#> [1] "Predicting bootstrapped TPCs 46.1 %"
#> [1] "Predicting bootstrapped TPCs 46.2 %"
#> [1] "Predicting bootstrapped TPCs 46.3 %"
#> [1] "Predicting bootstrapped TPCs 46.3 %"
#> [1] "Predicting bootstrapped TPCs 46.4 %"
#> [1] "Predicting bootstrapped TPCs 46.5 %"
#> [1] "Predicting bootstrapped TPCs 46.6 %"
#> [1] "Predicting bootstrapped TPCs 46.6 %"
#> [1] "Predicting bootstrapped TPCs 46.7 %"
#> [1] "Predicting bootstrapped TPCs 46.8 %"
#> [1] "Predicting bootstrapped TPCs 46.9 %"
#> [1] "Predicting bootstrapped TPCs 46.9 %"
#> [1] "Predicting bootstrapped TPCs 47 %"
#> [1] "Predicting bootstrapped TPCs 47.1 %"
#> [1] "Predicting bootstrapped TPCs 47.2 %"
#> [1] "Predicting bootstrapped TPCs 47.2 %"
#> [1] "Predicting bootstrapped TPCs 47.3 %"
#> [1] "Predicting bootstrapped TPCs 47.4 %"
#> [1] "Predicting bootstrapped TPCs 47.5 %"
#> [1] "Predicting bootstrapped TPCs 47.5 %"
#> [1] "Predicting bootstrapped TPCs 47.6 %"
#> [1] "Predicting bootstrapped TPCs 47.7 %"
#> [1] "Predicting bootstrapped TPCs 47.8 %"
#> [1] "Predicting bootstrapped TPCs 47.8 %"
#> [1] "Predicting bootstrapped TPCs 47.9 %"
#> [1] "Predicting bootstrapped TPCs 48 %"
#> [1] "Predicting bootstrapped TPCs 48.1 %"
#> [1] "Predicting bootstrapped TPCs 48.1 %"
#> [1] "Predicting bootstrapped TPCs 48.2 %"
#> [1] "Predicting bootstrapped TPCs 48.3 %"
#> [1] "Predicting bootstrapped TPCs 48.4 %"
#> [1] "Predicting bootstrapped TPCs 48.5 %"
#> [1] "Predicting bootstrapped TPCs 48.5 %"
#> [1] "Predicting bootstrapped TPCs 48.6 %"
#> [1] "Predicting bootstrapped TPCs 48.7 %"
#> [1] "Predicting bootstrapped TPCs 48.8 %"
#> [1] "Predicting bootstrapped TPCs 48.8 %"
#> [1] "Predicting bootstrapped TPCs 48.9 %"
#> [1] "Predicting bootstrapped TPCs 49 %"
#> [1] "Predicting bootstrapped TPCs 49.1 %"
#> [1] "Predicting bootstrapped TPCs 49.1 %"
#> [1] "Predicting bootstrapped TPCs 49.2 %"
#> [1] "Predicting bootstrapped TPCs 49.3 %"
#> [1] "Predicting bootstrapped TPCs 49.4 %"
#> [1] "Predicting bootstrapped TPCs 49.4 %"
#> [1] "Predicting bootstrapped TPCs 49.5 %"
#> [1] "Predicting bootstrapped TPCs 49.6 %"
#> [1] "Predicting bootstrapped TPCs 49.7 %"
#> [1] "Predicting bootstrapped TPCs 49.7 %"
#> [1] "Predicting bootstrapped TPCs 49.8 %"
#> [1] "Predicting bootstrapped TPCs 49.9 %"
#> [1] "Predicting bootstrapped TPCs 50 %"
#> [1] "Predicting bootstrapped TPCs 50 %"
#> [1] "Predicting bootstrapped TPCs 50.1 %"
#> [1] "Predicting bootstrapped TPCs 50.2 %"
#> [1] "Predicting bootstrapped TPCs 50.3 %"
#> [1] "Predicting bootstrapped TPCs 50.3 %"
#> [1] "Predicting bootstrapped TPCs 50.4 %"
#> [1] "Predicting bootstrapped TPCs 50.5 %"
#> [1] "Predicting bootstrapped TPCs 50.6 %"
#> [1] "Predicting bootstrapped TPCs 50.6 %"
#> [1] "Predicting bootstrapped TPCs 50.7 %"
#> [1] "Predicting bootstrapped TPCs 50.8 %"
#> [1] "Predicting bootstrapped TPCs 50.9 %"
#> [1] "Predicting bootstrapped TPCs 50.9 %"
#> [1] "Predicting bootstrapped TPCs 51 %"
#> [1] "Predicting bootstrapped TPCs 51.1 %"
#> [1] "Predicting bootstrapped TPCs 51.2 %"
#> [1] "Predicting bootstrapped TPCs 51.2 %"
#> [1] "Predicting bootstrapped TPCs 51.3 %"
#> [1] "Predicting bootstrapped TPCs 51.4 %"
#> [1] "Predicting bootstrapped TPCs 51.5 %"
#> [1] "Predicting bootstrapped TPCs 51.5 %"
#> [1] "Predicting bootstrapped TPCs 51.6 %"
#> [1] "Predicting bootstrapped TPCs 51.7 %"
#> [1] "Predicting bootstrapped TPCs 51.8 %"
#> [1] "Predicting bootstrapped TPCs 51.9 %"
#> [1] "Predicting bootstrapped TPCs 51.9 %"
#> [1] "Predicting bootstrapped TPCs 52 %"
#> [1] "Predicting bootstrapped TPCs 52.1 %"
#> [1] "Predicting bootstrapped TPCs 52.2 %"
#> [1] "Predicting bootstrapped TPCs 52.2 %"
#> [1] "Predicting bootstrapped TPCs 52.3 %"
#> [1] "Predicting bootstrapped TPCs 52.4 %"
#> [1] "Predicting bootstrapped TPCs 52.5 %"
#> [1] "Predicting bootstrapped TPCs 52.5 %"
#> [1] "Predicting bootstrapped TPCs 52.6 %"
#> [1] "Predicting bootstrapped TPCs 52.7 %"
#> [1] "Predicting bootstrapped TPCs 52.8 %"
#> [1] "Predicting bootstrapped TPCs 52.8 %"
#> [1] "Predicting bootstrapped TPCs 52.9 %"
#> [1] "Predicting bootstrapped TPCs 53 %"
#> [1] "Predicting bootstrapped TPCs 53.1 %"
#> [1] "Predicting bootstrapped TPCs 53.1 %"
#> [1] "Predicting bootstrapped TPCs 53.2 %"
#> [1] "Predicting bootstrapped TPCs 53.3 %"
#> [1] "Predicting bootstrapped TPCs 53.4 %"
#> [1] "Predicting bootstrapped TPCs 53.4 %"
#> [1] "Predicting bootstrapped TPCs 53.5 %"
#> [1] "Predicting bootstrapped TPCs 53.6 %"
#> [1] "Predicting bootstrapped TPCs 53.7 %"
#> [1] "Predicting bootstrapped TPCs 53.7 %"
#> [1] "Predicting bootstrapped TPCs 53.8 %"
#> [1] "Predicting bootstrapped TPCs 53.9 %"
#> [1] "Predicting bootstrapped TPCs 54 %"
#> [1] "Predicting bootstrapped TPCs 54 %"
#> [1] "Predicting bootstrapped TPCs 54.1 %"
#> [1] "Predicting bootstrapped TPCs 54.2 %"
#> [1] "Predicting bootstrapped TPCs 54.3 %"
#> [1] "Predicting bootstrapped TPCs 54.3 %"
#> [1] "Predicting bootstrapped TPCs 54.4 %"
#> [1] "Predicting bootstrapped TPCs 54.5 %"
#> [1] "Predicting bootstrapped TPCs 54.6 %"
#> [1] "Predicting bootstrapped TPCs 54.6 %"
#> [1] "Predicting bootstrapped TPCs 54.7 %"
#> [1] "Predicting bootstrapped TPCs 54.8 %"
#> [1] "Predicting bootstrapped TPCs 54.9 %"
#> [1] "Predicting bootstrapped TPCs 55 %"
#> [1] "Predicting bootstrapped TPCs 55 %"
#> [1] "Predicting bootstrapped TPCs 55.1 %"
#> [1] "Predicting bootstrapped TPCs 55.2 %"
#> [1] "Predicting bootstrapped TPCs 55.3 %"
#> [1] "Predicting bootstrapped TPCs 55.3 %"
#> [1] "Predicting bootstrapped TPCs 55.4 %"
#> [1] "Predicting bootstrapped TPCs 55.5 %"
#> [1] "Predicting bootstrapped TPCs 55.6 %"
#> [1] "Predicting bootstrapped TPCs 55.6 %"
#> [1] "Predicting bootstrapped TPCs 55.7 %"
#> [1] "Predicting bootstrapped TPCs 55.8 %"
#> [1] "Predicting bootstrapped TPCs 55.9 %"
#> [1] "Predicting bootstrapped TPCs 55.9 %"
#> [1] "Predicting bootstrapped TPCs 56 %"
#> [1] "Predicting bootstrapped TPCs 56.1 %"
#> [1] "Predicting bootstrapped TPCs 56.2 %"
#> [1] "Predicting bootstrapped TPCs 56.2 %"
#> [1] "Predicting bootstrapped TPCs 56.3 %"
#> [1] "Predicting bootstrapped TPCs 56.4 %"
#> [1] "Predicting bootstrapped TPCs 56.5 %"
#> [1] "Predicting bootstrapped TPCs 56.5 %"
#> [1] "Predicting bootstrapped TPCs 56.6 %"
#> [1] "Predicting bootstrapped TPCs 56.7 %"
#> [1] "Predicting bootstrapped TPCs 56.8 %"
#> [1] "Predicting bootstrapped TPCs 56.8 %"
#> [1] "Predicting bootstrapped TPCs 56.9 %"
#> [1] "Predicting bootstrapped TPCs 57 %"
#> [1] "Predicting bootstrapped TPCs 57.1 %"
#> [1] "Predicting bootstrapped TPCs 57.1 %"
#> [1] "Predicting bootstrapped TPCs 57.2 %"
#> [1] "Predicting bootstrapped TPCs 57.3 %"
#> [1] "Predicting bootstrapped TPCs 57.4 %"
#> [1] "Predicting bootstrapped TPCs 57.4 %"
#> [1] "Predicting bootstrapped TPCs 57.5 %"
#> [1] "Predicting bootstrapped TPCs 57.6 %"
#> [1] "Predicting bootstrapped TPCs 57.7 %"
#> [1] "Predicting bootstrapped TPCs 57.7 %"
#> [1] "Predicting bootstrapped TPCs 57.8 %"
#> [1] "Predicting bootstrapped TPCs 57.9 %"
#> [1] "Predicting bootstrapped TPCs 58 %"
#> [1] "Predicting bootstrapped TPCs 58 %"
#> [1] "Predicting bootstrapped TPCs 58.1 %"
#> [1] "Predicting bootstrapped TPCs 58.2 %"
#> [1] "Predicting bootstrapped TPCs 58.3 %"
#> [1] "Predicting bootstrapped TPCs 58.4 %"
#> [1] "Predicting bootstrapped TPCs 58.4 %"
#> [1] "Predicting bootstrapped TPCs 58.5 %"
#> [1] "Predicting bootstrapped TPCs 58.6 %"
#> [1] "Predicting bootstrapped TPCs 58.7 %"
#> [1] "Predicting bootstrapped TPCs 58.7 %"
#> [1] "Predicting bootstrapped TPCs 58.8 %"
#> [1] "Predicting bootstrapped TPCs 58.9 %"
#> [1] "Predicting bootstrapped TPCs 59 %"
#> [1] "Predicting bootstrapped TPCs 59 %"
#> [1] "Predicting bootstrapped TPCs 59.1 %"
#> [1] "Predicting bootstrapped TPCs 59.2 %"
#> [1] "Predicting bootstrapped TPCs 59.3 %"
#> [1] "Predicting bootstrapped TPCs 59.3 %"
#> [1] "Predicting bootstrapped TPCs 59.4 %"
#> [1] "Predicting bootstrapped TPCs 59.5 %"
#> [1] "Predicting bootstrapped TPCs 59.6 %"
#> [1] "Predicting bootstrapped TPCs 59.6 %"
#> [1] "Predicting bootstrapped TPCs 59.7 %"
#> [1] "Predicting bootstrapped TPCs 59.8 %"
#> [1] "Predicting bootstrapped TPCs 59.9 %"
#> [1] "Predicting bootstrapped TPCs 59.9 %"
#> [1] "Predicting bootstrapped TPCs 60 %"
#> [1] "Predicting bootstrapped TPCs 60.1 %"
#> [1] "Predicting bootstrapped TPCs 60.2 %"
#> [1] "Predicting bootstrapped TPCs 60.2 %"
#> [1] "Predicting bootstrapped TPCs 60.3 %"
#> [1] "Predicting bootstrapped TPCs 60.4 %"
#> [1] "Predicting bootstrapped TPCs 60.5 %"
#> [1] "Predicting bootstrapped TPCs 60.5 %"
#> [1] "Predicting bootstrapped TPCs 60.6 %"
#> [1] "Predicting bootstrapped TPCs 60.7 %"
#> [1] "Predicting bootstrapped TPCs 60.8 %"
#> [1] "Predicting bootstrapped TPCs 60.8 %"
#> [1] "Predicting bootstrapped TPCs 60.9 %"
#> [1] "Predicting bootstrapped TPCs 61 %"
#> [1] "Predicting bootstrapped TPCs 61.1 %"
#> [1] "Predicting bootstrapped TPCs 61.1 %"
#> [1] "Predicting bootstrapped TPCs 61.2 %"
#> [1] "Predicting bootstrapped TPCs 61.3 %"
#> [1] "Predicting bootstrapped TPCs 61.4 %"
#> [1] "Predicting bootstrapped TPCs 61.5 %"
#> [1] "Predicting bootstrapped TPCs 61.5 %"
#> [1] "Predicting bootstrapped TPCs 61.6 %"
#> [1] "Predicting bootstrapped TPCs 61.7 %"
#> [1] "Predicting bootstrapped TPCs 61.8 %"
#> [1] "Predicting bootstrapped TPCs 61.8 %"
#> [1] "Predicting bootstrapped TPCs 61.9 %"
#> [1] "Predicting bootstrapped TPCs 62 %"
#> [1] "Predicting bootstrapped TPCs 62.1 %"
#> [1] "Predicting bootstrapped TPCs 62.1 %"
#> [1] "Predicting bootstrapped TPCs 62.2 %"
#> [1] "Predicting bootstrapped TPCs 62.3 %"
#> [1] "Predicting bootstrapped TPCs 62.4 %"
#> [1] "Predicting bootstrapped TPCs 62.4 %"
#> [1] "Predicting bootstrapped TPCs 62.5 %"
#> [1] "Predicting bootstrapped TPCs 62.6 %"
#> [1] "Predicting bootstrapped TPCs 62.7 %"
#> [1] "Predicting bootstrapped TPCs 62.7 %"
#> [1] "Predicting bootstrapped TPCs 62.8 %"
#> [1] "Predicting bootstrapped TPCs 62.9 %"
#> [1] "Predicting bootstrapped TPCs 63 %"
#> [1] "Predicting bootstrapped TPCs 63 %"
#> [1] "Predicting bootstrapped TPCs 63.1 %"
#> [1] "Predicting bootstrapped TPCs 63.2 %"
#> [1] "Predicting bootstrapped TPCs 63.3 %"
#> [1] "Predicting bootstrapped TPCs 63.3 %"
#> [1] "Predicting bootstrapped TPCs 63.4 %"
#> [1] "Predicting bootstrapped TPCs 63.5 %"
#> [1] "Predicting bootstrapped TPCs 63.6 %"
#> [1] "Predicting bootstrapped TPCs 63.6 %"
#> [1] "Predicting bootstrapped TPCs 63.7 %"
#> [1] "Predicting bootstrapped TPCs 63.8 %"
#> [1] "Predicting bootstrapped TPCs 63.9 %"
#> [1] "Predicting bootstrapped TPCs 63.9 %"
#> [1] "Predicting bootstrapped TPCs 64 %"
#> [1] "Predicting bootstrapped TPCs 64.1 %"
#> [1] "Predicting bootstrapped TPCs 64.2 %"
#> [1] "Predicting bootstrapped TPCs 64.2 %"
#> [1] "Predicting bootstrapped TPCs 64.3 %"
#> [1] "Predicting bootstrapped TPCs 64.4 %"
#> [1] "Predicting bootstrapped TPCs 64.5 %"
#> [1] "Predicting bootstrapped TPCs 64.6 %"
#> [1] "Predicting bootstrapped TPCs 64.6 %"
#> [1] "Predicting bootstrapped TPCs 64.7 %"
#> [1] "Predicting bootstrapped TPCs 64.8 %"
#> [1] "Predicting bootstrapped TPCs 64.9 %"
#> [1] "Predicting bootstrapped TPCs 64.9 %"
#> [1] "Predicting bootstrapped TPCs 65 %"
#> [1] "Predicting bootstrapped TPCs 65.1 %"
#> [1] "Predicting bootstrapped TPCs 65.2 %"
#> [1] "Predicting bootstrapped TPCs 65.2 %"
#> [1] "Predicting bootstrapped TPCs 65.3 %"
#> [1] "Predicting bootstrapped TPCs 65.4 %"
#> [1] "Predicting bootstrapped TPCs 65.5 %"
#> [1] "Predicting bootstrapped TPCs 65.5 %"
#> [1] "Predicting bootstrapped TPCs 65.6 %"
#> [1] "Predicting bootstrapped TPCs 65.7 %"
#> [1] "Predicting bootstrapped TPCs 65.8 %"
#> [1] "Predicting bootstrapped TPCs 65.8 %"
#> [1] "Predicting bootstrapped TPCs 65.9 %"
#> [1] "Predicting bootstrapped TPCs 66 %"
#> [1] "Predicting bootstrapped TPCs 66.1 %"
#> [1] "Predicting bootstrapped TPCs 66.1 %"
#> [1] "Predicting bootstrapped TPCs 66.2 %"
#> [1] "Predicting bootstrapped TPCs 66.3 %"
#> [1] "Predicting bootstrapped TPCs 66.4 %"
#> [1] "Predicting bootstrapped TPCs 66.4 %"
#> [1] "Predicting bootstrapped TPCs 66.5 %"
#> [1] "Predicting bootstrapped TPCs 66.6 %"
#> [1] "Predicting bootstrapped TPCs 66.7 %"
#> [1] "Predicting bootstrapped TPCs 66.7 %"
#> [1] "Predicting bootstrapped TPCs 66.8 %"
#> [1] "Predicting bootstrapped TPCs 66.9 %"
#> [1] "Predicting bootstrapped TPCs 67 %"
#> [1] "Predicting bootstrapped TPCs 67 %"
#> [1] "Predicting bootstrapped TPCs 67.1 %"
#> [1] "Predicting bootstrapped TPCs 67.2 %"
#> [1] "Predicting bootstrapped TPCs 67.3 %"
#> [1] "Predicting bootstrapped TPCs 67.3 %"
#> [1] "Predicting bootstrapped TPCs 67.4 %"
#> [1] "Predicting bootstrapped TPCs 67.5 %"
#> [1] "Predicting bootstrapped TPCs 67.6 %"
#> [1] "Predicting bootstrapped TPCs 67.6 %"
#> [1] "Predicting bootstrapped TPCs 67.7 %"
#> [1] "Predicting bootstrapped TPCs 67.8 %"
#> [1] "Predicting bootstrapped TPCs 67.9 %"
#> [1] "Predicting bootstrapped TPCs 68 %"
#> [1] "Predicting bootstrapped TPCs 68 %"
#> [1] "Predicting bootstrapped TPCs 68.1 %"
#> [1] "Predicting bootstrapped TPCs 68.2 %"
#> [1] "Predicting bootstrapped TPCs 68.3 %"
#> [1] "Predicting bootstrapped TPCs 68.3 %"
#> [1] "Predicting bootstrapped TPCs 68.4 %"
#> [1] "Predicting bootstrapped TPCs 68.5 %"
#> [1] "Predicting bootstrapped TPCs 68.6 %"
#> [1] "Predicting bootstrapped TPCs 68.6 %"
#> [1] "Predicting bootstrapped TPCs 68.7 %"
#> [1] "Predicting bootstrapped TPCs 68.8 %"
#> [1] "Predicting bootstrapped TPCs 68.9 %"
#> [1] "Predicting bootstrapped TPCs 68.9 %"
#> [1] "Predicting bootstrapped TPCs 69 %"
#> [1] "Predicting bootstrapped TPCs 69.1 %"
#> [1] "Predicting bootstrapped TPCs 69.2 %"
#> [1] "Predicting bootstrapped TPCs 69.2 %"
#> [1] "Predicting bootstrapped TPCs 69.3 %"
#> [1] "Predicting bootstrapped TPCs 69.4 %"
#> [1] "Predicting bootstrapped TPCs 69.5 %"
#> [1] "Predicting bootstrapped TPCs 69.5 %"
#> [1] "Predicting bootstrapped TPCs 69.6 %"
#> [1] "Predicting bootstrapped TPCs 69.7 %"
#> [1] "Predicting bootstrapped TPCs 69.8 %"
#> [1] "Predicting bootstrapped TPCs 69.8 %"
#> [1] "Predicting bootstrapped TPCs 69.9 %"
#> [1] "Predicting bootstrapped TPCs 70 %"
#> [1] "Predicting bootstrapped TPCs 70.1 %"
#> [1] "Predicting bootstrapped TPCs 70.1 %"
#> [1] "Predicting bootstrapped TPCs 70.2 %"
#> [1] "Predicting bootstrapped TPCs 70.3 %"
#> [1] "Predicting bootstrapped TPCs 70.4 %"
#> [1] "Predicting bootstrapped TPCs 70.4 %"
#> [1] "Predicting bootstrapped TPCs 70.5 %"
#> [1] "Predicting bootstrapped TPCs 70.6 %"
#> [1] "Predicting bootstrapped TPCs 70.7 %"
#> [1] "Predicting bootstrapped TPCs 70.7 %"
#> [1] "Predicting bootstrapped TPCs 70.8 %"
#> [1] "Predicting bootstrapped TPCs 70.9 %"
#> [1] "Predicting bootstrapped TPCs 71 %"
#> [1] "Predicting bootstrapped TPCs 71.1 %"
#> [1] "Predicting bootstrapped TPCs 71.1 %"
#> [1] "Predicting bootstrapped TPCs 71.2 %"
#> [1] "Predicting bootstrapped TPCs 71.3 %"
#> [1] "Predicting bootstrapped TPCs 71.4 %"
#> [1] "Predicting bootstrapped TPCs 71.4 %"
#> [1] "Predicting bootstrapped TPCs 71.5 %"
#> [1] "Predicting bootstrapped TPCs 71.6 %"
#> [1] "Predicting bootstrapped TPCs 71.7 %"
#> [1] "Predicting bootstrapped TPCs 71.7 %"
#> [1] "Predicting bootstrapped TPCs 71.8 %"
#> [1] "Predicting bootstrapped TPCs 71.9 %"
#> [1] "Predicting bootstrapped TPCs 72 %"
#> [1] "Predicting bootstrapped TPCs 72 %"
#> [1] "Predicting bootstrapped TPCs 72.1 %"
#> [1] "Predicting bootstrapped TPCs 72.2 %"
#> [1] "Predicting bootstrapped TPCs 72.3 %"
#> [1] "Predicting bootstrapped TPCs 72.3 %"
#> [1] "Predicting bootstrapped TPCs 72.4 %"
#> [1] "Predicting bootstrapped TPCs 72.5 %"
#> [1] "Predicting bootstrapped TPCs 72.6 %"
#> [1] "Predicting bootstrapped TPCs 72.6 %"
#> [1] "Predicting bootstrapped TPCs 72.7 %"
#> [1] "Predicting bootstrapped TPCs 72.8 %"
#> [1] "Predicting bootstrapped TPCs 72.9 %"
#> [1] "Predicting bootstrapped TPCs 72.9 %"
#> [1] "Predicting bootstrapped TPCs 73 %"
#> [1] "Predicting bootstrapped TPCs 73.1 %"
#> [1] "Predicting bootstrapped TPCs 73.2 %"
#> [1] "Predicting bootstrapped TPCs 73.2 %"
#> [1] "Predicting bootstrapped TPCs 73.3 %"
#> [1] "Predicting bootstrapped TPCs 73.4 %"
#> [1] "Predicting bootstrapped TPCs 73.5 %"
#> [1] "Predicting bootstrapped TPCs 73.5 %"
#> [1] "Predicting bootstrapped TPCs 73.6 %"
#> [1] "Predicting bootstrapped TPCs 73.7 %"
#> [1] "Predicting bootstrapped TPCs 73.8 %"
#> [1] "Predicting bootstrapped TPCs 73.8 %"
#> [1] "Predicting bootstrapped TPCs 73.9 %"
#> [1] "Predicting bootstrapped TPCs 74 %"
#> [1] "Predicting bootstrapped TPCs 74.1 %"
#> [1] "Predicting bootstrapped TPCs 74.1 %"
#> [1] "Predicting bootstrapped TPCs 74.2 %"
#> [1] "Predicting bootstrapped TPCs 74.3 %"
#> [1] "Predicting bootstrapped TPCs 74.4 %"
#> [1] "Predicting bootstrapped TPCs 74.5 %"
#> [1] "Predicting bootstrapped TPCs 74.5 %"
#> [1] "Predicting bootstrapped TPCs 74.6 %"
#> [1] "Predicting bootstrapped TPCs 74.7 %"
#> [1] "Predicting bootstrapped TPCs 74.8 %"
#> [1] "Predicting bootstrapped TPCs 74.8 %"
#> [1] "Predicting bootstrapped TPCs 74.9 %"
#> [1] "Predicting bootstrapped TPCs 75 %"
#> [1] "Predicting bootstrapped TPCs 75.1 %"
#> [1] "Predicting bootstrapped TPCs 75.1 %"
#> [1] "Predicting bootstrapped TPCs 75.2 %"
#> [1] "Predicting bootstrapped TPCs 75.3 %"
#> [1] "Predicting bootstrapped TPCs 75.4 %"
#> [1] "Predicting bootstrapped TPCs 75.4 %"
#> [1] "Predicting bootstrapped TPCs 75.5 %"
#> [1] "Predicting bootstrapped TPCs 75.6 %"
#> [1] "Predicting bootstrapped TPCs 75.7 %"
#> [1] "Predicting bootstrapped TPCs 75.7 %"
#> [1] "Predicting bootstrapped TPCs 75.8 %"
#> [1] "Predicting bootstrapped TPCs 75.9 %"
#> [1] "Predicting bootstrapped TPCs 76 %"
#> [1] "Predicting bootstrapped TPCs 76 %"
#> [1] "Predicting bootstrapped TPCs 76.1 %"
#> [1] "Predicting bootstrapped TPCs 76.2 %"
#> [1] "Predicting bootstrapped TPCs 76.3 %"
#> [1] "Predicting bootstrapped TPCs 76.3 %"
#> [1] "Predicting bootstrapped TPCs 76.4 %"
#> [1] "Predicting bootstrapped TPCs 76.5 %"
#> [1] "Predicting bootstrapped TPCs 76.6 %"
#> [1] "Predicting bootstrapped TPCs 76.6 %"
#> [1] "Predicting bootstrapped TPCs 76.7 %"
#> [1] "Predicting bootstrapped TPCs 76.8 %"
#> [1] "Predicting bootstrapped TPCs 76.9 %"
#> [1] "Predicting bootstrapped TPCs 76.9 %"
#> [1] "Predicting bootstrapped TPCs 77 %"
#> [1] "Predicting bootstrapped TPCs 77.1 %"
#> [1] "Predicting bootstrapped TPCs 77.2 %"
#> [1] "Predicting bootstrapped TPCs 77.2 %"
#> [1] "Predicting bootstrapped TPCs 77.3 %"
#> [1] "Predicting bootstrapped TPCs 77.4 %"
#> [1] "Predicting bootstrapped TPCs 77.5 %"
#> [1] "Predicting bootstrapped TPCs 77.6 %"
#> [1] "Predicting bootstrapped TPCs 77.6 %"
#> [1] "Predicting bootstrapped TPCs 77.7 %"
#> [1] "Predicting bootstrapped TPCs 77.8 %"
#> [1] "Predicting bootstrapped TPCs 77.9 %"
#> [1] "Predicting bootstrapped TPCs 77.9 %"
#> [1] "Predicting bootstrapped TPCs 78 %"
#> [1] "Predicting bootstrapped TPCs 78.1 %"
#> [1] "Predicting bootstrapped TPCs 78.2 %"
#> [1] "Predicting bootstrapped TPCs 78.2 %"
#> [1] "Predicting bootstrapped TPCs 78.3 %"
#> [1] "Predicting bootstrapped TPCs 78.4 %"
#> [1] "Predicting bootstrapped TPCs 78.5 %"
#> [1] "Predicting bootstrapped TPCs 78.5 %"
#> [1] "Predicting bootstrapped TPCs 78.6 %"
#> [1] "Predicting bootstrapped TPCs 78.7 %"
#> [1] "Predicting bootstrapped TPCs 78.8 %"
#> [1] "Predicting bootstrapped TPCs 78.8 %"
#> [1] "Predicting bootstrapped TPCs 78.9 %"
#> [1] "Predicting bootstrapped TPCs 79 %"
#> [1] "Predicting bootstrapped TPCs 79.1 %"
#> [1] "Predicting bootstrapped TPCs 79.1 %"
#> [1] "Predicting bootstrapped TPCs 79.2 %"
#> [1] "Predicting bootstrapped TPCs 79.3 %"
#> [1] "Predicting bootstrapped TPCs 79.4 %"
#> [1] "Predicting bootstrapped TPCs 79.4 %"
#> [1] "Predicting bootstrapped TPCs 79.5 %"
#> [1] "Predicting bootstrapped TPCs 79.6 %"
#> [1] "Predicting bootstrapped TPCs 79.7 %"
#> [1] "Predicting bootstrapped TPCs 79.7 %"
#> [1] "Predicting bootstrapped TPCs 79.8 %"
#> [1] "Predicting bootstrapped TPCs 79.9 %"
#> [1] "Predicting bootstrapped TPCs 80 %"
#> [1] "Predicting bootstrapped TPCs 80 %"
#> [1] "Predicting bootstrapped TPCs 80.1 %"
#> [1] "Predicting bootstrapped TPCs 80.2 %"
#> [1] "Predicting bootstrapped TPCs 80.3 %"
#> [1] "Predicting bootstrapped TPCs 80.3 %"
#> [1] "Predicting bootstrapped TPCs 80.4 %"
#> [1] "Predicting bootstrapped TPCs 80.5 %"
#> [1] "Predicting bootstrapped TPCs 80.6 %"
#> [1] "Predicting bootstrapped TPCs 80.7 %"
#> [1] "Predicting bootstrapped TPCs 80.7 %"
#> [1] "Predicting bootstrapped TPCs 80.8 %"
#> [1] "Predicting bootstrapped TPCs 80.9 %"
#> [1] "Predicting bootstrapped TPCs 81 %"
#> [1] "Predicting bootstrapped TPCs 81 %"
#> [1] "Predicting bootstrapped TPCs 81.1 %"
#> [1] "Predicting bootstrapped TPCs 81.2 %"
#> [1] "Predicting bootstrapped TPCs 81.3 %"
#> [1] "Predicting bootstrapped TPCs 81.3 %"
#> [1] "Predicting bootstrapped TPCs 81.4 %"
#> [1] "Predicting bootstrapped TPCs 81.5 %"
#> [1] "Predicting bootstrapped TPCs 81.6 %"
#> [1] "Predicting bootstrapped TPCs 81.6 %"
#> [1] "Predicting bootstrapped TPCs 81.7 %"
#> [1] "Predicting bootstrapped TPCs 81.8 %"
#> [1] "Predicting bootstrapped TPCs 81.9 %"
#> [1] "Predicting bootstrapped TPCs 81.9 %"
#> [1] "Predicting bootstrapped TPCs 82 %"
#> [1] "Predicting bootstrapped TPCs 82.1 %"
#> [1] "Predicting bootstrapped TPCs 82.2 %"
#> [1] "Predicting bootstrapped TPCs 82.2 %"
#> [1] "Predicting bootstrapped TPCs 82.3 %"
#> [1] "Predicting bootstrapped TPCs 82.4 %"
#> [1] "Predicting bootstrapped TPCs 82.5 %"
#> [1] "Predicting bootstrapped TPCs 82.5 %"
#> [1] "Predicting bootstrapped TPCs 82.6 %"
#> [1] "Predicting bootstrapped TPCs 82.7 %"
#> [1] "Predicting bootstrapped TPCs 82.8 %"
#> [1] "Predicting bootstrapped TPCs 82.8 %"
#> [1] "Predicting bootstrapped TPCs 82.9 %"
#> [1] "Predicting bootstrapped TPCs 83 %"
#> [1] "Predicting bootstrapped TPCs 83.1 %"
#> [1] "Predicting bootstrapped TPCs 83.1 %"
#> [1] "Predicting bootstrapped TPCs 83.2 %"
#> [1] "Predicting bootstrapped TPCs 83.3 %"
#> [1] "Predicting bootstrapped TPCs 83.4 %"
#> [1] "Predicting bootstrapped TPCs 83.4 %"
#> [1] "Predicting bootstrapped TPCs 83.5 %"
#> [1] "Predicting bootstrapped TPCs 83.6 %"
#> [1] "Predicting bootstrapped TPCs 83.7 %"
#> [1] "Predicting bootstrapped TPCs 83.7 %"
#> [1] "Predicting bootstrapped TPCs 83.8 %"
#> [1] "Predicting bootstrapped TPCs 83.9 %"
#> [1] "Predicting bootstrapped TPCs 84 %"
#> [1] "Predicting bootstrapped TPCs 84.1 %"
#> [1] "Predicting bootstrapped TPCs 84.1 %"
#> [1] "Predicting bootstrapped TPCs 84.2 %"
#> [1] "Predicting bootstrapped TPCs 84.3 %"
#> [1] "Predicting bootstrapped TPCs 84.4 %"
#> [1] "Predicting bootstrapped TPCs 84.4 %"
#> [1] "Predicting bootstrapped TPCs 84.5 %"
#> [1] "Predicting bootstrapped TPCs 84.6 %"
#> [1] "Predicting bootstrapped TPCs 84.7 %"
#> [1] "Predicting bootstrapped TPCs 84.7 %"
#> [1] "Predicting bootstrapped TPCs 84.8 %"
#> [1] "Predicting bootstrapped TPCs 84.9 %"
#> [1] "Predicting bootstrapped TPCs 85 %"
#> [1] "Predicting bootstrapped TPCs 85 %"
#> [1] "Predicting bootstrapped TPCs 85.1 %"
#> [1] "Predicting bootstrapped TPCs 85.2 %"
#> [1] "Predicting bootstrapped TPCs 85.3 %"
#> [1] "Predicting bootstrapped TPCs 85.3 %"
#> [1] "Predicting bootstrapped TPCs 85.4 %"
#> [1] "Predicting bootstrapped TPCs 85.5 %"
#> [1] "Predicting bootstrapped TPCs 85.6 %"
#> [1] "Predicting bootstrapped TPCs 85.6 %"
#> [1] "Predicting bootstrapped TPCs 85.7 %"
#> [1] "Predicting bootstrapped TPCs 85.8 %"
#> [1] "Predicting bootstrapped TPCs 85.9 %"
#> [1] "Predicting bootstrapped TPCs 85.9 %"
#> [1] "Predicting bootstrapped TPCs 86 %"
#> [1] "Predicting bootstrapped TPCs 86.1 %"
#> [1] "Predicting bootstrapped TPCs 86.2 %"
#> [1] "Predicting bootstrapped TPCs 86.2 %"
#> [1] "Predicting bootstrapped TPCs 86.3 %"
#> [1] "Predicting bootstrapped TPCs 86.4 %"
#> [1] "Predicting bootstrapped TPCs 86.5 %"
#> [1] "Predicting bootstrapped TPCs 86.5 %"
#> [1] "Predicting bootstrapped TPCs 86.6 %"
#> [1] "Predicting bootstrapped TPCs 86.7 %"
#> [1] "Predicting bootstrapped TPCs 86.8 %"
#> [1] "Predicting bootstrapped TPCs 86.8 %"
#> [1] "Predicting bootstrapped TPCs 86.9 %"
#> [1] "Predicting bootstrapped TPCs 87 %"
#> [1] "Predicting bootstrapped TPCs 87.1 %"
#> [1] "Predicting bootstrapped TPCs 87.2 %"
#> [1] "Predicting bootstrapped TPCs 87.2 %"
#> [1] "Predicting bootstrapped TPCs 87.3 %"
#> [1] "Predicting bootstrapped TPCs 87.4 %"
#> [1] "Predicting bootstrapped TPCs 87.5 %"
#> [1] "Predicting bootstrapped TPCs 87.5 %"
#> [1] "Predicting bootstrapped TPCs 87.6 %"
#> [1] "Predicting bootstrapped TPCs 87.7 %"
#> [1] "Predicting bootstrapped TPCs 87.8 %"
#> [1] "Predicting bootstrapped TPCs 87.8 %"
#> [1] "Predicting bootstrapped TPCs 87.9 %"
#> [1] "Predicting bootstrapped TPCs 88 %"
#> [1] "Predicting bootstrapped TPCs 88.1 %"
#> [1] "Predicting bootstrapped TPCs 88.1 %"
#> [1] "Predicting bootstrapped TPCs 88.2 %"
#> [1] "Predicting bootstrapped TPCs 88.3 %"
#> [1] "Predicting bootstrapped TPCs 88.4 %"
#> [1] "Predicting bootstrapped TPCs 88.4 %"
#> [1] "Predicting bootstrapped TPCs 88.5 %"
#> [1] "Predicting bootstrapped TPCs 88.6 %"
#> [1] "Predicting bootstrapped TPCs 88.7 %"
#> [1] "Predicting bootstrapped TPCs 88.7 %"
#> [1] "Predicting bootstrapped TPCs 88.8 %"
#> [1] "Predicting bootstrapped TPCs 88.9 %"
#> [1] "Predicting bootstrapped TPCs 89 %"
#> [1] "Predicting bootstrapped TPCs 89 %"
#> [1] "Predicting bootstrapped TPCs 89.1 %"
#> [1] "Predicting bootstrapped TPCs 89.2 %"
#> [1] "Predicting bootstrapped TPCs 89.3 %"
#> [1] "Predicting bootstrapped TPCs 89.3 %"
#> [1] "Predicting bootstrapped TPCs 89.4 %"
#> [1] "Predicting bootstrapped TPCs 89.5 %"
#> [1] "Predicting bootstrapped TPCs 89.6 %"
#> [1] "Predicting bootstrapped TPCs 89.6 %"
#> [1] "Predicting bootstrapped TPCs 89.7 %"
#> [1] "Predicting bootstrapped TPCs 89.8 %"
#> [1] "Predicting bootstrapped TPCs 89.9 %"
#> [1] "Predicting bootstrapped TPCs 89.9 %"
#> [1] "Predicting bootstrapped TPCs 90 %"
#> [1] "Predicting bootstrapped TPCs 90.1 %"
#> [1] "Predicting bootstrapped TPCs 90.2 %"
#> [1] "Predicting bootstrapped TPCs 90.2 %"
#> [1] "Predicting bootstrapped TPCs 90.3 %"
#> [1] "Predicting bootstrapped TPCs 90.4 %"
#> [1] "Predicting bootstrapped TPCs 90.5 %"
#> [1] "Predicting bootstrapped TPCs 90.6 %"
#> [1] "Predicting bootstrapped TPCs 90.6 %"
#> [1] "Predicting bootstrapped TPCs 90.7 %"
#> [1] "Predicting bootstrapped TPCs 90.8 %"
#> [1] "Predicting bootstrapped TPCs 90.9 %"
#> [1] "Predicting bootstrapped TPCs 90.9 %"
#> [1] "Predicting bootstrapped TPCs 91 %"
#> [1] "Predicting bootstrapped TPCs 91.1 %"
#> [1] "Predicting bootstrapped TPCs 91.2 %"
#> [1] "Predicting bootstrapped TPCs 91.2 %"
#> [1] "Predicting bootstrapped TPCs 91.3 %"
#> [1] "Predicting bootstrapped TPCs 91.4 %"
#> [1] "Predicting bootstrapped TPCs 91.5 %"
#> [1] "Predicting bootstrapped TPCs 91.5 %"
#> [1] "Predicting bootstrapped TPCs 91.6 %"
#> [1] "Predicting bootstrapped TPCs 91.7 %"
#> [1] "Predicting bootstrapped TPCs 91.8 %"
#> [1] "Predicting bootstrapped TPCs 91.8 %"
#> [1] "Predicting bootstrapped TPCs 91.9 %"
#> [1] "Predicting bootstrapped TPCs 92 %"
#> [1] "Predicting bootstrapped TPCs 92.1 %"
#> [1] "Predicting bootstrapped TPCs 92.1 %"
#> [1] "Predicting bootstrapped TPCs 92.2 %"
#> [1] "Predicting bootstrapped TPCs 92.3 %"
#> [1] "Predicting bootstrapped TPCs 92.4 %"
#> [1] "Predicting bootstrapped TPCs 92.4 %"
#> [1] "Predicting bootstrapped TPCs 92.5 %"
#> [1] "Predicting bootstrapped TPCs 92.6 %"
#> [1] "Predicting bootstrapped TPCs 92.7 %"
#> [1] "Predicting bootstrapped TPCs 92.7 %"
#> [1] "Predicting bootstrapped TPCs 92.8 %"
#> [1] "Predicting bootstrapped TPCs 92.9 %"
#> [1] "Predicting bootstrapped TPCs 93 %"
#> [1] "Predicting bootstrapped TPCs 93 %"
#> [1] "Predicting bootstrapped TPCs 93.1 %"
#> [1] "Predicting bootstrapped TPCs 93.2 %"
#> [1] "Predicting bootstrapped TPCs 93.3 %"
#> [1] "Predicting bootstrapped TPCs 93.3 %"
#> [1] "Predicting bootstrapped TPCs 93.4 %"
#> [1] "Predicting bootstrapped TPCs 93.5 %"
#> [1] "Predicting bootstrapped TPCs 93.6 %"
#> [1] "Predicting bootstrapped TPCs 93.7 %"
#> [1] "Predicting bootstrapped TPCs 93.7 %"
#> [1] "Predicting bootstrapped TPCs 93.8 %"
#> [1] "Predicting bootstrapped TPCs 93.9 %"
#> [1] "Predicting bootstrapped TPCs 94 %"
#> [1] "Predicting bootstrapped TPCs 94 %"
#> [1] "Predicting bootstrapped TPCs 94.1 %"
#> [1] "Predicting bootstrapped TPCs 94.2 %"
#> [1] "Predicting bootstrapped TPCs 94.3 %"
#> [1] "Predicting bootstrapped TPCs 94.3 %"
#> [1] "Predicting bootstrapped TPCs 94.4 %"
#> [1] "Predicting bootstrapped TPCs 94.5 %"
#> [1] "Predicting bootstrapped TPCs 94.6 %"
#> [1] "Predicting bootstrapped TPCs 94.6 %"
#> [1] "Predicting bootstrapped TPCs 94.7 %"
#> [1] "Predicting bootstrapped TPCs 94.8 %"
#> [1] "Predicting bootstrapped TPCs 94.9 %"
#> [1] "Predicting bootstrapped TPCs 94.9 %"
#> [1] "Predicting bootstrapped TPCs 95 %"
#> [1] "Predicting bootstrapped TPCs 95.1 %"
#> [1] "Predicting bootstrapped TPCs 95.2 %"
#> [1] "Predicting bootstrapped TPCs 95.2 %"
#> [1] "Predicting bootstrapped TPCs 95.3 %"
#> [1] "Predicting bootstrapped TPCs 95.4 %"
#> [1] "Predicting bootstrapped TPCs 95.5 %"
#> [1] "Predicting bootstrapped TPCs 95.5 %"
#> [1] "Predicting bootstrapped TPCs 95.6 %"
#> [1] "Predicting bootstrapped TPCs 95.7 %"
#> [1] "Predicting bootstrapped TPCs 95.8 %"
#> [1] "Predicting bootstrapped TPCs 95.8 %"
#> [1] "Predicting bootstrapped TPCs 95.9 %"
#> [1] "Predicting bootstrapped TPCs 96 %"
#> [1] "Predicting bootstrapped TPCs 96.1 %"
#> [1] "Predicting bootstrapped TPCs 96.1 %"
#> [1] "Predicting bootstrapped TPCs 96.2 %"
#> [1] "Predicting bootstrapped TPCs 96.3 %"
#> [1] "Predicting bootstrapped TPCs 96.4 %"
#> [1] "Predicting bootstrapped TPCs 96.4 %"
#> [1] "Predicting bootstrapped TPCs 96.5 %"
#> [1] "Predicting bootstrapped TPCs 96.6 %"
#> [1] "Predicting bootstrapped TPCs 96.7 %"
#> [1] "Predicting bootstrapped TPCs 96.7 %"
#> [1] "Predicting bootstrapped TPCs 96.8 %"
#> [1] "Predicting bootstrapped TPCs 96.9 %"
#> [1] "Predicting bootstrapped TPCs 97 %"
#> [1] "Predicting bootstrapped TPCs 97.1 %"
#> [1] "Predicting bootstrapped TPCs 97.1 %"
#> [1] "Predicting bootstrapped TPCs 97.2 %"
#> [1] "Predicting bootstrapped TPCs 97.3 %"
#> [1] "Predicting bootstrapped TPCs 97.4 %"
#> [1] "Predicting bootstrapped TPCs 97.4 %"
#> [1] "Predicting bootstrapped TPCs 97.5 %"
#> [1] "Predicting bootstrapped TPCs 97.6 %"
#> [1] "Predicting bootstrapped TPCs 97.7 %"
#> [1] "Predicting bootstrapped TPCs 97.7 %"
#> [1] "Predicting bootstrapped TPCs 97.8 %"
#> [1] "Predicting bootstrapped TPCs 97.9 %"
#> [1] "Predicting bootstrapped TPCs 98 %"
#> [1] "Predicting bootstrapped TPCs 98 %"
#> [1] "Predicting bootstrapped TPCs 98.1 %"
#> [1] "Predicting bootstrapped TPCs 98.2 %"
#> [1] "Predicting bootstrapped TPCs 98.3 %"
#> [1] "Predicting bootstrapped TPCs 98.3 %"
#> [1] "Predicting bootstrapped TPCs 98.4 %"
#> [1] "Predicting bootstrapped TPCs 98.5 %"
#> [1] "Predicting bootstrapped TPCs 98.6 %"
#> [1] "Predicting bootstrapped TPCs 98.6 %"
#> [1] "Predicting bootstrapped TPCs 98.7 %"
#> [1] "Predicting bootstrapped TPCs 98.8 %"
#> [1] "Predicting bootstrapped TPCs 98.9 %"
#> [1] "Predicting bootstrapped TPCs 98.9 %"
#> [1] "Predicting bootstrapped TPCs 99 %"
#> [1] "Predicting bootstrapped TPCs 99.1 %"
#> [1] "Predicting bootstrapped TPCs 99.2 %"
#> [1] "Predicting bootstrapped TPCs 99.2 %"
#> [1] "Predicting bootstrapped TPCs 99.3 %"
#> [1] "Predicting bootstrapped TPCs 99.4 %"
#> [1] "Predicting bootstrapped TPCs 99.5 %"
#> [1] "Predicting bootstrapped TPCs 99.5 %"
#> [1] "Predicting bootstrapped TPCs 99.6 %"
#> [1] "Predicting bootstrapped TPCs 99.7 %"
#> [1] "Predicting bootstrapped TPCs 99.8 %"
#> [1] "Predicting bootstrapped TPCs 99.8 %"
#> [1] "Predicting bootstrapped TPCs 99.9 %"
#> [1] "Predicting bootstrapped TPCs 100 %"The bootstrapped uncertainty curves can be plotted easily with the
plot_uncertainties() function.
plot_uncertainties(bootstrap_uncertainties_tpcs = preds_boots_aphid,
temp = b.schwartzi_satar2002$temperature,
dev_rate = b.schwartzi_satar2002$rate_value,
species = "Brachycaudus schwartzi",
life_stage = "Nymphs")
#> Warning: Removed 89 rows containing missing values (`geom_line()`).
Once a model have been selected under both ecological realism and
statistical criteria, the user can estimate the thermal boundaries
defining the suitable range of temperatures for the studied population.
The thermal_suitability_bounds() function calculate these values given
the tibble output from predict_curves() function and the selected
model name (note that only one model is allowed each time for this
function). Additionally, a value of suitability defining the
quantile-upper part of the curve can be provided by the user
(predict_curves() function, this function inherits the bootstrapped
TPCs to calculate thermal suitability boundaries for each bootstrapped
curved in addition to the estimated curve.
boundaries_aphid <- therm_suit_bounds(preds_tbl = preds_boots_aphid,
model_name = "lactin2",
suitability_threshold = 80)
print(boundaries_aphid)
#> # A tibble: 102 × 6
#> model_name suitability tval_left tval_right pred_suit iter
#> <chr> <chr> <dbl> <dbl> <dbl> <int>
#> 1 lactin2 80 % NA NA NA NA
#> 2 lactin2 80 % 21.8 37.2 0.111 1
#> 3 lactin2 80 % NA NA 0.132 2
#> 4 lactin2 80 % 21.6 35.8 0.115 3
#> 5 lactin2 80 % 20.7 37.3 0.112 4
#> 6 lactin2 80 % 21.3 36.6 0.110 5
#> 7 lactin2 80 % 21.4 36.1 0.118 6
#> 8 lactin2 80 % 22.4 35.2 0.117 7
#> 9 lactin2 80 % 21.1 37.7 0.110 8
#> 10 lactin2 80 % 21.6 35.7 0.117 9
#> # ℹ 92 more rowsUsing the thermal boundaries provided by the previous function and a set of raster maps of monthly temperatures for a given region (which can be provided by the user or downloaded by the function), a map can be produced showing where (and for how many months a year) thermal conditions are suitable for the development of the pest.
# downloading data from geodata::wordlclim_global. It will take several minutes the first time you use the function on the same 'path'.
# risk_rast <- map_risk(t_vals = c(thermal_boundaries_sharpshooter$tval_left,
# thermal_boundaries_sharpshooter$tval_right),
# path = "~/downloaded_maps", # directory to download data
# region = "Réunion",
# verbose = TRUE)
# terra::plot(risk_rast[[13]]) # the last layer represents the sum of suitable months within a year; the first 12 layers, the monthly binary value (1, if suitable; 0, if not suitable).
#we can also save the raster with:
# terra::writeRaster(risk_rast, filename = "~/output_maps/risk_rast.tif")
# Alternatively, if you already have a raster of monthly average temperatures for your region of interest, you can use it as an input of `map_risk()`
## load it (here Luxembourg data)
#tavg_file <- system.file("extdata/tavg_lux.tif", package = "mappestRisk")
### convert it into a raster-compatible file with `terra`
#tavg_rast <- terra::rast(tavg_file)
### and apply the function
#risk_rast_binary <- map_risk(t_vals = c(thermal_boundaries_sharpshooter$tval_left,
# thermal_boundaries_sharpshooter$tval_right#),
# t_rast = tavg_rast)
# terra::plot(risk_rast_binary[[13]]) # the last layer represents the sum of suitable months within a year; the 12-th previous ones, the monthly binary value (1, if suitable; 0, if not suitable).#example <- interactive_map(x = risk_rast_binary, map_type = "high",
# path_out = paste0(tempdir(), "test_map.html"))
#example
#htmlwidgets::saveWidget(example,file = "index.html")A provisional example of the kind of output from interactive_map() is
shown in the following animated picture:
If using this package, please cite it:
citation("mappestRisk")
To cite mappestRisk in publications use:
San Segundo Molina, D., Barbosa, A.M., Pérez-Luque, A.J. &
Rodríguez-Sánchez, F. 2023. mappestRisk: Create Maps Forecasting Risk
of Pest Occurrence
https://ecologyr.github.io/templateRpackage/mappestRisk
A BibTeX entry for LaTeX users is
@Manual{,
title = {mappestRisk},
author = {Darío {San-Segundo Molina} and A. Márcia Barbosa and Antonio Jesús Pérez-Luque and Francisco Rodríguez-Sánchez},
year = {2024},
url = {https://ecologyr.github.io/templateRpackage/mappestRisk},
}The development of this software has been funded by Fondo Europeo de Desarrollo Regional (FEDER) and Consejería de Transformación Económica, Industria, Conocimiento y Universidades of Junta de Andalucía (proyecto US-1381388 led by Francisco Rodríguez Sánchez, Universidad de Sevilla).
Cheng, Joe, Bhaskar Karambelkar, and Yihui Xie. 2022. “Leaflet: Create Interactive Web Maps with the JavaScript ’Leaflet’ Library.” https://CRAN.R-project.org/package=leaflet.
Padfield, Daniel, and Granville Matheson. 2020. “Nls.multstart: Robust Non-Linear Regression Using AIC Scores.” https://CRAN.R-project.org/package=nls.multstart.
Padfield, Daniel, Hannah O’Sullivan, and Samraat Pawar. 2021. “rTPC and Nls.multstart: A New Pipeline to Fit Thermal Performance Curves in r.” Methods in Ecology and Evolution 12 (6): 1138–43. https://doi.org/10.1111/2041-210X.13585.
Pinheiro, José, Douglas Bates, and R Core Team. 2022. “Nlme: Linear and Nonlinear Mixed Effects Models.” https://CRAN.R-project.org/package=nlme.
Rebaudo, François, Quentin Struelens, and Olivier Dangles. 2018. “Modelling Temperature-Dependent Development Rate and Phenology in Arthropods: The devRate Package for r.” Methods in Ecology and Evolution 9 (4): 1144–50. https://doi.org/https://doi.org/10.1111/2041-210X.12935.
Taylor, Rachel A., Sadie J. Ryan, Catherine A. Lippi, David G. Hall, Hossein A. Narouei-Khandan, Jason R. Rohr, and Leah R. Johnson. 2019. “Predicting the Fundamental Thermal Niche of Crop Pests and Diseases in a Changing World: A Case Study on Citrus Greening.” Journal of Applied Ecology 56 (8): 2057–68. https://doi.org/10.1111/1365-2664.13455.
Footnotes
-
At least 4 unique temperatures are required. Fore more details, see documentation and vignettes. ↩