Linking yield with NLR PAV
Philipp Bayer
2020-09-22
Last updated: 2020-11-18
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Knit directory: R_gene_analysis/
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| Rmd | 92e2580 | Philipp Bayer | 2020-11-18 | fixed lme4 syntax |
| html | 262a76f | Philipp Bayer | 2020-11-05 | Build site. |
| Rmd | 69e9c29 | Philipp Bayer | 2020-11-05 | wflow_publish(“analysis/yield_link.Rmd”) |
| html | 5ddfe2b | Philipp Bayer | 2020-11-05 | Build site. |
| Rmd | 25f0f54 | Philipp Bayer | 2020-11-05 | wflow_publish(“analysis/yield_link.Rmd”) |
| html | fa5c0ff | Philipp Bayer | 2020-11-04 | Build site. |
| Rmd | 2d9c3db | Philipp Bayer | 2020-11-04 | wflow_publish(c(“analysis/index.Rmd”, “analysis/yield_link.Rmd”)) |
| html | f34dd48 | Philipp Bayer | 2020-11-02 | Build site. |
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| Rmd | 5166687 | Philipp Bayer | 2020-11-02 | wflow_publish(“analysis/yield_link.Rmd”) |
| Rmd | dae157b | Philipp Bayer | 2020-09-24 | Update of analysis |
| html | dae157b | Philipp Bayer | 2020-09-24 | Update of analysis |
knitr::opts_chunk$set(warning = FALSE, message = FALSE)
library(tidyverse)-- Attaching packages ------------------------------------------------------------------------------------------------------------------- tidyverse 1.3.0 --v ggplot2 3.3.2 v purrr 0.3.4
v tibble 3.0.2 v dplyr 1.0.0
v tidyr 1.1.0 v stringr 1.4.0
v readr 1.3.1 v forcats 0.5.0-- Conflicts ---------------------------------------------------------------------------------------------------------------------- tidyverse_conflicts() --
x dplyr::filter() masks stats::filter()
x dplyr::lag() masks stats::lag()library(patchwork)
library(ggsci)
library(dabestr)Loading required package: magrittr
Attaching package: 'magrittr'The following object is masked from 'package:purrr':
set_namesThe following object is masked from 'package:tidyr':
extractlibrary(dabestr)
library(cowplot)
********************************************************Note: As of version 1.0.0, cowplot does not change the default ggplot2 theme anymore. To recover the previous behavior, execute:
theme_set(theme_cowplot())********************************************************
Attaching package: 'cowplot'The following object is masked from 'package:patchwork':
align_plotslibrary(ggsignif)
library(ggforce)
library(lme4)Loading required package: Matrix
Attaching package: 'Matrix'The following objects are masked from 'package:tidyr':
expand, pack, unpacklibrary(lmerTest)
Attaching package: 'lmerTest'The following object is masked from 'package:lme4':
lmerThe following object is masked from 'package:stats':
steplibrary(sjPlot)Learn more about sjPlot with 'browseVignettes("sjPlot")'.
Attaching package: 'sjPlot'The following objects are masked from 'package:cowplot':
plot_grid, save_plotlibrary(dotwhisker)
theme_set(theme_cowplot())Data loading
npg_col = pal_npg("nrc")(9)
col_list <- c(`Wild-type`=npg_col[8],
Landrace = npg_col[3],
`Old cultivar`=npg_col[2],
`Modern cultivar`=npg_col[4])
pav_table <- read_tsv('./data/soybean_pan_pav.matrix_gene.txt.gz')nbs <- read_tsv('./data/Lee.NBS.candidates.lst', col_names = c('Name', 'Class'))
nbs# A tibble: 486 x 2
Name Class
<chr> <chr>
1 UWASoyPan00953.t1 CN
2 GlymaLee.13G222900.1.p CN
3 GlymaLee.18G227000.1.p CN
4 GlymaLee.18G080600.1.p CN
5 GlymaLee.20G036200.1.p CN
6 UWASoyPan01876.t1 CN
7 UWASoyPan04211.t1 CN
8 GlymaLee.19G105400.1.p CN
9 GlymaLee.18G085100.1.p CN
10 GlymaLee.11G142600.1.p CN
# ... with 476 more rows# have to remove the .t1s
nbs$Name <- gsub('.t1','', nbs$Name)
nbs_pav_table <- pav_table %>% filter(Individual %in% nbs$Name)names <- c()
presences <- c()
for (i in seq_along(nbs_pav_table)){
if ( i == 1) next
thisind <- colnames(nbs_pav_table)[i]
pavs <- nbs_pav_table[[i]]
presents <- sum(pavs)
names <- c(names, thisind)
presences <- c(presences, presents)
}
nbs_res_tibb <- new_tibble(list(names = names, presences = presences))groups <- read_csv('./data/Table_of_cultivar_groups.csv')
groups <- groups %>%
mutate(`Group in violin table` = str_replace_all(`Group in violin table`, 'landrace', 'Landrace')) %>%
mutate(`Group in violin table` = str_replace_all(`Group in violin table`, 'Old_cultivar', 'Old cultivar')) %>%
mutate(`Group in violin table` = str_replace_all(`Group in violin table`, 'Modern_cultivar', 'Modern cultivar'))
groups$`Group in violin table` <-
factor(
groups$`Group in violin table`,
levels = c('Wild-type',
'Landrace',
'Old cultivar',
'Modern cultivar')
)
nbs_joined_groups <-
inner_join(nbs_res_tibb, groups, by = c('names' = 'Data-storage-ID'))Linking with yield
Can we link the trajectory of NLR genes with the trajectory of yield across the history of soybean breeding? let’s make a simple regression for now
Yield
yield <- read_tsv('./data/yield.txt')
yield_join <- inner_join(nbs_res_tibb, yield, by=c('names'='Line'))yield_join %>% ggplot(aes(x=presences, y=Yield)) + geom_hex() + geom_smooth() +
xlab('NLR gene count')
Protein
protein <- read_tsv('./data/protein_phenotype.txt')
protein_join <- left_join(nbs_res_tibb, protein, by=c('names'='Line')) %>% filter(!is.na(Protein))protein_join %>% ggplot(aes(x=presences, y=Protein)) + geom_hex() + geom_smooth() +
xlab('NLR gene count')
summary(lm(Protein ~ presences, data = protein_join))
Call:
lm(formula = Protein ~ presences, data = protein_join)
Residuals:
Min 1Q Median 3Q Max
-11.8479 -2.1274 -0.3336 1.9959 10.0949
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -7.98158 7.24125 -1.102 0.271
presences 0.11786 0.01624 7.258 8.07e-13 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 3.106 on 960 degrees of freedom
Multiple R-squared: 0.05203, Adjusted R-squared: 0.05104
F-statistic: 52.69 on 1 and 960 DF, p-value: 8.075e-13Seed weight
Let’s look at seed weight:
seed_weight <- read_tsv('./data/Seed_weight_Phenotype.txt', col_names = c('names', 'wt'))
seed_join <- left_join(nbs_res_tibb, seed_weight) %>% filter(!is.na(wt))seed_join %>% filter(wt > 5) %>% ggplot(aes(x=presences, y=wt)) + geom_hex() + geom_smooth() +
ylab('Seed weight') +
xlab('NLR gene count')
summary(lm(wt ~ presences, data = seed_join))
Call:
lm(formula = wt ~ presences, data = seed_join)
Residuals:
Min 1Q Median 3Q Max
-12.2910 -2.8692 0.1462 2.7771 19.6962
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 91.40656 14.67990 6.227 8.28e-10 ***
presences -0.17636 0.03298 -5.348 1.21e-07 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 4.714 on 690 degrees of freedom
Multiple R-squared: 0.0398, Adjusted R-squared: 0.0384
F-statistic: 28.6 on 1 and 690 DF, p-value: 1.213e-07Oil content
And now let’s look at the oil phenotype:
oil <- read_tsv('./data/oil_phenotype.txt')
oil_join <- left_join(nbs_res_tibb, oil, by=c('names'='Line')) %>% filter(!is.na(Oil))
oil_join# A tibble: 962 x 3
names presences Oil
<chr> <dbl> <dbl>
1 AB-01 445 17.6
2 AB-02 454 16.8
3 BR-24 455 20.6
4 ESS 454 20.9
5 For 448 21
6 HN001 448 23.6
7 HN002 444 18.5
8 HN003 446 17.5
9 HN004 442 18.9
10 HN005 440 15.5
# ... with 952 more rowsoil_join %>% ggplot(aes(x=presences, y=Oil)) + geom_hex() + geom_smooth() +
xlab('NLR gene count')
summary(lm(Oil ~ presences, data = oil_join))
Call:
lm(formula = Oil ~ presences, data = oil_join)
Residuals:
Min 1Q Median 3Q Max
-10.4376 -1.9081 0.4846 2.2401 9.0361
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 118.03941 7.31646 16.13 <2e-16 ***
presences -0.22591 0.01641 -13.77 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 3.139 on 960 degrees of freedom
Multiple R-squared: 0.1649, Adjusted R-squared: 0.1641
F-statistic: 189.6 on 1 and 960 DF, p-value: < 2.2e-16OK there are many, many outliers here. Clearly I’ll have to do something fancier - for example, using the first two PCs as covariates might get rid of some of those outliers.
Boxplots per group
Yield
nbs_joined_groups %>%
filter(!is.na(`Group in violin table`)) %>%
inner_join(yield, by=c('names'='Line')) %>%
ggplot(aes(x=`Group in violin table`, y=Yield, fill = `Group in violin table`)) +
geom_boxplot() +
scale_fill_manual(values = col_list) +
theme_minimal_hgrid() +
theme(axis.text.x = element_text(size=12),
axis.text.y = element_text(size=12)) +
geom_signif(comparisons = list(c('Old cultivar', 'Modern cultivar')),
map_signif_level = T) +
guides(fill=FALSE) +
ylab('Protein') +
xlab('Accession group')
And let’s check the dots:
nbs_joined_groups %>%
filter(!is.na(`Group in violin table`)) %>%
inner_join(yield_join, by = 'names') %>%
ggplot(aes(y=presences.x, x=Yield, color=`Group in violin table`)) +
geom_point() +
scale_color_manual(values = col_list) +
theme_minimal_hgrid() +
theme(axis.text.x = element_text(size=12),
axis.text.y = element_text(size=12)) +
ylab('NLR gene count')
nbs_joined_groups %>%
filter(!is.na(`Group in violin table`)) %>%
inner_join(yield_join, by = 'names') %>%
filter(`Group in violin table` != 'Landrace') %>%
ggplot(aes(x=presences.x, y=Yield, color=`Group in violin table`)) +
geom_point() +
scale_color_manual(values = col_list) +
theme_minimal_hgrid() +
geom_smooth() +
theme(axis.text.x = element_text(size=12),
axis.text.y = element_text(size=12)) +
xlab('NLR gene count')
## Protein
protein vs. the four groups:
nbs_joined_groups %>%
filter(!is.na(`Group in violin table`)) %>%
inner_join(protein, by=c('names'='Line')) %>%
ggplot(aes(x=`Group in violin table`, y=Protein, fill = `Group in violin table`)) +
geom_boxplot() +
scale_fill_manual(values = col_list) +
theme_minimal_hgrid() +
theme(axis.text.x = element_text(size=12),
axis.text.y = element_text(size=12)) +
geom_signif(comparisons = list(c('Wild-type', 'Landrace'),
c('Old cultivar', 'Modern cultivar')),
map_signif_level = T) +
guides(fill=FALSE) +
ylab('Protein') +
xlab('Accession group')
Seed weight
And seed weight:
nbs_joined_groups %>%
filter(!is.na(`Group in violin table`)) %>%
inner_join(seed_join) %>%
ggplot(aes(x=`Group in violin table`, y=wt, fill = `Group in violin table`)) +
geom_boxplot() +
scale_fill_manual(values = col_list) +
theme_minimal_hgrid() +
theme(axis.text.x = element_text(size=12),
axis.text.y = element_text(size=12)) +
geom_signif(comparisons = list(c('Wild-type', 'Landrace'),
c('Old cultivar', 'Modern cultivar')),
map_signif_level = T) +
guides(fill=FALSE) +
ylab('Seed weight') +
xlab('Accession group')
Wow, that’s breeding!
Oil content
And finally, Oil content:
nbs_joined_groups %>%
filter(!is.na(`Group in violin table`)) %>%
inner_join(oil_join, by = 'names') %>%
ggplot(aes(x=`Group in violin table`, y=Oil, fill = `Group in violin table`)) +
geom_boxplot() +
scale_fill_manual(values = col_list) +
theme_minimal_hgrid() +
theme(axis.text.x = element_text(size=12),
axis.text.y = element_text(size=12)) +
geom_signif(comparisons = list(c('Wild-type', 'Landrace'),
c('Old cultivar', 'Modern cultivar')),
map_signif_level = T) +
guides(fill=FALSE) +
ylab('Oil content') +
xlab('Accession group')
Oha, a single star. That’s p < 0.05!
Let’s redo the above hexplot, but also color the dots by group.
nbs_joined_groups %>%
filter(!is.na(`Group in violin table`)) %>%
inner_join(oil_join, by = 'names') %>%
ggplot(aes(x=presences.x, y=Oil, color=`Group in violin table`)) +
geom_point() +
scale_color_manual(values = col_list) +
theme_minimal_hgrid() +
theme(axis.text.x = element_text(size=12),
axis.text.y = element_text(size=12)) +
xlab('NLR gene count')
Oha, so it’s the wild-types that drag this out a lot.
Let’s remove them and see what it looks like:
nbs_joined_groups %>%
filter(!is.na(`Group in violin table`)) %>%
inner_join(oil_join, by = 'names') %>%
filter(`Group in violin table` %in% c('Old cultivar', 'Modern cultivar')) %>%
ggplot(aes(x=presences.x, y=Oil, color=`Group in violin table`)) +
geom_point() +
scale_color_manual(values = col_list) +
theme_minimal_hgrid() +
theme(axis.text.x = element_text(size=12),
axis.text.y = element_text(size=12)) +
xlab('NLR gene count') +
geom_smooth()
Let’s remove that one outlier:
nbs_joined_groups %>%
filter(!is.na(`Group in violin table`)) %>%
inner_join(oil_join, by = 'names') %>%
filter(`Group in violin table` %in% c('Old cultivar', 'Modern cultivar')) %>%
filter(Oil > 13) %>%
ggplot(aes(x=presences.x, y=Oil, color=`Group in violin table`)) +
geom_point() +
scale_color_manual(values = col_list) +
theme_minimal_hgrid() +
theme(axis.text.x = element_text(size=12),
axis.text.y = element_text(size=12)) +
xlab('NLR gene count') +
geom_smooth()
Does the above oil content boxplot become different if we exclude the one outlier? I’d bet so
nbs_joined_groups %>%
filter(!is.na(`Group in violin table`)) %>%
inner_join(oil_join, by = 'names') %>%
filter(names != 'USB-393') %>%
ggplot(aes(x=`Group in violin table`, y=Oil, fill = `Group in violin table`)) +
geom_boxplot() +
scale_fill_manual(values = col_list) +
theme_minimal_hgrid() +
theme(axis.text.x = element_text(size=12),
axis.text.y = element_text(size=12)) +
geom_signif(comparisons = list(c('Wild-type', 'Landrace'),
c('Old cultivar', 'Modern cultivar')),
map_signif_level = T) +
guides(fill=FALSE) +
ylab('Oil content') +
xlab('Accession group')
Nope, still significantly higher in modern cultivars!
Mixed modeling
Alright here’s my hypothesis: There’s a link between cultivar status (Old, Wild, Landrace, Modern), r-gene count, and yield, but it’s ‘hidden’ by country differences.
Great tutorial here: https://ourcodingclub.github.io/tutorials/mixed-models
So we’ll have to build some lme4 models!
Oil
nbs_joined_groups$presences2 <- scale(nbs_joined_groups$presences, center=T, scale=T)
hist(nbs_joined_groups$presences2)
oil_nbs_joined_groups <- nbs_joined_groups %>% inner_join(oil_join, by = 'names')
oil_nbs_joined_groups$Oil2 <- scale(oil_nbs_joined_groups$Oil, center=T, scale=T)basic.lm <- lm(Oil2 ~ presences2, data=oil_nbs_joined_groups)ggplot(oil_nbs_joined_groups, aes(x = presences2, y = Oil2)) +
geom_point() +
geom_smooth(method = "lm")
Hm looks messy, you can see two groups
plot(basic.lm, which = 1)
which is confirmed by the messy line
plot(basic.lm, which = 2)
and this garbage qqplot.
So let’s build an lmer model!
mixed.lmer <- lmer(Oil2 ~ presences2 + (1|`Group in violin table`), data=oil_nbs_joined_groups)
summary(mixed.lmer)Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Oil2 ~ presences2 + (1 | `Group in violin table`)
Data: oil_nbs_joined_groups
REML criterion at convergence: 1872.4
Scaled residuals:
Min 1Q Median 3Q Max
-4.5879 -0.5672 0.0869 0.6631 3.2111
Random effects:
Groups Name Variance Std.Dev.
Group in violin table (Intercept) 1.3349 1.1554
Residual 0.4075 0.6384
Number of obs: 951, groups: Group in violin table, 4
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) -0.04360 0.57867 2.99844 -0.075 0.9447
presences2 -0.05350 0.02394 947.27006 -2.234 0.0257 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr)
presences2 -0.004So the Variance for Group in violin table is 1.3349, that means it’s 1.3349/(1.3349+0.4075) *100 = 76% of the variance is explained by the four groups!
plot(mixed.lmer)
qqnorm(resid(mixed.lmer))
qqline(resid(mixed.lmer))
These still look fairly bad - better than before, but the QQ plot still isn’t on the line.
Let’s quickly check yield too
Yield
yield_nbs_joined_groups <- nbs_joined_groups %>% inner_join(yield_join, by = 'names')
yield_nbs_joined_groups$Yield2 <-scale(yield_nbs_joined_groups$Yield, center=T, scale=T)mixed.lmer <- lmer(Yield2 ~ presences2 + (1|`Group in violin table`), data=yield_nbs_joined_groups)
summary(mixed.lmer)Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Yield2 ~ presences2 + (1 | `Group in violin table`)
Data: yield_nbs_joined_groups
REML criterion at convergence: 2060.4
Scaled residuals:
Min 1Q Median 3Q Max
-3.1643 -0.6819 0.0316 0.6948 2.8002
Random effects:
Groups Name Variance Std.Dev.
Group in violin table (Intercept) 0.6466 0.8041
Residual 0.8600 0.9274
Number of obs: 761, groups: Group in violin table, 3
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 0.23641 0.46910 1.98335 0.504 0.664692
presences2 -0.15364 0.04172 757.46580 -3.683 0.000247 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr)
presences2 0.025 Percentage explained by breeding group: 0.6466 / (0.6466+0.8600)*100 = 42%
plot(mixed.lmer)
qqnorm(resid(mixed.lmer))
qqline(resid(mixed.lmer))
:O
p-value of 0.000247 for the normalised presences while accounting for the breeding group, that’s beautiful.
ggplot(yield_nbs_joined_groups, aes(x = presences2, y = Yield2)) +
facet_wrap(~`Group in violin table`, nrow=2) + # a panel for each mountain range
geom_point(alpha = 0.5) +
theme_classic() +
geom_line(data = cbind(yield_nbs_joined_groups, pred = predict(mixed.lmer)), aes(y = pred), size = 1) +
theme_minimal_hgrid() +
theme(legend.position = "none") +
xlab('Scaled and centered NLR gene count') +
ylab('Scaled and centered yield')
Making the breeding group fixed
We have < 10 possible factors in the group, so making that fixed instead of random
# this doesn't work because you need at least one random effect
# mixed.lmer <- lmer(Yield2 ~ presences2 + `Group in violin table`, data=yield_nbs_joined_groups)Adding country
We should also add the country the plant is from as a random effect, that definitely has an influence too (perhaps a stronger one???)
Yield
country <- read_csv('./data/Cultivar_vs_country.csv')
names(country) <- c('names', 'PI-ID', 'Country')
yield_country_nbs_joined_groups <- yield_nbs_joined_groups %>% inner_join(country)mixed.lmer <- lmer(Yield2 ~ presences2 + (1|`Group in violin table`) + (1|Country), data=yield_country_nbs_joined_groups)
summary(mixed.lmer)Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Yield2 ~ presences2 + (1 | `Group in violin table`) + (1 | Country)
Data: yield_country_nbs_joined_groups
REML criterion at convergence: 1957
Scaled residuals:
Min 1Q Median 3Q Max
-3.09429 -0.56737 0.03072 0.65680 2.89981
Random effects:
Groups Name Variance Std.Dev.
Country (Intercept) 0.3807 0.6170
Group in violin table (Intercept) 0.4178 0.6464
Residual 0.7614 0.8726
Number of obs: 741, groups: Country, 40; Group in violin table, 3
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 0.07150 0.40194 2.28533 0.178 0.87336
presences2 -0.11258 0.04116 726.98206 -2.735 0.00639 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr)
presences2 0.051 Nice! Yield is negatively correlated with the number of NLR genes when accounting for breeding group AND country
ggplot(yield_country_nbs_joined_groups, aes(x = presences2, y = Yield2, colour = Country)) +
facet_wrap(~`Group in violin table`, nrow=2) + # a panel for each mountain range
geom_point(alpha = 0.5) +
theme_classic() +
geom_line(data = cbind(yield_country_nbs_joined_groups, pred = predict(mixed.lmer)), aes(y = pred), size = 1) +
theme_minimal_hgrid() +
theme(legend.position = "none") +
xlab('Scaled and centered NLR gene count') +
ylab('Scaled and centered yield')
Some diagnostics:
plot(mixed.lmer)
qqnorm(resid(mixed.lmer))
qqline(resid(mixed.lmer))
Hm, the qqplot looks slightly worse than when I use maturity group alone, interesting!
BIG DISCLAIMER: Currently, I treat country and group not as nested variables, they’re independent. I think that is the way it should be in this case but I’m thinking.
Making the breeding group fixed
mixed.lmer <- lmer(Yield2 ~ presences2 + `Group in violin table` + (1|Country), data=yield_country_nbs_joined_groups)
summary(mixed.lmer)Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Yield2 ~ presences2 + `Group in violin table` + (1 | Country)
Data: yield_country_nbs_joined_groups
REML criterion at convergence: 1951.8
Scaled residuals:
Min 1Q Median 3Q Max
-3.1864 -0.5700 0.0305 0.6525 2.8982
Random effects:
Groups Name Variance Std.Dev.
Country (Intercept) 0.3776 0.6145
Residual 0.7616 0.8727
Number of obs: 741, groups: Country, 40
Fixed effects:
Estimate Std. Error df t value
(Intercept) -0.15265 0.13488 33.06645 -1.132
presences2 -0.11149 0.04117 726.45969 -2.708
`Group in violin table`Old cultivar -0.29578 0.16164 734.95182 -1.830
`Group in violin table`Modern cultivar 1.00458 0.22335 360.40725 4.498
Pr(>|t|)
(Intercept) 0.26588
presences2 0.00693 **
`Group in violin table`Old cultivar 0.06768 .
`Group in violin table`Modern cultivar 9.28e-06 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) prsnc2 `Givt`Oc
presences2 0.119
`Grivtbl`Oc -0.112 -0.008
`Grivtbl`Mc -0.194 0.065 0.156 Non-normalised yield
Let’s see whether the ‘raw’ values perform the same.
mixed.lmer <- lmer(Yield ~ presences.x + (1|`Group in violin table`) + (1|Country), data=yield_country_nbs_joined_groups)
summary(mixed.lmer)Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Yield ~ presences.x + (1 | `Group in violin table`) + (1 | Country)
Data: yield_country_nbs_joined_groups
REML criterion at convergence: 1679.6
Scaled residuals:
Min 1Q Median 3Q Max
-3.09429 -0.56737 0.03072 0.65680 2.89981
Random effects:
Groups Name Variance Std.Dev.
Country (Intercept) 0.2602 0.5101
Group in violin table (Intercept) 0.2856 0.5345
Residual 0.5205 0.7215
Number of obs: 741, groups: Country, 40; Group in violin table, 3
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 9.011013 2.481360 677.994843 3.631 0.000303 ***
presences.x -0.015192 0.005555 726.982171 -2.735 0.006389 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr)
presences.x -0.991Oh, lower p-values for the intercept
ggplot(yield_country_nbs_joined_groups, aes(x = presences.x, y = Yield, colour = Country)) +
facet_wrap(~`Group in violin table`, nrow=2) + # a panel for each mountain range
geom_point(alpha = 0.5) +
theme_classic() +
geom_line(data = cbind(yield_country_nbs_joined_groups, pred = predict(mixed.lmer)), aes(y = pred), size = 1) +
theme_minimal_hgrid() +
theme(legend.position = "none") +
xlab('Raw NLR gene count') +
ylab('Raw yield')
plot(mixed.lmer)
qqnorm(resid(mixed.lmer))
qqline(resid(mixed.lmer))
#### Making the breeding group fixed
mixed.lmer <- lmer(Yield ~ presences.x + `Group in violin table` + (1|Country), data=yield_country_nbs_joined_groups)
summary(mixed.lmer)Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Yield ~ presences.x + `Group in violin table` + (1 | Country)
Data: yield_country_nbs_joined_groups
REML criterion at convergence: 1675.1
Scaled residuals:
Min 1Q Median 3Q Max
-3.1864 -0.5700 0.0305 0.6525 2.8982
Random effects:
Groups Name Variance Std.Dev.
Country (Intercept) 0.2581 0.5081
Residual 0.5206 0.7216
Number of obs: 741, groups: Country, 40
Fixed effects:
Estimate Std. Error df t value
(Intercept) 8.760056 2.465570 726.660933 3.553
presences.x -0.015045 0.005556 726.459065 -2.708
`Group in violin table`Old cultivar -0.244554 0.133648 734.951816 -1.830
`Group in violin table`Modern cultivar 0.830604 0.184672 360.407255 4.498
Pr(>|t|)
(Intercept) 0.000406 ***
presences.x 0.006929 **
`Group in violin table`Old cultivar 0.067680 .
`Group in violin table`Modern cultivar 9.28e-06 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) prsnc. `Givt`Oc
presences.x -0.999
`Grivtbl`Oc 0.003 -0.008
`Grivtbl`Mc -0.074 0.065 0.156 Oh, lower p-values for the intercept
ggplot(yield_country_nbs_joined_groups, aes(x = presences.x, y = Yield, colour = Country)) +
facet_wrap(~`Group in violin table`, nrow=2) + # a panel for each mountain range
geom_point(alpha = 0.5) +
theme_classic() +
geom_line(data = cbind(yield_country_nbs_joined_groups, pred = predict(mixed.lmer)), aes(y = pred), size = 1) +
theme_minimal_hgrid() +
theme(legend.position = "none") +
xlab('Raw NLR gene count') +
ylab('Raw yield')
plot(mixed.lmer)
qqnorm(resid(mixed.lmer))
qqline(resid(mixed.lmer))
plot(resid(mixed.lmer))
Plotting effect of each covariate
(re.effects <- plot_model(mixed.lmer, type = "re", show.values = TRUE))
#lmerTest breaks these other packages so I better unload it and reload only lme4
detach("package:lmerTest", unload=TRUE)
yield_country_nbs_joined_groups_renamed <- yield_country_nbs_joined_groups
names(yield_country_nbs_joined_groups_renamed) <- c('names', 'presences.x', 'PI-ID', 'Group', 'presences2', 'presences.y', 'Yield', 'Yield2', 'Country')
mixed.lmer <- lmer(Yield2 ~ presences2 + Group + (1|Country), data=yield_country_nbs_joined_groups_renamed)
dwplot(mixed.lmer,
vline = geom_vline(xintercept = 0, colour = "grey60", linetype = 2))
library(stargazer)
stargazer(mixed.lmer, type = "text",
digits = 3,
star.cutoffs = c(0.05, 0.01, 0.001),
digit.separator = "")
==================================================
Dependent variable:
-----------------------------
Yield2
--------------------------------------------------
presences2 -0.111**
(0.041)
GroupOld cultivar -0.296
(0.162)
GroupModern cultivar 1.005***
(0.223)
Constant -0.153
(0.135)
--------------------------------------------------
Observations 741
Log Likelihood -975.906
Akaike Inf. Crit. 1963.812
Bayesian Inf. Crit. 1991.460
==================================================
Note: *p<0.05; **p<0.01; ***p<0.001library(ggeffects)
ggpredict(mixed.lmer, terms = c("presences2", 'Group'), type = "re") %>%
plot() +
theme_minimal()
Let’s also plot that for non-normalised data
mixed.lmer <- lmer(Yield ~ presences.x + Group + (1|Country), data=yield_country_nbs_joined_groups_renamed)
ggpredict(mixed.lmer, terms = c("presences.x", 'Group'), type = "re") %>%
plot() +
theme_minimal_hgrid() +
xlab('Raw NLR count') +
ylab('Raw yield')
# alright back to regular programming
library(lmerTest)
mixed.lmer <- lmer(Yield2 ~ presences2 + `Group in violin table` + (1|Country), data=yield_country_nbs_joined_groups)More complex models
If I add random slopes to either groups not much changes, I do get warnings indicating that there’s not much in the data:
mixed.lmer <- lmer(Yield2 ~ presences2 + (presences2|`Group in violin table`) + (1|Country), data=yield_country_nbs_joined_groups)
summary(mixed.lmer)Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Yield2 ~ presences2 + (presences2 | `Group in violin table`) +
(1 | Country)
Data: yield_country_nbs_joined_groups
REML criterion at convergence: 1954.8
Scaled residuals:
Min 1Q Median 3Q Max
-3.09789 -0.56422 0.04471 0.67067 2.88976
Random effects:
Groups Name Variance Std.Dev. Corr
Country (Intercept) 0.3920 0.6261
Group in violin table (Intercept) 0.3858 0.6211
presences2 0.0310 0.1761 0.30
Residual 0.7564 0.8697
Number of obs: 741, groups: Country, 40; Group in violin table, 3
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 0.02964 0.38964 2.29148 0.076 0.945
presences2 -0.22515 0.12370 1.66243 -1.820 0.235
Correlation of Fixed Effects:
(Intr)
presences2 0.269 mixed.lmer <- lmer(Yield2 ~ presences2 + `Group in violin table` + (1 + presences2|Country), data=yield_country_nbs_joined_groups)
summary(mixed.lmer)Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Yield2 ~ presences2 + `Group in violin table` + (1 + presences2 |
Country)
Data: yield_country_nbs_joined_groups
REML criterion at convergence: 1951.5
Scaled residuals:
Min 1Q Median 3Q Max
-3.1904 -0.5715 0.0314 0.6551 2.9003
Random effects:
Groups Name Variance Std.Dev. Corr
Country (Intercept) 0.397511 0.63048
presences2 0.002137 0.04623 1.00
Residual 0.761491 0.87263
Number of obs: 741, groups: Country, 40
Fixed effects:
Estimate Std. Error df t value
(Intercept) -0.1470 0.1387 28.1820 -1.060
presences2 -0.1162 0.0430 30.8335 -2.702
`Group in violin table`Old cultivar -0.3010 0.1615 733.1173 -1.863
`Group in violin table`Modern cultivar 1.0093 0.2192 166.8461 4.605
Pr(>|t|)
(Intercept) 0.2982
presences2 0.0111 *
`Group in violin table`Old cultivar 0.0628 .
`Group in violin table`Modern cultivar 8.15e-06 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) prsnc2 `Givt`Oc
presences2 0.334
`Grivtbl`Oc -0.109 -0.017
`Grivtbl`Mc -0.188 0.044 0.158
convergence code: 0
boundary (singular) fit: see ?isSingularOh, a significant p-value, let’s plot plot that and compare with he previous plot:
ggplot(yield_country_nbs_joined_groups, aes(x = presences2, y = Yield2, colour = Country)) +
facet_wrap(~`Group in violin table`, nrow=2) + # a panel for each mountain range
geom_point(alpha = 0.5) +
theme_classic() +
geom_line(data = cbind(yield_country_nbs_joined_groups, pred = predict(mixed.lmer)), aes(y = pred), size = 1) +
theme_minimal_hgrid() +
theme(legend.position = "none") +
xlab('Scaled and centered NLR gene count') +
ylab('Scaled and centered yield')
Quite similar, mostly downwards trajectories for each country.
Let’s do that non-normalised:
mixed.lmer <- lmer(Yield ~ presences.x + `Group in violin table` + (1 + presences.x|Country), data=yield_country_nbs_joined_groups)
summary(mixed.lmer)Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Yield ~ presences.x + `Group in violin table` + (1 + presences.x |
Country)
Data: yield_country_nbs_joined_groups
REML criterion at convergence: 1675.2
Scaled residuals:
Min 1Q Median 3Q Max
-3.1863 -0.5679 0.0294 0.6532 2.8982
Random effects:
Groups Name Variance Std.Dev. Corr
Country (Intercept) 5.191e-01 0.7204930
presences.x 2.402e-07 0.0004901 -0.98
Residual 5.206e-01 0.7215284
Number of obs: 741, groups: Country, 40
Fixed effects:
Estimate Std. Error df t value
(Intercept) 8.73673 2.46492 709.51652 3.544
presences.x -0.01499 0.00555 412.58876 -2.702
`Group in violin table`Old cultivar -0.24420 0.13365 733.16976 -1.827
`Group in violin table`Modern cultivar 0.83046 0.18493 218.59478 4.491
Pr(>|t|)
(Intercept) 0.000419 ***
presences.x 0.007186 **
`Group in violin table`Old cultivar 0.068096 .
`Group in violin table`Modern cultivar 1.15e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) prsnc. `Givt`Oc
presences.x -0.999
`Grivtbl`Oc 0.002 -0.007
`Grivtbl`Mc -0.076 0.067 0.156
convergence code: 0
unable to evaluate scaled gradient
Model failed to converge: degenerate Hessian with 2 negative eigenvaluesggplot(yield_country_nbs_joined_groups, aes(x = presences.x, y = Yield, colour = Country)) +
facet_wrap(~`Group in violin table`, nrow=2) + # a panel for each mountain range
geom_point(alpha = 0.5) +
theme_classic() +
geom_line(data = cbind(yield_country_nbs_joined_groups, pred = predict(mixed.lmer)), aes(y = pred), size = 1) +
theme_minimal_hgrid() +
theme(legend.position = "none") +
xlab('Raw NLR gene count') +
ylab('Raw yield')
Quite similar, mostly downwards trajectories for each country.
And now both random slopes:
mixed.lmer <- lmer(Yield2 ~ presences2 + (presences2|`Group in violin table`) + (1 + presences2|Country), data=yield_country_nbs_joined_groups)
summary(mixed.lmer)Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Yield2 ~ presences2 + (presences2 | `Group in violin table`) +
(1 + presences2 | Country)
Data: yield_country_nbs_joined_groups
REML criterion at convergence: 1953.7
Scaled residuals:
Min 1Q Median 3Q Max
-3.11214 -0.56909 0.04459 0.66469 2.91084
Random effects:
Groups Name Variance Std.Dev. Corr
Country (Intercept) 0.42704 0.6535
presences2 0.01045 0.1022 0.81
Group in violin table (Intercept) 0.37523 0.6126
presences2 0.04201 0.2050 0.18
Residual 0.75392 0.8683
Number of obs: 741, groups: Country, 40; Group in violin table, 3
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 0.03595 0.38772 2.35869 0.093 0.933
presences2 -0.23848 0.14300 1.96304 -1.668 0.240
Correlation of Fixed Effects:
(Intr)
presences2 0.231 ggplot(yield_country_nbs_joined_groups, aes(x = presences2, y = Yield2, colour = Country)) +
facet_wrap(~`Group in violin table`, nrow=2) + # a panel for each mountain range
geom_point(alpha = 0.5) +
theme_classic() +
geom_line(data = cbind(yield_country_nbs_joined_groups, pred = predict(mixed.lmer)), aes(y = pred), size = 1) +
theme_minimal_hgrid() +
theme(legend.position = "none") +
xlab('Scaled and centered NLR gene count') +
ylab('Scaled and centered yield')
Yeah, nah
Oil
oil_country_nbs_joined_groups <- oil_nbs_joined_groups %>% inner_join(country)
mixed.lmer <- lmer(Oil2 ~ presences2 + `Group in violin table` + (1|Country), data=oil_country_nbs_joined_groups)
summary(mixed.lmer)Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Oil2 ~ presences2 + `Group in violin table` + (1 | Country)
Data: oil_country_nbs_joined_groups
REML criterion at convergence: 1808.3
Scaled residuals:
Min 1Q Median 3Q Max
-4.5285 -0.5605 0.0983 0.6472 3.2209
Random effects:
Groups Name Variance Std.Dev.
Country (Intercept) 0.07703 0.2775
Residual 0.39128 0.6255
Number of obs: 929, groups: Country, 41
Fixed effects:
Estimate Std. Error df t value
(Intercept) -1.66466 0.09388 57.11719 -17.732
presences2 -0.03579 0.02416 917.65081 -1.481
`Group in violin table`Landrace 1.93042 0.06953 911.95172 27.763
`Group in violin table`Old cultivar 2.25628 0.11897 922.58914 18.965
`Group in violin table`Modern cultivar 2.46605 0.14998 209.92967 16.443
Pr(>|t|)
(Intercept) <2e-16 ***
presences2 0.139
`Group in violin table`Landrace <2e-16 ***
`Group in violin table`Old cultivar <2e-16 ***
`Group in violin table`Modern cultivar <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) prsnc2 `Givt` `Givt`Oc
presences2 -0.232
`Grpivtbl`L -0.644 0.434
`Grivtbl`Oc -0.405 0.249 0.509
`Grivtbl`Mc -0.447 0.246 0.432 0.338 No significance here.
Protein
protein_nbs_joined_groups <- nbs_joined_groups %>% inner_join(protein_join, by = 'names')
protein_nbs_joined_groups$Protein2 <- scale(protein_nbs_joined_groups$Protein, center=T, scale=T)
protein_country_nbs_joined_groups <- protein_nbs_joined_groups %>% inner_join(country)
mixed.lmer <- lmer(Protein2 ~ presences2 + `Group in violin table` + (1|Country), data=protein_country_nbs_joined_groups)
summary(mixed.lmer)Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Protein2 ~ presences2 + `Group in violin table` + (1 | Country)
Data: protein_country_nbs_joined_groups
REML criterion at convergence: 2472.7
Scaled residuals:
Min 1Q Median 3Q Max
-3.6001 -0.6747 -0.0423 0.6274 3.5103
Random effects:
Groups Name Variance Std.Dev.
Country (Intercept) 0.07042 0.2654
Residual 0.81212 0.9012
Number of obs: 929, groups: Country, 41
Fixed effects:
Estimate Std. Error df t value
(Intercept) 0.52736 0.11992 77.94050 4.397
presences2 0.04347 0.03466 923.71757 1.254
`Group in violin table`Landrace -0.72486 0.09980 923.95960 -7.263
`Group in violin table`Old cultivar -1.20226 0.17045 923.25626 -7.053
`Group in violin table`Modern cultivar -1.10372 0.20076 140.80066 -5.498
Pr(>|t|)
(Intercept) 3.43e-05 ***
presences2 0.21
`Group in violin table`Landrace 8.04e-13 ***
`Group in violin table`Old cultivar 3.42e-12 ***
`Group in violin table`Modern cultivar 1.76e-07 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) prsnc2 `Givt` `Givt`Oc
presences2 -0.277
`Grpivtbl`L -0.712 0.438
`Grivtbl`Oc -0.445 0.253 0.511
`Grivtbl`Mc -0.507 0.270 0.463 0.340 No significance here.
Seed weight
seed_nbs_joined_groups <- nbs_joined_groups %>% inner_join(seed_join, by = 'names')
seed_nbs_joined_groups$wt2 <- scale(seed_nbs_joined_groups$wt, center=T, scale=T)
seed_country_nbs_joined_groups <- seed_nbs_joined_groups %>% inner_join(country)
mixed.lmer <- lmer(wt2 ~ presences2 + `Group in violin table` + (1|Country), data=seed_country_nbs_joined_groups)
summary(mixed.lmer)Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: wt2 ~ presences2 + `Group in violin table` + (1 | Country)
Data: seed_country_nbs_joined_groups
REML criterion at convergence: 1676
Scaled residuals:
Min 1Q Median 3Q Max
-2.9614 -0.6215 0.0110 0.5831 4.8138
Random effects:
Groups Name Variance Std.Dev.
Country (Intercept) 0.08566 0.2927
Residual 0.70082 0.8371
Number of obs: 664, groups: Country, 38
Fixed effects:
Estimate Std. Error df t value
(Intercept) -2.348857 0.183189 90.849260 -12.822
presences2 -0.007261 0.040531 656.652662 -0.179
`Group in violin table`Landrace 2.412123 0.166724 600.989922 14.468
`Group in violin table`Old cultivar 2.727120 0.224422 656.159635 12.152
`Group in violin table`Modern cultivar 2.782167 0.259555 67.478942 10.719
Pr(>|t|)
(Intercept) < 2e-16 ***
presences2 0.858
`Group in violin table`Landrace < 2e-16 ***
`Group in violin table`Old cultivar < 2e-16 ***
`Group in violin table`Modern cultivar 3.26e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) prsnc2 `Givt` `Givt`Oc
presences2 -0.267
`Grpivtbl`L -0.864 0.364
`Grivtbl`Oc -0.666 0.274 0.710
`Grivtbl`Mc -0.663 0.298 0.648 0.539 Again, no significance here.
sessionInfo()R version 3.6.3 (2020-02-29)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 17134)
Matrix products: default
locale:
[1] LC_COLLATE=English_Australia.1252 LC_CTYPE=English_Australia.1252
[3] LC_MONETARY=English_Australia.1252 LC_NUMERIC=C
[5] LC_TIME=English_Australia.1252
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] lmerTest_3.1-2 ggeffects_0.16.0 stargazer_5.2.2
[4] dotwhisker_0.5.0 sjPlot_2.8.6 lme4_1.1-21
[7] Matrix_1.2-18 ggforce_0.3.1 ggsignif_0.6.0
[10] cowplot_1.0.0 dabestr_0.3.0 magrittr_1.5
[13] ggsci_2.9 patchwork_1.0.0 forcats_0.5.0
[16] stringr_1.4.0 dplyr_1.0.0 purrr_0.3.4
[19] readr_1.3.1 tidyr_1.1.0 tibble_3.0.2
[22] ggplot2_3.3.2 tidyverse_1.3.0 workflowr_1.6.2.9000
loaded via a namespace (and not attached):
[1] TH.data_1.0-10 minqa_1.2.4 colorspace_1.4-1
[4] ellipsis_0.3.1 sjlabelled_1.1.7 rprojroot_1.3-2
[7] estimability_1.3 ggstance_0.3.4 parameters_0.9.0
[10] fs_1.5.0.9000 rstudioapi_0.11 glmmTMB_1.0.2.1
[13] hexbin_1.28.1 farver_2.0.3 fansi_0.4.1
[16] mvtnorm_1.1-1 lubridate_1.7.9 xml2_1.3.2
[19] codetools_0.2-16 splines_3.6.3 knitr_1.29
[22] sjmisc_2.8.5 polyclip_1.10-0 jsonlite_1.7.1
[25] nloptr_1.2.1 broom_0.5.6 dbplyr_1.4.4
[28] effectsize_0.3.0 compiler_3.6.3 httr_1.4.2
[31] sjstats_0.18.0 emmeans_1.4.5 backports_1.1.10
[34] assertthat_0.2.1 cli_2.0.2 later_1.1.0.1
[37] tweenr_1.0.1 htmltools_0.5.0 tools_3.6.3
[40] coda_0.19-3 gtable_0.3.0 glue_1.4.2
[43] Rcpp_1.0.5 cellranger_1.1.0 vctrs_0.3.1
[46] nlme_3.1-148 insight_0.10.0 xfun_0.17
[49] ps_1.3.4 rvest_0.3.5 lifecycle_0.2.0
[52] getPass_0.2-2 MASS_7.3-51.6 zoo_1.8-8
[55] scales_1.1.1 hms_0.5.3 promises_1.1.1
[58] sandwich_2.5-1 RColorBrewer_1.1-2 TMB_1.7.16
[61] yaml_2.2.1 stringi_1.5.3 bayestestR_0.7.5
[64] boot_1.3-25 rlang_0.4.7 pkgconfig_2.0.3
[67] evaluate_0.14 lattice_0.20-41 labeling_0.3
[70] processx_3.4.4 tidyselect_1.1.0 plyr_1.8.6
[73] R6_2.4.1 generics_0.0.2 multcomp_1.4-13
[76] DBI_1.1.0 mgcv_1.8-31 pillar_1.4.4
[79] haven_2.3.1 whisker_0.4 withr_2.2.0
[82] survival_3.2-3 performance_0.5.1 modelr_0.1.8
[85] crayon_1.3.4 utf8_1.1.4 rmarkdown_2.3
[88] grid_3.6.3 readxl_1.3.1 blob_1.2.1
[91] callr_3.4.4 git2r_0.27.1 reprex_0.3.0
[94] digest_0.6.25 xtable_1.8-4 httpuv_1.5.4
[97] numDeriv_2016.8-1.1 munsell_0.5.0