| title | output | ||||
|---|---|---|---|---|---|
Analyzing MLG distribution |
|
In this document, I will create a graph that shows the distribution of MLGs across populations
library('tidyverse')
library('poppr')
library('igraph')
library("ggraph")I'm loading the data and splitting it into the 11 locus and 16 locus versions
load("data/sclerotinia_16_loci.rda")Now we can inspect the genotype accumulation curves. Notice that the 16 loci version plateaus, but we know that these extra loci are inconsistent, so we might not want to trust them.
locus_table(dat)##
## allele = Number of observed alleles
## 1-D = Simpson index
## Hexp = Nei's 1978 gene diversity
## ------------------------------------------
## summary
## locus allele 1-D Hexp Evenness
## 5-2(F) 4.000 0.451 0.452 0.616
## 5-3(F) 12.000 0.839 0.841 0.790
## 6-2(F) 3.000 0.643 0.645 0.949
## 7-2(F) 7.000 0.727 0.729 0.764
## 8-3(H) 7.000 0.740 0.742 0.789
## 9-2(F) 9.000 0.347 0.348 0.406
## 12-2(H) 5.000 0.579 0.580 0.779
## 17-3(H) 7.000 0.551 0.553 0.526
## 20-3(F) 2.000 0.053 0.053 0.420
## 36-4(F) 4.000 0.255 0.256 0.502
## 50-4(F) 3.000 0.257 0.257 0.629
## 55-4(F) 10.000 0.721 0.723 0.656
## 92-4(F) 9.000 0.796 0.799 0.807
## 106-4(H) 32.000 0.918 0.920 0.605
## 110-4(H) 5.000 0.754 0.756 0.915
## 114-4(H) 10.000 0.828 0.831 0.801
## mean 8.062 0.591 0.593 0.685
set.seed(2017-06-28)
genotype_curve(dat, sample = 1000, quiet = TRUE)
gt16 <- last_plot() +
theme_bw(base_size = 16, base_family = "Helvetica") +
stat_smooth() +
ggtitle("Haplotype accumulation curve for 16 loci") +
ylab("Number of multilocus haplotypes")
genotype_curve(dat11, sample = 1000, quiet = TRUE)
gt11 <- last_plot() +
theme_bw(base_size = 16, base_family = "Helvetica") +
stat_smooth() +
ggtitle("Haplotype accumulation curve for 11 loci") +
ylab("Number of multilocus haplotypes")Creating contracted genotypes for use later
mlg.filter(dat, distance = bruvo.dist, replen = other(dat)$REPLEN) <- .Machine$double.eps
dat##
## This is a genclone object
## -------------------------
## Genotype information:
##
## 187 contracted multilocus genotypes
## (0) [t], (bruvo.dist) [d], (farthest) [a]
## 366 haploid individuals
## 16 codominant loci
##
## Population information:
##
## 5 strata - MCG, Region, Source, Year, Host
## 14 populations defined - NE, NY, MN, ..., France, Mexico, ND
mlg.filter(dat11, distance = bruvo.dist, replen = other(dat11)$REPLEN) <- .Machine$double.eps
dat11##
## This is a genclone object
## -------------------------
## Genotype information:
##
## 165 contracted multilocus genotypes
## (0) [t], (bruvo.dist) [d], (farthest) [a]
## 366 haploid individuals
## 11 codominant loci
##
## Population information:
##
## 5 strata - MCG, Region, Source, Year, Host
## 14 populations defined - NE, NY, MN, ..., France, Mexico, ND
mll(dat) <- "original"
mll(dat11) <- "original"We can use mlg.crosspop() to tabulte which MLGs cross populations.
I realized that it's possible to use an MLG table with matrix multiplication to get an adjency matrix. Here I'm making a function to create a list of graphs.
The vertices, representing populations, will have the following attributes:
- Size: equal to the number of MLGs within the population
- Weight: fraction of private MLGs
The edges, representing multilocus genotypes are a bit trickier to handle since multiple edges can represent a single MLG passing through populations. They have the following attributes:
- Label: the MLG this edge belongs to. Note that multiple edges can share the same label.
- Width: the number of populations this MLG passes through
- Weight: 1 - (probability of a second encounter by chance); 1 - psex
The reason why I'm weighting these nodes as 1 - psex is for subsequent community analysis. The more likely you are to encounter a genotype by chance, the less influence that genotype should have on the connectivity.
rerange <- function(x){
minx <- min(x, na.rm = TRUE)
maxx <- max(x, na.rm = TRUE)
if (minx < 0)
x <- x + abs(minx)
maxx <- maxx + abs(minx)
if (maxx > 1)
x <- x/maxx
return(x)
}
make_graph_list <- function(dat){ # dat is a genclone/snpclone object
# w <- pgen(dat, by_pop = FALSE) %>% rowSums() %>% exp() %>% setNames(paste0("MLG.", mll(dat)))
# w <- w[unique(names(w))]
w <- psex(dat, by_pop = FALSE, method = "multiple") %>% split(mll(dat))
names(w)<- paste0("MLG.", names(w))
datmlg <- mlg.table(dat, plot = FALSE) > 0 # presence/absence of MLG
crosses <- mlg.crosspop(dat, quiet = TRUE, df = TRUE) %>% tbl_df()
adjmat <- datmlg %*% t(datmlg)
cols <- sort(colnames(adjmat))
adjmat <- adjmat[cols, cols]
# Creating Graph
g <- graph_from_adjacency_matrix(adjmat, mode = "undirected", diag = FALSE)
V(g)$size <- diag(adjmat)
g <- delete_vertices(g, degree(g) == 0)
shared_mlg <- (crosses %>% group_by(Population) %>% summarize(n = n()))$n
V(g)$weight <- shared_mlg/V(g)$size # fraction of shared MLGs
el <- as_adj_edge_list(g)
el <- el[lengths(el) > 0]
popgraphs <- setNames(vector(mode = "list", length = length(el) + 1), c(names(el), "total"))
for (v in names(el)){
idx <- el[[v]]
mlgs <- crosses %>% # How to get all MLGs from a single population:
filter(Population == v) %>% # Grab only the population e and then
select(MLG) %>% # remove everything but the MLGs to do an
inner_join(crosses, by = "MLG") %>% # inner join of the original list and then
filter(Population != v) %>% # remove the query population to give
arrange(Population) # the neigboring populations in order.
MLGS <- as.character(mlgs$MLG)
E(g)[idx]$label <- substr(MLGS, 5, nchar(MLGS))
E(g)[idx]$width <- as.integer(table(MLGS)[MLGS]) # size == n populations visited
E(g)[idx]$weight <- 1 - map_dbl(w[MLGS], 2) # weight == 1 - psex 2nd encounter
popgraphs[[v]] <- subgraph.edges(g, eids = idx)
}
popgraphs[["total"]] <- g
popgraphs
}
plot_mlg_graph <- function(g, glayout = NULL, label = TRUE, seed = 2017-06-28){
set.seed(seed)
if (is.null(glayout)){
glayout <- layout_nicely(g)
colnames(glayout) <- c("x", "y")
} else {
glayout <- glayout[V(g)$name, ]
}
shared_mlg <- V(g)$weight * V(g)$size
g <- add_vertices(g, length(V(g)), size = V(g)$size - shared_mlg, color = "grey90")
g2 <- g
V(g2)$label <- ifelse(!is.na(V(g2)$name), sprintf("%s [(%d/%d)]", V(g2)$name, shared_mlg, V(g2)$size), NA)
glay <- create_layout(g2, "manual", node.positions = as.data.frame(rbind(glayout, glayout)))
x_nudge <- ifelse(abs(glay$x) == 1, -glay$x/10, glay$x/10)
breaks <- quantile(1 - E(g)$weight)
breaks <- setNames(breaks, format(breaks, digits = 2))
outg <- ggraph(glay) +
geom_edge_fan(aes(alpha = 1 - weight, width = width + 1)) +
geom_node_circle(aes(r = sqrt(size)/30, fill = size))
outg <- if (label) outg + geom_node_label(aes(label = label), repel = TRUE, parse = TRUE, label.size = 0.75, nudge_x = x_nudge, segment.size = 0, segment.alpha = 0) else outg
outg +
viridis::scale_fill_viridis(option = "C") +
scale_edge_alpha_continuous(range = c(1, 0.25), breaks = rev(breaks)) +
scale_edge_width_continuous(range = c(0.25, 1.25), breaks = c(2:5)) +
coord_fixed() +
theme_void() +
theme(text = element_text(size = 14)) +
labs(list(
# title = "Shared MLGs across regions",
fill = "Number of\nMLHs",
edge_alpha = "Probability of\nsecond encounter",
edge_width = "Populations\nper MLH"#,
#caption = "Outer circle: Number of MLGs in the region\nInner Circle: Number of private MLGs in the region"
))
}
plot_mlg_subgraph <- function(graphlist){
for (i in names(graphlist)){
pg <- graphlist[[i]]
labs <- ifelse(E(pg)$width > 1, E(pg)$label, NA)
labs <- ifelse(duplicated(labs), NA, labs)
plot(pg,
main = i,
layout = layout_as_star(pg, center = i),
edge.width = E(pg)$width,
edge.color = grey(rerange(1 - E(pg)$weight)),
edge.label = labs)
}
}
good_layout <- read.table(
text =
" x y
Australia 0.8090169943749470071737 5.877852522924730260812e-01
CA -1.0000000000000000000000 1.224646799147350002426e-16
CO -0.3090169943749480063744 -9.510565162951539752711e-01
France -0.3090169943749470071737 9.510565162951539752711e-01
MI 0.0000000000000000000000 0.000000000000000000000e+00
MN 1.0000000000000000000000 0.000000000000000000000e+00
ND 0.3090169943749470071737 -9.510565162951539752711e-01
NE -0.8090169943749470071737 -5.877852522924730260812e-01
NY 0.8090169943749470071737 -5.877852522924730260812e-01
OR 0.3090169943749470071737 9.510565162951539752711e-01
WA -0.8090169943749470071737 5.877852522924730260812e-01"
) %>% as.matrix()
alt_layout <- read.table(
text =
" x y
Australia 0.8090169943749470071737 5.877852522924730260812e-01
OR -1.0000000000000000000000 1.224646799147350002426e-16
CO -0.3090169943749480063744 -9.510565162951539752711e-01
WA -0.3090169943749470071737 9.510565162951539752711e-01
MI 0.0000000000000000000000 0.000000000000000000000e+00
MN 1.0000000000000000000000 0.000000000000000000000e+00
ND 0.3090169943749470071737 -9.510565162951539752711e-01
NE -0.8090169943749470071737 -5.877852522924730260812e-01
NY 0.8090169943749470071737 -5.877852522924730260812e-01
France 0.3090169943749470071737 9.510565162951539752711e-01
CA -0.8090169943749470071737 5.877852522924730260812e-01"
) %>% as.matrix()
alt_layout <- alt_layout[rownames(good_layout), ]With the fuctions above, we can create and plot the graphs.
# Creating the graphs
graph16loc <- make_graph_list(dat)
graph11loc <- make_graph_list(dat[loc = keeploci, mlg.reset = TRUE])g <- graph_from_adjacency_matrix(matrix(0, 2, 2))
V(g)$size <- c(43, 43 - 32)
V(g)$label <- c("Number of MLHs in Region", "Number of private MLHs")
lay <- as.data.frame(matrix(0, 2, 2, dimnames = list(NULL, c("x", "y"))))
glegend <- create_layout(g, "manual", node.positions = as.data.frame(lay)) %>% ggraph() +
geom_node_circle(aes(r = sqrt(size)*5, fill = size)) +
coord_fixed() +
viridis::scale_fill_viridis(option = "C", begin = 1 - 32/43, end = 43/56, guide = "none") +
ggrepel::geom_text_repel(aes(label = label),
x = c(6, -2) + 20,
y = c(20, -6),
nudge_x = 150,
segment.size = 1,
arrow = arrow(length = unit(0.15, "native")),
family = "Helvetica") +
theme_void() +
# theme(plot.background = element_rect(color = "black", fill = "grey98")) +
xlim(c(-60, 480))
glegend
Each subgraph shows all of the connections for a single population.
# Plotting the subgraphs
par(mfrow = c(3, 4))
plot_mlg_subgraph(graph16loc[-length(graph16loc)])
par(mfrow = c(3, 4))
plot_mlg_subgraph(graph11loc[-length(graph11loc)])
I'm plotting two graphs here because it's useful to see if both of them are congruent in their community predictions.
First, I'm going to show the results of a community analysis. I'm using the
igraph function cluster_optimal() to cluster the nodes.
par(mfrow = c(1, 1))
(g16o <- cluster_optimal(graph16loc$total))## IGRAPH clustering optimal, groups: 3, mod: 0.2
## + groups:
## $`1`
## [1] "Australia" "France" "MN"
##
## $`2`
## [1] "CA" "OR" "WA"
##
## $`3`
## [1] "CO" "MI" "ND" "NE"
##
gg16 <- plot_mlg_graph(graph16loc$total, alt_layout) #+ labs(list(subtitle = "(16 loci)"))
gg16## Warning: Removed 10 rows containing missing values (geom_label_repel).
ggsave(filename = "results/figures/publication/FigureS1Z.pdf", width = 88, height = (6.25/7)*88, units = "mm", scale = 2)## Warning: Removed 10 rows containing missing values (geom_label_repel).
suppressWarnings(
gg16cp <- cowplot::ggdraw(xlim = c(0, 1), ylim = c(0, 1)) +
cowplot::draw_plot(gg16, x = 0, y = 0.05) +
cowplot::draw_plot(glegend, x = -0.0125, y = 0, height = 0.1)
)
gg16cp
cowplot::ggsave(plot = gg16cp,
file = file.path(PROJHOME, "results", "figures", "publication", "mlg-16.pdf"),
width = 88,
height = (6.25/7)*88,
units = "mm",
scale = 2)What we see is that We are given three clusters showing a clustering of the plains states, the west coast, and Australia, France, and Minnesota. The last cluster is likely driven by the single genotype shared between these three regions that has a low probability of a second encounter.
(g11o <- cluster_optimal(graph11loc$total))## IGRAPH clustering optimal, groups: 3, mod: 0.17
## + groups:
## $`1`
## [1] "Australia" "France" "MN"
##
## $`2`
## [1] "CA" "NY" "OR" "WA"
##
## $`3`
## [1] "CO" "MI" "ND" "NE"
##
gg11 <- plot_mlg_graph(graph11loc$total, alt_layout)
gg11## Warning: Removed 11 rows containing missing values (geom_label_repel).
ggsave(filename = "results/figures/publication/Figure3Z.pdf", width = 88, height = (6.25/7)*88, units = "mm", scale = 2)## Warning: Removed 11 rows containing missing values (geom_label_repel).
suppressWarnings(
gg11cp <- cowplot::ggdraw(xlim = c(0, 1), ylim = c(0, 1)) +
cowplot::draw_plot(gg11, x = 0, y = 0.05) +
cowplot::draw_plot(glegend, x = -0.0125, y = 0, height = 0.1)
)
gg11cp
cowplot::ggsave(plot = gg11cp,
file = file.path(PROJHOME, "results", "figures", "publication", "mlg-11.pdf"),
width = 88,
height = (6.25/7)*88,
units = "mm",
scale = 2)save(graph16loc, graph11loc, alt_layout, file = "data/mlg-crosspop-graph.rda")Here I am using DAPC to assess how cohesive these artificial regions are.
g11o <- igraph::cluster_optimal(graph11loc$total)
comm <- igraph::communities(g11o)
names(comm) <- c("International", "Costal", "Midwest")
comm## $International
## [1] "Australia" "France" "MN"
##
## $Costal
## [1] "CA" "NY" "OR" "WA"
##
## $Midwest
## [1] "CO" "MI" "ND" "NE"
strata(dat11) <- strata(dat11) %>%
mutate(MLGRegion = case_when(
.$Region %in% comm$International ~ "International",
.$Region %in% comm$Costal ~ "Costal",
.$Region %in% comm$Midwest ~ "Midwest",
TRUE ~ as.character(.$Region)
))
setPop(dat11) <- ~MLGRegionset.seed(2017-07-12)
reg <- xvalDapc(tab(dat11), pop(dat11), n.rep = 100)## Warning in xvalDapc.matrix(tab(dat11), pop(dat11), n.rep = 100): 1
## group has only 1 member so it cannot be represented in both training and
## validation sets.
reg$DAPC## #################################################
## # Discriminant Analysis of Principal Components #
## #################################################
## class: dapc
## $call: dapc.data.frame(x = as.data.frame(x), grp = ..1, n.pca = ..2,
## n.da = ..3)
##
## $n.pca: 40 first PCs of PCA used
## $n.da: 5 discriminant functions saved
## $var (proportion of conserved variance): 0.985
##
## $eig (eigenvalues): 681.7 62.45 58.11 13.78 8.412 vector length content
## 1 $eig 5 eigenvalues
## 2 $grp 366 prior group assignment
## 3 $prior 6 prior group probabilities
## 4 $assign 366 posterior group assignment
## 5 $pca.cent 69 centring vector of PCA
## 6 $pca.norm 69 scaling vector of PCA
## 7 $pca.eig 58 eigenvalues of PCA
##
## data.frame nrow ncol
## 1 $tab 366 40
## 2 $means 6 40
## 3 $loadings 40 5
## 4 $ind.coord 366 5
## 5 $grp.coord 6 5
## 6 $posterior 366 6
## 7 $pca.loadings 69 40
## 8 $var.contr 69 5
## content
## 1 retained PCs of PCA
## 2 group means
## 3 loadings of variables
## 4 coordinates of individuals (principal components)
## 5 coordinates of groups
## 6 posterior membership probabilities
## 7 PCA loadings of original variables
## 8 contribution of original variables
scatter(reg$DAPC, col = viridis::viridis(6), bg = "grey90")
ggcompoplot::ggcompoplot(reg$DAPC, dat11, pal = viridis::viridis(6), cols = 2)
reg$DAPC$posterior %>%
as_tibble() %>%
bind_cols(data.frame(Population = reg$DAPC$grp)) %>%
group_by(Population) %>%
summarize_all(mean) %>%
gather(assignment, probability, -Population) %>%
ggplot(aes(x = assignment, y = probability)) +
geom_segment(aes(xend = assignment, yend = 0)) +
geom_point(pch = 21, fill = "grey") +
facet_wrap(~Population) +
scale_y_continuous(limits = c(0, 1),
minor_breaks = c(seq(0, 1, by = 0.125)),
breaks = c(0, 0.5, 1)) +
theme_bw(base_size = 16, base_family = "Helvetica") +
theme(legend.position = "top") +
theme(aspect.ratio = 1/2) +
theme(axis.text = element_text(color = "black")) +
theme(axis.ticks.y = element_blank()) +
theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust = 1)) +
theme(panel.grid.major.x = element_line(linetype = 0, color = "grey50")) +
theme(panel.grid.major = element_line(colour = "grey20")) +
theme(panel.grid.minor = element_line(linetype = 3, colour = "grey50")) +
theme(strip.background = element_rect(color = NA, fill = "grey90")) +
theme(strip.text = element_text(face = "bold", hjust = 0.05)) +
theme(panel.border = element_blank()) +
xlab("Population Assignment") +
ylab("Mean Probability")
Session Information
## Session info --------------------------------------------------------------------------------------
## setting value
## version R version 3.4.2 (2017-09-28)
## system x86_64, linux-gnu
## ui X11
## language (EN)
## collate en_US.UTF-8
## tz UTC
## date 2018-04-12
## Packages ------------------------------------------------------------------------------------------
## package * version date source
## ade4 * 1.7-8 2017-08-09 cran (@1.7-8)
## adegenet * 2.1.0 2017-10-12 cran (@2.1.0)
## ape 5.0 2017-10-30 cran (@5.0)
## assertr 2.0.2.2 2017-06-06 cran (@2.0.2.2)
## assertthat 0.2.0 2017-04-11 CRAN (R 3.4.2)
## base * 3.4.2 2018-03-01 local
## bindr 0.1 2016-11-13 CRAN (R 3.4.2)
## bindrcpp * 0.2 2017-06-17 CRAN (R 3.4.2)
## boot 1.3-20 2017-07-30 cran (@1.3-20)
## broom 0.4.3 2017-11-20 CRAN (R 3.4.2)
## cellranger 1.1.0 2016-07-27 CRAN (R 3.4.2)
## cli 1.0.0 2017-11-05 CRAN (R 3.4.2)
## cluster 2.0.6 2017-03-16 CRAN (R 3.4.2)
## coda 0.19-1 2016-12-08 cran (@0.19-1)
## codetools 0.2-15 2016-10-05 CRAN (R 3.4.2)
## colorspace 1.3-2 2016-12-14 CRAN (R 3.4.2)
## compiler 3.4.2 2018-03-01 local
## cowplot 0.9.1 2017-11-16 cran (@0.9.1)
## crayon 1.3.4 2017-09-16 CRAN (R 3.4.2)
## datasets * 3.4.2 2018-03-01 local
## deldir 0.1-14 2017-04-22 cran (@0.1-14)
## devtools 1.13.4 2017-11-09 CRAN (R 3.4.2)
## digest 0.6.12 2017-01-27 CRAN (R 3.4.2)
## dplyr * 0.7.4 2017-09-28 CRAN (R 3.4.2)
## evaluate 0.10.1 2017-06-24 CRAN (R 3.4.2)
## expm 0.999-2 2017-03-29 cran (@0.999-2)
## ezknitr 0.6 2016-09-16 cran (@0.6)
## fastmatch 1.1-0 2017-01-28 cran (@1.1-0)
## forcats * 0.2.0 2017-01-23 CRAN (R 3.4.2)
## foreign 0.8-69 2017-06-21 CRAN (R 3.4.2)
## gdata 2.18.0 2017-06-06 cran (@2.18.0)
## ggcompoplot 0.1.0 2018-04-09 Github (zkamvar/ggcompoplot@bcf007d)
## ggforce 0.1.1 2016-11-28 cran (@0.1.1)
## ggplot2 * 2.2.1 2016-12-30 CRAN (R 3.4.2)
## ggraph * 1.0.0 2017-02-24 cran (@1.0.0)
## ggrepel 0.7.0 2017-09-29 cran (@0.7.0)
## glue 1.2.0 2017-10-29 CRAN (R 3.4.2)
## gmodels 2.16.2 2015-07-22 cran (@2.16.2)
## graphics * 3.4.2 2018-03-01 local
## grDevices * 3.4.2 2018-03-01 local
## grid 3.4.2 2018-03-01 local
## gridExtra 2.3 2017-09-09 CRAN (R 3.4.2)
## gtable 0.2.0 2016-02-26 CRAN (R 3.4.2)
## gtools 3.5.0 2015-05-29 cran (@3.5.0)
## haven 1.1.0 2017-07-09 CRAN (R 3.4.2)
## highr 0.6 2016-05-09 CRAN (R 3.4.2)
## hms 0.4.0 2017-11-23 CRAN (R 3.4.2)
## htmltools 0.3.6 2017-04-28 CRAN (R 3.4.2)
## httpuv 1.3.5 2017-07-04 CRAN (R 3.4.2)
## httr 1.3.1 2017-08-20 CRAN (R 3.4.2)
## igraph * 1.1.2 2017-07-21 CRAN (R 3.4.2)
## jsonlite 1.5 2017-06-01 CRAN (R 3.4.2)
## KernSmooth 2.23-15 2015-06-29 cran (@2.23-15)
## knitr * 1.17 2017-08-10 CRAN (R 3.4.2)
## labeling 0.3 2014-08-23 CRAN (R 3.4.2)
## lattice 0.20-35 2017-03-25 CRAN (R 3.4.2)
## lazyeval 0.2.1 2017-10-29 CRAN (R 3.4.2)
## LearnBayes 2.15 2014-05-29 cran (@2.15)
## lubridate 1.7.1 2017-11-03 CRAN (R 3.4.2)
## magrittr 1.5 2014-11-22 CRAN (R 3.4.2)
## MASS 7.3-47 2017-04-21 CRAN (R 3.4.2)
## Matrix 1.2-12 2017-11-16 CRAN (R 3.4.2)
## memoise 1.1.0 2017-04-21 CRAN (R 3.4.2)
## methods * 3.4.2 2018-03-01 local
## mgcv 1.8-22 2017-09-19 CRAN (R 3.4.2)
## mime 0.5 2016-07-07 CRAN (R 3.4.2)
## mnormt 1.5-5 2016-10-15 CRAN (R 3.4.2)
## modelr 0.1.1 2017-07-24 CRAN (R 3.4.2)
## munsell 0.4.3 2016-02-13 CRAN (R 3.4.2)
## nlme 3.1-131 2017-02-06 CRAN (R 3.4.2)
## parallel 3.4.2 2018-03-01 local
## pegas 0.10 2017-05-03 cran (@0.10)
## permute 0.9-4 2016-09-09 cran (@0.9-4)
## phangorn 2.3.1 2017-11-01 cran (@2.3.1)
## pkgconfig 2.0.1 2017-03-21 CRAN (R 3.4.2)
## plyr 1.8.4 2016-06-08 CRAN (R 3.4.2)
## poppr * 2.5.0 2017-09-11 cran (@2.5.0)
## psych 1.7.8 2017-09-09 CRAN (R 3.4.2)
## purrr * 0.2.4 2017-10-18 CRAN (R 3.4.2)
## quadprog 1.5-5 2013-04-17 cran (@1.5-5)
## R.methodsS3 1.7.1 2016-02-16 cran (@1.7.1)
## R.oo 1.21.0 2016-11-01 cran (@1.21.0)
## R.utils 2.6.0 2017-11-05 cran (@2.6.0)
## R6 2.2.2 2017-06-17 CRAN (R 3.4.2)
## Rcpp 0.12.14 2017-11-23 CRAN (R 3.4.2)
## readr * 1.1.1 2017-05-16 CRAN (R 3.4.2)
## readxl 1.0.0 2017-04-18 CRAN (R 3.4.2)
## reshape2 1.4.2 2016-10-22 CRAN (R 3.4.2)
## rlang 0.1.4 2017-11-05 CRAN (R 3.4.2)
## rstudioapi 0.7 2017-09-07 CRAN (R 3.4.2)
## rvest 0.3.2 2016-06-17 CRAN (R 3.4.2)
## scales 0.5.0 2017-08-24 CRAN (R 3.4.2)
## seqinr 3.4-5 2017-08-01 cran (@3.4-5)
## shiny 1.0.5 2017-08-23 CRAN (R 3.4.2)
## sp 1.2-5 2017-06-29 CRAN (R 3.4.2)
## spData 0.2.6.7 2017-11-28 cran (@0.2.6.7)
## spdep 0.7-4 2017-11-22 cran (@0.7-4)
## splines 3.4.2 2018-03-01 local
## stats * 3.4.2 2018-03-01 local
## stringi 1.1.6 2017-11-17 CRAN (R 3.4.2)
## stringr * 1.2.0 2017-02-18 CRAN (R 3.4.2)
## tibble * 1.3.4 2017-08-22 CRAN (R 3.4.2)
## tidyr * 0.7.2 2017-10-16 CRAN (R 3.4.2)
## tidyselect 0.2.3 2017-11-06 CRAN (R 3.4.2)
## tidyverse * 1.2.1 2017-11-14 CRAN (R 3.4.2)
## tools 3.4.2 2018-03-01 local
## tweenr 0.1.5 2016-10-10 cran (@0.1.5)
## udunits2 0.13 2016-11-17 cran (@0.13)
## units 0.4-6 2017-08-27 cran (@0.4-6)
## utils * 3.4.2 2018-03-01 local
## vegan 2.4-4 2017-08-24 cran (@2.4-4)
## viridis 0.4.0 2017-03-27 CRAN (R 3.4.2)
## viridisLite 0.2.0 2017-03-24 CRAN (R 3.4.2)
## withr 2.1.0 2017-11-01 CRAN (R 3.4.2)
## xml2 1.1.1 2017-01-24 CRAN (R 3.4.2)
## xtable 1.8-2 2016-02-05 CRAN (R 3.4.2)