---
title: "Stable Isotope Trajectory Analysis (SITA)"
author: "Anthony STURBOIS"
date: "`r Sys.Date()`"
output: 
  rmarkdown::html_vignette:
    toc: TRUE
vignette: >
  %\VignetteIndexEntry{Stable Isotope Trajectory Analysis (SITA)}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignettePackage{ecotraj}
  \usepackage[utf8]{inputenc}
---

## 1. About this vignette

This vignette present some ecological applications used by Sturbois et al. (2021) in the new stable isotope trajectory analysis framework:

+ Sturbois, et al., Stable Isotope Trajectory Analysis (SITA): A new approach to quantify and visualize dynamics in stable isotope studies. Ecol. Monogr. (2021). https://doi.org/10.1002/ecm.1501

Example datasets have been included in the package for reproducibility. After the calculation of the necessary distance- and direction-based metrics, the vignette focuses, for each ecological applications, on the creation of trajectory charts.

## 2. Loading libraries
First of all, we load the required libraries, including `ecotraj`:
```{r load libraries, echo=FALSE}
library(ecotraj)
library(tidyr) ## For data manipulation
library(ggplot2) ## For plotting
library(hrbrthemes) ## Additional themes for ggplot2
library(scales) ## Scale functions for visualisation
library(viridis) ## Viridis color map
```

## 3. Spatial and temporal resource partitioning in fur seals


### 3.1 Fur seal stable isotope dataset
We begin by loading the package dataset `furseals`:

```{r load furseals, echo=T}
data("furseals")
```

This is a subset of the dataset provided in: 

+ Kernaléguen, L., Arnould, J.P.Y., Guinet, C., Cherel, Y., 2015.  Determinants of individual foraging specialization in large marine vertebrates, the Antarctic and subantarctic fur seals. *Journal of Animal Ecology* 1081–1091.

Briefly, fur seals [the Antarctic fur seal *Arctocephalus gazella* (AFS) and subantarctic fur seal *A. tropicalis* (SAFS)] whisker SI values yield unique long-term information on individual behaviour which integrates the spatial, trophic and temporal dimensions of the ecological niche. The foraging strategies of this two species of sympatric fur seals were examined in the winter 2001/2002 at Crozet, Amsterdam and Kerguelen Islands (Southern Ocean) using the stable isotope values of serially sampled whiskers. The method consists in the analysis of consecutive whisker sections (3 mm long) starting from the proximal (facial) end, with the most recently synthesized tissue remaining under the skin. Only individuals (n = 47) with whiskers totalizing at least 30 sections were selected in the initial data, and only those 30 sections were considered herein, from t1 (more recent values) to t30 (oldest values).



### 3.2 Trajectory metrics

In this section, we illustrate how to calculate trajectory metrics to characterize the foraging strategy of each fur seal. In the following sections, we show how to use these metrics as data to create plots. 

First, we calculate net changes relative to the initial state (i.e. the distance between stable isotope compositions (i.e state) of each whisker section and the initial stable isotope composition):
```{r, echo=T}
Net_changes<-trajectoryLengths2D(furseals[,c("d13C","d15N")],
                                 furseals$ID_SITA,
                                 furseals$Time, relativeToInitial=TRUE) 
head(Net_changes)
```

We then calculate trajectory segment lengths, i.e. the distance between the stable isotope composition of consecutive whisker sections in the stable isotope space:
```{r, echo=T}
Segment_lengths<-trajectoryLengths2D(furseals[,c("d13C","d15N")],
                                     furseals$ID_SITA,
                                     furseals$Time, relativeToInitial=FALSE) 
head(Segment_lengths)
```

Finally, we determine the angle ($\alpha$) of consecutive trajectory segments with respect to the second axis of the 2D stable isotope space:
```{r, echo=T}
Angles<-trajectoryAngles2D(furseals[,c("d13C","d15N")],
                           furseals$ID_SITA,
                           furseals$Time, betweenSegments=FALSE)
head(Angles)
```



### 3.3 Identification and characterization of trajectory clusters

Here we aim to define groups of fur seals depending on the similarity of their foraging strategy. We need first to calculate distances between pairs of complete trajectories in the stable isotope space:
```{r, echo=T}
D <- dist(furseals[,c("d13C","d15N")])
Ds<-trajectoryDistances(D, furseals$ID_SITA, surveys = NULL, distance.type = "DSPD",
                        symmetrization = "mean", add = TRUE, verbose = FALSE)
```

Then, we can use function `hclust()` to conduct a hierarchiacl clustering on the symmetric matrix `D`:
```{r, echo=TRUE, fig.height=4, fig.width=6}
colstd<-c("black","yellow","green","blue","grey","red")
pt<-c(16,16,16,16)
hsxy <- hclust(Ds, "ward.D2")
plot(hsxy,hang = -1, main="distance Fur Seals", cex=.6)
Hst=2 # Cutting height
x<-rect.hclust(hsxy, h=Hst,
               border = colstd)
```

We cut the dendrogram at height `Hst` to obtain a vector of cluster membership and copy it in `furseals` as a factor:
```{r}
groups <- cutree(hsxy, h=Hst)
furseals$cluster <- as.factor(groups)
```



#### 3.3.1 Individual trophic trajectories for males and females of *A. gazella* and *A. tropicalis*

Here we display trophic trajectories of all individuals, in plots corresponding to combinations of species and gender. To facilitate such plots, we create of a vector with the combination of species and gender:
```{r, echo=T}
furseals$sp_gender<-paste(furseals$Sexe, furseals$Species, sep=" ")
```

We now create a diagram to display fur seal trophic trajectories in the stable isotope space. Panels correspond to the combination of species and gender. In each panel, X-Y axes are defined by d13C and d15N stable isotope values. Arrows connects all whiskers section SI states from t1 to t30 (i.e. most recent to oldest SI state). Colors corresponds to trajectory clusters and shape to breeding sites:
```{r, echo=TRUE, fig.height=6, fig.width=6}
ggplot(data=furseals,aes(x=d13C,y=d15N,color=cluster,shape=Place))+
  geom_point()+
  geom_path(aes(x=d13C,y=d15N,group=ID_SITA,color=cluster),
            arrow = arrow(length = unit(0.10, "cm")))+
  xlab(expression(delta^13*"C"))+
  ylab(expression(delta^15*"N"))+
  facet_wrap(~sp_gender) +
  theme_classic()
```

#### 3.3.2 Net changes time series for males and females of both fur seal species

In this sub-section we display net changes time series for all individuals, in plots corresponding to combinations of species and gender
We prepare a subset of the data called `NC`: 
```{r}
NC<-Net_changes[,-30]
NC$cluster<-furseals$cluster[1:47]
NC$ID<-as.numeric(rownames(NC))
colnames(NC)<-c(2:30,"cluster","ID")
```

We then prepare the subset. We notably transform NC to a longer format, order the data set and add the vector sp_gender:
```{r}
NCline <- tidyr::pivot_longer(NC, 1:29, 
                              names_to ="Time_from_present", 
                              values_to="Net_changes", 
                              names_transform = function(x) {as.numeric(x)-1}) 
colnames(NCline)[1:2]<-c("Clusters", "ID")
NCline <- NCline[order(NCline$Time_from_present, decreasing=FALSE),]
NCline <- as.data.frame(NCline)
NCline$sp_gender<-c(furseals$sp_gender[1:47])
```

We now create the plot to display net changes time series for all individuals in panel corresponding Arrows connects all whiskers section stable isotope values from t1 to t30 (i.e. most recent to oldest stable isotope values). Colours corresponds to trajectory clusters:
```{r, fig.height=4, fig.width=6}
ggplot(data=NCline,aes(x=Time_from_present,y=Net_changes,color=Clusters))+
  geom_path(aes(x=Time_from_present,y=Net_changes,group=ID,color=Clusters),
            arrow = arrow(length = unit(0.10, "cm")))+
  facet_wrap(~sp_gender)+
  theme_classic()
```


#### 3.3.3 Angle $\alpha$ trajectory roses of Fur seals trajectory cluster.

In this sub-section, we plot the distribution of Angle $\alpha$ values in a trajectory rose  
We prepare the data set to compute the trajectory rose and transform to a long data structure.
We create a vector of direction to class Angle $\alpha$ values by range of 15°:
```{r}
Angl<-Angles
colnames(Angl)<-2:30
Angl$ID<-as.numeric(rownames(Angl))
Angl$cluster<-as.factor(groups)
Angl$sp_gender<-furseals$sp_gender[1:47]

Angline<- tidyr::pivot_longer(Angl, 1:29, 
                              names_to ="Time_from_present", 
                              values_to="Direction", 
                              names_transform = function(x) {as.numeric(x)-1}) 
colnames(Angline)[c(2,3)] = c("Clusters", "Group")

# range 15°
deg <- 15
# vector for range of direction of different bars
dir.breaks <- seq(0-(deg/2), 360+(deg/2), deg)
dir.binned <- cut(Angline$Direction,
                  breaks = dir.breaks,
                  ordered_result = TRUE)
# direction labels
dir.labels <- as.character(c(seq(0, 360-deg, by = deg), 0))
levels(dir.binned) <- dir.labels

# angles distribution in each range of direction
Angline$dir.binned <- dir.binned

# sort angles
df_sorted<-as.data.frame(table(Angline$dir.binned, Angline$Clusters))
colnames(df_sorted)<-c("dir.binned","Clusters","nb")
df_sorted = df_sorted[order(df_sorted$dir.binned),]
```

We now create the trajectory rose. Angles $\alpha$ were calculated in 2D $\Omega \delta$ space ($\delta 13C/\delta 15N$) and represented by range (15$\circ$) of direction. Bars size represent the number of trajectory segments (all individual within each trajectory clusters). 
```{r, fig.height=4, fig.width=6}
ggplot(data=df_sorted, aes(x=dir.binned, y=nb, fill=Clusters)) +
  geom_bar(stat="identity")+
  scale_y_continuous(limits = c(0,110), expand = c(0, 0), 
                     breaks = c(0,25,50,75,110), 
                     labels = c(0,25,50,75,110)) +
  labs(x = 'Trajectory segment directions within fur seals clusters', y = 'number of trajectory segments') +
  coord_polar(start = -(deg/2)*(pi/180)) +
  theme_minimal()
```

## 4. Ontogenic stable isotope trajectories of juvenile fishes

In this section, we illustrate how to calculate trajectory metrics to characterize the ontogenic stable isotope trajectories of juvenile fishes. In the following sections, we show how to use these metrics as data to create a trajectory diagram. 

### 4.1 Loading data

We begin by loading the package dataset `pike`:
```{r load Pike data}
data("pike")
```
This is a data set from :

+ Cucherousset, J., Paillisson, J.-M., Roussel, J.-M., 2013. Natal departure timing from spatially varying environments is dependent of individual ontogenetic status. *Naturwissenschaften* 100, 761–768.

Briefly, Cucherousset et al. (2013) released 192 individually tagged, hatchery-raised,  juvenile pike (*Esox lucius* L.) with variable initial trophic position (fin $\delta13C/\delta15N$ values). Based on $\delta15N$ values, individuals were classified into zooplanktivorous ($\delta15N$ < 10 ‰) and piscivorous ($\delta15N$ > 10 ‰) as cannibalism is commonly observed in this species. Individuals were released in a temporarily flooded grassland where pike eggs usually hatch of the Brière marsh (France) to identify the determinants of juvenile natal departure. The release site was connected through a unique point to an adjacent pond used as a nursery habitat. Fish were continuously recaptured when migrating from flooded grassland to adjacent pond. Recaptured individuals (n = 29) were anaesthetized, checked for tags, measured for fork length, fin-clipped to quantify changes in $\delta13C$ and $\delta15N$ values, and released. 


### 4.2 Calculating trajectory metrics and identification of trajectory clusters

First, we calculate net changes relative to the initial state for each individual (i.e. the distance between stable isotope compositions at release and at recapture):
```{r}
Net_changes<-trajectoryLengths2D(pike[,7:8],pike$ID,pike$Time, relativeToInitial=TRUE) 
colnames(Net_changes)<-c("Net_changes", "Trajectory")
pike$Net_Changes<-Net_changes$Net_changes
```

Then, we can use function `hclust()` to conduct a hierarchiacl clustering on the symmetric matrix `D`:
```{r}
D=dist(pike[,7:8])
Ds<-trajectoryDistances(D,pike$ID, surveys = NULL, distance.type = "DSPD",
                        symmetrization = "mean", add = TRUE, verbose = FALSE)
```

We cut the dendrogram at height `Hst` to obtain a vector of cluster membership and copy it in `pike`:
```{r, fig.height=4, fig.width=6}
Hst=3
colstd<-c("black","yellow","green","blue","grey","red")
hsxy <- hclust(Ds, "ward.D2")
plot(hsxy,hang = -1, main="distance Pike", cex=.6)
x<-rect.hclust (hsxy, h=Hst,
                border = colstd)
# Store clusters into a new data column
pike$Cluster<-cutree(hsxy, h=Hst)
```


### 4.3 Trajectory diagram of pike released in the flooded grassland and recaptured when emigrating into the adjacent pond

We prepare the data set to compute trajectory diagrams and density curves:
```{r}
Pike1<-pike[pike$Time %in% 1,]
Pike1<-Pike1[order(Pike1$ID, decreasing=FALSE),]
Pike1$Net_changes<-0
Pike2<-pike[pike$Time %in% 2,]
Pike2<-Pike2[order(Pike2$ID, decreasing=FALSE),]
Pike2$Net_changes<-Net_changes$Net_changes
data<-as.data.frame(rbind(Pike1,Pike2))
```

We create the trajectory diagram. Arrows represent trajectory path for each pit-tagged individual. Colors correspond to trajectory clusters. The dashed line separates piscivorous from zooplanktivorous individuals [zooplanktivorous ($\delta15N$ < 10) vs piscivorous ($\delta15N$ > 10)]. 
```{r, fig.height=4, fig.width=6}
ggplot(data=data,aes(x=d13C,y=d15N,shape=Trophic_status_initial))+
  geom_point(aes(size=Net_changes))+
  geom_path(aes(x=d13C,y=d15N,group=ID,color=factor(Cluster)),arrow = arrow(length = unit(0.30, "cm")))+
  geom_hline(yintercept=10, linetype="dashed", color = "black")+
  xlab(expression(delta^13*"C")) +
  ylab(expression(delta^15*"N"))+
  theme_minimal()
```

Density curves X represents the distribution of all samples according to $\delta13C$ values, and capture (green=release; red=departure):
```{r, fig.height=3, fig.width=4}
gg_dist_d13C = ggplot(data, aes(d13C, fill=TimeL)) + geom_density(alpha=.5) 
gg_dist_d13C = gg_dist_d13C + ylab(expression(delta^13*"C"*" density"))
gg_dist_d13C = gg_dist_d13C + theme(axis.title.y=element_blank(),
                                    axis.text=element_blank(),
                                    axis.line=element_blank(),
                                    axis.ticks=element_blank(),
                                    panel.grid.major = element_blank(),
                                    panel.grid.minor = element_blank(),
                                    panel.background =element_blank())
gg_dist_d13C = gg_dist_d13C + theme(legend.position = "none")
gg_dist_d13C + scale_x_continuous(limits = c(-33, -25))+scale_y_continuous(limits = c(0, 1))
```

Density curves Y represents the distribution of all samples according to $\delta15N$ values, and capture (green=release; red=departure):
```{r, fig.height=3, fig.width=4}
gg_dist_d15N = ggplot(data, aes(d15N, fill=TimeL)) + geom_density(alpha=.5) 
gg_dist_d15N = gg_dist_d15N + ylab(expression(delta^15*"N"*" density"))
gg_dist_d15N =gg_dist_d15N 
gg_dist_d15N =gg_dist_d15N + coord_flip()
gg_dist_d15N =gg_dist_d15N + theme(axis.title.y=element_blank(),
                                   axis.text=element_blank(),
                                   axis.line=element_blank(),
                                   axis.ticks=element_blank(),
                                   panel.grid.major = element_blank(),
                                   panel.grid.minor = element_blank(),
                                   panel.background =element_blank())
gg_dist_d15N =gg_dist_d15N +theme(legend.position = "none")
gg_dist_d15N + scale_x_continuous(limits = c(7, 14))+scale_y_continuous(limits = c(0, 1))
```

## 5. Spatio-temporal variability of $\delta 13C$ and $\delta 15N$ modelled isoscapes in the Northeast Pacific
In this section, we illustrate how to use trajectory metrics to characterize the spatio-temporal variability of $\delta 13C$ and $\delta 15N$ modelled isoscapes in the Northeast Pacific in an isoscape trajectory map and a trajectory heat map 

The datasets used in this application come from: 

+ Espinasse, B., Hunt, B.P.V., Batten, S.D., Pakhomov, E.A., 2020. Defining isoscapes in the Northeast Pacific as an index of ocean productivity. Global Ecol Biogeogr 29, 246–261.

Briefly, Espinasse et al. (2020) tested the application of isoscapes modelled from satellite data to the description of secondary production in the Northeast pacific. The output model fits in a 0.25° x 0.25° spatial grid covering the region spanning from 46 to 62°N and from 195 to 235°E and supporting $\delta13C$ and $\delta15N$ isoscapes from 1998 to 2017. We subset modelled $\delta13C$ and $\delta15N$ values of a 1° x 1° spatial grid from the original modelled dataset. Isoscapes modelled for 2013, 2015 and 2017 were selected as they were characterised by high stable isotope dynamics and consequently constitutes relevant inputs to test our isoscape trajectory map concept. Additionally, a long-term SITA analysis was performed from 1998 to 2017 using directions and net changes calculated for all pairs of dates (1998-1999,... ,2016-2017) as input for a trajectory heat map.

### 5.1 2013-2015 Isoscape trajectory maps 

We begin by loading the package dataset `isoscape`:
```{r load Alaska}
data("isoscape")
```


We calculate Segment lengths and Angle $\alpha$ for each stations to assess, respectively, the magnitude and the nature of change in the stable isotope space between 2013 and 2015. We then prepare a data set to compute the isoscape trajectory map with notably: Latitude, Longitude, Years, Angles and segment lenghts values:  
```{r}
sites<-isoscape$station
surveys<-isoscape$Year
Angl<-trajectoryAngles2D(isoscape[,3:4],sites,surveys, betweenSegments = FALSE)
Length<-trajectoryLengths2D(isoscape[,3:4],sites,surveys)
data<-as.data.frame(cbind(isoscape[1:489,],Angl,Length[,1]))
colnames(data)<-c("Latitude","Longitude","d13C","d15N","Stations","Years","Angles","Lengths")
head(data)
```

Angles $\alpha$ need to be transformed for the use with `geom_spoke`. We then add transformed values in a new column `Angles2`.
```{r}
angle<-data$Angles
Angles2<-c()
for (i in 1:length(angle)) {
  Angles2[i] <- c(ifelse(angle[i]==0,(angle[i]-270)*pi/180,
                         ifelse(angle[i]==180,(angle[i]-270)*pi/180,
                                ifelse(angle[i]==90,(angle[i]+270)*pi/180,
                                       ifelse(angle[i]==270,(angle[i]+270)*pi/180,
                                              ifelse(angle[i]==360,(angle[i]-270)*pi/180,  
                                                     ifelse(angle[i]>0 & angle[i]<90 ,(90-angle[i])*pi/180,
                                                            ifelse(angle[i]>90 & angle[i]<180 ,(90-angle[i])*pi/180,
                                                                   ifelse(angle[i]>180 & angle[i]<270,(180+(270-angle[i]))*pi/180,
                                                                          ifelse(angle[i]>270 & angle[i]<360,(90+(360-angle[i]))*pi/180,"ERROR"))))))))))
}

data$Angles2<-Angles2
```

We now create the Isoscape trajectory map. In this kind of map, Segment lengths and Angles $\alpha$ are mapped to illustrate stable isotope spatio-temporal dynamics. Direction of arrows (angle $\alpha$) illustrate direction (i.e. the nature of change) in the modelled 2D $\Omega \delta$ space according to increase and/or decrease in $\delta13C$ and $\delta15N$ values (0-90°: + $\delta13C$ and + $\delta15N$; 90-180°: + $\delta13C$ and - $\delta15N$; 90-180°: + $\delta13C$ and - $\delta15N$; 180-270°: + $\delta13C$ and - $\delta15N$). Length of arrows and colored background rasters illustrate modelled trajectory segment length at each station (i.e. the magnitude of change).
```{r, fig.height=4, fig.width=6}
ggplot(data, 
          aes(x = Longitude, 
              y = Latitude, 
              fill = Lengths, 
              angle = Angles2, 
              radius = rescale(Lengths, c(0.3, 1)))) +
  geom_raster(interpolate = TRUE) +
  geom_spoke(arrow = arrow(length = unit(.07, 'inches'))) + 
  scale_fill_distiller(palette = "RdYlBu") + 
  coord_equal(expand = 0) + 
  theme(legend.position = 'bottom', 
        legend.direction = 'horizontal',
        panel.background = element_rect(fill = "white"))
```

### 5.2 1998-2017 trajectory heatmap

We begin by loading the package dataset `heatmapdata`:
```{r load heatmap, echo=T}
data("heatmapdata")
```

`heatmapdata` is composed of trajectory metrics for all stations within all inter-annual consecutive periods between 1998 and 2017:
```{r}
head(heatmapdata)
```

We then prepare the data set to create the trajectory heat map. We create a vector of direction, ranging by 15° between 0 and 360°, to class Angle $\alpha$ values. We create the vector `ISPattern` to characterize the pattern of direction according to changes in both stable isotope values (0-90°: + $\delta13C$ and + $\delta15N$; 90-180°: + $\delta13C$ and - $\delta15N$; 90-180°: + $\delta13C$ and - $\delta15N$; 180-270°: + $\delta13C$ and - $\delta15N$):
```{r, echo=T}
#direction range
deg <- 15

dir.breaks <- c(0,15,30,45,60,75,90,105,120,135,150,165,180,195,210,225,240,255,270,285,300,315,330,345,360)


dir.binned <- cut(heatmapdata$Angles,
                  breaks = dir.breaks,
                  ordered_result = TRUE)

# bar labels
dir.labels <- as.character(c(seq(0, 360-deg, by = deg),0))

levels(dir.binned) <- dir.labels

heatmapdata$dir.binned <- dir.binned

data<-heatmapdata[,c(6,7,8,10)]

#direction vs SI patterns
data<-data[order(data$dir.binned, decreasing=FALSE),]
rownames(data)<-1:9206
data$ISpattern<- c(rep("+d13C/+d15N",2862),rep("+d13C/-d15N",1840),rep("-d13C/-d15N",2931), rep("-d13C/+d15N",1573))

data1<-as.data.frame(table(data$dir.binned,data$Years))

data2<-aggregate(x = data$Lengths, by = list(data$dir.binned, data$Years), FUN=sum, drop=FALSE)
data2[is.na(data2)] <- 0 


data1$Lengths<-data2$x
dfa<-data1
colnames(dfa)<-c("Directions","Periods","Nb_stations","Lengths")
```

The final dataset used to create the trajectory heat map is composed of four variables ("Directions","Periods","Nb_stations","Lengths"):
```{r}
head(dfa)
```

We plot trajectory metrics with respect to period and direction in a trajectory heat map. Angles $\alpha$ in the modelled 2D $\Omega \delta$ space
exhibited by all stations within all pairs of dates (1998-1999,…,2016-2017) are represented by range of direction (15°) according to period. Color gradient from dark blue to yellow indicate the number of stations exhibited by a given range of direction within a given period.
```{r, fig.height=4, fig.width=6}
ggplot(dfa, aes(Periods, Directions, fill= Nb_stations)) + 
  geom_tile() +
  scale_fill_viridis(discrete=FALSE) +
  theme_minimal()+
  theme(axis.text.x = element_text(size=10, angle=90))
```

The X bar plot represents the sum of segment lengths across stations and times, 1231 exhibiting the chosen angle. The blue gradient indicates the net change magnitude.
```{r, fig.height=3, fig.width=5}
df.Xbarplot<-aggregate(dfa$Lengths, by = list(dfa$Periods), FUN = sum)
colnames(df.Xbarplot)<-c("Periods","Lengths")
bp.x <- ggplot(data = df.Xbarplot, aes(x = factor(Periods), y = Lengths)) + 
  geom_bar(stat = "identity", aes(fill = Lengths)) + theme_minimal() +
  theme(axis.text.x = element_text(size = 10,angle=90), 
        axis.title.x = element_text(size = 20, margin = margin(10,0,0,0))) +
  labs(x = "Periods")
bp.x
```

The Y bar plot represents the overall net changes according to range of directions (angle $\alpha$). Bars are colored
according to increase and/or decrease in $\delta13C$ and $\delta15N$ values (Pink: 0-90°: + $\delta13C$ and + $\delta15N$ ; Blue: 90-180°: + $\delta13C$ and - $\delta15N$; Red: 90-180°: + $\delta13C$ and - $\delta15N$; Green: 180-270°: + $\delta13C$ and - $\delta15N$).
```{r, fig.height=4, fig.width=4}
df.Ybarplot<-aggregate(dfa$Lengths, by = list(dfa$Directions), FUN = sum)
colnames(df.Ybarplot)<-c("Directions","Lengths")
df.Ybarplot$ISpattern<- c(rep("+d13C/+d15N",6),rep("+d13C/-d15N",6),rep("-d13C/-d15N",6), rep("-d13C/+d15N",6))


bp.y <- ggplot(data = df.Ybarplot, aes(x = factor(Directions), y = Lengths,fill = ISpattern)) + 
  geom_bar(stat="identity") + theme_minimal() + coord_flip()
bp.y
```
