Analyzing Eagle Flight Characteristics and Patterns

By: Rylan O’Neill

Introduction

Information was gathered from 57 eagles over 4 Years in Iowa using GPS Biologgers on Various Flight Characteristics

Table 1 from Bergen et al.

Questions to Answer

Can we use the movement variables KPH, Sn, AGL, |Angle|, Vertical rate, and |VR|, to distinguish in-flight from perching points?
Of the in-flight points:

Are there distinct flight behaviors that can be identified?
What are the characteristics of these behaviors?
What are some visual examples of flight segments that demonstrate the different types of in-flight behaviors?

Silhouette and WSS Plot

WSS Plot shows “Elbows” at 2 and 4
Silhouette Plot Shows Highest Peak at 4 clusters
Silhouette Plot shows near Equal Values in 2, 3, 5, 6, and 7 clusters
We will now examine Kmeans plots for 2, 3, 4, 5, 6, and 7 clusters

Evaluating Kmeans Plots

The Best Plot for our Kmeans is our Clusters = 4
Distinct Groups by our Variables in 4 Clusters
PC1 accounts for 45% of Variation
PC2 accounts for 21% of Variation

Evaluating PCA Plots

PC1 defined by Velocity Variables (KPH & Sn)
PC2 defined by Vertical Rates. AGL, Angle
PC1 accounts for 45% of Variation
PC2 accounts for 21% of Variation

Characteristics of Flight Patterns

Orange Cluster (1)

Low KPH
Low AGL
Stable Vertical Rate
High Angle

Characteristics of Flight Patterns

Green Cluster (2)

Moderate KPH
High AGL
Ascending Vertical Rate
Moderate Angle

Characteristics of Flight Patterns

Blue Cluster (3)

Moderate KPH
Low AGL
Stable Vertical Rate
Moderate to Low Angle

Characteristics of Flight Patterns

Purple Cluster (4)

High KPH
High AGL
Descending Vertical Rate
Low Angle

Characteristics of Flight Patterns

Our Orange Cluster(1) is our “Perching” Cluster
Our Green Cluster (2) is our “Ascending” Cluster
Our Blue Cluster(3) is our “Flapping” Cluster
Our Purple Cluster(4) is our “Gliding” Cluster

Eagle Flight Segment Patterns

We can see that our Ascending Points steeply rise up
We can see the high angle our Flapping Points have.
We can see how spaced out and declining our Gliding Points are

We can see our Perching Points are stationary with barely any change

Eagle Flight Segment Patterns

Again we see that our Ascending Points steeply rise up
Again we see how spaced out our Gliding Points are

Appendix - Preparing Data

# Narrow Dataset to Numerics for Scaling
eagle_numerics <- (eagle_data
                  %>% select(KPH:absVR) 
)

# Scaling Dataset and Correcting Skew
scaled_eagle <- eagle_numerics %>% 
  mutate_at(vars(AGL, Sn, absVR,abs_angle), sqrt) %>% 
  scale()

# For reproducibility
set.seed(123)

# Sampling data so Computer can run and store the data
sample_indices <- sample(1:nrow(scaled_eagle), size = 10000, replace = TRUE)

#Grabbing Samples
eagle_subsampled <- scaled_eagle[sample_indices, ]

Appendix - Silhouette & WSS

# Plotting WSS plot to help determine number of clusters
fviz_nbclust(eagle_subsampled, 
             FUNcluster = kmeans,
             method='wss',
             ) + 
  labs(title = 'Plot of WSS vs k using kmeans')

# Plotting Silhouette Width plot to help determine number of clusters
fviz_nbclust(eagle_subsampled, 
             FUNcluster = kmeans,
             method='silhouette',
             ) + 
  labs(title = 'Plot of avg silhouette vs k using kmeans')

Appendix - Kmeans Plot

# testing kmeans for possible clusters determind from WSS and Silhouette width plot; This was repeated for 2:7
kmeans2 <- kmeans(eagle_subsampled, centers = 2, nstart = 10, iter.max = 30)

#Making PCA variable arrows for Kmeans plots 
eagle_pca <- prcomp(eagle_subsampled, center=TRUE)

#Combining PC to Dataset for Plotting Variables and clusters; This was repeated for 2:7
eagle_update2 <- bind_cols(eagle_subsampled,k2=factor(kmeans2$cluster),eagle_pca$x[,1:2])

# Plotting PCA plots with clusters and Variable arrows to compare clusters with variable arrows; This was repeated for 2:7
p2 <- fviz_pca(eagle_pca, 
         axes= c(1,2),
         label = 'var', 
         col.ind = 'white')  + 
  geom_point(aes(x = PC1, y = PC2, col=factor(kmeans2$cluster)), data = eagle_update2, shape = '.', alpha = 1) +
guides(color = "none")+ 
  labs(title = 'Plot of Kmeans 2')

# Patchwork to combine all plots together 
p2 + p3 + p4 + p5 + p6 + p7

Appendix - PCA Plots

# PCA Repeated for Loading Plots 
eagle_pca <- prcomp(scaled_eagle, center=TRUE)

#Creating Dataframe for plotting Loadings 
loadings_df <- data.frame(eagle_pca$rotation) %>% 
  rownames_to_column('Variable')

# Base plot for loadings 
base_plot <- ggplot(loadings_df) + 
  theme_classic(base_size = 12) +
  theme(axis.text.x = element_text(angle = 45,hjust=1,vjust=1)) + 
  labs(x = 'Variable') + 
  geom_hline(aes(yintercept= 0), linetype=2)

#Entering Specific dimension Loadings information
l1 <- base_plot + 
  geom_col(aes(x = reorder(Variable,PC1, decreasing=TRUE), y = PC1))
l2 <- base_plot+
  geom_col(aes(x = reorder(Variable,PC2, decreasing=TRUE), y = PC2))

#Showing PC1 and PC2 loading plots
(l1+l2)+
  plot_annotation(title = 'Loadings plots for Eagle PCA',
                  theme=theme(plot.title = element_text(hjust = 0.5)))

Appendix - Characteristics of Flight Patterns

#Kmeans of 4 Clusters for Boxplots
kmeans4eagle <- kmeans(scaled_eagle, center = 4, nstart = 10, iter.max = 30)

#Adding k4 to my numerics information
eagle_numerics_cluster <- eagle_numerics %>% 
  mutate(k4 = kmeans4eagle$cluster)

#Repeated PCA for Larger Eagle Data set
eagle_pca <- prcomp(scaled_eagle, center=TRUE)

#Adding PCA to larger eagle data set for boxplots
eagle_updatebig <- bind_cols(eagle_data,k4=factor(kmeans4eagle$cluster),eagle_pca$x[,1:2])

#Code for Boxplot with larger eagle dataset to compare characteristics to cluster group to help determine groupings; Repeated for all 4 boxplots
bp1 <- ggplot(data = eagle_numerics_cluster) + 
  geom_boxplot(aes(x = factor(kmeans4eagle$cluster), 
                   fill = factor(kmeans4eagle$cluster), 
                   y = AGL),outlier.shape = NA) +
                   ylim(c(0,1500)) +
  xlab("Clusters") + 
  labs(fill = "Clusters")

#Patchwork to combine Plots
bp1+bp2+bp3+bp4

Appendix - Eagle Flight Segments

#Creating Segment Group to help determine which segments to use for analyzing 
eagle_segment <- eagle_updatebig %>% select(segment_id,segment_length)

#Grouping segments to allow easier identification of lengths for segments
eagle_segment_grouped <- (eagle_segment 
                    %>% group_by(segment_id)
                    %>%summarize(n = n())
)

#Sorting Segment lengths and then choosing a value around 400 for easier analyzation of plotted points; This was repeated for both segments
eagle_segment_sorted_desc <- arrange(eagle_segment_grouped,desc(n))
#head(eagle_segment_sorted_desc,1000)
filtered_segment1 <- eagle_updatebig %>% 
  filter(segment_id==72341)

#Code for plotting segments by longitude and latitude with defined characteristics cluster coloring for points; This was repeated for both flight segments
ggplot(data = filtered_segment1,aes(x = Longitude, y = Latitude)) +
  geom_point(aes(col = factor(k4)),size=.5) +
scale_color_discrete(
    name = "Flight Characteristics", 
    labels = c(
      "1" = "Perching",
      "2" = "Ascending",
      "3" = "Flapping",
      "4" = "Gliding"
    ) 
  )