In 1898, Hermon Bumpus, an American biologist working at Brown University, collected data on one of the first examples of natural selection directly observed in nature. Immediately following a bad winter storm, he collected 136 English house sparrows, Passer domesticus, and brought them indoors. Of these birds, 64 had died during the storm, but 72 recovered and survived. By comparing measurements of physical traits, Bumpus demonstrated physical differences between the dead and living birds. He interpreted this finding as evidence for natural selection as a result of this storm:
bumpus <- read_csv("http://wilkelab.org/classes/SDS348/data_sets/bumpus_full.csv")## Parsed with column specification:
## cols(
## Sex = col_character(),
## Age = col_character(),
## Survival = col_character(),
## Length = col_integer(),
## Wingspread = col_integer(),
## Weight = col_double(),
## Skull_Length = col_double(),
## Humerus_Length = col_double(),
## Femur_Length = col_double(),
## Tarsus_Length = col_double(),
## Sternum_Length = col_double(),
## Skull_Width = col_double()
## )head(bumpus)## # A tibble: 6 x 12
## Sex Age Survival Length Wingspread Weight Skull_Length Humerus_Length
## <chr> <chr> <chr> <int> <int> <dbl> <dbl> <dbl>
## 1 Male Adult Alive 154 241 24.5 31.2 17.4
## 2 Male Adult Alive 160 252 26.9 30.8 18.7
## 3 Male Adult Alive 155 243 26.9 30.6 18.6
## 4 Male Adult Alive 154 245 24.3 31.7 18.8
## 5 Male Adult Alive 156 247 24.1 31.5 18.2
## 6 Male Adult Alive 161 253 26.5 31.8 19.8
## # ... with 4 more variables: Femur_Length <dbl>, Tarsus_Length <dbl>,
## # Sternum_Length <dbl>, Skull_Width <dbl>The data set has three categorical variables (Sex, with levels Male and Female, Age, with levels Adult and Young, and Survival, with levels Alive and Dead) and nine numerical variables that hold various aspects of the birds’ anatomy, such as wingspread, weight, etc.
Question 1: Perform a PCA on the numerical columns of this data set. Then make three plots potting the data as PC2 vs. PC1, colored by (i) sex, (ii) age, (iii) survival.
# R code goes here.Question 2: Now visualize the rotation matrix of the PCA obtained under Question 1.
# R code goes here.Question 3: Given the four plots from Questions 1 and 2, how do you interpret PC1 and PC2? What does PC1 tell you about a data point? What does PC2 tell you about a data point?
Answer goes here.
Question 4: What percentage of the variation in the data does PC1 explain?
# R code goes here.Answer goes here.
Question 5: Does the PCA suggest any specific physical characteristics for birds that survived? Consider only PC1 and PC2 for your answer.
Answer goes here.