Regression Data Exploration: Skibiel et al 2013 milk data

Introduction to Regression Modeling

Data for today: comparative zology of milk

How does milk compositon vary with animal life history & biology?

Skibiel et al 2013. Journal of Animal Ecology. The evolution of the nutrient composition of mammalian milks.

• Table S1. Milk composition of mammals at mid-lactation
• Table S2. Ecology and life histories of mammals whose milk composition has been described

The milk dataset

• Focus on % of fat in milk
• Several “continous predictors” / covariates
  • mass of female = mass.female
  • duration of pregnancy/gestation = gest.month.NUM
    
  • how long young fed = lacat.mo.NUM
    
  • how big are babies = mass.litter
    
• Several “categorical predictors”
  • diet = meat, plants, everything
  • arid = desert or other
  • biome = aquatic or terrestrial (includes bats)

Look at data

# Hom much data?
dim(milk2)

## [1] 130  13

#focal columns
##(use negative indexing to drop some)
summary(milk2[,-c(2,3,8,9)])

##            order     mass.female        gest.month.NUM    lacat.mo.NUM   
##  Artiodactyla :23   Min.   :        8   Min.   : 0.400   Min.   : 0.300  
##  Carnivora    :23   1st Qu.:      857   1st Qu.: 1.405   1st Qu.: 1.625  
##  Primates     :22   Median :     5716   Median : 5.000   Median : 4.500  
##  Rodentia     :17   Mean   :  2229475   Mean   : 5.624   Mean   : 6.092  
##  Chiroptera   :10   3rd Qu.:   107500   3rd Qu.: 8.365   3rd Qu.: 8.225  
##  Diprotodontia:10   Max.   :170000000   Max.   :21.460   Max.   :42.000  
##  (Other)      :25                                                        
##   mass.litter               diet     arid            biome    
##  Min.   :      0.3   carnivore:32   no :91   aquatic    : 22  
##  1st Qu.:     42.0   herbivore:61   yes:39   terrestrial:108  
##  Median :    423.5   omnivore :37                             
##  Mean   :  52563.8                                            
##  3rd Qu.:   7038.2                                            
##  Max.   :2272500.0                                            
##                                                               
##   fat.percent    
##  Min.   : 0.200  
##  1st Qu.: 4.575  
##  Median : 8.550  
##  Mean   :14.068  
##  3rd Qu.:17.575  
##  Max.   :61.100  
##  NA's   :2

Focal families in dataset

• Artiodactyla = 23; Even-toed ungulate
• Carnivora = 23
• Primates = 22
• Rodentia = 17
• Chiroptera = 10; bats
• Diprotodontia = 10; marsupials
• Cetacea = 6
• Perrissodactyla = 7; odd-toed ungulates
• Lagomorpha = 3

Explore milk data with ggplot2

• ggplot2::qplot is an excellent function for rapid data exploration
• different synatax than R’s “base” plot functions
• (another R plotting system is “trellis”)

Look at % milk fat vs. mass of female

• Plot is dominated by whales!

library(ggplot2)

#set font
theme_set(theme_bw(base_size = 18))

qplot(y = fat.percent,
      x = mass.female,
      data = milk2,
      main = "Regression data: continous vs continuous",
      xlab = "Continous x: mass of female",
      ylab = "Continous y: mass of female") 

Look at % milk fat vs. log(mass of female)

• Logging helps
• NOTE: statiticians typically use natural log = ln()
• Biologists, especially when allometry is invovled, typically use base 10 = log10()
• Original authors used log10, but I just realized this, so I’ll stick with ln()
• I believe (?) give similar answers, but log10 I think (?) makes biological interpretation easier (???)

Compare log10

• Looks very similar

Add “smoother”

• “geom = c(”point“,”smooth“)”
• Multiple types of smoothers
  • loess
  • spline
  • GAM

qplot(y = fat.percent,
      x = log(mass.female),
      geom = c("point","smooth"),
      data = milk2,
            main = "Regression data: continous vs log(continuous)",
      xlab = "Continous x: log(mass of female)",
      ylab = "Continous y: mass of female")

Look at % milk fat by a categorical variable (diet)

Look at % milk fat by diet AND biome

• “facets” are a powerful tool in ggplot
• Turns out ALL of our aquatic spp are carnivores (sorry, no manatees)
• This shows that “aquatic” and “diet” are “Confounded”

library(ggplot2)

qplot(y = fat.percent,
      x = diet,
      data = milk2,
      facets = ~ biome)

Look at % milk fat by diet AND biome, colored by body mass

• The color scale is DOMINATED by a whale

…Look at % milk fat by diet AND biome, colored by log(body mass)

• logging should equalize things

Change to boxplot using “geoms”

Overlay raw data on boxplots

• geom = c(“boxplot”, “point”)

Focal data subset: Primates & Relatives

• Primates
• Rodents (this is why we use mouse models)
• Rabbits

Subset data

This is a fairly fancy subsetting * Note use of with() * which() * %in%

#Select subset
i.use <- with(milk2, which(order %in% c("Rodentia",
                                        "Primates",
                                        "Lagomorpha")))
#make subset using row indexing
milk3 <- milk2[i.use,]

write.csv(milk3, file = "Skibiel_clean_milk_focal_genera.csv")

Compare original data and our working subset

• Original = 130 speices
• Working data = 42

# Original data
dim(milk2)

## [1] 130  13

#out sowkring subset
dim(milk3)

## [1] 42 13

Plot working data:

milk fat.percent ~ female size

The big animal is a Gorrilla!

Plot logged data

milk fat.percent ~ log(female size)

Add smoother

% Fat generally declines as body mass increases

Add regression line

• % Fat generally declines as body mass increases
• Grey areas is “confidence band”
• ggplot makes these really easily
• harder using plot()

Alternate predictor: Duration of gestation

fat.percent ~ log(gest.month.NUM)

• % Fat generally declines as gestation duration increases
• (the longer animal is pregnant, the less fatty the milk is)
• longer pregnancy, lower milk fat

Duration of lactation

fat.percent ~ log(lacat.mo.NUM)

• % Fat generally declines as lactation duration increases
• longer time kids are dependent, lower milk fat

Mass of litter

fat.percent ~ log(mass.litter)

• % Fat generally declines as litter size increases
• more or bigger babies, less milk fat