Common Code 05 — mutate()

Creating and transforming columns — ecological math, logarithms, and regression equations

how to do math and add columns based on calculations or mutations

Creating new columns with mutate()

mutate() adds new columns to a data frame, or overwrites existing ones. Each new column is computed row by row from whatever expression you give it — simple arithmetic, logarithms, conditional logic, or a full regression equation applied to every observation at once.

⬇️ Download the companion R script — all examples ready to run: 05_mutate.R

💡 Following along? Examples use penguins from palmerpenguins. The ecological math sections apply directly to any field data you collect.

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Packages needed

library(tidyverse)
library(palmerpenguins)

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1 · The basics

mutate() always goes at the end of a pipe, after your filter() and select() steps. New columns can immediately reference other columns just created in the same mutate() call:

penguins |>
  mutate(
    mass_kg       = body_mass_g / 1000,
    flipper_m     = flipper_length_mm / 1000,
    mass_per_flip = mass_kg / flipper_m    # uses both columns just made above
  )

💡 Key idea: mutate() never changes existing rows or drops columns — it only adds or replaces. The original data frame is untouched unless you overwrite it with <-. Store results in a new object with a descriptive name.

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2 · Simple arithmetic

The operators are what you expect: +, -, *, /, ^ for power. Reference any column by name, mix columns with constants freely:

penguins |>
  mutate(
    mass_kg       = body_mass_g / 1000,              # unit conversion g → kg
    bill_ratio    = bill_length_mm / bill_depth_mm,  # length-to-depth ratio
    bill_area_mm2 = bill_length_mm * bill_depth_mm,  # rough bill area proxy
    mass_centered = body_mass_g - mean(body_mass_g, na.rm = TRUE)  # centre on mean
  )

💡 Bill ratios and shape indices are a classic ecology move — dividing two measurements to capture shape independent of size. The same idea appears in body condition indices, cephalic indices, and leaf shape metrics.

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3 · Logarithms — the most important transformation in ecology

Log-transformation is everywhere in ecology: species–area relationships, metabolic scaling, abundance distributions, allometric growth. Understanding which log function to use matters.

penguins |>
  mutate(
    log10_mass = log10(body_mass_g),   # base-10 — most interpretable
    ln_mass    = log(body_mass_g),     # natural log (base e) — used in models
    log2_mass  = log2(body_mass_g)     # base-2 — used in some genetics work
  )

⚠️ Watch out! log() in R is the natural log (base e ≈ 2.718), NOT base-10. This catches almost everyone the first time. Use log10() when you want base-10. When in doubt, be explicit.

Which log to use:

Log	R function	Use when
Base 10	log10()	Plotting, interpreting orders of magnitude, species–area
Natural (base e)	log()	Statistical models (GLMs, regression), likelihood
Base 2	log2()	Gene expression, information theory

Back-transforming

Always know how to undo a transformation — you will need it when reporting model predictions on the original scale:

penguins |>
  mutate(
    log10_mass   = log10(body_mass_g),
    mass_back    = 10 ^ log10_mass,     # undo log10:  10^x

    ln_mass      = log(body_mass_g),
    mass_back_ln = exp(ln_mass)         # undo natural log: e^x
  )

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4 · Exponents and powers

The ^ operator raises to any power. This is directly useful for allometric and metabolic scaling, which follow power laws:

penguins |>
  mutate(
    mass_kg       = body_mass_g / 1000,
    metabolic_est = mass_kg ^ 0.75,          # Kleiber's Law: metabolic rate ∝ mass^0.75
    flipper_area  = flipper_length_mm ^ 2,   # area scales as length²
    flipper_vol   = flipper_length_mm ^ 3    # volume scales as length³
  )

💡 Kleiber’s Law — basal metabolic rate scales to body mass to the power of ¾ across animals spanning 20 orders of magnitude. A single ^ 0.75 in mutate() lets you compute a metabolic estimate for every row in your data frame instantly.

# sqrt() is ^ 0.5 — sometimes used to stabilise variance in count data
penguins |>
  mutate(sqrt_mass = sqrt(body_mass_g))

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5 · Applying a regression equation

After you fit a linear model, mutate() is the cleanest way to apply the equation back to your data frame — either to generate predicted values for plotting or to calculate residuals.

Simple linear regression: y = mx + b

Say your regression of body mass on flipper length gave:

body_mass_g = 49.7 × flipper_length_mm − 5781

penguins |>
  mutate(mass_predicted = 49.7 * flipper_length_mm - 5781)

Plot observed vs. predicted:

penguins |>
  mutate(mass_predicted = 49.7 * flipper_length_mm - 5781) |>
  ggplot(aes(x = flipper_length_mm)) +
  geom_point(aes(y = body_mass_g),    color = "steelblue", alpha = 0.6) +
  geom_line(aes(y = mass_predicted),  color = "tomato", linewidth = 1) +
  labs(
    x     = "Flipper length (mm)",
    y     = "Body mass (g)",
    title = "Observed vs. predicted body mass"
  ) +
  theme_classic()

Log-log (allometric) regression

Log-log regression is the backbone of allometric studies: log₁₀(mass) = −3.41 + 1.52 × log₁₀(flipper length)

Apply it and back-transform predictions to the original scale:

penguins |>
  mutate(
    log10_flip     = log10(flipper_length_mm),
    log10_mass_hat = -3.41 + 1.52 * log10_flip,
    mass_predicted = 10 ^ log10_mass_hat          # back-transform to grams
  )

💡 Key idea: Back-transforming a log-scale prediction with 10^x (or exp(x) for natural log) gives you the geometric mean prediction on the original scale — which is what you want for a log-normal relationship. Report these back-transformed values, not the log-scale ones.

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6 · Conditional columns

Two categories — if_else()

penguins |>
  mutate(
    size_class = if_else(body_mass_g >= 4000, "large", "small")
  )

if_else(test, value_if_TRUE, value_if_FALSE) — all three arguments must return the same data type.

Three or more categories — case_when()

penguins |>
  mutate(
    size_class = case_when(
      body_mass_g >= 5000 ~ "large",
      body_mass_g >= 3500 ~ "medium",
      body_mass_g <  3500 ~ "small",
      .default            = "unknown"   # catches NA and anything else
    )
  )

💡 case_when() evaluates conditions top to bottom and stops at the first match — just like an if/else if chain. Put the most specific conditions first. .default catches anything that matched nothing, including NA.

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7 · Overwriting an existing column

Use the same name on the left to replace a column in place. The most common use is fixing a type that imported incorrectly:

# Year imported as numeric — treat it as a category for plotting
penguins |>
  mutate(year = as.factor(year))

# A measurement column that imported as character
my_data |>
  mutate(length_mm = as.numeric(length_mm))

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8 · Complete ecological pipeline

Putting it all together — bill shape index, log-transformation, size classification, factor ordering — all in one readable pipe:

penguins_analysis <- penguins |>
  drop_na() |>
  mutate(
    bill_ratio = bill_length_mm / bill_depth_mm,
    log10_mass = log10(body_mass_g),
    log10_flip = log10(flipper_length_mm),
    size_class = case_when(
      body_mass_g >= 5000 ~ "large",
      body_mass_g >= 3500 ~ "medium",
      TRUE                ~ "small"
    ),
    species = factor(species, levels = c("Adelie", "Chinstrap", "Gentoo"))
  ) |>
  select(species, sex, bill_ratio, log10_mass, log10_flip, size_class)

glimpse(penguins_analysis)

Then the classic allometric log–log plot:

ggplot(penguins_analysis,
       aes(x = log10_flip, y = log10_mass, color = species)) +
  geom_point(size = 2, alpha = 0.7) +
  labs(
    title = "Allometric scaling: body mass vs. flipper length",
    x     = "log₁₀ Flipper length (mm)",
    y     = "log₁₀ Body mass (g)",
    color = "Species"
  ) +
  theme_classic()

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Quick reference

Task	Code
Unit conversion	mutate(mass_kg = body_mass_g / 1000)
Ratio	mutate(bill_ratio = bill_length_mm / bill_depth_mm)
Base-10 log	mutate(log10_mass = log10(body_mass_g))
Natural log	mutate(ln_mass = log(body_mass_g))
Undo log10	mutate(mass = 10 ^ log10_mass)
Undo natural log	mutate(mass = exp(ln_mass))
Power / exponent	mutate(metabolic = mass_kg ^ 0.75)
Square root	mutate(sqrt_mass = sqrt(body_mass_g))
Linear regression eq.	mutate(predicted = 49.7 * flipper_length_mm - 5781)
Log-log prediction	mutate(pred = 10 ^ (-3.41 + 1.52 * log10(flipper_length_mm)))
Binary category	mutate(size = if_else(body_mass_g >= 4000, "large", "small"))
Multiple categories	mutate(size = case_when(... ~ ..., .default = "unknown"))
Fix column type	mutate(year = as.factor(year))
Centre on mean	mutate(mass_c = body_mass_g - mean(body_mass_g, na.rm = TRUE))

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End of Common Code 05 — mutate(). Next: Common Code 06 — Advanced plotting and themes.