Statistics Using R with Biological Examples: The free and open-source programming language R has evolved into a pillar of statistical analysis in biological science. Its rich set of tools, systems for reproducibility, and packages make it perfect for assignments ranging from basic data summaries to difficult genomic analysis. This book discusses important statistical techniques in R supplemented with biological illustrations to show its practical applications in answering real-world research questions.
Basic Statistical Methods in R with Biological Applications
1. Descriptive Statistics
Descriptive statistics summarize data, offering insights into trends and variability. Biologists often use them to report baseline results.
Example: Measuring the body lengths of Anolis lizards.
# Load data
lizard_data <- read.csv("lizard_lengths.csv")
mean_length <- mean(lizard_data$length)
sd_length <- sd(lizard_data$length)
cat("Mean length:", mean_length, "±", sd_length, "cm")
2. Hypothesis Testing
t-test: Compare means between two groups.
Example: Testing if a new fertilizer increases plant height (control vs. treatment groups).
t_test_result <- t.test(height ~ group, data = plant_data)
print(t_test_result$p.value) # p < 0.05 implies significant difference
3. Linear Regression
Model relationships between variables.
Example: Predicting coral growth rate based on seawater pH.
model <- lm(growth_rate ~ pH, data = coral_data)
summary(model) # R² and p-value for pH
Advanced Techniques for Biological Data
1. Generalized Linear Models (GLMs)
Handle non-normal distributions (e.g., Poisson for count data).
Example: Modeling insect abundance based on habitat type.
glm_model <- glm(abundance ~ habitat, data = insect_data, family = poisson)
2. Principal Component Analysis (PCA)
Reduce dimensionality in high-throughput data.
Example: Analyzing morphological traits in bird populations.
pca_result <- prcomp(bird_traits[,2:5], scale = TRUE)
biplot(pca_result) # Visualize clusters
3. Clustering
Identify groups in unsupervised data.
Example: Classifying microbial communities using 16S rRNA data.
dist_matrix <- dist(microbe_data, method = "euclidean")
hclust_result <- hclust(dist_matrix)
plot(hclust_result) # Dendrogram
Data Visualization with ggplot2
Compelling visuals are critical for interpreting biological data.
Scatter Plot: Predator-prey dynamics.
ggplot(predator_data, aes(x = prey_density, y = predator_growth)) +
geom_point() +
geom_smooth(method = "lm") +
labs(title = "Predator Growth vs. Prey Density")
Bar Plot: Species abundance across habitats.
ggplot(abundance_data, aes(x = habitat, y = count, fill = species)) +
geom_col(position = "dodge") +
theme_minimal()
Case Study: Temperature Effects on Bacterial Growth
Objective: Determine if higher temperatures (30°C vs. 20°C) affect E. coli growth rates.
Steps:
- Import Data:
growth_data <- read.csv("bacterial_growth.csv")- Exploratory Analysis:
summary(growth_data)
boxplot(growth_rate ~ temperature, data = growth_data)- t-test:
t.test(growth_rate ~ temperature, data = growth_data) # p < 0.001- Visualize:
ggplot(growth_data, aes(x = temperature, y = growth_rate)) +
geom_boxplot() +
ggtitle("E. coli Growth at Different Temperatures")Conclusion: Significant growth increase at 30°C (p < 0.001).
Learning Resources for Biologists
- Books: R for Data Science (Wickham & Grolemund), Biostatistics with R (Kabacoff).
- Packages:
ggplot2(visualization),dplyr(data wrangling),vegan(ecology). - Communities: Bioconductor (genomics), RStudio Community, Stack Overflow.
Conclusion
R allows biologists to run reliable, thorough studies from elementary statistics to sophisticated machine learning. Researchers can quickly reveal patterns in complicated biological systems and hence speed up discoveries in ecology, genetics, and beyond by including R in their process of work.