Meta-analysis

Meta-analysis is a statistical approach for combining results from multiple independent studies to estimate an overall effect and identify factors that explain variation among studies.

What is a meta-analysis?

Ecological studies often report different results because they are conducted in different environments, use different methods, or examine different species and systems. Meta-analysis provides a quantitative framework for synthesizing these findings.

A typical meta-analysis involves:

  1. Defining a research question
  2. Systematically searching the literature
  3. Screening and selecting relevant studies
  4. Extracting data from individual studies
  5. Calculating effect sizes
  6. Fitting meta-analytic models
  7. Examining heterogeneity and moderators
  8. Assessing the robustness of the results

Effect sizes

An effect size provides a common metric that allows results from different studies to be compared. For continuous ecological responses, the log response ratio (lnRR) is commonly used:

[ = () ]

where ({X}{T}) is the mean response in the treatment group and ({X}{C}) is the mean response in the control group.

Positive values indicate higher values in the treatment relative to the control, whereas negative values indicate lower values.

Meta-analytic models

A basic meta-analysis estimates an overall effect across studies. However, ecological datasets commonly contain multiple observations from the same study, site, or experiment. Multilevel meta-analysis can account for this non-independence by including appropriate random effects.

For example:

library(metafor)

model <- rma.mv(
  yi,
  vi,
  random = ~ 1 | StudyID/CohortID,
  method = "REML",
  data = dat
)

summary(model)

Exploring moderators

The effectiveness of an ecological treatment may depend on environmental conditions, species characteristics, or management practices. These factors can be examined using moderator analyses.

model_mod <- rma.mv(
  yi,
  vi,
  mods = ~ Habitat + MAT + MAP,
  random = ~ 1 | StudyID/CohortID,
  method = "REML",
  data = dat
)

summary(model_mod)

Moderator analyses can help identify when, where, and under what conditions an ecological intervention is most effective.

Visualizing results

Forest plots provide a useful way to visualize individual study effects and the overall meta-analytic estimate.

forest(model)

A well-designed meta-analysis should combine rigorous study selection, transparent data extraction, appropriate statistical models, and clear visualization of the results.