Additive mixed meta-analysis with spline meta-regression for nonlinear ecological trends

Ecologists use meta-analysis models to propagate uncertainty from statistical models of independent datasets into a higher-level analysis. Meta-analysis can be used to combine independent studies or as a two-stage method for hierarchical modeling of data components from a large-scale or long-term study that are impractical to analyze in a single statistical model. While linear meta-regression against study-level covariates is common, ecological patterns are frequently nonlinear. For such cases, meta-analysis methodology lacks tools to estimate semiparametric smooth meta-regression models. We propose new spline meta-regression methods by melding meta-analysis with additive mixed models, resulting in the class of additive mixed meta-analysis (AMMA) models. In a simulation study, when first-stage SEs are heterogeneous, meta-splines perform better than naive approaches such as simple generalized additive models (GAMs). In a case study to investigate 43-year patterns of seasonally averaged phytoplankton levels in San Francisco Bay, California, USA, meta-splines give notably different results than naive methods in such heterogeneous cases. Seasonal averages and SEs are estimated annually, then combined with meta-splines to investigate long-term, nonlinear changes in the season-scale averages. The meta-analysis approach is practical, fully propagates the statistical information and uncertainties, and provides advantages for visualization. The methods are available in the R package splinemixmeta.