Improving the accuracy of meta-analysis for datasets with missing measures of variance: Elevated [CO2] effect on plant growth as a case study.

Abstract Ongoing increases in atmospheric carbon dioxide (CO2) are expected to stimulate biomass and yield of plants possessing the C3 photosynthetic pathway; however, the extent of stimulation is likely to vary both intra- and inter-species specifically. Meta-analytic approaches can be applied to decrease variation and uncertainty by delineating and characterizing variation, allowing results to be used in modeling plant responses to elevated [CO2]. However, the use of meta-analysis in this effort could be limited by missing measures of variance, including standard deviations (SDs) of the compiled dataset. Here, we examined whether there were differences in effect sizes of elevated [CO2] on plant growth using various weighting and imputation approaches. Our results showed that the efficacy of different weighting functions and data interpolation methods on meta-analysis outcomes depended on the SDs provided by the studies. Comparing different methodologies for [CO2] fumigation as a case study, if the ratio of missing SD was low, the overall trend of effect values and 95% confidence interval (CI) were not changed. For datasets of greenhouse and growth chamber [CO2] methodologies, which had a high ratio of missing SDs, effect sizes and 95% confidence intervals using different weighing and imputation methods were influenced relative to that of the raw dataset, with reduced effect sizes and broader CI. Overall these results suggest that application of meta-analysis to discern general biological responses could be influenced by the number of missing SDs. As such, efforts should be made to check the proportion of missing SDs of the compiled dataset and if necessary, to apply various weighting functions and imputation methods to fully discern meta-analysis implications. Our findings could improve the assessment of methodological choices for future [CO2] experimentation and discerning long-term trends for agricultural productivity and food security.