Data Analysis
To estimate the overall effect of microbial inoculants on above-ground
biomass, we used the natural log response ratio as our effect size,
calculated as lnRR = ln (Vi/Vc) (Hedges
et al., 1999), where Vi is the mean of the treatments
(inoculated) and Vc is the mean of the control
(uninoculated). Thus, the lnRR is positive when the magnitude of the
above-ground plant biomass of inoculated plants is greater than the
biomass of uninoculated plants, and vice versa. Statistical significance
was determined when 95% confidence intervals did not overlap with zero.
We used hierarchical meta-analytic models using the rma.mvfunction from the metafor package (Viechtbauer, 2010; version
3.0.2) to test for the mean effect of microbial inoculation on plant
growth. Study type, site, and species were found to be non-independent
so we included them as random variables in the analyses.
We performed a meta-analytic model to determine the overall mean effect
of inoculation on plant growth, using an intercept-only model with
random effects for study type, site, and species. We then performed
meta-regressions using the moderators; microbial source (either native
or commercial), microbial type (either bacteria or fungi), and microbial
composition (single or multiple inoculants) in separate models to test
our hypotheses. All statistical analyses were conducted in R version
4.2.1 (2022). Statistical significance was determined when 95%
confidence intervals did not overlap with zero. We reported
back-transformed effect sizes converted to the percentage scale to
facilitate interpretation (a percentage increase in plant growth in
inoculated plants versus non-inoculated plants). We also reported 95%
prediction intervals (PI), which represent 95% of the expected values
from future empirical studies, and also to put the result in perspective
to climate-specific comparisons (Moles, 2018). Plots were created with
the orchaRd package (Nakagawa et al., 2021) supported under theggplot2 package (Wickham 2016).
Publication bias implies that statistically significant findings are
more likely to be published than non-statistically significant findings.
We assessed publication bias in our dataset by using hierarchical
meta-regressions using standard error or sampling variance as moderators
in our models (Nakagawa et al., 2022) and assessed it using Egger’s
regression test (Figure Appendix 2). We also assessed the robustness of
our findings by performing sensitivity analysis (leave one out
analysis), where each study from the 62 studies was iteratively removed,
and the resulting data were fitted in an intercept-only meta-analytic
model.
We obtained a total of 172 effect sizes comparing inoculated from
uninoculated plants from 62 studies across the globe (Figure S1).
Ninety-four of the effect sizes were from restoration studies, 63 from
agriculture, and 15 from phytoremediation studies. The most commonly
used genus of fungi in plant inoculation was Rhizophagus spp.
(N=34) while Pseudomonas spp. (N=20) was the most abundant genus
of bacteria used in plant inoculation.
We found no strong evidence for publication bias nor an association
between plant responses to inoculation and either standard error (slope
= -0.48, CI = -0.78 - 1.11, N = 172). Our results were also robust to
the iterative removal of one study at a time. Across all models, the
inoculated increased plant biomass by 43.76% (CI = 29.69% - 58.8%),
which is consistent with the overall effect previously reported (43.3%,
CI = 29.69% - 58%, Figure 1A).