Overview of approach to analysis
We employed multi-factor statistical models to assess the relative importance of different factors to the response of plants to mycorrhizal inoculation. The methods for multi-factor meta-analysis are not well developed in the statistical literature, and widely available meta-analysis software (e.g., Metawin 2.0, Rosenberg et al. 2000) do not accommodate such a multi-factor approach. Datasets for multi-factor meta-analysis are inherently observational in nature because the values of the explanatory variables have not been independently manipulated. Some combinations of study characteristics used as explanatory variables are likely to be much more common than other combinations, generating autocorrelation and incomplete orthogonality among the explanatory variables. The commonly used stepwise multiple regression approach to selecting a single statistical model based on P-values associated with individual factors can lead to substantial errors in model selection and parameter estimation (Chatfield 1995; Burnham & Anderson 2002; Whittingham et al. 2006). We used information–theoretic criteria to rank candidate multiple regression models having different combinations of explanatory variables and to rank the relative importance of the variables in those models. We also estimated the parameters associated with important explanatory variables, while controlling for the effects of other explanatory variables in the best multi-factor models, rather than testing their statistical significance (Burnham & Anderson 2002). Overall, this analytical approach allows for inference from multiple models and focuses inference on the weight of evidence in the data for different models and factors and on the size and direction of effects. Furthermore, this approach avoids testing null hypotheses about individual factors that may not belong in the best model or models.
Literature search and dataset construction
We searched the ISI Web of Science database (1968–2004) using the key words mycorrhiz* and inocul* on 22 January 2005 to generate a set of 1852 publications. Because we did not anticipate screening all 1852 publications, we screened a random subset (c. 20%) of those publications for studies to be included in our meta-analysis. We defined a ‘study’ as any comparison of average plant performance between plants that were inoculated with mycorrhizal fungi (AM or EM) and plants that were not inoculated. We did not include studies in which different levels of mycorrhizal colonization were produced by adding fungicide to the roots of a subset of plants. Individual publications frequently yielded multiple studies, for example comparing the response of different host plants to inoculation or the response of the same host plant to inoculation with different fungi and our initial screening identified 1167 studies (from 134 publications) containing appropriate data. Because this initial compilation of studies included substantially fewer studies involving EM fungi compared with AM fungi, we added an additional 827 studies (from 49 publications) on EM fungi that were used in a previous meta-analysis and that met our criteria for inclusion (Karst et al. 2008). The latter studies were originally selected by screening, using similar criteria as our original search, the 3591 publications produced by a search of the ISI Web of Science database (1965–2006) using the key word ectomycorrhiza.
From each study, we collected data on plant performance with and without mycorrhizal inoculation, as well as the following 14 study characteristics to be used as explanatory variables in multi-factor meta-analyses:
PlantFunctionalGroup: A categorical fixed-effect variable with up to six levels corresponding to putative plant functional groups: C4 grasses, C3 grasses, N-fixing forbs (i.e. forbs with N-fixing bacterial symbionts), non-N-fixing forbs, N-fixing woody plants and non-N-fixing woody plants.
MycorrhizaType: A categorical fixed-effect variable with two levels, AM and EM.
FungalGenus: A categorical fixed-effect variable with seven levels, including five EM levels (Laccaria, Pisolithus, Hebeloma, Scleroderma and ‘other EM genera’) and two arbuscular-mycorrhizal (AM) levels (Glomus and ‘other AM genera’).
InoculumComplexity: A categorical fixed-effect variable with three levels: whole soil inoculum (presumably containing multiple fungal species as well as diverse non-mycorrhizal microbes and other biota), multiple-species inoculum (containing multiple fungal species but little or no other soil biota) and single-species inoculum (containing only a single fungal species and little or no other soil biota).
Sterility: A categorical fixed-effect variable with two levels: sterilized (background soil medium was sterilized before the experiment was conducted) and not sterilized.
MicrobeControl: A categorical fixed-effect variable with three levels: No added non-mycorrhizal microbes (non-mycorrhizal microbes were not added or supplemented in the experiment, either to all the background soil or to the non-inoculated pots), microbial wash (an aqueous filtrate of non-mycorrhizal microbes was added), or other microbial addition (non-mycorrhizal microbes were supplemented in another form, usually using rhizosphere soil from non-mycorrhizal culture plants).
Location: A categorical fixed-effect variable with two levels, laboratory (greenhouse or growth chamber) and field (e.g. agricultural field, forest).
N-fertilization, P-fertilization and Fertilization: Categorical fixed-effect variables. N-fertilization and P-fertilization had two levels (fertilized or not) and Fertilization had four levels (fertilized with N but not P, fertilized with P but not N, fertilized with both N and P, and fertilized with neither N nor P). Fertilization was not used in the same statistical models with N-fertilization and P-fertilization, but rather was used as an alternative to those two separate factors. Because actual levels of soil fertility were rarely reported, these fertilization variables are the best available approach to assess the potential importance of N and P availability for mycorrhizal function (also see Univariate tissue nutrient analyses below).
N-fertilization × MycorrhizaType: A fixed-effect variable, testing the interaction between two variables described above, N-fertilization and MycorrhizaType.
PlantSpecies and PlantFamily: Categorical random-effect variables. Each level of PlantSpecies is designated by a unique combination of plant genus and specific epithet. The largest data subset (Analysis 1) contained more than 130 plant species in 27 different plant families.
PlantSpecies × PlantFunctionalGroup: A random-effect variable included only in models containing PlantFunctionalGroup as a fixed factor.
Because most studies lacked information on one or more of these 14 variables and missing data were not compatible with our approach to multi-factor meta-analysis, we created four different subsets of the data for analysing different subsets of the 14 explanatory variables in separate meta-analyses. Each of these data subsets contained complete information on a subset of the explanatory variables, allowing analyses of the relative importance of those variables in that data subset. Table 1 lists the explanatory variables analysed for each of the four data subsets and Appendix S1 provides additional details on how candidate explanatory variables were chosen and scored and how multiple data subsets were chosen for meta-analysis. Appendices S2 and S3 contain, respectively, the data used in each of the analyses and the full bibliographic references for the publications from which those data were extracted. Chaudhary et al. (2010) provide a detailed description of the database and web interface tools that we developed to facilitate efficient and accurate compilation of data for complex multi-factor meta-analysis.
Table 1. Summary of which candidate explanatory variables were included in analysis of each of the four data subsets. An ‘X’ indicates inclusion of a candidate explanatory variable in the analysis of a particular data subset
|Explanatory variables||1: AM and EM fungi (n = 616 studies)||2: AM fungi only (n = 420 studies)||3: Single-species inocula only (n = 524 studies)||4: Laboratory studies of AM fungi only (n = 306 studies)|
|MycorrhizaType||X|| || || |
|FungalGenus|| || ||X|| |
|Sterility|| || || ||X|
|MicrobeControl|| || || ||X|
|N-fertilization × MycorrhizaType||X|| || || |
|PlantSpecies × PlantFunctionalGroup||X||X||X||X|
Calculation of effect sizes
Whole plant (root and shoot) biomass and shoot biomass were the most commonly reported measures of plant response to mycorrhizal inoculation; in our analyses, we used whole plant biomass when it was available and otherwise used shoot biomass. For each experimental comparison between inoculated treatments and non-inoculated controls, we calculated an effect size for plant biomass based on mean values in the inoculated and non-inoculated groups. Specifically, effect size of inoculation was calculated as the log response ratio of inoculated to non-inoculated plant biomass: ln(Xi/Xn), where Xi is the mean biomass in an inoculated treatment and Xn is the mean biomass in a non-inoculated control. This metric is positive for a beneficial effect of inoculation on plant biomass, and negative for a detrimental effect on plant biomass. We used the log response ratio (rather than other commonly used metrics for effect size such as Hedges’d ) because it provides a standardized, unit-less measure of overall performance in inoculated treatments relative to non-inoculated controls, allowing valid comparisons among studies. Moreover, log response ratios have particularly favourable statistical properties for meta-analysis (Hedges et al. 1999). Scatter plots of effect size vs. the sample size of each study did not reveal any patterns indicative of publication bias, for example a lack of studies with both low effect size and low sample size.
We used the MIXED procedure in SAS (SAS v. 9.1; SAS Institute, Inc., Cary, NC, USA) for all analyses, employing restricted maximum likelihood estimation of parameters. We first used a pure random-effects model to estimate the overall weighted mean effect size (i.e. the log response ratio of plant response to mycorrhizal inoculation) and random between-studies variance component (sensuvan Houwelingen et al. 2002), with each effect size estimate weighted by the reciprocal of the within-study variance (which we estimated as the summed number of replicates in the inoculated treatments and non-inoculated controls) plus the maximum likelihood estimate of the residual between-studies variance component. We used this weighting method in lieu of the actual estimated effect size variance from each study, because far more studies reported levels of replication than reported actual measures of dispersion (SD, SE or confidence intervals) that could be used to calculate variance. Thus, we made the assumption that studies with higher levels of replication provided more precise estimates of effect size and those studies were given higher weight in the meta-analysis.
For each of the four separate analyses (Table 1), we explored the relative importance of different fixed factors by analysing a series of mixed-effect multiple meta-regression models, including the global model containing all of the fixed factors being considered for that dataset, as well as each of the nested subset models containing at least one fixed factor. Within each analysis, each candidate model was ranked according to an information-theoretic criterion (AICc, Akaike’s Information Criterion corrected for small samples, which converges on AIC for large samples). An Akaike weight (wi) was calculated for each model, which corresponds approximately to the likelihood that model is the best model among those being considered. Inference was then based on a 95% confidence set of models, based on cumulative wi of the best models. For each predictor variable, its relative importance with regards to plant response to mycorrhizal inoculation was then determined based on the sum of wi of the models in the 95% confidence set in which that predictor appeared. Predictor variables with a summed wi less than 0.5 were considered relatively unimportant (Burnham & Anderson 2002). Further details on how these analyses and calculations were carried out can be found in Appendix S4.
Univariate tissue nutrient analyses
Overall, plants benefit most from mycorrhizal mutualisms in nutrient limited soils and benefit least in high fertility soils since plants have less to gain from trading C for fungal-derived nutrients (Koide 1991; Schwartz & Hoeksema 1998; Jones & Smith 2004); however, interactions between concentration levels of different nutrients may also be important for determining symbiosis function. For example, mycorrhizal benefits to plants may be greatest when plants are P-limited but not N-limited because N limitation reduces plant photosynthetic capacity and thus C supply for the symbiosis (Johnson et al. 2003; Johnson 2010). Although soil and plant tissue nutrient concentration data were not reported frequently enough to be included as predictor variables in our multi-factor analyses, plant tissue nutrient concentration data – which can be useful indicators of plant nutrient status – were reported often enough (95 AM studies and 35 EM studies from 25 publications) for some separate, supportive univariate analyses, to aid interpretation of our multifactor meta-analysis results with respect to P- and N-fertilization. In particular, tissue N : P ratios < 14 or > 16 have been postulated to indicate N limitation or P limitation, respectively, with ratios between 14 and 16 likely indicating that the two elements are not limiting or are co-limiting (Koerselman & Meuleman 1996). Therefore, the tissue N : P ratios of non-mycorrhizal plants may also be a useful indicator of plant responsiveness to mycorrhizal inoculation. Because plant response to mycorrhizal inoculation depends on relative limitation of plant growth by C, N and P; and because photosynthesis (C acquisition) is often reduced in N-limited plants due to the high relative abundance of N in the photosynthetic enzymes (Chapin 1980), we predicted that mycorrhizas should be most beneficial when P is relatively more limited than N. We tested this prediction with two analyses: First, we estimated the linear relationship between plant biomass response to inoculation (log response ratio) and final tissue N : P ratio (natural log-transformed) of control (non-inoculated) plants using un-weighted maximum-likelihood parameter estimation in SAS PROC MIXED. Second, we used a t-test to compare plant biomass response to inoculation between N-limited (tissue N : P < 14 in non-inoculated plants) and P-limited (tissue N : P > 16 in non-inoculated plants) studies. Finally, to better understand the relationship between N-fertilization and P-fertilization (predictor variables in our meta-analyses) and the tissue N and P data used in these univariate analyses, we used t-tests to compare tissue N : P ratios of non-inoculated plants between studies that were N-fertilized and those that were not and between studies that were P-fertilized and those that were not.