NCEAS

Data extraction

Studies analyzed in this contribution are a subset from the ELSIE database (EcoLogical Synthesis of Interactive Experiments), created within a workshop hosted by the National Center for Ecological Analysis and Synthesis (metadata available at knb.ecoinformatics.org/). Studies were selected by examining the abstracts of all publications returned from searches on ISI Web of Science (1965-2006) using the following search strings: [herbivor* or graz* or consum*] and [resourc* or nutrient* or fertili*]; [â??top-downâ?? and â??bottom-upâ?? and ecolog*]. We also included data from studies reported in other syntheses (Proulx & Mazumder 1998; Hillebrand 2002; Shurin et al. 2002; Borer et al. 2005; Hillebrand 2005; Burkepile & Hay 2006; Elser et al. 2007; Hillebrand et al. 2007) and searched both the literature cited in those papers and all subsequent citations of those analyses. Citations for the 83 included papers (containing 191 independent experiments) are listed in the supplementary material (Appendix S1).

Studies were included only if they 1) directly manipulated nutrient resource availability through fertilization of nitrogen (N), phosphorus (P), or both; 2) manipulated herbivorous animal assemblages through mechanical exclusion, enclosure (such as in mesocosms), or chemical or manual removal; 3) crossed these treatments in a full factorial design; and 4) reported mean community-level biomass responses of producers to these factorial manipulations. Population-level studies and single species responses of producers were only considered if they were 1) drawn from a mono-dominant community (as judged by the original authors), or 2) mean community-level biomass response(s) could be calculated from single species responses within a study. In several cases where all criteria were met but published data presentation was incomplete, we requested original data from authors. Although multiple levels of a factor (e.g. multiple nutrient levels) were extremely rare in the dataset, as standard practice we used the highest resource additions and most comprehensive herbivore removals that retained the full factorial design. Previous analyses expanding greatly on the present dataset showed that fertilization effect sizes across systems were independent of rates or quantities of applied nutrients (Elser et al. 2007). Those analyses did not demonstrate the rates are unimportant; instead, they showed that most investigators added nutrients in excess and successfully removed nutrient limitation in their experiments.

We defined a study as a temporally and spatially distinct sample with appropriate, consistent controls. Multiple studies could be reported from within one publication if the same experimental treatments were performed in multiple locations with differing physical and/or biological conditions. When multiple measures were reported over time from the same experiment, we used the last temporal sample in order to avoid phases of transient dynamics. Exceptions were made if some unusual disturbance affected some or all of the treatments or replicates. In these cases, we used the most robust values by deferring to the working knowledge and intuition of the original authors.

At the most basic level, studies were classified into three broadly recognized system categories: freshwater, marine and terrestrial. We divided these classes further into habitats defined primarily by physical habitat structure or strata (e.g. aquatic studies focused on benthic or pelagic producers) and the dominant producers in that medium or substrate (e.g. terrestrial habitats were grouped as herbaceous â??grasslandsâ?? or woody â??forestsâ??). Examples such as salt marshes or wetlands were more difficult to classify. Operationally, studies addressing periphyton or macrophytes, submerged or floating, were defined as aquatic (marine or freshwater); whereas studies on above-water, rooted plants were assigned to terrestrial systems (e.g. Spartina, Gough & Grace 1998). The resulting eight habitat categories were defined as follows: lake pelagic, lake benthic, stream benthic (freshwater); coastal soft bottom, coastal rocky temperate reef, coral reef, and oceanic (marine); grassland and forest (terrestrial). Other classification schemes are plausible, and other categories are possible within our scheme but were not included because appropriate empirical studies were lacking (e.g. stream pelagic). We could find only one oceanic pelagic study that met our criteria (Sommer 2000); this study was used in broad comparisons but dropped from habitat-level analyses.

Data were extracted from tables or digitized figures using the GrabIt! XP add-in for Microsoft Excel (Datatrend Software Inc.). The preferred producer community metric was standing dry biomass per unit area, although we also accepted the following proxy variables that have been shown to be highly correlated with standing biomass (Buck et al. 2000): chlorophyll, ash-free dry mass, wet biomass, fixed carbon, biovolume, percent cover or net (total, aboveground, belowground) primary production per area. These inclusive criteria incorporated more studies into the database and allowed broad comparisons across systems. Where multiple acceptable biomass measures were reported, we entered all measures and calculated mean standardized response ratios for each study. While productivity is often decoupled from standing stock biomass, particularly in systems with high turnover, twelve studies in our dataset reported both measurements and showed strong positive correlations (LRRH: r = 0.682, p = 0.0146; LRRF: r = 0.859, p = 0.0003; LRRI: r = 0.622, p = 0.031; df = 10 for all). Counts of individuals within a community were excluded because organisms can vary in body size by orders of magnitude between systems, and because body size usually relates inversely to abundance (Cohen et al. 1993; Cyr et al. 1997). Because multiple studies were often reported from a single publication, and from a smaller pool of principal investigators, we assigned categorical variables indicating publication units and the identities of principal investigators. The robustness of our results was checked with diagnostics, for instance by comparison of log ratios computed from different biomass metrics within the same studies or after pooling studies by publication or laboratory source (Englund et al. 1999).

Calculation of effect sizes

We used the log response ratio as the effect size metric (generally: ln[treatment/control]). The log response ratio (LRR) is one of the most commonly used effect metrics in ecological meta-analysis (Hedges et al. 1999; Lajeunesse & Forbes 2003). The analysis of treatment responses relative to that of the control is more meaningful than standardized absolute differences between means when comparing between systems. Unlike Hedgeâ??s d, the log response ratio does not require a measure of sample variability and does not weight individual studies by their variance, which would favor small-scale well-replicated studies over large-scale, presumably more realistic studies. Moreover, the distributions of log ratios typically conform to a normal distribution, making them suitable for a wide range of parametric statistical tests (Hedges et al. 1999). Finally, the log response ratio simplifies the interpretation of statistical interactions as in the cases of multiple predator interactions (Wootton 1994) and trait-mediated interactions (Okuyama & Bolker 2007). Calculating effects on the log response scale allows interpretation of positive and negative statistical interactions in terms of specific ecological interactions (Box).

We used factorial meta-analysis to calculate LRR effect sizes (Gurevitch et al. 2000; Hawkes & Sullivan 2001; Borer et al. 2006). To ease interpretation and facilitate direct comparison between the magnitudes of nutrient and herbivore main factors, we constructed the log ratios such that main effects were expected to be positive. That is, we assigned the controls as unfertilized (F0) and with herbivores present (H1); the fertilization and herbivore absence treatments were expected on average to increase producer biomass. For all factorial experiments included herein, we calculated the main fertilization (LRRF), main herbivore (LRRH), and the interaction effect size (LRRI) as:

LRRF = (ln[H0F1] + ln[H1F1]) - (ln[H0F0] + ln[H1F0])

LRRH = (ln[H0F1] + ln[H0F0]) - (ln[H1F1] + ln[H1F0])

LRRI = (ln[H1F0] + ln[H0F1]) - (ln[H1F1] + ln[H0F0])

We used the average biomass of grazed unfertilized (H1F0), grazed fertilized (H1F1), ungrazed unfertilized (H0F0) and ungrazed fertilized (H0F1) treatment combinations to calculate these log response ratios. Nonparametric 95%-confidence intervals (CIs) were calculated by bootstrap sampling from effect size pools with 999 iterations (Rosenberg et al. 2000). Non-overlapping CIs were used as conservative tests for statistically significant differences in effect sizes among groups or a significant deviation of an effect size from zero.