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Figure 1 shows the reflectance spectra collected over turfgrass at three different levels of water stress, specifically turfgrass at 16 days without watering, the intermediate situation at 7 days and at the end of the trial with the saturated cores (0 days without water), which serves as control. The differences across the curves are well evident. The major difference is the increase of reflectance at all wavelengths at 16 days without watering, where LRWC was at about 18% (Fig. 2), with respect to the other two spectral reflectance curves. It is so evident from the three different curves that in the Near-infrared (NIR 750–1,300 nm) and Short-wavelength infrared (SWIR 1,300–2,500 nm) four major absorption troughs are present. These strong reflectance troughs, located approximately in the NIR at 970 and 1,175, in the SWIR at 1,450 and 1,950 nm, are due to the absorption by water11. The troughs around 1,450 and 1,950 nm are less accentuated in the turf with high degree of desiccation (16 days without watering). Also González-Fernández et al.47 recommend calculating the band area for 1,450 nm and for 1,950 nm because of its link to equivalent water thickness, thus to estimate vine water status. Rallo et al.48 observed typical spectral responses in the SWIR region, where at leaf scale, absorbance bands near 1,450 and 1,900 nm could be related to the leaf water content of an olive grove.
Figure 2

Decline in volumetric soil water content (SWC) (%) and leaf relative water content (LRWC) (%) after watering ceased. Each point is the mean of six replications. Bars indicate one standard deviation error.

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However, in the regions of 1,350–1,480, 1,800–2,000 and 2,350–2,500 nm measurements of spectral reflectance of crop leaves are not possible in nature, also with fully sun-light conditions, because of the strong atmospheric absorption of light due to water vapor14,32,49 and are generally not exploited for landscape level studies. Consequently, to correctly measure these regions of wavelengths, a portable spectroradiometer system with an artificial light source must be chosen49. In fact, in our experiment an artificial light source was used, thus 1,430 and 1,950 can be considered key wavelengths for the measurements under artificial light source.
In the NIR spectral region there is a more commonly exploited troughs around 970 nm and in the region of 1,150–1,260, which are the most studied spectral ranges for estimation of vegetation water content14. It was interesting to note that the troughs of reflectance spectra underwent a gradual reduction in depth as the turfgrass desiccation increased, up to almost disappear in most cases, as showed in the 16 days without water curve. Some of the wavelengths associated with these troughs are, in fact, exploited by the spectral indices used in this study (see Table 1).
Figure 2 shows SWC and LRWC values, averaged over each set of six replicates with one standard deviation error bars, plotted with respect to the number of days without watering. Volumetric SWC declined as the days without watering increased. Starting from a value of 43.78% for the control cores with 0 days without watering, it decreased reaching a much lower value of 5.19% after two weeks without watering. Similarly, also LRWC declined as the number of days without watering increased. LRWC rate of decline was smaller than SWC as the days without watering were 4 or less (LRWC equal to 98.7%, 94.3% and 94.2% for 0, 1 and 4 days without watering, respectively). Then LRWC steeply decreased as the number of days without watering increased above 4. Observing the two parameters it is interesting to note that, with the exception of data collected in cores at 4 days without water, the trend of SWC and LRWC is similar (Fig. 2). In fact, from 1 to 4 days without water, turfgrass leaves try to preserve more water even if the soil water content decreases.
Figure 3 plots bar graphs of the selected indices in Table 1, where the indices are averaged over each set of six replicates of turfgrass at same water stress condition. One standard deviation error bars are also plotted. As is evident, all selected indices correlate with water stress level (Fig. 3).
Figure 3

Bar graphs of spectral indices averaged over each set of six replicates at same water stress condition, with one standard deviation error bar. (a) NDVI, (b) WI, (c) NDWI2130, (d) NDWI1240, (e) WI/NDVI.

Full size image

A quantitative analysis of these correlations, and specifically with respect to SWC, LRWC and SM, is reported in Table 2, which reports the Pearson product-moment correlation coefficients evaluated among the various parameters and indexes studied in this work.
Table 2 Pearson product-moment correlation coefficients (r) among volumetric soil water content (%) (SWC) measured using a time domain reflectometry (TDR); leaf relative water content (%) (LRWC); soil moisture (%) (SM) and vegetation indices selected for the study.
Full size table

Volumetric soil water content (SWC)
As expected, SWC was found to be highly correlated with SM (r = 0.98, p  More

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Regionally-downscaled climate change projections
We used a management strategy evaluation (MSE) applied to ensemble projections of a climate-enhanced multispecies stock assessment within the integrated modeling framework of the Alaska Climate Change Integrated Modeling project (ACLIM)19. For this, six high resolution downscaled projections of oceanographic and lower trophic level conditions in the Bering Sea (using the Regional Ocean Modeling System49,50) were coupled to the BESTNPZ nutrient-phytoplankton-zooplankton model51; we refer to this model complex throughout this paper as the Bering10K ROMSNPZ, or just ROMSNPZ, model. Boundary conditions were driven by three global general circulation models (GFDL-ESM2M52, CESM153, and MIROC-ESM54) projected (2006–2099) under the high-baseline emission scenario Representative Concentration Pathway 8.5 (RCP 8.5) and midrange global carbon mitigation (RCP 4.5; note, that for CESM under RCP 4.5, projections from 2080–2100 were unavailable so conditions from 2080–2099 were held constant at 2080 conditions for that scenario only) future scenarios from the Coupled Model Intercomparison Project phase 5 (CMIP5)29,55. Hermann et al.30,56 also report on downscaled hindcasts of oceanographic and lower trophic conditions in the EBS from 1970–2012 (see refs. 30,56,57 for detailed descriptions of model evaluation and performance). For each downscaled model simulation, we replicated the National Marine Fisheries Service Alaska Fisheries Science Center annual summer bottom-trawl survey in time and space in the ROMSNPZ model (using historical mean survey date at each latitude and longitude of each gridded survey station) to derive estimates of sea surface and bottom temperatures (Fig. 1). We additionally used a polygon mask of the survey area to estimate the average zooplankton abundance in the system during spring, summer, winter, and fall months. These indices were derived for each climate projection scenario, as well as a persistence scenario where conditions were held constant at the average of those for 2006–2017 from a hindcast simulation. All index projections were bias corrected to the 2006–2017 hindcast period using the delta method assuming unequal variance in the GCM projections and hindcast58 such that:

$$T_{mathop {{{mathrm{fut}}}}limits^prime ,y} = bar T_{{mathrm{hind}},overrightarrow {scriptstyle{mathrm{ref}}} } + frac{{sigma _{{mathrm{hind}},overrightarrow {scriptstyle{mathrm{ref}}} }}}{{sigma _{{mathrm{fut}}, overrightarrow{scriptstyle{mathrm{ ref}}} }}}left( {T_{{mathrm{fut}},y} – bar T_{{mathrm{fut}},overrightarrow {scriptstyle{mathrm{ref}}} }} right)$$
(1)

where (T_{mathop {{{mathrm{fut}}}}limits^prime ,y}) is the bias-corrected projected timeseries, (T_{{mathrm{fut}},y}) is the raw projected timeseries, (bar T_{{mathrm{hind}},overrightarrow {scriptstyle{mathrm{ref}}} }) is the mean of the hindcast during the reference years (overrightarrow {{mathrm{ref}}}) (2006–2017), (bar T_{{mathrm{fut}},overrightarrow {scriptstyle{mathrm{ref}}} }) is the mean of the raw projected timeseries during the reference years (overrightarrow {{mathrm{ref}}}), (sigma _{{mathrm{hind}},overrightarrow {scriptstyle{mathrm{ref}}} }) is the standard deviation of the hindcast during the reference years (overrightarrow {{mathrm{ref}}}), (sigma _{{mathrm{fut}},overrightarrow {scriptstyle{mathrm{ref}}} }) is the standard deviation of the raw projection timeseries during the reference years (overrightarrow {{mathrm{ref}}}).
Climate-enhanced multispecies stock assessment model
Bias-corrected indices were then used as covariates in the climate-enhanced multispecies stock assessment model for the Bering Sea (hereafter CEATTLE)59 to evaluate the performance of alternative management approaches on future fish biomass and catch. CEATTLE is a climate-enhanced multispecies statistical age-structured assessment model with parameters for growth that are functions of temperature (i.e., temperature-specific average weight-at-age) and predation that are functions of temperature (via a bioenergetics-based predation sub-model)59,60,61. Since 2016, the model has been used operationally in the Bering sea as a supplement to the annual BSAI pollock stock assessment61. Various configurations of CEATTLE are possible; for this study we chose one where temperature-specific predator and prey interactions influenced natural mortality, temperature influenced weight-at-age, and the spawner-recruit relationship was a function of physical and biological future conditions as well as random variability (i.e., a climate-informed multispecies model). We fit the model using penalized maximum likelihood to survey biomass, diet, and fishery harvest data for three groundfish species pollock, Pacific cod, and arrowtooth flounder from the EBS in the EBS over the period 1979–2017. We also used the Bering10K ROMSNPZ model to produce detailed hindcasts of temperature for the period 1970–2017. We used hindcast-extracted timeseries from the ROMSNPZ model and CEATTLE model estimates of recruitment ((R_{i,y,l})) and spawning biomass ((B_{i,y – 1})) in hindcast year y for each species i to fit a climate-enhanced logistic recruitment per spawner model36, such that:

$$ln left( {hat R_{i,y}} right) = alpha _i – beta _{0,i}B_{i,y – 1} + ln left( {B_{i,y – 1}} right) + {{{bf{B}}}}_i{{{bf{X}}}} + varepsilon _{i,y}$$
(2)

where ({{{bf{B}}}}_i{{{bf{X}}_l}}) is the summed product of each covariate parameter (beta _{ij}) and the corresponding environmental covariate (X_{j,y}) for each bias-corrected environmental index (j = ( {1,2…n_j} )). We selected indices representative of ecological conditions important for groundfish recruitment in the Bering sea39; spring and fall large zooplankton abundances, survey replicated bottom temperature, and extent of the residual cold pool of extremely dense and cold sea water that persists across the EBS shelf following spring sea ice retreat. We assumed normally distributed (in log space) residual errors for each species ((varepsilon _{i,y} sim Nleft( {0,sigma _i^2} right))). The CEATTLE model was then projected forward where ROMSNPZ indices from individual projections drove growth, predation, and recruitment in each future simulation year36,62.
Evaluation of harvest management approaches
Previous authors have defined EM (i.e., the incorporation of ecosystem information into marine resource management) as a continuum between two paradigms of management and focus18. On one end is within-sector single-species management that considers ecosystem information (EAFM) and on the other is cross-sectoral whole of ecosystem management (i.e., EBM). EBFM is intermediate between these and is defined by quantitative incorporation of ecosystem interactions into assessment models and target setting (EBFM). Most fisheries management in the Bering Sea can be characterized as EBFM or EAFM, with increasing trends toward cross-sectoral coordination at the scale of EBM. Here we focus on one aspect on this scale of potential management options, operational EBFM and EAFM as captured through the CEATTLE multispecies stock assessment model and harvest policies decisions made annually under the constraint of the 2 MT cap (modeled via the ATTACH model).
MSE is a process of “assessing the consequences of a range of management strategies or options and presenting the results in a way which lays bare the tradeoffs in performance across a range of management objectives”63. MSE has been frequently used to evaluate alternative management strategies based on single-species estimation methods64. It is increasingly used to evaluate ecosystem management performance, although these evaluations are far less commonplace due to the complexity of modeling and assessing the performance of ecosystem level metrics64. Importantly, MSE “does not seek to proscribe an optimal strategy or decision”63, rather it aims to describe the uncertainty and tradeoffs inherent in alternative strategies and scenarios. In this case, through a series of workshops, we worked with managers and stakeholders to identify priority scenarios and outputs19. From this, risk, sensitivity, and uncertainty under contrasting climate scenarios were requested outputs of the analysis, as was the performance of current climate-naive EBFM policies.
A key component of MSE is identifying and quantifying uncertainty (i.e., process, observation, estimation, model, and implementation error) and representing it using an operating model. In the case of this MSE, the focus was on process error uncertainty due to variation in recruitment about the fitted stock-recruitment relationship, one major source of model error in the form of alternative climate scenarios, and implementation error. The MSE does not account for estimation error (uncertainty in the parameters of the operating model) nor observation error. This is because the estimates of recruitment and spawning biomass from CEATTLE for the BSAI are very precise (see Fig. 10 in ref. 60) and the estimation and operating models are therefore very similar. Thus, CEATTLE is the operating model for this MSE and implicitly the estimation method. In this approach we assume that while allowing for observation error would have increased overall error, the effect would have been minor compared to the investigated uncertainties. Future analyses using a full MSE (i.e., separate operating and estimation models) could evaluate the effect of observation error, but perhaps more importantly, the potential for model error, whereby the population dynamics model (on which the estimation method is based) differs from that of the operating model such that the estimates on which management decisions are made are biased relative to the true values in the operating model.
Given this we summarized the relative change in catch and biomass for the three species in the model under the following fishing scenarios (Fig. 1): (a) projections without harvest ((F_{i,y} = 0)) in each year y of scenario l for each species i, (b) projections under target harvest rate (Supplementary Fig. 7 left) and with a sloping harvest control rule (HCR) (Supplementary Fig. 7 right), (c) as in 2 but with the constraint of a 2 MT cap applied dynamically to the three focal species only.
Under the North Pacific Fishery Management Council (NPFMC) constraint of the 2 MT cap on cumulative total annual catch, realized harvest (i.e., catch) and specification of individual species harvest limits known as Total Allowable Catch (TAC; metric tons) are a function of the acceptable biological catch (ABC) for the given species, as well as ABC of other valuable species in the aggregate complex19,34 (https://github.com/amandafaig/catchfunction). TAC must be set at or below ABC for each species, therefore TAC of individual species are traded-off with one another to avoid exceeding the 2 MT cap. From 1981 to 1983, the TAC of pollock was reduced significantly below the ABC and in 1984 the 2 MT cap became part of the BSAI fishery management plan21,34,65. Pacific cod regulations have changed markedly over recent decades and it was only in the 1990s that in many years the catch and TAC approached its ABC. Thus, we used the socioeconomic ATTACH model (the R package ATTACHv1.6.0 is available with permission at https://github.com/amandafaig/catchfunction34) to model realized catch in each simulation year as a function of CEATTLE assessment estimates of ABC (tons) for pollock, Pacific cod, and arrowtooth flounder under future projections (2018–2100). This entailed three steps for each future simulation year (y):
1.
project the population forward from (y – 1) to (y) using estimated parameters from the multispecies mode of the CEATTLE model fit to data from 1979 to 2017 and recruitment based on biomass in simulation year (y) and future environmental covariates from the ROMSNPZ model downscaled projections (see “Methods” above) to determine ({mathrm{ABC}}_{i,y,l}) for each species (i) under each scenario (l) given the sloping harvest control rule for pollock, Pacific cod, and arrowtooth flounder in each simulation year (y);

2.
use ({mathrm{ABC}}_{i,y,l}) of each species from step 1 as inputs to the ATTACH model in order to determine the North Pacific Marine Fishery Council Total Allowable Catch (TACi,y,l) for the given simulation l year y;

3.
use TACi,y,l from step 2 to estimate catch (tons) in the simulation year (Fig. 1); remove catch from the population and advance the simulation forward 1 year.

Determine the annual ABC
We used end-of-century projections (2095–2099) to derive a maximum sustainable yield (MSY) proxy for future harvest recommendations (ABCi,y,l) for each scenario l. To replicate current management, we used a climate-specific harvest control rule that uses climate-naive unfished and target spawning biomass reference points ((B_{0,i}) and (B_{{mathrm{target},i}}), respectively) and corresponding harvest rates ((F_{i,y} = 0) and (F_{i,y} = F_{{mathrm{target}}}) and (B_{i,y,l}) in each simulation l year (y) for each species (i)

$${mathrm{ABC}}_{i,y,l} = mathop {sum }limits_a^{A_i} left( {frac{{S_{i,a}F_{{mathrm{ABC}},i,y,l}}}{{Z_{i,a,y,l}}}left( {1 – e^{ – Z_{i,a,y,l}}} right)N_{i,a,y,l}W_{i,a,y,l}} right)$$
(3)

where (W_{i,a,y,l}), (N_{i,a,y}), and (Z_{i,a,y,l}) is the climate-simulation specific annual weight, number, and mortality (i.e., influenced through temperature effects on recruitment, predation, and growth) at age (a) for (A_i) ages in the model, and (S_{i,a}) is the average fishery age selectivity from the estimation period 1979–201759,60. (F_{{mathrm{ABC}},i,y,l}) and was determined in each simulation timestep using an iterative approach66 whereby we: (i) first determined average (B_{0,i}) values in years 2095–2099 by projecting the model forward without harvest (i.e., (F_{i,y} = 0)) for each species under the persistence scenario. We then (ii) iteratively solved for the harvest rate that results in an average spawning biomass ((B_{i,y})) during 2095–2099, that is, 40% of (B_{0,i}) (i.e., (F_{{mathrm{target}},i})) for pollock and Pacific cod simultaneously, with arrowtooth flounder (F_{i,y}) set to the historical average (as historical F for arrowtooth flounder ≪(F_{40% })); once (F_{{mathrm{target}},i}) for pollock and Pacific cod were found, we then iteratively solved for (F_{{mathrm{target}},i}) for arrowtooth flounder (Supplementary Fig. 7 left panel)59,60. Last, (iii) to derive a climate-informed ({mathrm{ABC}}_{i,y,l}) in each simulation year, the North Pacific Marine Fisheries Council (hereafter, “Council”) Tier 3 sloping harvest control rule with an ecosystem cutoff at (B_{20% }) was applied to adjust (F_{{mathrm{ABC}},i,y,l}) lower than (F_{{mathrm{target}},i}) if the simulation specific (climate-informed) (B_{i,y,l}) was lower than 40% of the climate-naive (B_{0,i}) at the start of a given year or set to 0 if (B_{i,y,l} , More

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We first describe the development of the method and its validation under controlled laboratory settings for both Synechococcus and Prochlorococcus host-phage systems. Then we apply the method to quantify the contribution of T4-like and T7-like cyanophage infection to the mortality of Prochlorococcus over the diel cycle in the upper mixed layer of the North Pacific Subtropical Gyre during the summer of 2015.
Development of the iPolony method for the detection of viral infection
Our goal was to develop a sensitive, high-throughput method amendable to analysis of field samples that can assess infection by virus families of interest. The polony method (named for PCR colonies that form during the reaction) is a direct PCR-based method that detects virus DNA inside infected cells. The original polony method was developed by Mitra and Church [45] and was subsequently adapted for the enumeration of free virus particles from the two major cyanophage lineages, the T4-like cyanomyoviruses [34] and the T7-like cyanopodoviruses [33]. Here we describe further development of the method to simultaneously detect viral infection in thousands of individual cells embedded in a solid-phase gel in a high-throughput manner. We term this method for the quantification of infected cells ‘iPolony’.
The iPolony method has two steps (Fig. 1). In the first step, infection is arrested by fixation with glutaraldehyde, and target cells are isolated and concentrated (Fig. 1a). In its use here, Prochlorococcus and Synechococcus are sorted by flow cytometry based on forward angle light scattering, a proxy for cell size, and the autofluorescence of chlorophyll a and phycoerythrin, respectively. The concentration of cells is then quantified to calculate the number of cells analyzed in the downstream molecular analysis. In the second step, the cells are screened for the presence of intracellular virus DNA using the polony method (Fig. 1b). Polyacrylamide gels are cast with embedded sorted cells and a 5′-acrydite-modified primer to anchor the primer to the gel. PCR reagents are diffused into the gels. Degenerate PCR primers target a signature gene shared by the virus group of interest, in this case the DNA polymerase gene for the T7-like cyanopodoviruses [33] and the portal protein gene (g20) for the T4-like cyanomyoviruses [34]. Prior to thermal cycling, cells are permeabilized to allow amplification of virus DNA with an in-gel heat lysis step (Supplementary text, Supplementary Fig. 3). During thermal cycling, a cell that contained virus DNA results in an anchored sphere of amplification or polony. After amplification, polonies in gels are hybridized with fluorescently labeled degenerate cyanophage group-specific probes, and gels are scanned with a microarray scanner. Each individual cell is counted as infected whether there is a single or multiple virus genome copies, which enables quantification of infection in a presence–absence manner per cell. Percent infection is calculated by dividing the number of polonies by the number of cells in the gel.
Fig. 1: iPolony: a polony method for quantifying virally infected cyanobacteria.

a First, Prochlorococcus and Synechococcus are sorted based on size and their autofluorescence properties using a flow cytometer from fixed samples. b Then, thousands of sorted cells per slide are screened for the presence of intracellular viral DNA using a solid-phase PCR polony method. Percent infection is determined based on the fraction of input cells that resulted in polonies at the end of the analysis.

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Validation of the iPolony method in controlled virus growth experiments
The method was first developed and tested on model lab systems under known conditions. We assessed the ability of the iPolony method to detect virus DNA inside cyanobacterial cells throughout the infection cycle. Two model systems were used: Synechococcus sp. strain WH8109 infected with the T7-like cyanophage, Syn5, and Prochlorococcus sp. strain MIT9515 infected with the T4-like cyanophage, S-TIM4. Virus DNA was detected inside cells at all stages of the infection cycle (Fig. 2). The efficiency of detection was lower prior to virus genome replication and was 43% for Syn5 and 11% for S-TIM4 (Fig. 2a–d). Detection of infected cells rose with the onset of DNA replication, reaching 86% of maximal infection levels based on host gDNA degradation, midway through genome replication for Syn5 and at the end of genome replication for S-TIM4 (Fig. 2a–d). Since more than a single phage can enter cells in these experiments, we verified that single gene copies can be detected inside cells for a single copy host gene, rbcL, in Synechococcus WH8109, as well as for E. coli carrying a single plasmid with a cyanophage g20 copy (see Supplementary results and discussion). These findings indicate the method is sensitive enough to detect infection throughout the entire infection process even when a single molecule of phage DNA is present prior to genome replication and reaches maximal levels after the onset of DNA replication.
Fig. 2: The iPolony method detects viral infection throughout the infection cycle.

Cultures of Synechococcus sp. strain WH8109 infected by the T7-like cyanopodovirus, Syn5 (a, c, e) and Prochlorococcus sp. strain MIT9515 infected by the T4-like cyanomyovirus, S-TIM4 (b, d, f) at MOI = 3. a, b Percent infection was determined using the polony method over the infection cycle. c, d Virus DNA replication (solid lines) and host genomic DNA degradation (dashed lines) were assessed by qPCR in infected cultures. Host and virus DNA concentrations were normalized to initial or maximum concentrations, respectively. Shaded regions indicate the period of virus genome replication. Lysis was assessed from an increase in plaque forming units measured by the plaque assay for Syn5 (e) or the appearance of extracellular virus DNA measured by qPCR for S-TIM4 (f). Note that Syn5 infections shown in (c) and (e) were not synchronized at 5 min post infection as in (a) and are shown for comparison of the timing of different phases of infection. Average and standard deviation of biological triplicates are shown in all panels.

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Next, we assessed whether the method could accurately detect varying levels of infection by exposing Synechococcus sp. strain WH8109 to different numbers of the Syn5 phage, such that the infective virus-to-host ratios (multiplicities of infection, MOIs) ranged from 0.1 to 3, spanning infection percentages that theoretically range from 10 to 95% based on encounter theory estimates (Supplementary Table 3). The percent infection determined by the iPolony method was significantly and positively correlated with the MOI (Fig. 3a) (F = 143.1, R2 = 0.87, p  More

We primarily relied on the “tidyverse”61, “metafor”30, “lmerTest”62, “effects”63, “maptools”64, “sf”65, and “raster”66 packages of the R software67 for organizing and analyzing data, and visualizing the results.
Data assembly
To support the use of meta-analysis to quantify the effects of species richness on plant litter decomposition (i.e., species-mixing effects), we searched the literature using the ISI Web of Science (WoS) database (https://clarivate.com/products/web-of-science/; up to and including December 2018). We used a combination of “decomposition” AND “litter”. These keywords matched 12,278 publications. We then reduced this list of the literature with the keywords of “mix* litter,” OR “litter diversity,” OR “litter mix*,” OR “litter species diversity,” OR “litter species richness,” OR “species mix*,” OR “mix* plant litter,” OR “multi* species litter,” OR “mixing effect*,” resulting in 416 publications. We also searched the literature using Scopus (https://www.scopus.com/home.uri) and Google Scholar (https://scholar.google.ca/) and the latter set of keywords, resulting in 765 publications. An anonymous expert identified 15 additional publications. We decided not to include reports in the grey literature among the papers we found, as we could not verify whether, as in all WoS-listed papers, the papers had undergone independent peer review as a quality check. We read through the papers carefully to select those that focused on quantifying the effects of litter diversity on decomposition rates based on a litter-bag experiment using both mixed- and mono-species litter. We focused on the publications that reported values of either mass loss (or mass remaining) or a decomposition rate constant k that quantified the decomposition rate. Specifically, some papers for litter-mixing effects reported only for the additive effects of mixture and had no reports on mass loss or the constant k. In some cases, no sample size nor standard deviations/errors were reported. Mass loss or standard deviations/errors values were reported only for mono-species or multi-species litter. These publications were not included in the present analyses. In cases that had no report on means but instead showed median values, we estimated means and standard errors based on individual data points or percentile values of boxplots. Note that, standard deviations/errors were often invisible because they were too small to read and thus hidden by their data points; in this case, a conservative approach was adopted by using possible maximum values of deviations/errors (i.e., the size of these symbols). Based on these criteria, we extracted information required for our meta-analysis (see below) from a total of 151 studies (Supplementary Data 1). Out of these 151 studies, 131 and 45 studies measured mass loss and the decomposition rate constant k, respectively. Also see the PRISMA work flow diagram (Supplementary Fig. 6).
For the selected studies, we identified the sets of comparisons between mixed- and mono-species litter bags in each publication. That is, a single study could have multiple treatments that focused on different litter substrates, using different mesh sizes for litter bags, having multiple experiments in different locations, changing abiotic conditions, and so on. The decomposition rate should be comparable in a given treatment under the same set of environmental conditions except for differences caused by a different number of plant species. Even for a given treatment, decomposition rates were often reported multiple times in the literature; in such cases, we only included comparisons for litter retrieved at the same time (i.e., after the same incubation period). Note that in a given treatment, the same mono-species litter could be used for multiple comparisons; for instance, mass loss from a litter bag that contained a three-species mixture (species A, B, and C simultaneously) can be compared with the mass loss in three different mono-species litter bags (only species A, B, or C). This could lead to issues related to pseudo replication, which we considered based on a multilevel random effects meta-analysis (see Data analyses). As a result, we identified 6535 comparisons (across 1949 treatments from the 131 studies) for the values of mass loss and 1423 comparisons (across 504 treatments from the 45 studies) for values of the decomposition rate constant k.
After identifying the sets of comparisons, we extracted the sample size (number of litter-bag replicates, n), and the mean and standard deviation (SD) of the decomposition rate from the main text, from any tables and figures, and from the supplemental materials of the selected studies. If standard errors or 95% confidence intervals (CI) were given, we transformed them into SD values. If only figures were given, we used version 3.4 of the Webplot-digitizer software (https://automeris.io/WebPlotDigitizer/) to extract these parameters from the graphs. We also recorded the study location (longitude, latitude, elevation), climatic region (subarctic, boreal, temperate, subtropical, tropical, or other), ecosystem type (forest, grassland, shrubland, desert, wetland, stream, seagrass, lake, or ex situ microcosm), and litter substrate (leaf, root, stem, branch, straw, or other). Microcosm studies were further divided into two categories: terrestrial or aquatic. The former and latter, respectively, placed litter bags on the soil and in water. For litter substrate, most studies used terrestrial plants, but two studies used macrophytes for their decomposition experiment; these data were included in the main analysis and excluded from the subsequent analyses that focused on leaf litter. Note that authors reported the decomposition rate for mixed-species litter bags in different ways, as the values for all species together or for individual species in the same bag. Removing data based on the latter classification had little effect on our results, so we retained that data. Because of the limited data availability, we did not consider the potential influences of species richness (here, the number of litter species; more than 74% of the comparisons used two- or three-species mixtures) and instead considered species richness as a random term (see Data analyses). Based on the geographic locations of the studies, we estimated their present bioclimatic conditions based on the WorldClim database (www.worldclim.org).
Species-mixing effects on litter decomposition
We calculated the unbiased standardized mean difference (Hedges’ d)30 of the decomposition rate between the mean values for the mixed- and mono-species litter. Hedges’ d is a bias-corrected, unit-free index that expresses the magnitude of the deviation from no difference in the response variable between comparisons. Note that many studies performed multiple comparisons for the decomposition rate between mixed- and mono-species litter, potentially causing issues of pseudo-replication and non-independence in the dataset, as is often the case for ecological syntheses68. We thus applied a multilevel random effects meta-analysis30,69 to account for this problem. In a random effects model, the effect sizes for individual comparisons are weighted by the sum of two values: the inverse of the within-study variance and the between-study variance. The multilevel model can also account for a nested structure in the dataset (in which different treatments and multiple comparisons were nested within each study) and is thus appropriate for dealing with non-independence within a dataset. To calculate the effect sizes, we defined their values to be positive for comparisons in which decomposition was faster in mixed-species litter than in mono-species litter and negative when mono-species litter decomposed faster. This is based on a species gain perspective. Note that some have mono- and two-species mixtures, and others could have for instance from 1 to 16 species in their experiments. Considering mono-species litter as a control is therefore the only way to be consistent across all studies. That is, quantification based on a species loss perspective requires us to obtain the effect sizes using mixed-species litter as a control. In this case, different studies have different levels of richness for a control, making it impossible to have a quantification in a standardized way. We first calculated the effect sizes based on mass loss and the decomposition rate constant k (Fig. 1b, c); because of the limited data availability for the constant k, we only calculated the effect sizes for the entire dataset and the subset of data for leaf litter. For mass loss, we further calculated the effect sizes for the different ecosystem types in different climatic regions; subsets of the data that originated from at least three different studies were used. We conducted a multilevel mixed effects meta-regression by considering random effects due to non-independence among some data points, resulting from a nested structure of the dataset that individual data points were nested within a treatment and treatments were also nested within a study. We used the Q statistic for the test of significance.
Note that, because publication bias is a problem in meta-analysis, we visually evaluated the possibility of such a potential bias by plotting the values of the effect sizes and their variances against sample size. If there is no publication bias, studies with small sample sizes should have an increased sampling error relative to those with larger sample sizes, and the variance should decrease with increasing sample size. In addition, the effect size should be independent of the sample size. Also, there should be large variation in effect sizes at the smallest sample sizes. Prior to the meta-analysis, we confirmed that these conditions existed (Supplementary Fig. 1), and found no publication bias large enough to invalidate our analysis.
We also visually confirmed that the datasets were normally distributed based on normal quantile plots. Furthermore, following the method of Gibson et al.70, we randomly selected only one comparison per treatment and then calculated the effect sizes for the decomposition rate (based on mass loss); we repeated this procedure 10,000 times (with replacement) and found that the species-mixing effects on decomposition were significantly positive (0.247 ± 0.045 for the mean ± 95% CI; Supplementary Fig. 2). We thus confirmed that the overall results were not affected by a publication bias or by non-independence of the dataset. We additionally focused on a subset of the entire dataset, which reported mass loss data for each component species from mixtures and thus had comparisons between mass loss of mono-species litter and that of the same species in a mixture (e.g., mass loss of mono-species litter for species A, B, and C was only compared with that for species A, B, and C within a three-species mixture, respectively). We found the results for this subset of the data (Supplementary Fig. 3) almost identical to the main results (Fig. 2a, b). Note that because of the limited data availability, we did not consider the effects of using different equation forms to estimate the rate constant k and instead considered these among-study differences based on a random term in our multilevel meta-analysis. We also calculated the influence of incubation period (days) on the effect size for the decomposition rate (based on mass loss of leaf litter) for the subsets of the dataset using a mixed effects meta-regression30 (Supplementary Fig. 4). We limited this analysis to studies that retrieved litter bags at least two different time points. To account for non-independence of data points, the study identity was included as a random term.
Impacts of global change drivers on litter decomposition
Litter decomposition is primarily controlled by three factors: the environment (e.g., climate), the community of decomposers, and litter traits46,47,48. By relying on the dataset of Makkonen et al.50, who conducted a full reciprocal litter transplant experiment with 16 plant species that varied in their traits and origins (four forest sites from subarctic to tropics), we aimed to obtain a standardized equation to estimate how decomposition rate changed along a climatic gradient (hereafter, the “standardized climate–decomposition relationship”). First, by considering litter decomposition rates at the coldest location (i.e., the subarctic site) as a reference (control), we calculated the effect sizes (i.e., standardized mean difference based on Hedges’ d) for their decomposition rate constant k for all possible comparisons (i.e., between data from the coldest site and the value, one at a time, for the three other warmer sites). As explained above, the effect sizes were calculated only for the comparisons between decomposition rates of litter that were obtained using the same protocol (litter species, origin, and decomposers). The effect sizes therefore represent the climatic effects on litter decomposition after removing the effects of the decomposer community and litter traits.
We obtained the bioclimatic variables for these four study sites from the WorldClim database, and then modelled the standardized climate–decomposition relationships using a multilevel mixed effects meta-regression30,69. Annual mean temperature, the mean temperature of the wettest quarter, or precipitation of the driest quarter were used as an explanatory variable, with the protocol as a random term. This allowed us to evaluate how decomposition rate can be altered by climate along a latitudinal gradient from tropics to subarctic. We then calculated the decomposition rate constant k for our dataset in exactly the same manner as Makkonen et al.50 and calculated the effect sizes; because of limited datasets for most biomes, we performed this analysis only for the subset of our dataset that we obtained for forest biomes, and we used only leaf litter (57 studies) so the results would be comparable with those of Makkonen et al.50. We used these effect sizes and the standardized climate–decomposition relationships to convert the species-mixing effects into climatic effects; that is, based on the temperature or precipitation required to alter the effect size to the same magnitude as the litter diversity effect, we estimated the climate-equivalency of the diversity effects. This means that we relied on the slope of the relationships to quantify the diversity effects, as has been done in previous analyses38,71. We also compared these estimates to the future projections of changes in decomposition rates in response to climate change (with estimates for the 2070s for two of the representative concentration pathway scenarios of CO2 used in the 5th Climate Model Intercomparison Project; CMIP5 RCP 2.6 and 8.5) for the locations of the original studies (the coordinates of individual studies were collected using the Google Map; www.google.com). This comparison was aimed at quantifying the impacts of different global change drivers (biodiversity and climate change) on decomposition processes. Note that we additionally conducted the above analysis after excluding data with no species identity information for mono and/or mixed-species litter bags, those that measured ash-free dry mass loss (this exclusion was to be consistent with the procedure used in Makkonen et al.50), or both of them (Table S1). As an additional confirmation, we also relied on an alternative method used by Hooper et al.45 to convert the species-mixing effects into climatic effects (mean annual temperature), and compared the impacts of different global change drivers on the decomposition rate (Supplementary Fig. 5).
We further analyzed the potential changes in decomposition resulting from litter diversity and climate change. For the dataset of Makkonen et al.50, we first modelled the relationship between climate (annual mean temperature) and the decomposition rate constant k using an LMM with the protocol as a random term. The constant k was log-transformed to improve homoscedasticity. With this equation and the values of annual mean temperature at the 57 study locations in the forest biomes included in our dataset, we then estimated the expected values of k at these study locations (the present k values). Note that because the experiment of Makkonen et al.50 had no mixed-species litter, the expected k using the above LMM was used primarily to estimate the decomposition rate of mono-species litter at a given annual mean temperature. By combining this estimate with the aforementioned estimate of the climate-equivalency of the litter diversity effect (for annual mean temperature; Fig. 3a), it was possible to estimate the potential changes in the k that resulted from increasing litter diversity from mono- to mixed-species litter at the 57 forest study locations. Specifically, the diversity effect converted into the temperature effect (Fig. 3a) was added to present estimates of annual mean temperature at these study locations, and these values of temperature change were used as an explanatory variable to project changes in k based on the above LMM (the projected k values). In other words, we quantified the projected k values under a scenario in which we brought mono-species litter to areas with a warmer annual mean temperature equivalent to the temperature increase in the climate-equivalency effect. We then converted the present and projected values of the decomposition rate constant k to a mass loss per unit time, making it possible to calculate percentage changes in the decomposition rate due to litter diversification. Furthermore, using the above LMM for the temperature–decomposition relationship with the projected changes in mean annual temperature (based on the CMIP5 RCP 2.6 and 8.5 scenarios) as an explanatory variable, we projected future changes in the decomposition rate constant k at these study locations.
Again, we converted these estimates to a litter mass loss to obtain the percentage changes in the decomposition rate that would result from climate change. The rationale for using the temperature–decomposition relationship was as follows: A similar magnitude of increase in k can, in absolute terms, have different influences on decomposition rates at different locations with a different k. For instance, a change in the value of k from 0.1 to 0.2 and a change from 3.0 to 3.1 are substantially different when considered based on litter mass loss or litter amount remaining after decomposition. We thus included annual mean temperature in our model for quantifying the effects of litter diversity on decomposition. More