Are high-throughput root phenotyping platforms suitable for informing root system architecture models with genotype-specific parameters? An evaluation based on the root model ArchiSimple and a small panel of wheat cultivars.

Given the difficulties in accessing plant roots in situ, high-throughput root phenotyping (HTRP) platforms under controlled conditions have been developed to meet the growing demand for characterizing root system architecture (RSA) for genetic analyses. However, a proper evaluation of their capacity to provide the same estimates for strictly identical root traits across platforms has never been achieved. In this study, we performed such an evaluation based on six major parameters of the RSA model ArchiSimple, using a diversity panel of 14 bread wheat cultivars in two HTRP platforms that had different growth media and non-destructive imaging systems together with a conventional set-up that had a solid growth medium and destructive sampling. Significant effects of the experimental set-up were found for all the parameters and no significant correlations across the diversity panel among the three set-ups could be detected. Differences in temperature, irradiance, and/or the medium in which the plants were growing might partly explain both the differences in the parameter values across the experiments as well as the genotype × set-up interactions. Furthermore, the values and the rankings across genotypes of only a subset of parameters were conserved between contrasting growth stages. As the parameters chosen for our analysis are root traits that have strong impacts on RSA and are close to parameters used in a majority of RSA models, our results highlight the need to carefully consider both developmental and environmental drivers in root phenomics studies.

Neglecting acclimation of photosynthesis under drought can cause significant errors in predicting leaf photosynthesis in wheat.

Extreme climatic events, such as heat waves, cold snaps and drought spells, related to global climate change, have become more frequent and intense in recent years. Acclimation of plant physiological processes to changes in environmental conditions is a key component of plant adaptation to climate change. We assessed the temperature response of leaf photosynthetic parameters in wheat grown under contrasting water regimes and growth temperatures (Tgrowth ). Two independent experiments were conducted under controlled conditions. In Experiment 1, two wheat genotypes were subjected to well-watered or drought-stressed treatments; in Experiment 2, the two water regimes combined with high, medium and low Tgrowth were imposed on one genotype. Parameters of a biochemical C3 -photosynthesis model were estimated at six leaf temperatures for each factor combination. Photosynthesis acclimated more to drought than to Tgrowth . Drought affected photosynthesis by lowering its optimum temperature (Topt ) and the values at Topt of light-saturated net photosynthesis, stomatal conductance, mesophyll conductance, the maximum rate of electron transport (Jmax ) and the maximum rate of carboxylation by Rubisco (Vcmax ). Topt for Vcmax was up to 40°C under well-watered conditions but 24-34°C under drought. The decrease in photosynthesis under drought varied among Tgrowth but was similar between genotypes. The temperature response of photosynthetic quantum yield under drought was partly attributed to photorespiration but more to alternative electron transport. All these changes in biochemical parameters could not be fully explained by the changed leaf nitrogen content. Further model analysis showed that both diffusional and biochemical parameters of photosynthesis and their thermal sensitivity acclimate little to Tgrowth , but acclimate considerably to drought and the combination of drought and Tgrowth . The commonly used modelling approaches, which typically consider the response of diffusional parameters, but ignore acclimation responses of biochemical parameters to drought and Tgrowth , strongly overestimate leaf photosynthesis under variable temperature and drought.

The extreme 2016 wheat yield failure in France.

France suffered, in 2016, the most extreme wheat yield decline in recent history, with some districts losing 55% yield. To attribute causes, we combined the largest coherent detailed wheat field experimental dataset with statistical and crop model techniques, climate information, and yield physiology. The 2016 yield was composed of up to 40% fewer grains that were up to 30% lighter than expected across eight research stations in France. The flowering stage was affected by prolonged cloud cover and heavy rainfall when 31% of the loss in grain yield was incurred from reduced solar radiation and 19% from floret damage. Grain filling was also affected as 26% of grain yield loss was caused by soil anoxia, 11% by fungal foliar diseases, and 10% by ear blight. Compounding climate effects caused the extreme yield decline. The likelihood of these compound factors recurring under future climate change is estimated to change with a higher frequency of extremely low wheat yields.

Importance of the description of light interception in crop growth models.

Canopy light interception determines the amount of energy captured by a crop, and is thus critical to modeling crop growth and yield, and may substantially contribute to the prediction uncertainty of crop growth models (CGMs). We thus analyzed the canopy light interception models of the 26 wheat (Triticum aestivum) CGMs used by the Agricultural Model Intercomparison and Improvement Project (AgMIP). Twenty-one CGMs assume that the light extinction coefficient (K) is constant, varying from 0.37 to 0.80 depending on the model. The other models take into account the illumination conditions and assume either that all green surfaces in the canopy have the same inclination angle (θ) or that θ distribution follows a spherical distribution. These assumptions have not yet been evaluated due to a lack of experimental data. Therefore, we conducted a field experiment with five cultivars with contrasting leaf stature sown at normal and double row spacing, and analyzed θ distribution in the canopies from three-dimensional canopy reconstructions. In all the canopies, θ distribution was well represented by an ellipsoidal distribution. We thus carried out an intercomparison between the light interception models of the AgMIP-Wheat CGMs ensemble and a physically based K model with ellipsoidal leaf angle distribution and canopy clumping (KellC). Results showed that the KellC model outperformed current approaches under most illumination conditions and that the uncertainty in simulated wheat growth and final grain yield due to light models could be as high as 45%. Therefore, our results call for an overhaul of light interception models in CGMs.

Drought exerts a greater influence than growth temperature on the temperature response of leaf day respiration in wheat (Triticum aestivum).

We assessed how the temperature response of leaf day respiration (Rd ) in wheat responded to contrasting water regimes and growth temperatures. In Experiment 1, well-watered and drought-stressed conditions were imposed on two genotypes; in Experiment 2, the two water regimes combined with high (HT), medium (MT) and low (LT) growth temperatures were imposed on one of the genotypes. Rd was estimated from simultaneous gas exchange and chlorophyll fluorescence measurements at six leaf temperatures (Tleaf ) for each treatment, using the Yin method for nonphotorespiratory conditions and the nonrectangular hyperbolic fitting method for photorespiratory conditions. The two genotypes responded similarly to growth and measurement conditions. Estimates of Rd for nonphotorespiratory conditions were generally higher than those for photorespiratory conditions, but their responses to Tleaf were similar. Under well-watered conditions, Rd and its sensitivity to Tleaf slightly acclimated to LT, but did not acclimate to HT. Temperature sensitivities of Rd were considerably suppressed by drought, and the suppression varied among growth temperatures. Thus, it is necessary to quantify interactions between drought and growth temperature for reliably modelling Rd under climate change. Our study also demonstrated that the Kok method, one of the currently popular methods for estimating Rd , underestimated Rd significantly.

Omics Data Reveal Putative Regulators of Einkorn Grain Protein Composition under Sulfur Deficiency.

Understanding the molecular mechanisms controlling the accumulation of grain storage proteins in response to nitrogen (N) and sulfur (S) nutrition is essential to improve cereal grain nutritional and functional properties. Here, we studied the grain transcriptome and metabolome responses to postanthesis N and S supply for the diploid wheat einkorn (Triticum monococcum). During grain filling, 848 transcripts and 24 metabolites were differentially accumulated in response to N and S availability. The accumulation of total free amino acids per grain and the expression levels of 241 genes showed significant modifications during most of the grain filling period and were upregulated in response to S deficiency. Among them, 24 transcripts strongly responded to S deficiency and were identified in coexpression network analyses as potential coordinators of the grain response to N and S supply. Sulfate transporters and genes involved in sulfate and Met metabolism were upregulated, suggesting regulation of the pool of free amino acids and of the grain N-to-S ratio. Several genes highlighted in this study might limit the impact of S deficiency on the accumulation of grain storage proteins.

Sensitivities to temperature and evaporative demand in wheat relatives.

There is potential sources of alleles and genes currently locked into wheat-related species that could be introduced into wheat breeding programs for current and future hot and dry climates. However, neither the intra- nor the inter-specific diversity of the responses of leaf growth and transpiration to temperature and evaporative demand have been investigated in a large diversity of wheat-related species. By analysing 12 groups of wheat-related sub-species, we questioned the n-dimensional structure of the genetic diversity for traits linked to plant vegetative structures and development, leaf expansion and transpiration together with their responses to "non-stressing" range of temperature and evaporative demand. In addition to provide new insight on how genome type, ploidy level, phylogeny and breeding pressure together structure this genetic diversity, this study provides new mathematical formalisms and the associated parameters of trait responses in the large genetic diversity of wheat-related species. This potentially allow crop models predicting the impact of this diversity on yield, and indicate potential sources of varietal improvement for modern wheat germplasms, through interspecific crosses.

Leaf elongation response to blue light is mediated by stomatal-induced variations in transpiration in Festuca arundinacea.

Reduced blue light irradiance is known to enhance leaf elongation rate (LER) in grasses, but the mechanisms involved have not yet been elucidated. We investigated whether leaf elongation response to reduced blue light could be mediated by stomata-induced variations of plant transpiration. Two experiments were carried out on tall fescue in order to monitor LER and transpiration under reduced blue light irradiance. Additionally, LER dynamics were compared with those observed in the response to vapour pressure deficit (VPD)-induced variations of transpiration. Finally, we developed a model of water flow within a tiller to simulate the observed short-term response of LER to various transpiration regimes. LER dramatically increased in response to blue light reduction and then reached new steady states, which remained higher than the control. Reduced blue light triggered a simultaneous stomatal closure which induced an immediate decrease of leaf transpiration. The hydraulic model of leaf elongation accurately predicted the LER response to blue light and VPD, resulting from an increase in the growth-induced water potential gradient in the leaf growth zone. Our results suggest that the blue light signal is sensed by stomata of expanded leaves and transduced to the leaf growth zone through the hydraulic architecture of the tiller.

Maize yields over Europe may increase in spite of climate change, with an appropriate use of the genetic variability of flowering time.

Projections based on invariant genotypes and agronomic practices indicate that climate change will largely decrease crop yields. The comparatively few studies considering farmers' adaptation result in a diversity of impacts depending on their assumptions. We combined experiments and process-based modeling for analyzing the consequences of climate change on European maize yields if farmers made the best use of the current genetic variability of cycle duration, based on practices they currently use. We first showed that the genetic variability of maize flowering time is sufficient for identifying a cycle duration that maximizes yield in a range of European climatic conditions. This was observed in six field experiments with a panel of 121 accessions and extended to 59 European sites over 36 years with a crop model. The assumption that farmers use optimal cycle duration and sowing date was supported by comparison with historical data. Simulations were then carried out for 2050 with 3 million combinations of crop cycle durations, climate scenarios, management practices, and modeling hypotheses. Simulated grain production over Europe in 2050 was stable (-1 to +1%) compared with the 1975-2010 baseline period under the hypotheses of unchanged cycle duration, whereas it was increased (+4-7%) when crop cycle duration and sowing dates were optimized in each local environment. The combined effects of climate change and farmer adaptation reduced the yield gradient between south and north of Europe and increased European maize production if farmers continued to make the best use of the genetic variability of crop cycle duration.

The bZIP transcription factor SPA Heterodimerizing Protein represses glutenin synthesis in Triticum aestivum.

The quality of wheat grain is mainly determined by the quantity and composition of its grain storage proteins (GSPs). Grain storage proteins consist of low- and high-molecular-weight glutenins (LMW-GS and HMW-GS, respectively) and gliadins. The synthesis of these proteins is essentially regulated at the transcriptional level and by the availability of nitrogen and sulfur. The regulation network has been extensively studied in barley where BLZ1 and BLZ2, members of the basic leucine zipper (bZIP) family, activate the synthesis of hordeins. To date, in wheat, only the ortholog of BLZ2, Storage Protein Activator (SPA), has been identified as playing a major role in the regulation of GSP synthesis. Here, the ortholog of BLZ1, named SPA Heterodimerizing Protein (SHP), was identified and its involvement in the transcriptional regulation of the genes coding for GSPs was analyzed. In gel mobility shift assays, SHP binds cis-motifs known to bind to bZIP family transcription factors in HMW-GS and LMW-GS promoters. Moreover, we showed by transient expression assays in wheat endosperm that SHP acts as a repressor of the activity of these gene promoters. This result was confirmed in transgenic lines overexpressing SHP, which were grown with low and high nitrogen supply. The phenotype of SHP-overexpressing lines showed a lower quantity of both LMW-GS and HMW-GS, while the quantity of gliadin was unchanged, whatever the nitrogen availability. Thus, the gliadin/glutenin ratio was increased, which suggests that gliadin and glutenin genes may be differently regulated.

Estimation of Plant and Canopy Architectural Traits Using the Digital Plant Phenotyping Platform.

The extraction of desirable heritable traits for crop improvement from high-throughput phenotyping (HTP) observations remains challenging. We developed a modeling workflow named "Digital Plant Phenotyping Platform" (D3P), to access crop architectural traits from HTP observations. D3P couples the Architectural model of DEvelopment based on L-systems (ADEL) wheat (Triticum aestivum) model (ADEL-Wheat), which describes the time course of the three-dimensional architecture of wheat crops, with simulators of images acquired with HTP sensors. We demonstrated that a sequential assimilation of the green fraction derived from Red-Green-Blue images of the crop into D3P provides accurate estimates of five key parameters (phyllochron, lamina length of the first leaf, rate of elongation of leaf lamina, number of green leaves at the start of leaf senescence, and minimum number of green leaves) of the ADEL-Wheat model that drive the time course of green area index and the number of axes with more than three leaves at the end of the tillering period. However, leaf and tiller orientation and inclination characteristics were poorly estimated. D3P was also used to optimize the observational configuration. The results, obtained from in silico experiments conducted on wheat crops at several vegetative stages, showed that the accessible traits could be estimated accurately with observations made at 0° and 60° zenith view inclination with a temporal frequency of 100 °Cd (degree day). This illustrates the potential of the proposed holistic approach that integrates all the available information into a consistent system for interpretation. The potential benefits and limitations of the approach are further discussed.

Temperature increase reduces global yields of major crops in four independent estimates.

Wheat, rice, maize, and soybean provide two-thirds of human caloric intake. Assessing the impact of global temperature increase on production of these crops is therefore critical to maintaining global food supply, but different studies have yielded different results. Here, we investigated the impacts of temperature on yields of the four crops by compiling extensive published results from four analytical methods: global grid-based and local point-based models, statistical regressions, and field-warming experiments. Results from the different methods consistently showed negative temperature impacts on crop yield at the global scale, generally underpinned by similar impacts at country and site scales. Without CO2 fertilization, effective adaptation, and genetic improvement, each degree-Celsius increase in global mean temperature would, on average, reduce global yields of wheat by 6.0%, rice by 3.2%, maize by 7.4%, and soybean by 3.1%. Results are highly heterogeneous across crops and geographical areas, with some positive impact estimates. Multimethod analyses improved the confidence in assessments of future climate impacts on global major crops and suggest crop- and region-specific adaptation strategies to ensure food security for an increasing world population.

A Model of Leaf Coordination to Scale-Up Leaf Expansion from the Organ to the Canopy.

Process-based crop growth models are popular tools with which to analyze and understand the impact of crop management, genotype-by-environment interactions, or climate change. The ability to predict leaf area development is critical to predict crop growth, particularly under conditions of limited resources. Here, we aimed at deciphering growth coordination rules between wheat (Triticum aestivum) plant organs (i.e. between leaves within a stem, between laminae and sheaths, and between the mainstem and axillary tillers) to model the dynamics of canopy development. We found a unique relationship between laminae area and leaf rank for the mainstem and its tillers, which was robust across a range of sowing dates and plant densities. Robust relationships between laminae and sheath areas also were found, highlighting the tight control of organ growth within and between phytomers. These relationships identified at the phytomer scale were used to develop a simulation model of leaf area dynamics at the canopy level that was integrated in the wheat model SiriusQuality. The model was then evaluated using several independent experiments. The model accurately predicts leaf area dynamics under different scenarios of nitrogen and water limitations. It accounted for 85%, 64%, and 73% of the variability of the surface area of leaf cohorts, total leaf area index, and total green area index, respectively. The process-based model of the dynamics of leaf area described here is a key element to quantify the value of candidate traits for use in plant breeding and to project the impact of climate change on wheat growth.

Experimental and modeling evidence of carbon limitation of leaf appearance rate for spring and winter wheat.

Accurate predictions of the timing of physiological stages and the development rate are crucial for predicting crop performance under field conditions. Plant development is controlled by the leaf appearance rate (LAR) and our understanding of how LAR responds to environmental factors is still limited. Here, we tested the hypothesis that carbon availability may account for the effects of irradiance, photoperiod, atmospheric CO2 concentration, and ontogeny on LAR. We conducted three experiments in growth chambers to quantify and disentangle these effects for both winter and spring wheat cultivars. Variations of LAR observed between environmental scenarios were well explained by the supply/demand ratio for carbon, quantified using the photothermal quotient. We therefore developed an ecophysiological model based on the photothermal quotient that accounts for the effects of temperature, irradiance, photoperiod, and ontogeny on LAR. Comparisons of observed leaf stages and LAR with simulations from our model, from a linear thermal-time model, and from a segmented linear thermal-time model corrected for sowing date showed that our model can simulate the observed changes in LAR in the field with the lowest error. Our findings demonstrate that a hypothesis-driven approach that incorporates more physiology in specific processes of crop models can increase their predictive power under variable environments.

Invited review: Intergovernmental Panel on Climate Change, agriculture, and food-A case of shifting cultivation and history.

Since 1990, the Intergovernmental Panel on Climate Change (IPCC) has produced five Assessment Reports (ARs), in which agriculture as the production of food for humans via crops and livestock have featured in one form or another. A constructed database of the ca. 2,100 cited experiments and simulations in the five ARs was analyzed with respect to impacts on yields via crop type, region, and whether adaptation was included. Quantitative data on impacts and adaptation in livestock farming have been extremely scarce in the ARs. The main conclusions from impact and adaptation are that crop yields will decline, but that responses have large statistical variation. Mitigation assessments in the ARs have used both bottom-up and top-down methods but need better to link emissions and their mitigation with food production and security. Relevant policy options have become broader in later ARs and included more of the social and nonproduction aspects of food security. Our overall conclusion is that agriculture and food security, which are two of the most central, critical, and imminent issues in climate change, have been dealt with an unfocussed and inconsistent manner between the IPCC five ARs. This is partly a result of not only agriculture spanning two IPCC working groups but also the very strong focus on projections from computer crop simulation modeling. For the future, we suggest a need to examine interactions between themes such as crop resource use efficiencies and to include all production and nonproduction aspects of food security in future roles for integrated assessment models.

Global wheat production with 1.5 and 2.0°C above pre-industrial warming.

Efforts to limit global warming to below 2°C in relation to the pre-industrial level are under way, in accordance with the 2015 Paris Agreement. However, most impact research on agriculture to date has focused on impacts of warming >2°C on mean crop yields, and many previous studies did not focus sufficiently on extreme events and yield interannual variability. Here, with the latest climate scenarios from the Half a degree Additional warming, Prognosis and Projected Impacts (HAPPI) project, we evaluated the impacts of the 2015 Paris Agreement range of global warming (1.5 and 2.0°C warming above the pre-industrial period) on global wheat production and local yield variability. A multi-crop and multi-climate model ensemble over a global network of sites developed by the Agricultural Model Intercomparison and Improvement Project (AgMIP) for Wheat was used to represent major rainfed and irrigated wheat cropping systems. Results show that projected global wheat production will change by -2.3% to 7.0% under the 1.5°C scenario and -2.4% to 10.5% under the 2.0°C scenario, compared to a baseline of 1980-2010, when considering changes in local temperature, rainfall, and global atmospheric CO2 concentration, but no changes in management or wheat cultivars. The projected impact on wheat production varies spatially; a larger increase is projected for temperate high rainfall regions than for moderate hot low rainfall and irrigated regions. Grain yields in warmer regions are more likely to be reduced than in cooler regions. Despite mostly positive impacts on global average grain yields, the frequency of extremely low yields (bottom 5 percentile of baseline distribution) and yield inter-annual variability will increase under both warming scenarios for some of the hot growing locations, including locations from the second largest global wheat producer-India, which supplies more than 14% of global wheat. The projected global impact of warming <2°C on wheat production is therefore not evenly distributed and will affect regional food security across the globe as well as food prices and trade.

Climate change impact and adaptation for wheat protein.

Wheat grain protein concentration is an important determinant of wheat quality for human nutrition that is often overlooked in efforts to improve crop production. We tested and applied a 32-multi-model ensemble to simulate global wheat yield and quality in a changing climate. Potential benefits of elevated atmospheric CO2 concentration by 2050 on global wheat grain and protein yield are likely to be negated by impacts from rising temperature and changes in rainfall, but with considerable disparities between regions. Grain and protein yields are expected to be lower and more variable in most low-rainfall regions, with nitrogen availability limiting growth stimulus from elevated CO2 . Introducing genotypes adapted to warmer temperatures (and also considering changes in CO2 and rainfall) could boost global wheat yield by 7% and protein yield by 2%, but grain protein concentration would be reduced by -1.1 percentage points, representing a relative change of -8.6%. Climate change adaptations that benefit grain yield are not always positive for grain quality, putting additional pressure on global wheat production.

Grain subproteome responses to nitrogen and sulfur supply in diploid wheat Triticum monococcum ssp. monococcum.

Wheat grain storage proteins (GSPs) make up most of the protein content of grain and determine flour end-use value. The synthesis and accumulation of GSPs depend highly on nitrogen (N) and sulfur (S) availability and it is important to understand the underlying control mechanisms. Here we studied how the einkorn (Triticum monococcum ssp. monococcum) grain proteome responds to different amounts of N and S supply during grain development. GSP composition at grain maturity was clearly impacted by nutrition treatments, due to early changes in the rate of GSP accumulation during grain filling. Large-scale analysis of the nuclear and albumin-globulin subproteomes during this key developmental phase revealed that the abundance of 203 proteins was significantly modified by the nutrition treatments. Our results showed that the grain proteome was highly affected by perturbation in the N:S balance. S supply strongly increased the rate of accumulation of S-rich α/ß-gliadin and γ-gliadin, and the abundance of several other proteins involved in glutathione metabolism. Post-anthesis N supply resulted in the activation of amino acid metabolism at the expense of carbohydrate metabolism and the activation of transport processes including nucleocytoplasmic transit. Protein accumulation networks were analyzed. Several central actors in the response were identified whose variation in abundance was related to variation in the amounts of many other proteins and are thus potentially important for GSP accumulation. This detailed analysis of grain subproteomes provides information on how wheat GSP composition can possibly be controlled in low-level fertilization condition.

Contribution of crop model structure, parameters and climate projections to uncertainty in climate change impact assessments.

Climate change impact assessments are plagued with uncertainties from many sources, such as climate projections or the inadequacies in structure and parameters of the impact model. Previous studies tried to account for the uncertainty from one or two of these. Here, we developed a triple-ensemble probabilistic assessment using seven crop models, multiple sets of model parameters and eight contrasting climate projections together to comprehensively account for uncertainties from these three important sources. We demonstrated the approach in assessing climate change impact on barley growth and yield at Jokioinen, Finland in the Boreal climatic zone and Lleida, Spain in the Mediterranean climatic zone, for the 2050s. We further quantified and compared the contribution of crop model structure, crop model parameters and climate projections to the total variance of ensemble output using Analysis of Variance (ANOVA). Based on the triple-ensemble probabilistic assessment, the median of simulated yield change was -4% and +16%, and the probability of decreasing yield was 63% and 31% in the 2050s, at Jokioinen and Lleida, respectively, relative to 1981-2010. The contribution of crop model structure to the total variance of ensemble output was larger than that from downscaled climate projections and model parameters. The relative contribution of crop model parameters and downscaled climate projections to the total variance of ensemble output varied greatly among the seven crop models and between the two sites. The contribution of downscaled climate projections was on average larger than that of crop model parameters. This information on the uncertainty from different sources can be quite useful for model users to decide where to put the most effort when preparing or choosing models or parameters for impact analyses. We concluded that the triple-ensemble probabilistic approach that accounts for the uncertainties from multiple important sources provide more comprehensive information for quantifying uncertainties in climate change impact assessments as compared to the conventional approaches that are deterministic or only account for the uncertainties from one or two of the uncertainty sources.

Multimodel ensembles improve predictions of crop-environment-management interactions.

A recent innovation in assessment of climate change impact on agricultural production has been to use crop multimodel ensembles (MMEs). These studies usually find large variability between individual models but that the ensemble mean (e-mean) and median (e-median) often seem to predict quite well. However, few studies have specifically been concerned with the predictive quality of those ensemble predictors. We ask what is the predictive quality of e-mean and e-median, and how does that depend on the ensemble characteristics. Our empirical results are based on five MME studies applied to wheat, using different data sets but the same 25 crop models. We show that the ensemble predictors have quite high skill and are better than most and sometimes all individual models for most groups of environments and most response variables. Mean squared error of e-mean decreases monotonically with the size of the ensemble if models are added at random, but has a minimum at usually 2-6 models if best-fit models are added first. Our theoretical results describe the ensemble using four parameters: average bias, model effect variance, environment effect variance, and interaction variance. We show analytically that mean squared error of prediction (MSEP) of e-mean will always be smaller than MSEP averaged over models and will be less than MSEP of the best model if squared bias is less than the interaction variance. If models are added to the ensemble at random, MSEP of e-mean will decrease as the inverse of ensemble size, with a minimum equal to squared bias plus interaction variance. This minimum value is not necessarily small, and so it is important to evaluate the predictive quality of e-mean for each target population of environments. These results provide new information on the advantages of ensemble predictors, but also show their limitations.