Is the Rice Yield Response to Elevated CO₂ a Source Effect or a Sink Effect?

1. Introduction

Grain yield in cereals is set by the balance between assimilate supply (the source: flag leaves and the crop canopy) and assimilate demand (the sink: developing panicles and grains), not by the capacity of any single organ [1]. The standard way to separate the two is source sink perturbation: shading or defoliation lowers carbon supply, whereas spikelet thinning or partial panicle removal lowers demand. How the untreated tissue compensates then shows which process limits yield [2]. Two conclusions from this work are now widely accepted. First, grain number is source limited: it is fixed within a narrow pre-heading window, tracks crop growth rate over that window, and responds plastically to changes in assimilate supply [2]. Second, from heading onwards the crop is largely sink limited. During grain filling, treatments that leave potential grain size unchanged, moderate shading, or removing spikelets after grain number is set, have little effect on the mass of the remaining grains. Grain growth therefore appears to be capped by the capacity of the grain itself rather than by current photosynthate supply [2]. Savin et al. (2026) add a caveat that matters here: conclusions of source limitation drawn from severe treatments (50–90% shading) or from manipulations applied before grain number is fixed describe treated plants only and should not be extended to intact crops [2]. Any synthesis that adopts a source sink framework must therefore treat the pre-heading period, when grain number is set, and the grain-filling period that follows as separate stages.

Elevated atmospheric CO_₂ concentration (eCO_₂) is usually presented as a fertilization effect that strengthens the source: a steeper CO_₂ gradient between atmosphere and chloroplast suppresses photorespiration in C_₃ species. That view is incomplete in three respects. First, eCO_₂ does not act on source processes alone. Exposure normally begins early in vegetative growth and runs through the pre-heading window in which grain number is set, so extra assimilate arriving in that window may enlarge the sink rather than only fill a sink of fixed size. Second, surplus photosynthate raises yield only if sink tissue can import and use it, and this is where the source sink literature bears directly on eCO_₂ work. Prolonged exposure often depresses photosynthetic capacity, the phenomenon known as photosynthetic acclimation; in a cross species meta-analysis, Arp (1991) found this down-regulation to be strongest where abundant carbohydrate coincides with a small sink [3]. Acclimation is therefore better read as a symptom of a disturbed source sink balance than as a direct effect of CO_₂ on the photosynthetic apparatus. Paul and Foyer (2001) supplied the mechanism: weak sink demand lets carbohydrate accumulate in leaves, which represses photosynthetic genes and accelerates senescence, and this sink-dependent control can override the stimulation by light and CO_₂ [4]. Ainsworth and Bush (2011) identified carbohydrate export from the leaf as the node through which sink demand acts back on source capacity [5], and work on rice genotypes traced the same feedback to triose phosphate utilization, placing the constraint inside the leaf rather than at the CO_₂ supply step [6,7]. Third, source and sink act on different schedules, so their balance shifts during development: eCO_₂ raises source activity at once, whereas sink capacity is largely fixed before heading. Under eCO_₂ the source:sink ratio is therefore not constant through the life cycle.

Rice is the most intensively studied cereal in Asian eCO_₂ experiments, and several syntheses have quantified its yield response [8,9,10,11]. Pooled estimates converge on roughly 20%, yet field studies consistently report smaller gains than enclosed facilities [8,12]. Few of these analyses, however, divide the eCO_₂ yield benefit into source and sink derived parts: most report final yield, sometimes alongside photosynthesis, without resolving the mechanism. Primary studies share the limitation. One experiment addressed it directly, Gao et al. manipulated source sink balance under free-air CO_₂ enrichment (FACE) and found that the yield response to eCO_₂ changed with that manipulation [13], and trials across inbred lines generally find single grain weight to be stable and insensitive to eCO_₂ [14]. Source side responses are better documented: canopy carbon assimilation rises under eCO_₂, but the size of the response depends on growth stage and leaf nitrogen [15]; carbohydrate reserves reflect when the carbon was fixed during development [16]; and photosynthetic capacity declines as the season advances [17,18,19]. Nitrogen uptake acclimates to high CO_₂ and canopy nitrogen allocation is rearranged [20,21], and dry matter and nitrogen partitioning among organs have been quantified under combined warming and CO_₂ enrichment [22]. Where assimilate supply is experimentally reduced, final yield tracks the source sink imbalance that develops during grain filling, not the instantaneous photosynthetic rate [23]. What is still missing is a framework that treats source and sink together and asks which one sets the ceiling on yield.

This study asks whether the eCO_₂ yield gain in rice comes mainly from a stronger source or from a larger sink. Our hypothesis, fixed before the dataset was assembled and grounded in the source sink work outlined above, is that the gain comes from more sinks. Extra assimilate during the pre-heading critical window should raise panicle and spikelet number, whereas grain mass and harvest index should change little, because grain filling in undisturbed stands is sink limited. The distinction has practical consequences. Breeding programmes for future CO_₂ conditions must choose between greater photosynthetic capacity and larger sink size, and the evidence shows the two are not interchangeable [24,25,26]. Crop models face the same choice: most implement CO_₂ by scaling photosynthesis or radiation use efficiency, which assumes yield is source limited; if the gain is instead set by yield components established before heading, those models will carry a directional bias [11,27,28,29].

2. Materials and Methods

2.1. Study Design and Literature Collection

The study has two parts. The first is an evidence map [30], a scoping assessment of how much primary experimental literature exists on rice responses to elevated CO_₂, what it covers and where the gaps lie [31,32,33]. The second is a secondary synthesis, in which pooled estimates already published in meta-analyses are read together within a single source sink framework. We did not re-extract primary data, recompute effect sizes or fit new random effects models. Re-pooling published estimates would break the assumption of independence and would count the same primary experiment repeatedly wherever it appears in more than one meta-analysis [34].

Two independent literature searches were executed on 10 September 2026, one in the Web of Science (WoS) (TS field) and one in China National Knowledge Infrastructure (CNKI) (professional search, SU field). Adding CNKI was necessary because a substantial share of Chinese free-air CO₂ enrichment (FACE) rice experiments is published in Chinese language journals that are not indexed in the WoS. Search (TS=("elevated CO2" OR "elevated CO2 concentration" OR "elevated atmospheric CO2" OR "elevated atmospheric carbon dioxide" OR "elevated [CO2]" OR "high CO2" OR "high CO2 concentration" OR "increased CO2" OR "increased CO2 concentration" OR "increased atmospheric CO2" OR "rising CO2" OR "rising atmospheric CO2" OR "future CO2" OR "CO2 enrichment" OR "CO2 elevation" OR "enriched CO2" OR "CO2 fertilization" OR "carbon dioxide enrichment" OR "elevated carbon dioxide" OR "eCO2" OR "free-air CO2 enrichment" OR "free-air carbon dioxide enrichment" OR "FACE") AND TS=(rice OR "Oryza sativa" OR Oryza OR paddy OR "paddy rice" OR "paddy field")) was run in both databases.

2.2. Coding the Evidence Map

Screening for the evidence map used titles, abstracts, author keywords and Keywords Plus from full WoS and CNKI exported files. Five categorical variables were coded for each record. Study type separated empirical experiments from reviews, editorials and modelling work, combining the native Web of Science document label with textual indicators such as “crop model” and “DSSAT”; a record was classed as modelling only when no experimental facility was described. Crop separability recorded whether rice was grown alone, grown alongside other crops, or not measured at all. Trait class recorded source traits, sink traits, both or neither. A fourth code flagged studies that reported grain yield but no yield component. A fifth code was added after the first pass. Harvest index (HI) can be reached in two ways: it is sometimes reported directly, and it is also grain yield divided by above-ground biomass at maturity, so a study giving both quantities has the information even if it never uses the term. The two routes were kept apart. HI was recorded only where the term appeared; derivable cases were coded separately, noting whether biomass was measured at maturity, at harvest or at physiological maturity, because the quotient is undefined for biomass cut earlier than that.

Source traits encompassed light-saturated photosynthesis, net photosynthesis, leaf gas exchange parameters, chlorophyll content, rubisco, stomatal conductance, leaf area index, tiller count, plant height, plus leaf, stem and root biomass. Sink traits included panicle number, spikelet count per panicle, spikelet density, grain number per unit ground area, filled grain percentage, individual grain mass, thousand grain weight, and HI. This classification follows conventions established by prior source sink manipulation experiments [35,36].

Coding applied the predefined keyword rules to title, abstract, author keywords and Keywords Plus. Because the rules are deterministic, the same record and the same rules always return the same code, so simply repeating the procedure proves little. What matters is whether the rules capture the intended categories, and that was tested twice. In the first test a 10% random sample of records (256) was drawn with a fixed seed and coded by hand from the same four metadata fields, without sight of the automated codes; some of these records were also checked against the full text. Disagreements were discussed, and where they traced to ambiguous wording in the rules, the rules were amended. Agreement on the trait variable was then measured with Cohen’s kappa [37] and its 95% confidence interval. Gwet’s AC1 [38] was reported as well, because kappa is unstable when one class dominates the distribution and can fall far below raw agreement [39,40]; for rare trait classes we also report raw agreement, since both coefficients are unreliable at low prevalence.

In the second test the rule set was frozen. A different seed drew a further 100 records that had played no part in any rule revision, and these were coded under the same conventions with no further adjustment. Comparing the two samples therefore shows how the finished rules perform on unseen records, free of the optimism that comes from having tuned them against the first sample.

2.3. Eligibility Criteria for Included Syntheses

Published quantitative syntheses were retained only when satisfying all eligibility criteria below:

(i) the work implemented quantitative synthesis methods (meta-analysis, meta-regression, or formal data aggregation) using empirical experimental data;

(ii) rice (Oryza sativa) was a target crop, with either rice specific analysis or effect estimates reported separately from other plant species;

(iii) the study reported at least one source trait, sink trait, or grain yield;

(iv) elevated and ambient CO₂ treatments were clearly defined.

We excluded purely narrative reviews lacking quantitative synthesis, modelling papers that did not synthesize empirical experimental data, syntheses restricted to noncereal species, and datasets where rice outcomes could not be decoupled from other crops. If multiple syntheses reported estimates for the same trait using overlapping primary datasets, all eligible publications were retained; we report the full range of observed effect sizes rather than adopting a single summary value.

Traits were preassigned to three categories following standard physiological definitions: source tissues export fixed assimilates, while sink tissues receive and store assimilates:

(i) Source traits: light-saturated photosynthetic rate (A_sat), net photosynthetic rate (P_n), leaf area index (LAI), plant height, leaf biomass, stem biomass, root biomass, and biochemical determinants of photosynthetic capacity (Rubisco concentration, V_cmax, J_max).

(ii) Sink traits: panicle number, spikelet number per panicle, spikelet density, grain number per unit area, filled grain percentage, individual grain mass, grain size, and HI.

(iii) Integrated traits: grain yield and reported source: sink ratio.

Two classification ambiguities are explicitly acknowledged. First, tiller number is reported separately as sink associated morphology rather than assigned to either class, because tiller number largely determines panicle number and therefore lies at the boundary between the two domains; counting it as an unambiguous source trait would bias the source to sink ratio downwards. Second, vegetative biomass (leaf, stem, root) is treated here as a source associated structural variable because leaves function as the primary assimilates exporting organs. In contrast, panicle biomass falls under sink traits: panicles act as assimilate receiving structures, and mature panicle biomass is dominated by grain mass. We emphasize that this grouping represents a working convention. Biomass partitioning between vegetative and reproductive tissues is itself an emergent outcome of source-sink balance rather than an unambiguous marker of source or sink status. To make this distinction checkable, the proportion of biomass allocated to roots, stems, leaves and panicles was coded as a separate allocation class.

2.4. Selection of Individual Experiments and Supplementary Materials

A small number of individual experiments were considered as possible illustrations alongside the synthesis level estimates, and were identified through targeted searching rather than through the systematic searches. To prevent selection bias, these entries were admitted only under the following pre-specified conditions: (i) the study reported both a source side and a sink side trait for the same CO_₂ treatment contrast; (ii) the CO_₂ treatment was applied at field scale under free-air or open-top conditions; and (iii) the study was published between 2010 and 2026. Studies not meeting all three conditions were excluded. These experiments serve only to illustrate specific mechanisms. They were excluded from all frequency counts, source to sink ratios and proportional statistics reported in Section 3.1, so they cannot have influenced the quantitative conclusions. The selection was nevertheless informed by our prior expectation of a sink directed response, and we state that openly.

All materials required to reproduce this analysis accompany the article. Supplementary Table S1 reports harvest index frequencies under three alternative counting definitions. Supplementary Table S2 gives the full search strings, the stage by stage record counts for both databases, and the list of eligible syntheses. Supplementary Table S3 lists the trait classification rules, the noise exclusion rules and the treatment of ambiguous cases.

2.5. Data Extraction and Synthesis

From each contributing synthesis we extracted the target crop, the experimental platform (FACE, open-top chamber, controlled-environment chamber) and the elevated and ambient CO_₂ concentrations. We also recorded the number of primary studies and observations behind each pooled estimate, the trait name, the direction and size of the response, and the significance or confidence interval reported with it.

The source syntheses used different effect size metrics, log response ratios, percentage change and standardized mean differences, and we converted every response to percentage change where that was possible. Responses were then grouped by trait class and compared descriptively. No new pooled estimate was produced and no statistical test was applied across trait classes, for two reasons: the primary datasets behind the syntheses overlap substantially, and confidence intervals were not reported consistently. The comparison therefore rests on the direction, relative size and consistency of the responses as published.

3. Results

3.1. How the Coding Held up, and What the Literature Contains

Agreement between the automated coding and the human coding was acceptable but not high. Before any rule was revised, Cohen’s κ for the trait variable was 0.46, with 64.8% raw pairwise agreement. Reading the 90 discordant records showed three systematic gaps in the rules rather than scattered disagreement. The source trait keyword list omitted common standalone terms for photosynthesis and biomass. The bare keyword yield caught papers on methane or nitrous oxide fluxes, where yield was mentioned only in passing. And unqualified root and canopy keywords misclassified work on rhizosphere carbon cycling or heavy metal accumulation as source trait research. The rules were therefore revised, and a noise exclusion class was added at title screening to flag papers centered on greenhouse gas dynamics, soil microbial processes or contaminant biogeochemistry, in which crop traits are peripheral. Coding was then repeated on the same calibration sample: κ = 0.56 (95% CI 0.47-0.65), raw agreement 74.6%. By conventional benchmarks [41] that is moderate rather than substantial. Two qualifications apply. κ is depressed when one class dominates the distribution [39,40], and the neither-trait class accounted for 58% of coded records; on the same data Gwet’s AC1, which is less sensitive to class prevalence, reached 0.70.

Applying the two searches described in Section 2.1 retrieved 6,120 records (2,940 from the Web of Science Core Collection and 3,180 from CNKI). Removing 2 duplicate records and 1,666 records excluded at download by document-type restriction left 4,452 records screened. Automated title and keyword level prescreening removed a further 2,223 records as clearly ineligible, leaving 2,229 records that underwent semantic screening against the three eligibility criteria. Application of those criteria retained 668 studies, which form the denominator for all descriptive analyses reported below. PRISMA stage-by-stage counts are given in Supplementary Table S2 and Figure 1a. Publication years spanned 1986-2026; records without a resolved publication year were retained in the corpus but excluded from temporal trend analyses.

Within this corpus, 460 studies (68.9%) reported source traits and 194 (29.0%) reported sink traits, a source to sink ratio of 2.37:1 (Figure 1). The gap is widest for the traits that matter most when deciding whether a yield response is source or sink driven. Photosynthesis was measured in 261 studies (39.1%), spikelet or grain number in 91 (13.6%), grain filling in 54 (8.1%), individual grain mass in 49 (7.3%), and HI in only 22 (3.3%). The reporting classes overlap: 114 studies (17.1%) covered both source and sink traits, 346 source traits alone, 80 sink traits alone, and 128 (19.2%) gave grain yield with no yield component, so their gain cannot be attributed to either more grains or heavier grains. The ratio is similar in the Chinese language subset (136 source versus 49 sinks; 2.78:1) and the English language subset (324 versus 145; 2.23:1), which argues against language or database coverage as the cause (Figure 1b).

Time windows over three decades show no narrowing of the imbalance. The share of studies reporting both source and sink traits rose from 10.0% (1995-2004) to 19.0% (2020-2029), which is real progress; even so, studies reporting source traits alone stayed dominant at 44.2-51.0% in every period, and those reporting neither rose from 6.7% to 20.4% as climate scenario modelling became common. Because classification used titles and abstracts only, every proportion here is a lower bound on how often a trait was actually measured. HI needs separate treatment, because it can be calculated rather than measured. It was named explicitly in 22 studies (3.3%). Because HI is the quotient of grain yield and aboveground biomass measured at maturity, a further 37 studies (5.5%) reported both quantities and stated that biomass was sampled at physiological maturity or at harvest, so HI is derivable although unnamed. Three counts are therefore possible (Supplementary Table S1): named HI only (n = 22, 3.3%); derivable cases with maturity-stage biomass confirmed (n = 37, 5.5%); or the combined upper bound (n = 59, 8.8%). These move the photosynthesis to HI ratio from 11.9:1 to 6.9:1 and 4.4:1. The main analysis uses the strict count. Two cautions attach to the looser counts. HI cannot be derived from biomass cut before physiological maturity, which is why definition B requires an explicit maturity or harvest statement rather than an inferred one; and even on the most permissive count the imbalance is reduced, not removed. Studies reporting nutrient (N, P or K) HI were excluded from all three counts, since that metric describes nutrient recovery, not carbon partitioning to grain.

These reporting patterns set two limits on what the literature can support. First, it cannot yet separate source from sink mediated yield responses. Only 114 studies measured both classes, and fewer still provide paired observations from which a within-study source sink contrast could be computed; the syntheses summarised in Section 3.2 supply paired estimates for fewer again. Second, the set of studies that measure photosynthesis under eCO_₂ is not a neutral sample, because choosing to measure photosynthesis usually presumes that CO_₂ acts through photosynthesis. Pooling that set to test a source limited model therefore risks testing the hypothesis on literature already inclined towards it. This is a property of the evidence base, not something that reanalyzing published data can correct.

3.2. The Published Syntheses

The same two searches also retrieved syntheses of this literature. Applying criteria (i)-(iv) to those records identified 14 quantitative syntheses of eCO_₂ effects in rice, of which seven contributed estimates to Table 1. The remaining seven met all four criteria but were not extracted, either because rice specific estimates could not be separated from other crops [52,72] or because we prioritised syntheses reporting a source or sink trait contrast. A further 58 candidate records were excluded. Those reporting only greenhouse gas fluxes [46,47,48,49,50,51] or only grain quality and nutrient composition [43,44,45,75] do not satisfy criterion (iii), and those projecting future climate scenarios or crop responses to drivers other than an applied CO_₂ contrast [53,54,55,56,57,58,59,60,61] do not satisfy criterion (iv).

Across the seven contributing syntheses, grain yield was the most frequently reported outcome, followed by source-side physiological and biomass traits. Sink-side yield components appeared less often, and harvest index in only two of the seven. This asymmetry repeats the bias measured in the primary literature (Section 3.1) and is the main obstacle to decomposing the eCO_₂ yield gain into source and sink parts. Figure 2 describes all 14 eligible syntheses and marks those that contribute data.

The most cited rice focused synthesis is Ainsworth (2008), followed by Wang et al. (2015) and the FACE series of Hu et al. (2021, 2022). Since then, the literature has moved into questions this framework does not address grain composition and human nutrition, greenhouse gas fluxes, and interactions with warming, nitrogen and water, and cross-cereal syntheses of biomass and yield components, nutrient cycling and contaminant loads have appeared as well.

3.3. A Gradient from Source to Sink

Table 1 and Figure 3 collect the estimates from the seven contributing syntheses. Because the underlying primary datasets overlap and confidence intervals were reported unevenly, we did not test the ordering statistically; the sequence should be read as a description of published values, not as a ranking. Read that way, from source traits through allocation to sink traits, grain yield and grain quality, the responses fall along a gradient: source side and allocation variables move strongly, sink capacity variables barely move, and grain yield rises by substantially less than the source side. HI appears in only two syntheses and the two estimates disagree in sign (+9% and -2%); we record the disagreement rather than resolve it, because the estimates come from different primary datasets with different platform composition. Allocation ratios, available from one synthesis only, put the extra carbon below ground: the root fraction rose while the leaf fraction fell, and the panicle fraction did not change.

On the source side, almost every measured trait increased. Under FACE, eCO_₂ raised light-saturated photosynthesis by 21.9%, root biomass by 27.9%, shoot biomass by 19.0%, maximum tiller number by 11.4%, leaf area index by 8.7% and plant height by 3.7% [10]. Shoot organs differed: leaf biomass rose 8.8%, stems 23.7% and panicles 25.4%, so allocation shifted towards reproductive tissue, with panicles responding about 2.9 times more than leaves. Carbohydrate pools grew as well, stem nonstructural carbohydrate by 18.8%, leaf soluble sugar by 11.9% (n = 8) and leaf starch by 26.3% (n = 7), which suggests that much of the extra carbon stayed in vegetative tissue instead of moving to grain.

Three patterns recur along this sequence: responses weaken from source to sink; within the shoot, allocation favours panicles over leaves; and the source side increases in Table 1 are not matched by equivalent gains in sink capacity, a point taken up in Section 4.2.

3.4. What Modifies the Response

Each included synthesis conducted independent moderator analyses. Although we did not re-pool effect sizes, we compare the directional trends of these moderators. Experimental fumigation platform exerted the most consistent influence on yield response. Ainsworth [8] found yield enhancement diminished under field realistic conditions: 12% stimulation under FACE versus 23% across all chamber and field platforms. This aligns with broader consensus that enclosure-based systems tend to overestimate crop responses observed in open fields [12,63]. Likewise, genotypic responses differed markedly. Hybrid rice achieved a 24.7% yield gain, compared with a cultivar mean of 14.0%; within conventional lines, indica rice gained 20.4% versus 12.7% for japonica rice [42]. This advantage of hybrid and indica cultivars arose primarily from greater spikelet density, reflecting expanded sink number rather than improved source capacity. Organ-scale observations support this interpretation [64,65].

Warming consistently attenuated the eCO_₂ benefit. Yield rose 16.2% at ambient temperature but only 10.1% with 1-2 °C of warming [42], and further warming removed the gain altogether [8]. In source sink terms the loss came from lower filled grain percentage and lighter grains, both sink traits, rather than from impaired photosynthesis, and experiments that warmed the crop at flowering or during early grain filling show the same thing [66,67,68]. Nitrogen mattered as well: the yield response peaked at 21.1% at 21-30 g m^-2 and fell away at both lower and higher rates, for different reasons at each end [42]. A higher nitrogen supply amplified the biomass response to eCO_₂ while warming suppressed it [10], and nitrogen uptake itself acclimates to elevated CO_₂ [20,69].

Fabre et al. [6] provide a useful test case. They defined a genotype specific index as flag leaf area divided by the spikelet number of the corresponding panicle, and compared five genotypes of differing source: sink balance. Under eCO_₂, genotypes with a low ratio showed stronger photosynthetic stimulation, less nonstructural carbohydrate in flag leaves and larger gains in biomass and grain yield; high ratio genotypes became sink limited, which the authors attributed to limited triose phosphate utilization [7].

Across genotypes, photosynthetic responsiveness fell as the ratio rose, and the ratio itself is reported as stable across environments. The stimulation was also transient: biomass increments and light-saturated photosynthesis both diminished as the crop matured [10], and progressive downregulation of leaf photosynthesis under FACE has been recorded directly [17,19,70].

4. Discussion

4.1. Source-Limited and Sink-Limited Phases in Sequence

The three core patterns identified in Section 3.3 are not independent observational outcomes. Instead, they arise from a single developmental sequence in which the operative constraint differs before and after heading. Separating these two growth windows resolves what would otherwise appear as three unrelated observations.

Genotypic comparisons point the same way. Two syntheses that partition the yield response by cultivar type agree that hybrid and indica rice gain more than japonica. Hu et al. [42] report +24.7% for hybrid, +20.4% for indica, +14.2% for conventional and +12.7% for japonica; the updated FACE synthesis of Lv et al. [11] reports +32.8% for hybrid, +22.6% for indica and +13.5% for japonica. Ainsworth and Long [63] instead report a cultivar mean of +14.0% and a high potential cultivar class of +35.0%, a contrast that indicates genotypic rather than class level differences.

The constraint reverses after heading. In intact field grown rice populations, grain filling is predominantly sink limited. External manipulations during the filling stage cannot increase individual grain weight if the maximum potential grain size is already fixed [2]. Consistently, the expanded sink size formed pre-heading fails to produce heavier grains under elevated CO_₂. Existing evidence confirms no significant changes in individual grain mass and HI under eCO_₂ conditions [9]. A targeted pot-transfer experiment further verified this rule: shifting rice plants between ambient and elevated CO_₂ environments at heading (when sink number was fully determined) exerted no influence on final grain weight [14].

The same sequence explains why photosynthetic acclimation is so common in eCO_₂-treated rice. Extra carbon before heading enlarges the sink, but the sink size fixed after heading cannot absorb the surplus, so carbohydrate builds up in leaves and feeds back on photosynthesis. Early work showed acclimation to be strongest where abundant carbon supply meets limited sink storage [3]. The pathways are now well characterized: leaf carbon export capacity governs photosynthetic plasticity [4,5], and in rice the limitation has been traced to triose phosphate utilization, which restricts carbon fixation inside the leaf once supply is surplus [6,7]. Acclimation is therefore not an artefact of CO_₂ enrichment but the expected adjustment when source capacity runs ahead of sink demand (Figure 4).

4.2. What Changes, and What Does Not

The syntheses assembled here retain their own internal validity and conclusions; the present work does not overturn those results but reexamines the mechanistic reading offered for them. The contribution of the present work is therefore a change in the organising framework, not a revision of the published estimates themselves.

A synthesis of two decades of FACE data attributed the eCO_₂ gain in rice productivity to higher leaf photosynthesis, while noting that the stimulation weakens late in the season [10]. That observation matches ours; the causal reading differs. We argue that post-heading sink limitation caps final yield, so surplus assimilate raises yield only where sink size was enlarged before heading. Photosynthesis is the route; sink capacity is the constraint. This matters in practice: a genotype or a management practice that raises photosynthesis without enlarging the sink should show strong acclimation and little yield gain, whereas one that enlarges the sink should hold on to the CO_₂ effect. Cross crop comparisons support the same reading: eCO_₂ stimulates growth far more in C_₃ than in C_₄ crops, plasticity indices of 1.97 versus 1.23 for root biomass and 2.04 versus 1.16 for shoot biomass, without altering growth balance [71].

The comparison of Fabre et al. [6] is worth restating here because it is the closest available approximation to a direct test: low ratio cultivars gained more, and high ratio cultivars became sink limited. It rests on one experiment rather than on pooled estimates, so it illustrates the proposed mechanism rather than confirming it statistically. What it does add is a measurable index, flag leaf area per spikelet, that a breeding programme could score directly.

This framework also clarifies field to chamber response discrepancies in existing models. Enclosure based experiments consistently overestimate rice CO₂ fertilization effects relative to open-field FACE conditions, with yield gains of 23% versus 12% respectively [8,12]. Part of this deviation originates from source sink imbalance rather than inherent enclosure artefacts. Controlled enclosure environments alter pre-heading growth conditions critical for sink formation, inducing artificial sink expansion; meanwhile, fixed sink capacity in enclosed plants inevitably triggers late-stage photosynthetic acclimation. Recent temperature moderator analyses further confirm that photosynthesis-only models fail to predict interactive climate responses accurately in specific regions [52,72]. This testable mechanistic discrepancy is formally proposed as a targeted prediction in Section 4.6.

4.3. What the Primary Literature Cannot Yet Do

Section 3.1 does more than describe the corpus: it sets the boundary of what the primary evidence can support. Three findings define that boundary. Sink determinants of yield are seldom measured: HI in 3.3% of studies and individual grain mass in 7.3%, against photosynthesis in 39.1% and any biomass trait in 28.7%. The source to sink ratio of 2.37:1 is therefore a fact about the field’s measurement habits, not about rice physiology. The asymmetry is also persistent, as the time windows show. And the subset that measures photosynthesis under eCO_₂ is not neutral, because that choice already assumes CO_₂ acts through photosynthesis; testing a source limited model on that subset risks confirming the assumption built into it.

Together these constraints explain why we did not re-pool primary data, and they point to what a future rice eCO_₂ meta-analysis should do differently. Syntheses should give priority to studies that measured source and sink traits together. Models should treat grain mass, spikelet number and HI as the response variables, with photosynthesis as a covariate rather than the outcome. And publications should state whether the eCO_₂ treatment covered the pre-heading window in which sink size is set, a detail usually omitted, although it decides the answer. Methods for handling missing measured variables in crop meta-analysis already exist and could be applied here [34].

Secondary synthesis has known weaknesses that carry over here: publication bias, screening criteria that differ between source studies, and uneven trait coverage. Non-independent primary datasets and inconsistent confidence intervals also limit how far trait classes can be compared quantitatively. The sequential source sink model proposed below is therefore offered as a mechanistic reading of the evidence, and every inference drawn from it is stated as a testable prediction rather than as a statistical result.

4.4. Practical Implications for Rice Breeding and Field Management

The sequential model has three implications for breeding and management, given in the order of how firmly the evidence supports them.

Sink capacity, not photosynthetic rate, is the breeding target for rice adapted to future CO_₂. eCO_₂ raises panicle number, spikelet density and spikelets per panicle, whereas individual grain mass and harvest index stay unchanged [9,42]. Spikelet number has already been identified as the constraint on japonica yield under FACE, where spikelet degeneration occurs under high CO_₂ [29,65]. Any sink-focused selection also has to be checked against lodging, which does not always move in the same direction as yield [73].

The canopy source:sink ratio could serve as a screening index, because the flag leaf area to spikelet number ratio is stable across environments, which is what a selection criterion requires [6]. Genotypes with a low intrinsic ratio show less flag leaf carbohydrate accumulation and weaker photosynthetic acclimation under elevated CO_₂.

Temperature is the third piece, and it matters for climate resilient cultivation. Warming erodes the CO_₂ benefit through the sink: filled grain percentage falls and grains finish lighter, whereas photosynthesis is not the failing step [8,42]. Heat tolerance of the sink, rather than thermal stability of photosynthesis, therefore appears to govern yield stability under combined eCO_₂ and warming. Heat stress at flowering or early grain filling removes the CO_₂ advantage by causing spikelet sterility and incomplete filling, independently of carbon supply [66,67,68], and interactions of the same sign have been reported in barley [62]. Whether the effect is specific to pre-heading warming is not yet established: few experiments separate warming applied before heading from warming applied after it, and we state this as a hypothesis to be tested.

Two qualifications temper this reading. Sink focused breeding has to be judged together with grain quality, because eCO_₂ changes the nutritional composition of rice independently of yield [74,75,76], and nitrogen supply shifts the response in both directions, through demand as well as uptake [69,77,78]. Beyond rice, the framework predicts that any crop whose sink capacity is fixed before reproductive growth will show the same attenuation once the sink is filled, which offers a general explanation for why enclosure based screening overstates eCO_₂ responsiveness. It also reframes the practical question: not how far photosynthesis can be pushed, but how large a sink can be built before it becomes self limiting. The predictions in Section 4.6 are stated so that this can be checked against new data.

4.5. Study Limitations

Five limitations qualify the present analysis. Screening was title- and abstract-level, so a small number of records may be misclassified. The searches covered the WoS and CNKI but not Scopus, PubMed or CAB Abstracts, and Chinese language theses were not searched; because a substantial share of Chinese FACE rice experiments originates in theses, this likely underestimates long-term FACE datasets. Secondary synthesis cannot remove publication bias or selective outcome reporting in the primary studies. Effect estimates in Table 1 are statistically non-independent, since individual experiments appear in more than one meta-analysis, which is why none was re-pooled and why each is reported as its authors derived it. Finally, the trait-class comparisons in Figure 3 are semi-quantitative: no significance test of the source to sink gradient was performed, and the ordering should not be read as a statistical ranking. None of these limits bears on the reporting frequencies of Section 3.1, which are counts of what the literature contains, nor on the direction of the effects in Table 1, which are reproduced as published.

4.6. Testable Mechanistic Predictions

The sequential source sink limitation framework developed above generates three predictions that are testable with data either already available or straightforward to generate. Each is stated together with the observation that would falsify it, so that the framework can be assessed rather than merely illustrated.

(i) Yield responses to eCO_₂ are explained better by spikelet number plasticity than by the enhancement of light-saturated photosynthesis; residual variation left unexplained by sink traits should be attributed to late season photosynthetic acclimation rather than to initial stimulation. The assembled estimates already offer a check. If the source limited model were right, the FACE yield increment (+12%) should track the photosynthesis increment (+21.9%) more closely than the panicle density increment (+9.2%); in fact it lies closer to the sink-side change, which is not the pattern that model predicts.

(ii) Whatever their intrinsic photosynthetic capacity under ambient CO_₂, genotypes with a low local source:sink ratio should gain more yield, keep less carbohydrate in the flag leaf and acclimate less under eCO_₂ than genotypes with a high ratio.

(iii) Elevated CO_₂ treatments applied exclusively after heading (with fixed sink size) will produce negligible yield improvement and stronger photosynthetic acclimation, compared with treatments covering the pre-heading sink formation window. Existing pot-transfer experiments have already validated the absent yield response of post heading CO_₂ enrichment [14], supporting the core premise of this prediction.

5. Conclusions

Reading the published syntheses of rice under eCO_₂ through one source sink framework gives a picture that no single synthesis provides. Three patterns recur. eCO_₂ raises leaf photosynthetic capacity and vegetative biomass, most strongly root biomass (+27.9%) and panicle biomass (+25.4%). Individual grain mass and harvest index do not change consistently: the two syntheses that report harvest index give +9% and -2%, and the latter does not differ from zero. Grain yield nevertheless rises by 12-20%, less under free-air conditions than in enclosures, and more in hybrid and indica cultivars than in japonica. These estimates are listed side by side rather than reduced to a single conversion efficiency, because they come from partly disjoint primary datasets in which one trial may appear more than once; they are a range of published values, not measurements that can be added together. Milling also matters: brown and white rice yield rise by 18.8% and 15.7% while head rice yield does not change, so part of the apparent gain is lost in processing. The pattern is descriptive, rests on published estimates rather than on tests of our own, and should be read as a hypothesis consistent with the evidence rather than as an established mechanism.

These divergent responses fit a sequential constraint. Before heading, grain number depends on assimilate supply, so extra CO_₂ enlarges the sink through more spikelets. After heading, filling responds little: the larger sink population does not produce heavier grains, and surplus carbohydrate accumulates in leaves, where it depresses photosynthesis through feedback. Allocation data now show this directly, under FACE the fraction of biomass in roots rose 8.5% while that in leaves fell 8.4%, with no change in the panicle fraction [10]. Carbon therefore goes below ground and into leaves rather than into grain, which is why harvest index does not rise even though total yield does.

Two consequences follow, one for modelling and one for breeding. Crop models that implement CO_₂ responses by scaling photosynthesis or radiation-use efficiency implicitly assume that yield is source limited; if the increment is instead set largely by yield components established before heading, such models will carry a directional bias. And breeding for future eCO_₂ environments should not treat greater photosynthetic capacity and larger sink size as interchangeable targets: the evidence assembled here indicates that sink capacity, not photosynthetic potential, sets the ceiling on realized yield. That conclusion comes from a descriptive comparison of published estimates and should be treated as a well-supported hypothesis rather than an established causal mechanism; the tests proposed in Section 4.6 provide the means to evaluate it.