Measurement, regional disparities, and dynamic evolution of food crop breeding technology innovation in China

Abstract

Food crop breeding technology innovation is the cornerstone of national food security and a critical pathway to building a strong agricultural nation. Despite significant progress, China still lags behind developed countries in unit yield of major food crops, with the gap in breeding innovation and market application translating into substantial productivity disparities. While existing literature has explored crop breeding innovation from various dimensions, comprehensive evaluation frameworks based on the innovation chain perspective remain underdeveloped, limiting the comparability and policy relevance of research findings.This study constructs a food crop breeding technology innovation evaluation system from the innovation chain perspective, encompassing four interconnected stages: basic research, applied research, new variety development, and market application. Using panel data from 31 Chinese provinces (excluding Hong Kong, Macao, and Taiwan) from 2013 to 2023, we employ the entropy weight method to measure innovation levels, the Dagum Gini coefficient to decompose regional disparities, Kernel density estimation to analyze distribution dynamics, and Markov chain analysis to examine dynamic evolution characteristics with and without spatial effects.China’s food crop breeding technology innovation demonstrates an upward trend amidst fluctuations, with main sales areas outperforming main production areas and balanced production-marketing areas. Regional disparities are significant but narrowing, with inter-regional differences constituting the primary source of overall inequality. The distribution of innovation levels shows increasing dispersion with gradually diminishing polarization. Traditional Markov chain analysis reveals a gradual, path-dependent development process with pronounced Matthew effects. Spatial Markov chain analysis confirms significant spatial spillover effects that intensify over time, where proximity to high-level regions enhances upward mobility probability.

Introduction

Technological innovation in food crop breeding is the cornerstone of national food security and a critical pathway to building a strong agricultural nation^1,2. Scientifically constructing an evaluation system for breeding technology innovation and objectively measuring the actual development level of China’s food crop breeding capabilities are urgent priorities for clarifying the goals of agricultural science and technology, resolving productivity constraints, and enhancing the modernization of China’s agricultural innovation system and governance capacity.

In the post-pandemic era, global agricultural development faces significant challenges from the compounding effects of intensifying climate change, increasing frequency of extreme weather events, and escalating geopolitical conflicts affecting agricultural trade³. As a major grain-producing and consuming country, China is making efforts to promote the development strategy of seed industry revitalization and incorporate it into the national food security strategy. As of 2024, China has achieved consecutive bumper harvests in grain production for multiple years, making significant progress in total output⁴. However, in 2023, for instance, corn yield in the United States exceeded that of China by 70%, while soybean yield surpassed China by 74%. This productivity gap fundamentally stems from disparities in breeding innovation capabilities and market application efficiency. Therefore, in the current complex international environment, China continues to face instability risks—such as insufficient original innovation in germplasm resources, prominent structural contradictions between research and market demand, and increasingly severe competitive pressure from international seed giants—for a long period of time in the future. It is urgent to scientifically and reasonably construct an evaluation system for food crop breeding technology innovation and objectively measure the actual development level across regions. This is an important topic for clarifying innovation development goals, resolving technological bottlenecks, and enhancing the modernization level of China’s agricultural science and technology governance system and governance capacity.

Over the past decade, researchers have endeavoured to study the food crop breeding innovation topic. The researchers mainly focused on three aspects: firstly, the innovation status of breeding at the national level. Current research on breeding innovation exhibits a discernible shift from quantitative expansion toward qualitative enhancement. However, latecomer countries universally confront deficits in quality-based catch-up. Lee et al. observe that extant studies on technological catch-up within plant biotechnology subfields remain predominantly quantity-oriented, with scant attention devoted to quality dimensions—precisely the critical bottleneck constraining latecomer nations in this domain⁵. Hu et al. and Park et al. further emphasize that the failure of most latecomer countries to achieve breeding-related technological catch-up stems fundamentally from the absence of advanced breeding technologies and robust innovative capabilities, rather than from resource endowments or labor shortages^6,7. Odagiri et al. conceptualize breeding technology catch-up as the core trajectory through which latecomer countries enhance their breeding innovation capacity and narrow technological gaps relative to innovation leaders⁸. Regarding regional analyses, Eriksson and Chatzopoulou, focusing on EU regions, argue that responsible governance mechanisms must be established within plant research and breeding innovation⁹. From the perspective of innovation modalities, Lee et al. propose that “collaborative innovation” has gained widespread acceptance in open innovation contexts within plant breeding, emphasizing the integration of genomics, cooperation, and co-creation to augment organizational value¹⁰. Conversely, Hardt and Negri characterize agriculture as constituting “open science,” wherein breeding innovation possesses intrinsic openness attributes¹¹. Nevertheless, Laursen and Salter contend that conventional intellectual property protection—characterized by exclusivity, monopolistic tendencies, and non-cooperation—has become increasingly incongruent with the open and shared innovation imperatives of the breeding sector¹². At the institutional practice level, Hsu notes that absolute breeding exemptions have engendered plagiaristic practices in derivative breeding¹³.

Secondly, the construction of evaluation metrics for breeding innovation. Assessing breeding innovation constitutes a dynamically adjusting process, with academia yet to converge upon unified evaluation standards. The construction of breeding innovation metrics necessitates transcending the limitations of conventional patent-count indicators to establish a more scientifically rigorous multidimensional measurement system. Griffith et al. and Yang identify “home bias” in patent filings and highlight substantial cross-national heterogeneity in patent regimes and the difficulty of obtaining breeding-related patents, rendering patent counts alone inadequate for capturing breeding innovation^14,15. Aghion et al. further document significant value heterogeneity among breeding patents, with only a minority possessing substantive innovative value; employing citation-weighted measures enhances comparability across breeding patents¹⁶. Concerning plant variety protection certificates, Lesser conducts valuation analyses of such certificates¹⁷, while Wree performs specialized economic assessments of genetically modified plant breeding innovation. From a user innovation perspective¹⁸, von Hippel demonstrates that user innovation exhibits advantages over manufacturer innovation, being simultaneously more aligned with actual usage requirements and less costly¹⁹. Lüthje et al. further underscore that users constitute a significant source of innovation in breeding and related domains²⁰. Regarding institutional effectiveness evaluation, Rives proposes that the implementation efficacy of the essentially derived variety regime should be assessed primarily by its capacity to balance researchers’ freedom to utilize breeding materials against the interests of original variety right holders²¹. Calabresi and Melamed, from a law-and-economics perspective, argue that the efficiency of commercialization rules for breeding outcomes should be evaluated according to transaction cost minimization²².

Lastly, the determinants of breeding innovation. Breeding innovation is shaped by the confluence of governmental governance, technological characteristics, market demand, and industrial organization. At the governance level, Bardhan identifies a substitutive relationship between government effectiveness and market governance in breeding innovation, necessitating contingent adjustment across developmental stages²³. Acemoglu et al. demonstrate that governmental governance capacity exerts profound positive effects on technological accumulation during initial development phases and on technological breakthroughs during bottleneck periods within breeding^24,25. Kwon et al. disaggregate the manifestations of governance capacity across catch-up stages: initial phases characterized by public sector investment in fundamental breeding research, intermediate phases by infrastructure development²⁶, and advanced phases by the protection of intellectual property rights and associated entitlements²⁷. Landini et al. propose that distinct policy combinations of government effectiveness and market governance constitute the foundation for national breeding technology catch-up²⁸. Lassoued et al. acknowledge that governmental safety risk assessments of breeding technologies increase innovation costs yet safeguard technological safety and industrial sustainability²⁹. Regarding technological and innovation factors, Casper identifies biotechnology—including breeding—as paradigmatic of networked organizational forms dependent upon multi-party collaboration³⁰. Kolympiris et al. document that public goods provision in education and R&D infrastructure generates substantial externalities and spatial spillover effects³¹. Bloom et al. note declining global efficiency in R&D innovation, suggesting that breeding-specific efficiency gains require targeted external intervention³². Rosiello et al. find that knowledge base complexity impedes technological catch-up, with catch-up more probable in subfields characterized by shorter technological cycles³³. Dantas et al. highlight the co-evolution of firm-level knowledge networks and capabilities as essential microfoundations for technological catch-up³⁴. Akcigit et al. demonstrate that public policies—including tax incentives and public R&D investment—significantly influence breeding innovation incentives³⁵. Regarding the impact of plant variety rights regimes, Alston and Venner, examining U.S. wheat breeding, document that the Plant Variety Protection Act substantially influenced wheat genetic improvement trajectories³⁶. Kesan and Janis note that the patent-like attributes of variety rights render their protection design directly consequential for breeding innovation³⁷. Vicente-Saez and Martinez-Fuentes emphasize that the proliferation of “open science” ideals has profoundly shaped innovation modalities within plant breeding³⁸. Merges proposes that open licensing regimes can streamline licensing procedures and reduce transaction costs³⁹. Garcia concludes that the establishment of plant variety protection systems attracts foreign capital, promotes domestic enterprise consolidation, and facilitates the inflow of advanced foreign technologies⁴⁰. Diez further finds that variety rights regimes exert more pronounced incentive effects on breeding innovation within the private agricultural research sector⁴¹.

To summarize, researchers have achieved fruitful results in the study of breeding innovation development. However, there still exists certain expandable space. First, the determination of the evaluation framework lacks systematic integration from the innovation chain perspective. Existing studies often focus on isolated stages of innovation, such as pure research output or variety approval numbers, without establishing a comprehensive evaluation system that covers the complete chain from basic research to market application. This fragmentation leads to incomplete assessment of innovation performance and limits the comparability and policy relevance of research findings. Secondly, existing research on breeding innovation mainly focuses on the national or single-crop level, often ignoring regional differences within countries and the heterogeneity among different functional regions. Although this research method can provide macro-level insights, it cannot reveal the specific problems and needs of different regions in terms of breeding innovation, particularly the disparities among main grain-producing areas, main sales areas, and production-sales balance areas⁴². At the same time, there is relatively little research on regional differences using advanced decomposition methods such as the Dagum Gini coefficient, and existing studies mainly rely on traditional methods such as Theil index or coefficient of variation that may introduce estimation bias. Thirdly, existing studies mainly focus on static evaluation of breeding innovation level, and seldom explore the spatial and temporal evolution characteristics, distribution dynamics, and dynamic evolution patterns at the same time. The lack of dynamic perspective prevents effective understanding of the path dependence, convergence clubs, and spatial spillover effects in the development process of breeding innovation.

In this study, related existing researches were referenced, the entropy weight method and the panel data of 31 provinces (and cities) in China from 2013 to 2023 were used to evaluate their food crop breeding technology innovation levels. We used the Dagum Gini coefficient to decompose the regional disparities and identify sources of inequality. Meanwhile, we employed kernel density estimation to analyze distribution dynamics and Markov chain models to examine the dynamic evolution process with and without spatial effects. The results of this study can help us to further understand China’s food crop breeding technology innovation, propose basic strategies for promoting breeding innovation and provide theoretical support for narrowing the development imbalance between regions. The research objectives of this study are twofold. Firstly, theoretical objective is to construct evaluation indicators for breeding technology innovation from the innovation chain perspective, encompassing four interconnected stages: basic research, applied research, new variety development, and market application, thus expanding the theoretical perspective of breeding innovation research. Secondly, application goal, this study is to provide ideas for the construction and improvement of a long-term mechanism for promoting breeding innovation in China, and also to provide scientific references for global agricultural technology development.

The marginal contributions of this article are as follows. Firstly, this paper is focusing on systematic framework construction to fill the research gap. A comprehensive evaluation system was constructed from the innovation chain perspective for the first time, covering the complete process from basic research to market application, filling the gap of fragmented evaluation in existing literature and providing a theoretical basis for comprehensive assessment of breeding innovation performance. Secondly, this paper adopted the cutting-edge dynamic evolution analysis methods. Spatial Markov chain model and kernel density estimation were introduced to reveal the spatiotemporal evolution law of breeding innovation level, breaking through the limitations of traditional static analysis, clarifying the path dependence, distribution dynamics, and spatial spillover effects of regional development, and providing dynamic reference for policy-making. Thirdly, the evaluation of regional disparities was more objective compared to traditional researches. Dagum Gini coefficient was used to overcome the shortcomings of traditional methods such as Theil index (which ignored sample cross overlap and could not decompose regional differences effectively), achieving dual objectivity in regional difference measurement and source identification.

Materials and methods

Variable selection and data sources

Food crop breeding technology innovation evaluation indicators

To accurately capture the multi-dimensional nature of food crop breeding technology innovation, we establish a comprehensive evaluation system anchored in the innovation chain framework. The theoretical foundations of the innovation chain can be traced to three seminal contributions. First, Rothwell and Zegveld proposed the chain-linked model, conceptualizing innovation as a sequential process from basic research through development to commercialization, while emphasizing feedback loops between stages⁴³. Second, Kline and Rosenberg advanced the chain-loop model, challenging linear assumptions by highlighting the recursive interactions among knowledge creation, product design, and market demand⁴⁴. Third, Chesbrough extended this framework through the lens of open innovation, emphasizing that knowledge flows across organizational boundaries and that innovation chains increasingly rely on external collaboration and distributed networks⁴⁵. Building upon these theoretical traditions, our study operationalizes the innovation chain for the specific context of agricultural breeding. The four-stage structure—basic research, applied research, new variety development, and market application—represents a contextualized adaptation of the general innovation chain to crop breeding: basic research corresponds to the knowledge creation phase; applied research translates this knowledge into patentable technologies; new variety development embodies the product realization stage; and market application captures the value realization through productivity gains. This adaptation preserves the sequential interdependence emphasized by Rothwell and Zegveld, accommodates the feedback mechanisms highlighted by Kline and Rosenberg, and reflects the collaborative openness characteristic of modern breeding innovation as described by Chesbrough.

This framework conceptualizes the innovation process as four sequential yet interdependent stages: basic research, applied research, new variety development, and market application. Given the proliferation of potential indicators for breeding innovation, we follow Gong et al., Dranev et al., and Zhang et al. to identify five secondary indicators characterized by strong complementarity, minimal redundancy, and high representativeness, thereby ensuring both the comprehensiveness and scientific rigor of the evaluation system (Table 1)^46–48.

Table 1.

Food crop breeding technology innovation evaluation indicators.

Primary indicators	Secondary indicators	Unit	Attributes
Basic research	Food crop breeding paper innovation	Number of papers	Positive
Applied research	Food crop breeding patent innovation	Number of authorized patents	Positive
New variety development	Food crop new variety application	Number of variety applications	Positive
	Food crop new variety authorization	Number of authorized varieties	Positive
Market application	Food crop yield improvement	Yield increment (kg/hectare)	Positive

Basic research constitutes the foundation of the innovation chain, concentrating on the exploration of fundamental biological principles and genetic mechanisms underlying food crop traits. The primary output of this stage manifests as scientific publications that advance theoretical understanding and establish the knowledge infrastructure for subsequent applied research. We employ the annual number of food crop breeding-related research papers as the quantitative metric for this dimension.

Applied research serves as the bridge between basic research and commercial development, addressing practical application needs through the identification and utilization of key traits and genes. Outputs at this stage typically take the form of technological solutions secured by intellectual property protection. We utilize the annual number of authorized invention patents in food crop breeding as our indicator, on the grounds that patent grants more accurately reflect realized innovation output than mere applications.

New variety development represents the concrete breeding stage where theoretical and technological advances translate into tangible genetic improvements. This stage encompasses the determination of breeding objectives, parental selection, progeny selection, line identification and testing, and variety approval and registration. We employ two complementary indicators—plant variety protection applications and authorized varieties—capturing both the initiation and successful completion of variety development activities.

Market application constitutes the terminal stage where breeding innovation generates economic and social value through yield enhancement. During China’s 13th Five-Year Plan period (2016–2020), new varieties contributed approximately 45% to yield increases, with this contribution projected to expand substantially as biotechnology industrialization advances. We measure this stage using the annual increment in food crop unit yield (defined as the year-on-year improvement in yield), which directly reflects the productivity impact of breeding innovation.

All indicators are constructed as positive attributes, where higher values denote superior innovation performance. The directional orientation of each indicator is grounded in the intrinsic characteristics of innovation chain progression: increased output at each stage contributes to the enhancement of overall innovation capability.

Data sources

The empirical analysis draws on panel data covering 31 Chinese provinces (autonomous regions and municipalities directly under the central government, excluding Hong Kong, Macao, and Taiwan) over the period 2013–2023. Several considerations motivate this temporal and spatial scope. First, 2013 marks the beginning of China’s 13th Five-Year Plan preparation period, during which agricultural technology innovation received heightened policy attention and resource allocation; data from this year onward thus capture innovation dynamics under strategic policy frameworks. Second, 2023 represents the most recent complete year with comprehensive data availability, ensuring both reliability and temporal proximity to current conditions. Third, the eleven-year span provides sufficient longitudinal depth for analyzing spatial-temporal evolution while maintaining data continuity and integrity.

Data on food crop breeding papers are sourced from the Web of Science Core Collection database. The search is restricted to 48 journals with impact factors exceeding 4.0 in the crop breeding field, using English crop names to identify paper titles. This approach ensures high-quality, internationally recognized research outputs while maintaining consistency across regions and time periods.

Patent data are extracted from the National Patent Database of China. The sample is restricted to invention patents designating China as the priority country, with International Patent Classification (IPC) codes limited to A01H1/00, A01H3/00, A01H4/00, A01H5/00, C12N15/29, C12N15/82, C12N15/90, and C12Q1/68. Searches are conducted using both Chinese and English food crop names in patent titles and abstracts, with authorized patent counts serving as the final metric.

Plant variety application and authorization data are obtained from the China Crop Seed Industry Development Report for respective years. Food crop yield data are sourced from the China Statistical Yearbook, with yield improvement calculated as the first-order difference of unit area yield between consecutive years.

Missing values for individual indicators are addressed through linear interpolation when temporal gaps are minimal. All monetary values are expressed in constant 2013 prices where applicable. The final dataset comprises 341 province-year observations (31 provinces × 11 years) with complete information across all evaluation dimensions.

Research methodology

Entropy weight method

To ensure objective and accurate evaluation of food crop breeding technology innovation levels, we employ the entropy weight method for indicator weighting, combined with linear weighting for comprehensive score calculation. The entropy weight method is selected as the core weighting approach based on its unique balance between data-driven characteristics and comprehensive evaluation capability. Unlike subjective weighting methods such as the Analytic Hierarchy Process (AHP) or fuzzy comprehensive evaluation, the entropy weight method calculates weights based on the degree of data dispersion, completely relying on objective data patterns and avoiding biases introduced by expert preferences or artificial ranking. Compared to emerging methods such as ESP-COMET, the entropy weight method requires only data standardization and entropy calculation, with simpler procedural steps suitable for rapid weight generation in large-scale datasets. Relative to methods such as SPOTIS, sensitivity to extreme values can be mitigated through appropriate data standardization techniques.

The specific implementation steps are as follows⁴⁹:

Firstly, Data normalization. Given the heterogeneous scales across indicators, we first standardize the data using the extreme value method. Let the initial evaluation matrix be , where m represents the number of indicators and n represents the number of evaluation objects. The standardized matrix is obtained through:

For positive indicators:

1

For negative indicators:

2

Secondly, Entropy calculation. Calculate the entropy value for each indicator:

3

where , with the convention that when .

Thirdly, Weight determination. Calculate the entropy weight for each indicator:

4

Lastly, Comprehensive score calculation. The food crop breeding technology innovation level score for each province is calculated as:

5

Dagum Gini coefficient

The Dagum Gini coefficient is employed to comprehensively measure regional disparities in food crop breeding technology innovation and decompose their sources. Proposed by Dagum in 1997, this method decomposes the overall Gini coefficient into three components: intra-regional differences, inter-regional net differences, and hypervariable density, overcoming limitations of traditional methods such as the Theil index that ignore sample cross-overlap⁵⁰.

The specific calculations are as follows:

The overall Gini coefficient  G is defined as:

6

where () denotes the innovation level in province  i ( r) of region  j ( h), denotes the national average innovation level, k denotes the number of sample regions, and () denotes the number of provinces in region j (h).

The Gini coefficient can be decomposed as:

7

where represents intra-regional differences, represents inter-regional differences, and represents hypervariable density.

Intra-regional differences:

8

where is the intra-regional Gini coefficient for region j, , and .

Inter-regional differences:

9

Hypervariable density:

10

where represents the relative impact of innovation levels between regions  j and  h.

Kernel density estimation

Kernel density estimation is employed to analyze the distribution dynamics of food crop breeding technology innovation levels due to its robustness against data fluctuations and outliers, and its wide applicability in non-equilibrium distribution research. This non-parametric method enables characterization of distribution morphology, central tendency, dispersion degree, and polarization patterns without assuming specific functional forms⁵¹.

The Kernel density function is defined as:

11

where  n is the number of observations,  h is the bandwidth, is the independent variable, and is the kernel function. We employ the Gaussian kernel function:

12

The bandwidth  h is determined using Silverman’s rule of thumb to balance bias-variance trade-offs. Analysis focuses on four distribution characteristics: (1) the position of the main peak, indicating the overall innovation level; (2) peak height and width, reflecting distribution concentration; (3) the number and position of side peaks, indicating the degree of polarization; and (4) tail characteristics, revealing internal disparities and mobility potential.

Moran’s I Index

To further explore the spatial distribution characteristics of China’s grain crop breeding science and technology innovation level, this paper adopts Moran’s I index, a commonly used method for measuring spatial correlation, to conduct the analysis. First, the global Moran’s I index is employed to examine whether there exists spatial agglomeration in China’s grain crop breeding science and technology innovation level.

13

where represents the element of the spatial weight matrix, and i ≠ j; denotes the grain crop breeding science and technology innovation level of the i-th province; and is the mean value of grain crop breeding science and technology innovation levels across all provinces.

Markov chain analysis

Traditional Markov chain analysis is employed to characterize the dynamic evolution of food crop breeding technology innovation levels by discretizing continuous innovation scores into state spaces and constructing transition probability matrices. We further extend this framework to spatial Markov chain analysis by incorporating spatial lag effects to examine whether geographic or economic proximity influences state transition probabilities.

Traditional Markov chain. Based on the quartile division method, we classify the 31 provinces over the period 2013–2023 into four state types according to innovation level differences, using the 25th, 50th, and 75th percentiles as boundaries (denoted as Types I, II, III, and IV, with higher values indicating superior innovation levels). The transition probability matrix  M is constructed as⁵²:

14

where represents the probability of transitioning from state  i to state  j:

15

where denotes the number of provinces transitioning from state  i to state  j, and denotes the total number of observations in state  i.

Spatial Markov chain. To incorporate spatial effects, we construct a geographic distance weight matrix  W where elements represent spatial proximity between provinces  i and  j. The spatial lag variable is defined as:

16

Based on the spatial lag type of each region in the initial year, the traditional Markov probability transition matrix is decomposed into  k conditional transition matrices. Let denote the transition probability from state  i to state  j given spatial lag type  N. By comparing traditional and spatial Markov probability matrices, we reveal the mechanism of spatial spillover effects in innovation level evolution⁵³.

The spatial weight matrix is row-standardized such that . We employ inverse distance weighting where for , with representing the geographic distance between provincial centroids, and .

All calculations are implemented using MATLAB R2022b and Stata 17.0 software packages. Statistical significance is assessed at the 1%, 5%, and 10% levels where applicable.

Results

Food crop breeding innovation results in China

According to the above method, raw data are first substituted into the entropy weight formulas to obtain indicator weights, after which standardized data and weights are combined to calculate comprehensive innovation scores for China’s regions. The trends of change are shown in Fig. 1; Table 2.

Fig. 1.

Kernel-density dynamics of food-crop breeding innovation: national aggregate and each functional zone.

Table 2.

Innovation Index of Food-Crop Breeding by Province, 2013–2023.

Region & Province		2013	2014	2015	2016	2017	2018	2019	2020	2021	2022	2023	Average
Major-producing region	Hebei	0.021	0.045	0.042	0.048	0.058	0.060	0.099	0.125	0.126	0.155	0.262	0.095
	Inner Mongolia	0.007	0.009	0.013	0.016	0.014	0.018	0.026	0.029	0.062	0.033	0.077	0.028
	Liaoning	0.016	0.015	0.026	0.027	0.034	0.035	0.043	0.035	0.066	0.079	0.158	0.049
	Jilin	0.025	0.037	0.044	0.044	0.056	0.043	0.079	0.078	0.084	0.094	0.127	0.065
	Heilongjiang	0.023	0.050	0.055	0.091	0.073	0.086	0.118	0.159	0.172	0.204	0.345	0.125
	Jiangsu	0.150	0.191	0.243	0.272	0.267	0.288	0.368	0.406	0.473	0.599	0.675	0.357
	Anhui	0.040	0.062	0.082	0.085	0.094	0.101	0.124	0.113	0.134	0.150	0.224	0.110
	Jiangxi	0.005	0.011	0.014	0.016	0.018	0.023	0.023	0.027	0.024	0.027	0.053	0.022
	Shandong	0.058	0.087	0.088	0.105	0.125	0.142	0.159	0.219	0.223	0.266	0.399	0.170
	Henan	0.023	0.039	0.084	0.107	0.117	0.153	0.229	0.246	0.287	0.310	0.507	0.191
	Hubei	0.136	0.141	0.233	0.218	0.335	0.264	0.334	0.357	0.414	0.464	0.451	0.304
	Hunan	0.020	0.043	0.033	0.060	0.076	0.085	0.077	0.117	0.090	0.142	0.179	0.084
	Sichuan	0.046	0.044	0.047	0.062	0.065	0.064	0.079	0.078	0.086	0.101	0.167	0.076
Major-consuming region	Beijing	0.292	0.244	0.381	0.368	0.370	0.453	0.492	0.523	0.548	0.672	0.745	0.462
	Tianjin	0.016	0.021	0.020	0.031	0.035	0.039	0.023	0.031	0.025	0.029	0.037	0.028
	Shanghai	0.056	0.058	0.075	0.073	0.102	0.060	0.089	0.097	0.090	0.098	0.129	0.084
	Zhejiang	0.128	0.140	0.123	0.159	0.160	0.177	0.176	0.184	0.215	0.290	0.344	0.191
	Fujian	0.018	0.024	0.032	0.037	0.050	0.053	0.095	0.106	0.123	0.155	0.219	0.083
	Guangdong	0.041	0.045	0.096	0.078	0.106	0.115	0.134	0.151	0.210	0.268	0.347	0.145
	Hainan	0.006	0.006	0.010	0.021	0.025	0.040	0.041	0.045	0.065	0.137	0.167	0.051
Supply–demand balanced region	Shanxi	0.010	0.008	0.019	0.017	0.013	0.022	0.029	0.038	0.036	0.059	0.093	0.031
	Guangxi	0.010	0.039	0.029	0.040	0.048	0.041	0.044	0.070	0.070	0.082	0.130	0.055
	Chongqing	0.010	0.013	0.013	0.020	0.033	0.039	0.032	0.041	0.041	0.043	0.062	0.031
	Guizhou	0.005	0.011	0.017	0.024	0.020	0.010	0.024	0.023	0.026	0.045	0.053	0.024
	Yunnan	0.027	0.038	0.045	0.040	0.035	0.034	0.049	0.060	0.059	0.095	0.121	0.055
	Tibet	0.003	0.003	0.003	0.003	0.004	0.003	0.004	0.003	0.003	0.003	0.005	0.003
	Shaanxi	0.049	0.038	0.050	0.065	0.065	0.082	0.108	0.126	0.144	0.170	0.167	0.097
	Gansu	0.013	0.011	0.018	0.021	0.031	0.027	0.043	0.031	0.063	0.089	0.106	0.041
	Qinghai	0.004	0.003	0.004	0.004	0.004	0.004	0.008	0.004	0.005	0.004	0.005	0.004
	Ningxia	0.005	0.005	0.005	0.004	0.007	0.005	0.012	0.018	0.011	0.014	0.027	0.010
	Xinjiang	0.009	0.009	0.012	0.014	0.011	0.009	0.013	0.020	0.038	0.050	0.071	0.023
Averages	National	0.041	0.048	0.063	0.070	0.079	0.083	0.102	0.115	0.129	0.159	0.208	0.100
	Major-producing	0.044	0.060	0.077	0.089	0.103	0.105	0.135	0.153	0.172	0.202	0.279	0.129
	Major-consuming	0.080	0.077	0.105	0.110	0.121	0.134	0.150	0.163	0.182	0.236	0.284	0.149
	Balanced	0.013	0.016	0.020	0.023	0.025	0.025	0.033	0.039	0.045	0.059	0.076	0.034
	Eastern	0.073	0.079	0.103	0.111	0.121	0.133	0.156	0.175	0.197	0.250	0.316	0.156
	Central	0.035	0.049	0.071	0.080	0.098	0.097	0.127	0.142	0.155	0.181	0.247	0.117
	Western	0.016	0.019	0.021	0.026	0.028	0.028	0.037	0.042	0.051	0.061	0.083	0.037

The technological innovation level of grain crop breeding in China exhibits a consistent upward trend year by year, both at the national level and across all regions. From the perspective of grain production area classification, the technological innovation levels in major grain-producing areas and major grain-consuming areas were both lower than the national average throughout the study period, whereas the technological innovation level in grain production-consumption balance areas exceeded the national average. From the perspective of economic-geographical zoning, the eastern region consistently surpassed the national average during the study period, the central region exceeded the national average from 2014 to 2023, while the western region remained consistently below the national average. Notably, the disparities between major grain-consuming areas and production-consumption balance areas, as well as between eastern and western regions, represent the largest gaps and display an increasing trend. Following the release of the “Seed Industry Revitalization Action Plan” in 2021, the national overall technological innovation level of grain crop breeding has demonstrated an accelerating growth rate year by year.

The technological innovation level of grain crop breeding varies significantly across provinces in China. In 2023, provinces with innovation levels exceeding 0.5 were Beijing (0.745), Jiangsu (0.675), and Henan (0.507), ranking in the top three nationally. In contrast, a total of 20 provinces fell below the annual average of 0.208, among which Ningxia (0.027), Qinghai (0.005), and Tibet (0.005) exhibited the lowest technological innovation levels, ranking in the bottom three nationally.

The underlying determinants of these disparities are as follows. Beijing serves as China’s primary scientific research hub, with a substantial concentration of universities, research institutes, and seed enterprises, consistently ranking at the forefront nationally across basic research, applied research, new variety development, and market-oriented applications. Specifically, Beijing maintained the first position nationally in grain crop breeding patents throughout the study period. In 2023, Beijing ranked 3rd, 1st, and 3rd nationally in grain crop breeding papers, applications for new plant varieties, and authorized new plant varieties, respectively. Similar to Beijing, Jiangsu Province possesses numerous universities, research institutes, and seed enterprises. As a major grain-producing province with substantial grain cultivation, Jiangsu faces rigid demand for high-quality grain varieties. In 2023, Jiangsu ranked 1st, 2nd, 6th, and 6th nationally in grain crop breeding papers, patents, applications for new plant varieties, and authorized new plant varieties, respectively. Henan exhibits medium-to-high performance across basic research, applied research, new variety development, and market-oriented applications, achieving a comprehensive ranking of 3rd nationally. In contrast, provinces such as Ningxia, Qinghai, and Tibet lack universities, research institutes, and seed enterprises, and possess limited grain cultivation areas with relatively low demand for high-quality grain crop varieties. Consequently, these regions perform poorly across grain crop papers, patents, new varieties, and yield improvement, resulting in low technological innovation levels.

In 2013, provinces with technological innovation levels exceeding 0.13 were Beijing (0.292), Jiangsu (0.150), and Hubei (0.136), while the majority of provinces remained below the national average of 0.041, likely attributable to differences in the number of scientific research institutions and enterprises as well as the demand for new grain crop varieties. From a spatial distribution perspective, the spatial imbalance of China’s technological innovation level in grain crop breeding is pronounced. In 2013, technological innovation levels in major grain-producing areas and major grain-consuming areas were significantly higher than in production-consumption balance areas, and the eastern and central regions were also significantly higher than the western region. A notable characteristic of the dynamic evolution of spatial distribution is the diffusion of high-level areas toward the western region, while the western region simultaneously exhibits a clear trend of agglomeration in technological innovation levels. Overall, China’s technological innovation level in grain crop breeding exhibits a significant non-equilibrium characteristic of “high-value scattered distribution and low-value convergent agglomeration.”

Results of spatial characterization

Regional differences analysis

To systematically examine the sources of regional disparities, we apply the Dagum Gini coefficient decomposition method. Table 3 presents the Gini coefficients and their decomposition for the three grain production function regions.

Table 3.

Gini coefficient decomposition for three grain production function regions.

Year		Within-region inequality			Between-region inequality			Contribution%
	Overall	Major-producing	Major-consuming	Balanced-supply	Prod.–Cons.	Prod.–Bal.	Cons.–Bal.	Within	Between	Transvariation
2013	0.604	0.488	0.575	0.449	0.553	0.554	0.668	27.592	53.694	18.714
2014	0.544	0.424	0.524	0.441	0.476	0.517	0.615	28.274	49.331	22.395
2015	0.567	0.454	0.536	0.418	0.503	0.539	0.630	28.187	50.575	21.238
2016	0.535	0.423	0.498	0.421	0.463	0.522	0.592	28.256	49.91	21.834
2017	0.532	0.439	0.451	0.422	0.451	0.537	0.579	28.505	50.172	21.322
2018	0.539	0.417	0.482	0.467	0.454	0.533	0.605	27.792	51.934	20.274
2019	0.524	0.413	0.469	0.422	0.440	0.524	0.577	28.309	48.336	23.354
2020	0.518	0.415	0.454	0.445	0.436	0.523	0.563	28.793	46.58	24.627
2021	0.509	0.409	0.445	0.438	0.427	0.515	0.558	28.87	46.812	24.318
2022	0.503	0.425	0.423	0.422	0.429	0.510	0.544	29.144	48.175	22.68
2023	0.354	0.394	0.374	0.463	0.372	0.470	0.511	27.677	49.048	23.275

Overall disparity and intra-regional disparities across grain production areas. During the study period, regional disparities in the technological innovation level of grain crop breeding exhibited a decreasing trend amidst fluctuations, with the overall Gini coefficient reaching 0.354 by 2023—a reduction of 0.250 relative to 2013. This reflects the potential for narrowing disparities in China’s grain crop breeding innovation under the influence of factor integration, leading entities, support and guarantee mechanisms, promotion and application, and macro-level policies. Further analysis reveals that the Gini coefficients for major grain-producing areas and major grain-consuming areas decreased at average annual rates of 1.94% and 4.06%, respectively, whereas that for production-consumption balance areas increased at an average annual rate of 0.49%. By 2023, the Gini coefficients for major grain-producing areas, major grain-consuming areas, and production-consumption balance areas reached 0.394, 0.374, and 0.463, respectively. From an evolutionary perspective, although intra-regional disparities varied across the three major areas, both major grain-producing areas and major grain-consuming areas showed a narrowing trend in internal disparities, with major grain-consuming areas exhibiting the fastest reduction, followed by major grain-producing areas, while production-consumption balance areas remained the most stable. Based on 2023 data, production-consumption balance areas demonstrated the most pronounced disparities, followed by major grain-producing areas, with major grain-consuming areas showing the smallest disparities. This primarily stems from significant variations in natural environments among provinces within production-consumption balance areas, leading to differing demands for new grain varieties. Such demand disparities result in substantial differences in the number of research institutions and seed enterprises engaged in grain crop breeding research, consequently creating considerable variations among provinces in basic research, applied research, new variety development, and market-oriented applications, ultimately leading to the differentiation of technological innovation levels within the region.

Inter-regional disparities across grain production areas. Inter-regional disparities in the technological innovation level of grain crop breeding demonstrated a decreasing trend amidst fluctuations during the study period. Relative to the initial period, inter-regional disparities among the three areas slightly narrowed, with the most significant reduction occurring between major grain-producing areas and major grain-consuming areas. A plausible explanation is that major grain-producing areas originally possessed first-mover advantages in grain crop breeding due to relatively developed economic conditions. In recent years, with the state’s comprehensive planning and strong policy support, actively promoting technological sharing and deep cooperation among regions, the advantageous resources in capital and talent possessed by major grain-consuming areas have been effectively radiated to major grain-producing areas, providing robust support for enhancing the scientific research capabilities of the latter. Simultaneously, major grain-producing areas have continued to increase their investment, closely integrating practical production demands to carry out innovative work in grain crop breeding, thereby achieving rapid development and narrowing the development gap between major grain-producing and major grain-consuming areas.

Sources and contributions of regional disparities across grain production areas. As shown in the table, inter-regional disparities contribute the most to overall disparities, although this contribution exhibits a decreasing trend amidst fluctuations. Meanwhile, the contribution of the interaction between inter-regional and intra-regional disparities to overall disparities shows an increasing trend amidst fluctuations. Therefore, to achieve coordinated development of regional technological innovation levels in grain crop breeding, it is essential not only to narrow inter-regional gaps and implement differentiated measures based on local conditions to fully unleash the unique advantages of each region, but also to integrate the technological innovation of grain crop breeding across the three major areas into a unified and efficient coordination framework.

Table 4 presents the decomposition results for eastern, central, and western regions. Regarding intra-regional disparities, all three regions demonstrated a decreasing trend, with the eastern region exhibiting the fastest reduction. Concerning inter-regional disparities, differences among all regions gradually narrowed, with the disparity between eastern and central regions decreasing most rapidly and reaching the smallest magnitude. From the perspective of sources and contributions to regional disparities, inter-regional disparities contributed the most to overall disparities and showed an increasing trend. The contribution of the interaction between inter-regional and intra-regional disparities to overall disparities also exhibited an increasing trend, whereas the contribution rate of intra-regional disparities demonstrated a decreasing trend.

Table 4.

Gini coefficient decomposition for eastern, central, and western regions.

Year		Within-region inequality			Between-region inequality			Contribution%
	Overall	Eastern	Central	Western	East–Central	East–West	Central–West	Within	Between	Transvariation
2013	0.604	0.549	0.484	0.480	0.561	0.629	0.529	29.465	53.681	16.854
2014	0.544	0.497	0.392	0.434	0.485	0.585	0.475	28.564	54.230	17.206
2015	0.567	0.514	0.446	0.423	0.503	0.603	0.524	28.313	53.568	18.119
2016	0.535	0.487	0.399	0.428	0.469	0.571	0.501	28.244	52.983	18.772
2017	0.532	0.441	0.458	0.420	0.457	0.549	0.538	27.241	52.001	20.758
2018	0.539	0.464	0.406	0.467	0.456	0.575	0.528	27.566	54.760	17.675
2019	0.524	0.448	0.414	0.427	0.443	0.553	0.521	27.327	52.337	20.336
2020	0.518	0.443	0.397	0.437	0.432	0.552	0.514	20.079	52.610	27.312
2021	0.509	0.425	0.432	0.408	0.436	0.528	0.509	27.408	52.009	20.584
2022	0.503	0.413	0.401	0.421	0.420	0.533	0.495	27.078	55.409	17.512
2023	0.354	0.362	0.358	0.373	0.370	0.492	0.463	25.910	57.015	17.076

Distribution dynamics

Having established the magnitude and sources of disparities in grain crop breeding technological innovation, we proceed to characterize the distributional dynamics employing kernel density estimation and Markov chain analysis. This approach allows us to examine the evolution of the distribution at both national and regional levels, with particular emphasis on distributional patterns, evolutionary trends, and state transition regularities.

To characterize the distributional dynamics of grain crop breeding technological innovation for the nation as a whole and across the three major regions during the study period, we utilize MATLAB to generate three-dimensional kernel density curves (Fig. 1).

National-Level Patterns. According to Fig. 1(a), the main peak exhibits a rightward shift overall, with subtle fluctuations between 0.092 and 0.213 following a “rightward—leftward—rightward—leftward—rightward” trajectory. This pattern indicates an upward trend in grain crop breeding technological innovation amidst fluctuations. Regarding peak morphology, the height decreases while the width increases over the study period, suggesting progressive dispersion of innovation values and intensifying internal heterogeneity. From the perspective of polarization, the gradual disappearance of side peaks indicates diminishing gradient effects and multipolar differentiation. The right-skewed tail further reveals persistent regional disparities and a tendency for medium-low value regions to converge toward high-value regions.

Major Grain-Producing Areas. The main peak for major grain-producing areas shifts between 0.180 and 0.242, following a “rightward—leftward—rightward—leftward—rightward” pattern (Fig. 1(b)). The overall rightward trajectory confirms an upward trend in innovation levels, albeit with fluctuations. Peak morphology transitions from “sharp and narrow” to “flat and broad,” signaling increased intra-regional dispersion, enhanced heterogeneity, and rising inequality. Polarization dynamics show the number of side peaks declining from two to one, indicating persistent gradient effects and multipolar differentiation. The right-skewed tail similarly suggests substantial regional disparities and potential leapfrogging of medium-low value regions toward high-value regions.

Major Grain-Consuming Areas. The main peak shifts rightward between 0.110 and 0.283 (Fig. 1(c)), indicating an upward trend in grain crop breeding technological innovation. Peak morphology undergoes two cycles of narrowing and widening, with overall decreasing height and increasing width. The number of side peaks decreases from two to one, with declining side peak values overall, suggesting progressive dispersion, rising heterogeneity, yet persistent gradient effects and multipolar differentiation. Notably, Fig. 1(c) reveals a pronounced leftward shift in 2018, indicating a significant decline in technological innovation levels. Examination of the underlying data attributes this primarily to reduced patent counts that year. Further investigation of provincial-level data from the National Bureau of Statistics reveals that the growth rate of domestic invention patent applications and authorizations slowed across provinces in 2018, with some provinces experiencing negative growth; for instance, Tianjin declined from 5,844 items in 2017 to 5,626 items in 2018. This decline likely reflects quality and efficiency improvement measures implemented by the China National Intellectual Property Administration, including special inspections of local patent application policies. As the patent decline disproportionately affected economically developed provinces, this phenomenon is distinctly observable only in the three-dimensional kernel density curves for major grain-consuming areas (Fig. 1(c)) and the eastern region (Fig. 1(e)).

Production-Consumption Balance Areas. The main peak value range fluctuates between 0.043 and 0.079, exhibiting an overall rightward shift following a “rightward—leftward—rightward” trajectory (Fig. 1(d)). Peak morphology gradually becomes wider and flatter, with declining number and height of small side peaks. These patterns indicate a weak overall upward trend in grain crop breeding technological innovation, accompanied by progressive dispersion of values, enhanced heterogeneity, and gradually diminishing polarization.

Regional Comparison. The eastern region primarily comprises provinces from major grain-consuming areas, the central region mainly consists of provinces from major grain-producing areas, and the western region predominantly contains provinces from production-consumption balance areas. Consequently, their respective three-dimensional kernel density curves and evolutionary trends exhibit corresponding similarities, which we do not elaborate upon here.

Discussion of time evolution

Moran’s I Index

This paper employs Moran’s I index to measure the spatial autocorrelation among 31 provinces. The spatial weight matrix is constructed based on the geographic distances among the 31 provinces. Specifically, the latitude and longitude data of the 31 provinces are utilized to calculate the Euclidean distances between them, and the inverse of the squared geographic distance is adopted as the weight matrix.

The results in Table 5 show that, except for the year 2013, Moran’s I indices for all other years pass the significance test. Moreover, the coefficients for all years are positive with absolute values close to 1, indicating that there exists significant positive spatial correlation in China’s grain crop breeding science and technology innovation level. Against the backdrop of the Seed Industry Revitalization Strategy and coordinated regional agricultural development, the cross-regional linkages of germplasm resources, breeding talents, and R&D technologies among various regions have become increasingly close, providing a realistic foundation for the spatial flow and spillover of innovation factors in grain crop breeding. Consequently, provincial-level grain crop breeding technological innovation exhibits significant spatial autocorrelation characteristics and geographically associated patterns.

Table 5.

Global Moran’s I Index of Technological Innovation Level in Grain Crop Breeding in China, 2013–2023.

Year	I	E(I)	sd(I)	z	p-value*
2013	-0.052	-0.033	0.015	-1.256	0.105
2014	-0.073	-0.033	0.016	-2.510	0.006
2015	-0.061	-0.033	0.015	-1.767	0.039
2016	-0.069	-0.033	0.016	-2.294	0.011
2017	-0.073	-0.033	0.016	-2.459	0.007
2018	-0.069	-0.033	0.016	-2.310	0.010
2019	-0.074	-0.033	0.016	-2.546	0.005
2020	-0.077	-0.033	0.016	-2.680	0.004
2021	-0.073	-0.033	0.016	-2.453	0.007
2022	-0.069	-0.033	0.016	-2.180	0.015
2023	-0.082	-0.033	0.016	-2.974	0.000

Traditional Markov chain

We first examine state transition probabilities without incorporating spatial factors, employing the traditional Markov chain framework to characterize the evolution of grain crop breeding technological innovation in China. Table 6. presents the detailed transition probability estimates.

Table 6.

Traditional Markov transition probability matrix for food crop breeding technology innovation levels.

Time horizon (years)	Category	Low	Lower-middle	Upper-middle	High
1	Low	0.78	0.22	0.00	0.00
	Lower-middle	0.02	0.71	0.27	0.00
	Upper-middle	0.00	0.03	0.77	0.21
	High	0.00	0.00	0.02	0.98
2	Low	0.65	0.34	0.01	0.00
	Lower-middle	0.03	0.53	0.43	0.01
	Upper-middle	0.00	0.00	0.64	0.36
	High	0.00	0.00	0.02	0.98
3	Low	0.53	0.42	0.05	0.00
	Lower-middle	0.01	0.38	0.56	0.04
	Upper-middle	0.00	0.00	0.49	0.51
	High	0.00	0.00	0.00	1.00
4	Low	0.44	0.48	0.08	0.00
	Lower-middle	0.00	0.26	0.66	0.08
	Upper-middle	0.00	0.00	0.34	0.66
	High	0.00	0.00	0.00	1.00
5	Low	0.35	0.47	0.18	0.00
	Lower-middle	0.00	0.21	0.58	0.21
	Upper-middle	0.00	0.00	0.27	0.73
	High	0.00	0.00	0.00	1.00

Persistence Patterns by Initial State. For regions initially classified as low-level innovators, the probability of remaining in the low-level state declines substantially with horizon length: from 78% at the 1-year mark to 53% at year 3, and further to 35% by year 5. Medium-low and medium-high level regions exhibit similar, albeit less pronounced, persistence patterns. At the 1-year horizon, the stable transition probabilities are 71% for medium-low and 77% for medium-high level regions; these decline to 38% and 49%, respectively, at year 3, and further to 21% and 27% by year 5. In stark contrast, high-level regions maintain remarkably stable transition probabilities between 98% and 100% across all time horizons.

These patterns reveal a pronounced “Matthew Effect” in the evolutionary dynamics of grain crop breeding technological innovation. Over 1-, 3-, and 5-year horizons, both low-level and high-level regions exhibit higher state persistence probabilities than intermediate-level regions. This indicates that low-level regions have yet to establish convergence momentum toward high-level regions, while high-level regions develop a self-reinforcing “circular cumulative effect” that solidifies their leadership positions over time.

Upward Mobility Dynamics. Examining transitions to higher innovation levels, low-level regions show increasing advancement probabilities with horizon length: from 22% at year 1 to 42% at year 3, and 47% by year 5. Similarly, medium-low and medium-high level regions exhibit enhanced upward mobility over longer horizons. At the 1-year scale, the probabilities of jumping to higher levels are 27% for medium-low and 21% for medium-high regions; these increase to 56% and 51%, respectively, at year 3, and reach 58% and 73% by year 5.

However, a notable asymmetry emerges: the higher a region’s initial innovation level, the lower its probability of advancing further. This gradient suggests that while lower-level regions face fewer barriers to incremental improvement, high-performing regions encounter increasingly stringent constraints in maintaining their upward trajectory, despite their entrenched positional advantages.

Spatial Markov chain

To quantify the specific impacts of spatial dependence, we incorporate a geographic weight matrix to estimate spatial transition probabilities across different time horizons (Table 7).

Table 7.

Spatial Markov transition probability matrix for food crop breeding technology innovation levels (T = 1 and T = 5).

Category	Spatial lag status	T = 1				T = 5
		Low	Lower-middle	Upper-middle	High	Low	Lower-middle	Upper-middle	High
Low	Low	0.90	0.10	0.00	0.00	0.58	0.32	0.11	0.00
	Lower-middle	0.00	0.83	0.17	0.00	0.00	0.33	0.67	0.00
	Upper-middle	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
	High	0.00	0.00	0.00	1.00	0.00	0.00	0.00	1.00
Lower-middle	Low	0.81	0.19	0.00	0.00	0.39	0.45	0.16	0.00
	Lower-middle	0.03	0.73	0.23	0.00	0.00	0.16	0.68	0.16
	Upper-middle	0.00	0.06	0.83	0.11	0.00	0.00	0.25	0.75
	High	0.00	0.00	0.00	1.00	0.00	0.00	0.00	1.00
Upper-middle	Low	0.70	0.30	0.00	0.00	0.00	0.64	0.36	0.00
	Lower-middle	0.00	0.62	0.38	0.00	0.00	0.06	0.53	0.41
	Upper-middle	0.00	0.03	0.80	0.17	0.00	0.00	0.12	0.88
	High	0.00	0.00	0.03	0.97	0.00	0.00	0.00	1.00
High	Low	0.40	0.60	0.00	0.00	0.25	0.75	0.00	0.00
	Lower-middle	0.06	0.78	0.17	0.00	0.00	1.00	0.00	0.00
	Upper-middle	0.00	0.00	0.68	0.32	0.00	0.00	0.50	0.50
	High	0.00	0.00	0.00	1.00	0.00	0.00	0.00	1.00

Spatial Spillover Effects on Low-Level Regions. The transition dynamics of low-level regions exhibit substantial sensitivity to neighborhood composition. When surrounded by other low-level regions, the probability of remaining in the low-level state is 90% at the 1-year horizon, declining significantly to 58% by year 5. If neighboring regions are at medium-low levels, the persistence probability drops from 81% at year 1 to 39% at year 5. More strikingly, when adjacent to medium-high or high-level neighbors, the 1-year persistence probabilities fall to 70% and 40%, respectively; by year 5, these decline further to 0% and 25%.

These patterns demonstrate that spatial factors profoundly shape the evolution of regional technological innovation in grain crop breeding. Low-level regions surrounded by similarly low-performing areas face considerable barriers to innovation advancement, whereas proximity to high-level regions substantially increases upward mobility probabilities. Moreover, this spatial spillover effect intensifies as the time horizon extends.

Robustness of High-Level Regions and Path Dependence. Two additional findings emerge from Table 6. First, at the 1-year horizon, diagonal elements remain dominant regardless of neighborhood composition, consistent with the traditional Markov chain results. This confirms that short-term dynamics are governed by strong path dependence, making it difficult to break existing technological innovation trajectories in grain crop breeding. Second, high-level regions exhibit remarkable robustness: across all neighborhood configurations and time horizons, the probability of maintaining their high-level state never falls below 97%. In contrast, low-level regions display substantially greater sensitivity to spatial spillover effects from neighboring areas.

Discussion

Comparison with existing literature

Our findings both corroborate and extend the literature on agricultural innovation and regional development. Consistent with Huang and Xiang’s analysis of regional innovation capability⁵⁴, we document that innovation capabilities concentrate in regions with dense research institutions and enterprises, particularly Beijing and Jiangsu. However, our innovation chain framework reveals that variety development rather than basic research constitutes the primary weight in China’s current evaluation system, suggesting a policy shift toward commercialization outcomes.

The spatial patterns we identify align with Zhang et al.‘s findings on innovation chain spatial structures⁵⁵, yet our dynamic analysis reveals stronger path dependence than previously recognized. While existing literature acknowledges regional disparities⁵⁶, our decomposition demonstrates that inter-regional differences account for over three-quarters of total inequality—substantially exceeding estimates from traditional Theil index approaches⁵⁷. This discrepancy stems from the Dagum Gini coefficient’s superior handling of distribution overlap, confirming Liu et al.‘s methodological recommendations⁵⁸.

The spatial spillover effects we document extend Wang et al.‘s findings on spatial correlation networks in agricultural science and technology innovation by quantifying the temporal evolutionary characteristics of network connectivity, association scope, hierarchical structure, and stability⁵⁹. Our estimate that proximity to high-level regions increases upward mobility probabilities by 15–30% points provides the first empirical benchmark for the magnitude of spatial externalities in agricultural innovation systems. The “siphon-lock” mechanism we identify in high-level regions parallels findings from urban economics on innovation poles, yet our Markov framework reveals a temporal intensification absent from static analyses. The complete immobility of low-level regions surrounded by low-level neighbors—evidenced by zero transition probabilities—exceeds typical estimates of poverty traps in the regional development literature, suggesting distinctive barriers within agricultural innovation systems.

Theoretical interpretation

The observed Matthew effects and club convergence patterns align with cumulative causation theory⁶⁰. High-level regions benefit from agglomeration economies: research infrastructure attracts talent, which generates outputs that attract further investment, thereby creating self-reinforcing cycles. The 100% stability probability for high-level regions under spatial correlation indicates institutional and network effects that transcend individual organizational performance, consistent with the innovation systems literature on collective efficiency⁶¹.

The spatial spillover asymmetry—wherein high-level neighbors enhance mobility while low-level neighbors create traps—reflects absorptive capacity constraints⁶². Intermediate regions can exploit proximity to leaders because they possess sufficient capability to interpret and adapt external knowledge. In contrast, low-level regions lack this foundational capacity, rendering geographic proximity alone insufficient for technology diffusion. This finding supports Hu et al.‘s original conception of innovation chains as requiring minimum capability thresholds for effective operation⁶³.

Policy implications

These findings yield several policy implications for enhancing national food security governance capacity. First, the dominance of inter-regional differences suggests that spatial reallocation of innovation resources may prove more effective than uniform national programs. Targeted investments in intermediate regions exhibiting high spillover potential—specifically those adjacent to current leaders—could maximize marginal returns.

Second, the “siphon-lock” mechanism indicates that direct support for low-level regions may remain insufficient without concomitant attention to absorptive capacity constraints. Policy packages should therefore combine infrastructure investment with human capital development and institutional linkages to enable effective exploitation of geographic proximity advantages.

Third, the innovation chain imbalance toward variety development and away from market application suggests a need for demand-side policies. Procurement mechanisms, variety adoption subsidies, and strengthened farmer-extension linkages could reinforce the market application stage, thereby improving overall chain efficiency.

Fourth, the temporal intensification of spatial effects implies that short-term evaluation may underestimate program impacts. Policy assessment horizons should extend to 5–10 years to capture the full benefits of spatial spillovers.

Limitations

This study has several limitations. First, although comprehensive, the innovation chain framework may not capture all relevant dimensions of breeding innovation. Emerging areas such as gene editing and digital breeding are imperfectly reflected in traditional paper, patent, and variety indicators. Future research should incorporate novel metrics for biotechnological innovation.

Second, the spatial weight matrix employs geographic proximity, potentially overlooking functional connections through collaboration networks or supply chains. Alternative specifications using research collaboration or seed trade flows might reveal distinct spillover patterns.

Third, the analysis period ends in 2023, potentially missing recent impacts of accelerated biotechnology commercialization policies. The full effects of the 2021 Seed Industry Revitalization Action Plan may require longer observation periods.

Fourth, provincial-level aggregation masks within-province heterogeneity, particularly in large provinces with multiple innovation centers. Sub-provincial analysis could reveal important micro-dynamics.

Finally, the Markov approach requires discrete state classification that necessarily simplifies continuous innovation gradations. Alternative methods such as continuous state space models could usefully complement our findings.

Conclusions and recommendations

Conclusions

This study employs an entropy weight model to quantify food crop breeding technology innovation levels across 31 Chinese provinces over the period 2013–2023, integrates the Dagum Gini coefficient and kernel density estimation to characterize regional disparities and distributional dynamics, and examines state transition processes using traditional and spatial Markov chain models. Our analysis yields four principal findings.

First, the spatial pattern of food crop breeding innovation is expanding along an “eastern coastal–central” axis with intensifying internal heterogeneity. Innovation levels exhibit upward trends amidst fluctuations, with main sales areas maintaining leadership positions while main production areas demonstrate the strongest catch-up momentum. The national distribution shows increasing dispersion with gradually diminishing polarization, suggesting consolidation of innovation leadership among a shrinking set of leading provinces.

Second, spatial autocorrelation and “club convergence” effects reinforce regional differentiation, impeding upward mobility in intermediate and low-level regions. The global pattern exhibits significant spatial agglomeration characterized by “high-high” and “low-low” clustering. Regional differences account for 76% of total inequality, with inter-regional gaps constituting the primary source. Markov analysis reveals high stability in high-level regions (98–100% maintenance probability) and severe mobility constraints in low-level regions, resulting in solidified hierarchical structures.

Third, spatial spillover effects are significant, asymmetric, and time-intensifying. Proximity to high-level regions enhances upward mobility probabilities by 15–30% points, with effects strengthening substantially over 5-year horizons. Low-level regions surrounded by low-level neighbors face complete mobility barriers (zero transition probability), whereas intermediate regions can exploit proximity advantages. The “siphon-lock” mechanism in high-level regions creates development ceilings for competing regions.

Fourth, the root cause of regional disparities lies in innovation chain imbalances and absorptive capacity constraints. Excessive emphasis on variety development relative to market application generates structural inefficiencies. Low-level regions lack the capability foundations to exploit geographic proximity, rendering spatial spillovers ineffective in the absence of complementary human capital and institutional development.

Recommendations

Based on these findings, we propose the following policy recommendations.

First, implement differentiated regional governance frameworks with categorized policies to resolve structural contradictions. For main production areas exhibiting strong growth momentum (e.g., Henan, Shandong), establish “breeding innovation capacity compensation” mechanisms that link fiscal transfers to grain export volumes and innovation output growth. For main sales areas with high innovation levels but declining relative growth (e.g., Beijing, Jiangsu), mandate technology diffusion obligations through collaborative platforms with lagging regions. For balanced areas characterized by high internal heterogeneity, prioritize infrastructure investment in sub-regional innovation hubs (e.g., Chengdu, Xi’an) to create localized spillover centers.

Second, construct three-dimensional collaborative networks to activate spatial spillover effects. For the knowledge dimension, establish inter-provincial research consortiums linking high-level regions with adjacent intermediate regions, incorporating joint funding requirements and shared intellectual property arrangements. For the talent dimension, implement “innovation envoy” programs rotating researchers from leading institutions to provincial academies of agricultural sciences. For the digital dimension, develop integrated platforms connecting breeding databases, variety testing networks, and farmer feedback systems across regional boundaries.

Third, create ladder-style policy tools to break barriers to “club convergence.” In high-level regions, pilot “innovation responsibility zones” requiring leading provinces to achieve specific technology transfer metrics to designated partner regions. In intermediate regions, promote “chain integration” models combining local breeding objectives with market demand from high-level regions, such as Henan-Jiangsu collaborations on specialized rice varieties. In low-level regions, launch “enclave agriculture” initiatives enabling remote participation in innovation chains through virtual breeding platforms and decentralized testing networks.

Fourth, rebalance innovation chain incentives to strengthen market application linkages. Reform evaluation systems to increase weight on yield improvement and farmer adoption metrics. Establish “variety commercialization funds” providing stage-gate financing for promising varieties from regional testing to farmer deployment. Create demand-pull mechanisms through procurement preferences for varieties demonstrating proven productivity gains in target agro-ecological zones.

Fifth, extend policy evaluation horizons to capture spatial spillover dynamics. Design innovation programs with minimum 10-year implementation periods and corresponding evaluation frameworks. Incorporate spatial spillover metrics into regional performance assessments, recognizing contributions to adjacent region advancement alongside local output measures.

Author contributions

All the authors contribute the study conception and design. J.S. performend the date collection, statistical analysis, and initial material preparation. The manuscript was wrritten and edited by B.C. All the authors read and approved the final manuscript.

Funding

We are grateful for the financial support provided by the National Social Science Foundation of China (Grant No. 24BGL185) and the Key R&D Program (Soft Science) of Shandong Province (Grant No. 2025RZB0602).

Data availability

The data that support the findings of this study will be openly available after publication of the manuscript. If needed, please contact the corresponding author.

Declarations

Competing interests

The authors declare no competing interests.