The relationship between interdisciplinarity and citation impact—a novel perspective on citation accumulation

The study addresses how interdisciplinarity influences the dynamic accumulation of citations for scientific papers. Motivated by mixed findings on whether interdisciplinary research (IDR) yields higher citation impact, the paper explores this relationship by focusing on the citation accumulation process rather than static citation counts. It poses two research questions: (1) What are the differences between Rao-Stirling diversity (RS) and Diversity (DIV) in measuring interdisciplinarity? (2) How does interdisciplinarity influence the citation accumulation process in Chemistry? The context emphasizes the growing importance of IDR for tackling complex problems, widespread use of bibliometric databases to quantify interdisciplinarity, and the crucial role of citation windows in interpreting IDR’s impact. The purpose is to clarify contradictory prior results by examining when papers peak in citations (PEAK_YEAR) and how sustainable citations are after the peak (SUS), thereby informing evaluation practices for IDR.

Prior research shows heterogeneous relationships between interdisciplinarity and citation impact. Several studies report positive associations: higher-IDR work tends to receive more citations (Levitt and Thelwall, 2008; Okamura, 2019; Wang et al., 2015), interdisciplinary teams deliver higher scientific gains (Abramo et al., 2017), and atypical combinations correlate with higher impact (Schilling and Green, 2011; Uzzi et al., 2013). Integrated indicators like Rao-Stirling and Leinster-Cobbold diversity have been linked to positive citation effects (Chen et al., 2022), and societal impact can be broader for more interdisciplinary publications (Zhang et al., 2021). However, null or negative relationships also appear: UK IDR sometimes shows lower citation rates (Elsevier, 2015); mono-disciplinary publications can receive more citations than multidisciplinary ones in certain domains (Levitt and Thelwall, 2008); and disadvantages for IDR have been observed in peer review and funding (Lyall et al., 2013; Woelert and Millar, 2013; Bromham et al., 2016; Nicholson and Ioannidis, 2012). At the individual level, IDR can initially depress citations but improve long-term performance (Sun et al., 2021). Importantly, citation window choice is pivotal: shorter windows (e.g., 3 years) can mask delayed recognition, while longer windows (e.g., 13 years) may reveal advantages for variety and disparity dimensions (Wang et al., 2015) and for diverse referencing (van Noorden, 2015). Chen et al. (2022) reviewed IDR studies’ varied citation windows (3–15 years) and noted that effects can depend on the chosen interdisciplinarity metric. The present paper contributes by analyzing citation accumulation dynamics over 10 years in Chemistry across different IDR levels.

Design: Quantitative bibliometric study of Chemistry papers examining how interdisciplinarity (RS, DIV) relates to citation accumulation dynamics characterized by PEAK_YEAR and citation sustainability (SUS). Data: Clarivate Web of Science Core Collection, seven Chemistry WoS Categories: Chemistry, Analytical; Chemistry, Inorganic & Nuclear; Chemistry, Applied; Chemistry, Medicinal; Chemistry, Physical; Chemistry, Organic; Chemistry, Multidisciplinary. Publication years 2009–2011; document types Article and Review; at least one author affiliated with China or the USA. Exclusions: >20 authors; <10 matched references. Final dataset: 148,123 papers (China 79,954; USA 71,768). References matched to Journal Citation Reports (JCR) sources and mapped to WoS Categories; 90.1% of 6,074,052 references matched to WoS-indexed journals. Citation data: Annual citations by year; citation percentiles from Clarivate InCites to identify globally top-5% highly cited papers within field and document type. Interdisciplinarity metrics: - Rao-Stirling diversity (RS): RS = Σ_i Σ_j p_i p_j d_ij, where p_i is the reference share in category i and d_ij is 1 minus co-citation similarity between categories i and j (from 2015 WoS co-citation data). Captures variety, balance, and disparity in principle, though criticized for insufficiently separating dimensions. - Diversity (DIV) (Leydesdorff): integrates relative variety (n/N), balance (Gini coefficient based on references per category), and disparity. Computed using the 2015 JCR category system. Categorization: Papers sorted into deciles separately by RS (rs1–rs10) and by DIV (div1–div10) to compare citation curves and top-5% “hit” rates across citation windows. Dependent variables: - PEAK_YEAR: the year (1–10 since publication) of maximum annual citations. - SUS (citation sustainability): SUS = (10 − PEAK_YEAR) × (C10 / C_peak), where C_peak is the maximum annual citations within 10 years and C10 citations in year 10. Higher SUS indicates slower post-peak decay. For SUS regressions, included only papers peaking within 6 years to ensure at least 4 years of observed decline. Statistical analysis: OLS regressions for PEAK_YEAR and SUS. Key independent variables: RS (and RS^2), square root of DIV (and its square when relevant). Controls: review (dummy), open access (dummy), international collaboration (dummy), ln(number of authors), ln(number of references), publication year dummies, subfield dummies; for SUS models also included peak-year dummies. Analyses performed on the full sample and on the globally top-5% highly cited subset.

Descriptives (Table 1): PEAK_YEAR mean 4.43 (SD 2.27); C_peak mean 8.48; C10 mean 3.96; SUS mean 0.548; RS mean 0.305; sqrt(DIV) mean 0.111; globally top-5% share 9.6%. Citation curves: - Across both RS and DIV deciles, higher interdisciplinarity is associated with higher average annual citations. - RS deciles: peak generally in year 3–4; decline rates similar across groups; magnitude differs more than shape. - DIV deciles: higher DIV groups (e.g., div10) show delayed peaks and flatter tails. Example: in year 10, div10 averages 5.76 citations per paper, 95.7% of its year-3 peak; div1 averages 2.73, 50.7% of its year-3 peak—indicating greater long-term sustainability at higher DIV. Hit-rate heatmaps: - By DIV (Fig. 4): For low DIV (div1–div3), hit rates decrease with longer windows (short-term advantage). For mid DIV (div4–div5), hit rates stable across 3–10 years. For high DIV (div6–div10), hit rates increase with longer windows (delayed recognition). Overall, higher DIV tends to higher hit rates across windows, except the lowest group. - By RS (Fig. 5): Hit rates increase with both RS category and citation window length; RS appears less tied to curve shape and more to overall level. PEAK_YEAR regressions (Table 2): - Full sample: RS shows a U-shaped association with peak year (RS coef −4.720; RS^2 8.266; turning point ≈ RS 0.286): very low and very high RS papers peak later; mid-RS peak earlier. DIV positively associated with peak year (DIV 11.937; DIV^2 −14.527, with the peak beyond the observed range), indicating higher DIV leads to later peaks. - Top-5% subset: DIV positively associated with later peaks; RS negatively associated with peak year (greater RS linked to earlier peaks among highly cited papers). Controls: reviews and international collaboration associated with later peaks; open access linked to later peaks in full sample; larger teams and more references generally reach peaks earlier. SUS regressions (Table 3): - Full sample: RS positively related to SUS with acceleration at higher RS (RS −0.129; RS^2 0.777, net positive over most observed range). DIV strongly positively associated with SUS (coef 0.360). - Top-5% subset: RS positively associated with SUS (0.101). DIV positive with SUS (1.247) with a small negative quadratic (−2.241), but over 99% of observed DIV values lie in the increasing region. Interpretation: Higher interdisciplinarity (by RS or DIV) is associated with more sustainable citations post-peak (higher SUS). DIV is more sensitive to citation window length and aligns more closely with novelty, showing delayed peaks and slower decay at higher values. These dynamics help explain mixed prior findings: short windows can understate the impact of high-IDR work, while longer windows reveal advantages.

The findings address the research questions by clarifying differences between RS and DIV and by demonstrating how interdisciplinarity shapes citation accumulation. RS correlates more with the level of cumulative citations and, in the full sample, exhibits a U-shaped relation with time to peak; among highly cited papers, higher RS corresponds to earlier peaks. DIV, in contrast, tracks novelty-related features: higher DIV consistently delays the citation peak and enhances long-term sustainability. This distinction explains why short citation windows can produce null or negative associations between interdisciplinarity and impact: high-DIV research requires more time for recognition. Consequently, evaluation practices that rely on short windows may disadvantage interdisciplinary and novel works. These results reinforce the delayed recognition hypothesis for IDR and underscore the importance of aligning citation windows with the temporal dynamics characteristic of interdisciplinary contributions.

The study contributes a dynamic perspective on how interdisciplinarity relates to citation impact in Chemistry (2009–2011). Key contributions: - Demonstrates that both RS and DIV are positively associated with long-term citation sustainability (SUS), but DIV more strongly captures delayed recognition and sustained impact, indicating greater sensitivity to citation window length and closer alignment with novelty. - Shows RS’s U-shaped relationship with time to peak in the full sample and a negative association with time to peak among highly cited papers, whereas DIV is generally positively associated with later peaks. - Highlights that higher interdisciplinarity leads to delayed recognition but ultimately greater and more durable impact, particularly evident under longer citation windows. Practical recommendations: - Carefully select citation windows when assessing IDR; longer windows should be used as alternatives or supplements to short-term metrics, especially for evaluating high-interdisciplinarity papers, centers, and projects. Future research directions: - Expand beyond China/US and Chemistry to additional countries and disciplines. - Test robustness under alternative field classification systems and granularities. - Extend citation windows beyond 10 years and incorporate additional dynamic indicators (e.g., residual citations, citation bursts, citation speed/decay).

• Scope limited to two countries (China and USA) within Chemistry; findings may not generalize to other countries or disciplines, especially those with higher inherent interdisciplinarity. - Dependence on integrated interdisciplinarity metrics (RS and DIV) that rely on WoS Categories and distances; results may vary with changes in classification granularity or structure. - Focus on two accumulation descriptors (PEAK_YEAR and SUS) and a 10-year window for computational tractability; other dynamic indicators and longer windows could yield further insights.