Research universities form the backbone of regional innovation systems

The U.S. state is a regional scale that aligns with the governance, funding and related agenda of state governments. At this scale, research institutions operate under policies shaped by regional agencies that coordinate funding and resource distribution to address region-specific challenges – such as wildfire, illicit wildlife trade, invasive species, and deforestation [43–45] – by promoting collaborative solutions, and fostering a more integrated approach to regional development and innovation.

Accordingly, we analyze the composition and structure of multi-institutional collaboration within and between two prominent US states – California and Texas – building on the tradition of two-region models in economic geography that serve as a foundation for studying more complex multi-region systems [19]. Notably, CA and TX represent geographically and politically distinct RIS within the US innovation system, each featuring extensive RU ecosystems that generate a sizable high-skilled workforce and attract investments into specialized R&D infrastructure that are critical to state and national research agendas.

Despite their strength, these innovation systems remain sensitive to disruptions at multiple scales – ranging from institutional changes (e.g., entry, exit, or mergers [46]) to large-scale macroeconomic shocks [47]. To investigate this sensitivity, we exploit the 2007-08 financial crisis to examine how the institutional ecosystem structure responds to external resource shock. This case-event analysis sheds light on how structural changes influence research outcomes, offering insights into the structure–function dynamics of innovation system.

In order to measure and evaluate the persistence of research co-production within and between innovation systems over time, we selected the most prominent research-oriented institutions within each state. As such, a principal component of our institutional sample are the research-oriented multi-campus university systems (MUS) in each state: the University of California (UC) system comprised of 10 distinct institutions (or ‘campuses’), and the University of Texas (UT) system comprised of 12 institutions (7 traditional university campuses offering multi-disciplinary graduate education, and 5 specialized health science centers). We complement these MUS institutions with six prominent private universities that form a non-MUS comparison group – see Fig 1A. Due to the labor intensive collection of disambiguated institutional profiles from our primary data source, the Clarivate Analytics Web of Science Core Collection (WOS), we focus on the largest single MUS along with the three most prominent private universities in each RIS. Together the 28 select institutions in our sample are affiliated with roughly 3 million distinct WOS publications – see Fig 1B – alltogether accounting for >5% of all publications indexed by WOS over our focal sample period.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 1. Framework for evaluating RIS according to the integration of research university ecosystems.

(A) Geographic distribution of universities and health science centers belonging to the University of California (UC) and University of Texas (UT) systems, along with the three most prominent private research universities within CA and TX (approximate locations to avoid overlaps). The outline of each state administrative boundary was generating using public-domain U.S. Census Bureau TIGER shape files from https://catalog.data.gov/. (B) Research output N_s(t) of six university subgroups. UC_N are the 5 UC campuses located in the greater Bay Area mega-region: the exponential growth rate over the 21-year period shown is ; UC_S are the UC campuses located in southern California: . PU_CA represents Stanford, USC and Caltech combined: g_PU,CA = 0.046(1). UT_A denotes the 7 UT campuses: ; and UT_H denotes the 5 UT health science centers: . PU_TX represents Rice, SMU and Baylor combined: g_PU,TX = 0.060(2). For each g value reported, the digit in parenthesis is the standard error in the last digit shown. (C) Base rate of multi-university research co-production, for three non-overlapping university subgroups and all 28 universities considered together. Distinct levels observed for UC + PU_CA and reflect different degrees of co-production (dashed lines indicate mean values), and show that CA features higher levels of RIS integration than TX. (D) Universities ranked according to the total number of research articles N_i co-produced by scholars at each university i over 2000-2020. As an indicator of regional embeddedness, each data point is colored according to the fraction of the N_i articles that involved multi-university collaboration within its RIS (home state); the mean and standard deviation across these RU are .

https://doi.org/10.1371/journal.pcsy.0000088.g001

A configurational perspective on university ecosystems

According to evolutionary principles applied to organizational and industrial dynamics, the knowledge economy can be understood as a dynamic system in which organizations and institutional environments co-evolve over time [48]. Drawing from Durham’s prescription of the model of evolutionary change [48,49], knowledge takes the role of the unit of transmission. Accordingly, we then consider institutional environments – encompassing (research and researcher) governance, culture, legacy, policy and norms – as endogenous sources of variation. Meanwhile, the localization of institutions to particular regions and cities generates sources of isolation that shape how knowledge develops and diffuses across space over time.

Given the multi-disciplinary composition of research universities, then the variation in institutional research area profiles within a given region is a fundamental determinant of its distinct configurational space – the set of all possible configurations of a system. At a more granular level, the configurational space reflects the various ways that subcomponents (such as researchers, research labs, specialized infrastructure, strategic industry partnerships, etc.) can be arranged and interact within the system.

In reality, we only observe the subset of realized ecosystem configurations that emerge as a result of constraints (financial, geographic, etc.) and related selection mechanisms. By analyzing the relative magnitude and persistence of realized institutional relationships and overall system structure, we are able to evaluate various dimensions of variation and selection – i.e., assortativity channels that promote research synergies that persist within and across the university ecosystem. From this perspective, the configurational space uniquely characterizes each university ecosystem and conditions the integration of regional innovation systems.

Yet the configurational space is also subject to principles of strategic design, which thereby confronts these institutions with the organizational innovator’s dilemma of whether to focus on existing institutional strengths or pursue new, cross-institutional opportunities. As a relevant scenario pertaining to multi-campus systems, consider a breakthrough research area or technological breakthrough such as quantum computing: should a MUS invest in a new research center at a particular campus, or should it develop a cross-cutting consortium that distributes critical investment resources more broadly across the system? To this end, the University of California established the Multicampus Research Programs and Initiatives (MRPI) as a dedicated funding mechanism designed to strategically channel financial resources towards system-level synergies.

Four assortativity channels that contribute to ecosystems structure

Conceptually, configurational entities that are more closely related tend to be more ‘proximal’ within the configuration space. From a configurational perspective, this principle means fewer and smaller changes are required to align one entity with another. This concept is generalizable across various domains, including cognitive, organizational, institutional, and geographical contexts [50–52]. Within the present context, assortativity channels refers to particular institution-level factors that generate different pathways for alignment, thereby fostering persistent research co-production between institutions. The following four channels reflect both latent and observable characteristics of research universities.

The 2007-08 global financial crisis: An exogenous shock to research production

The 2007-08 financial crisis extended globally, generating a significant shock to the international economy that lasted for several years. While not the principal focus of this study, it is worth describing the contextual backdrop behind the major socio-economic shock occurring during the focal period of our analysis and how it impacted academic research institutions, and why its signatures would be evident in our analysis.

The pervasiveness of the financial crisis strained academic institutions by triggering rapid and significant endowment losses at private universities [70,71]. While also true for public universities, they additionally faced severe state budget cuts that generated hiring freezes, furloughs and staff cuts, raised student-faculty ratios, and limited research capacity. Together, these sudden resource constraints generating funding allocation gaps can be expected to directly affect faculty research output, graduate student funding resources, and general morale.

A sudden shift toward fiscal austerity occurred across the US and Europe, marked by unexpected reductions in public and private R&D spending as well as cuts to educational expenditures [47,72]. At the same time, there was significant reduction to industrial research productivity as firms pivoted available resources away from basic research towards product development [73], likely mirroring adjustments within the academic sector. In the US, stimulus response measures like the American Recovery and Reinvestment Act (ARRA) provided temporary relief to mitigate the immediate effects of this shock [74–76]. Among academic institutions, labor markets proved particularly susceptible, with public universities experiencing sharper declines in new faculty hires and salary growth compared to private institutions [77]. Accordingly, in what follows we observe the response dynamics of this socio-economic shock and therefore examine how this socio-economic shock reshaped the institutional ecosystem, in particular regarding patterns of institutional stratification relating to homophily and prestige.

Related literature

A substantial body of research has mapped international collaboration and mobility networks, highlighting how the flow of human and intellectual capital across borders shapes the globalization of science [12,13,17,18,78–83]. However, accounting for variations in regional and institutional contexts poses significant challenges for studies conducted on a global scale.

To address this limitation, some studies downscale by aggregating counts at the level of national regions [9,13,14,38,53,84]. Here we further downscale the focal unit of analysis to the level of institutions, which aligns with a resource-based view on the relationship between institutional environment and scientific productivity [57,85]. Another motivation for focusing on regional ecosystems is to support the literature developing diagnostic and place-based policy guidance for seeding and incubating innovation hubs, which often develop and evolve around universities that draw investment into specialized facilities and equipment [3,4,8,10,20,25,38,39,86]. A relevant study on patent co-production found that higher levels of regional integration, measured by the size of the largest network component, played a crucial role in driving the development of innovation hubs in Silicon Valley and Boston in the 1990s [87]. Against this backdrop, our work contributes to the longstanding economics and science policy literature on research universities [22,29–33,86] and university systems [8,24,25] as potent vehicles for direct investment.

Mapping institutional interactions reveals key insights into the organizational ecology of complex systems tasked with collective problem-solving [8,22,88]. In particular, our analysis contributes to the literature on social homophily, whereby shared backgrounds, attributes, values, and experiences promotes the formation of lasting in-group propensities [67] that can be readily quantified using network metrics, such as the assortativity coefficient and the clustering coefficient [41,89,90]. Homophily is particularly relevant in the academic context, where educational pedigree is widely emphasized. For example, scholars find that sharing common educational histories is an important factor supporting entrepreneurial team formation [91], and that institutional homophily is a key factor driving the digital media co-visibility of research institutions [66]. Extending to other sectors, another study found that non-governmental organizations are more likely to develop partnerships with peers sharing common funding sources and common consultative agreements with intergovernmental organizations [92]

In addition to institutional-specific factors, multi-university (XU) research co-production is also sensitive to exogenous economic shocks. In particular, the 2007-08 financial crisis generated a sudden decline in public funding for research and development (R&D) that extended from the national to regional scale, which translated into significant university budget reductions. One particularly relevant study of R&D appropriations in Spain before and after the global crisis showed that the adverse effects of the crisis extended well into the early 2010s [47]. Interestingly, we observe a rapid reaction to the crisis at the regional level, with XU research among TX health science centers (UT_H) exhibiting a sudden burst during the 2007-08 financial crisis, indicative of within-MUS resource-sharing during this period of resource constraints. Contrariwise, rates of XU research observed among all 28 universities exhibited a downturn during the same period, indicative of the sensitivity of across-region activity to heightened financial constraints and uncertainty – see Fig 1C.

Our focus on institutional networks at the regional scale complements prior work analyzing multi-university collaboration at the global scale. In particular, in their seminal study on XU research over the period 1975-2005, Jones et al. [55] found that multi-university collaborations tend to occur between scholars at prestigious universities; they also found that roughly 90% of multi-university collaborations involve just 2 distinct universities, which supports our choice of a pairwise measure of research co-production developed in what follows. Another perspective focusing on the global scale analyzes the increasing prevalence of multi-national collaborations [42,78,79]. A recent study found that research produced by scholar extending across 2-4 countries to be the largest growth mode, which accounted for roughly 17% of research in 2010, whereas mono-national research accounted for roughly 80% [81].

Data collection

We collected 2,965,198 records published between 1970-2020 from the Clarivate Analytics Core Collection (WOS) using their in-house institutional disambiguation tool to identify publications with at least one author from a particular campus. Exploiting the WOS “Affiliation Index” (available only within the WOS web portal search interface) specifically addresses limitations in the availability and consistency of the C1 “Author Address” WOS field tag in the raw data, which we found to be largely void prior to 1997 in our downloaded data records. The publication counts and metrics used in our analysis reflect the same journal selection process as WOS, which periodically reviews and updates its journal coverage to maintain a focus on high-quality, reputable sources.

Why not extend beyond these 28 RU? Due to limited access to the WOS database, we manually collected data through their web portal, which restricts downloads to 500 publications at a time. These constraints are the primary reason for limiting our sample to 28 RUs, selected to represent the most prominent institutions in each state, which together represent roughly 5% of global research indexed in the entire WOS database, and 10% of US research. While there are numerous RU and other research-generating institutions in each state that were not included in our representation of each RIS, these 28 institutions represent the majority of research produced in each state – i.e., 70% of all publications produced by CA, with the largest excluded institution being San Diego State; and 55% in the case of TX, with the largest excluded institution being Texas A&M Univ. at College Station.

While our analysis is restricted to these two states, this focused approach provides a practical foundation for extending to more regions, as in the tradition of extending two-region to multi-region spatial models [19]. Extending to other regions would need to account for the variable levels of institutional concentration that occur, especially in large megacities globally. Another institutional dimension that would need to be accounted for is the nature and extent of satellite campuses that are increasingly prevalent, as in the case of New York University (NYU) Abu Dhabi and NYU Shanghai.

As this institutional sample includes the most prominent research producers in each region, it also captures the most prominent sources of co-production in each region. In terms of the connectivity generated by these institutions, we find that roughly ∼6% of the articles feature two or more universities from our sample – see S2 Fig. For a base rate comparison, our companion study analyzing the brand co-visibility among the same set of institutions across a comprehensive collection of 2 million digital media articles published between 2000-2020 identifies ∼10% of the articles featuring two or more institutions [66].

Quantifying the intensity of institutional research co-production

As a proxy for regional integration, we analyze the principal mode of institution-specific knowledge (co-)production, which is peer-reviewed scientific research. While patents, grants and other formal multi-institutional agreements and products may offer complementary information that enhances the representation of innovative activities in a particular region, their metadata are less available in standardized formats that extend across substantial time periods on the order of decades. Moreover, in the particular case of patents, federal grants and other forms of joint R&D contracts, the research teams and thus the number of distinct assignee institutions tend to be much smaller than in the domain of academic publication [93], which would limit the resolvability of persistent multi-institutional relationships and their cofactors. Hence, in this study we exploit the consistent data generated by research scholars that constitute the principal data source in the science of science [34].

Regarding the generating mechanisms contributing to institutional co-production, there are two principal contributions: collaboration by scholars at two distinct institutions; and individual scholars with multiple affiliations. Recent analysis has identified an increasing prevalence of the latter multi-affiliation mode, rising to roughly 16% of authors in 2019, on average, albeit with substantial national and disciplinary variation [94,95]. While we do not distinguish between the two mechanisms, as we are focused on the institutional layer of science, we expect that the number of individual scholars with multiple affiliations at the particular set of institutions we analyzed to make a marginal contribution to the overall rate of institutional co-production relative to the mechanism of distinct scholars collaborating across institutional boundaries. Indeed, additional analysis is merited to analyze the relative contributions of these two author-level mechanisms to measures of institutional co-production.

To facilitate accounting for both institutional attributes (MUS membership, research specialization, and prestige) and relational attributes (spatial proximity and research area alignment), we adopt a pairwise (dyadic) representation of the institutional ecosystem. We test the fidelity of this representation by tabulating the frequency of research articles featuring N_c individual MUS campuses – see S2 Fig. for the frequency distribution P(N_c). Results indicate that the vast majority of multi-university publications feature N_c = 2 MUS campuses, consistent with prior work extending across a larger sample of universities [55].

We quantify the intensity of research co-produced by universities i and j in a given time period t by way of the Jaccard similarity index,

(1)

where the quantity N_i,t is the total number of publications by i in a given period t, and N_ij,t is the number of publications featuring authors from both i and j during the same period. J_ij measures the intersection over union of the two publication sets, corresponding to the fraction of the total possible research articles that were co-produced by those two entities.

This quantity is preferred over N_ij for the following reasons. By construction, J_ij,t is intensive (a fraction), and so its distribution is more stationary than the distribution of N_ij,t, which is instead an extensive quantity that is systematically biased by the persistent exponential growth of scientific publication output [96] – see Fig 1B. Thus, J_ij,t supports analyzing relationships that persist and develop in excess of baseline secular growth patterns. At the same time, the denominator of J_ij explicitly controls for the wide variation in publication volume N_i across institutions – see Fig 1D. In the same way that traditional gravity model approaches control for the size of the units as explicit cofactors [5,7]), in what follows this cofactor (i.e., N_i) is implicitly incorporated into our dependent variable definition. Together, this dependent variable standardization accommodates cross-temporal regression analysis spanning multiple decades.

The Jaccard index is a valid proxy of intersection when the sample sizes N_i and N_j are sufficiently large, a condition that applies to most statistical metrics. Otherwise, the Jaccard index can be biased by the minimum-bound inequality , which generates relatively small J_ij,t values when . This scenario can be difficult to distinguish from small J_ij,t values reflecting genuinely weak intersection (i.e., ). A similar problem associated with sample sizes significantly smaller than the average (), is that relatively large can occur due to random chance. As our institutional sample focuses on research-intensive institutions, N_i,t values are sufficiently large so as to avoid these small-sample issues – see Fig 1D. The average and standard deviation of J_ij in our data sample is with (min, max) values of (0.0001, 0.0955).

Quantifying the research area profile of institutions

A reliable classification of scientific research areas is essential for consistently measuring specialization across institutions and time. To this end, we exploit the longstanding classification of journals indexed by WOS according to research areas (corresponding to the SC field tag), which facilitates measuring the disciplinary profile of individual universities. This journal classification is comprised of 153 individual research areas that map onto 5 broad categories (denoted here by SC), with some journals featuring two compounded SC. As such, we focus on the six most frequent SC associated with co-produced research, which together span 87% of the entire data sample. Four of these categories are singular SC, and two represent compound SC (e.g.“Life Sciences & Biomedicine × Physical Sciences”). Thus, for a given set of publications, we denote the proportion of publications featuring a particular SC distribution by the vector , where individual components are bounded and the vector is normalized, .

For each institution i, we calculate a research area profile (denoted by ) for two non-overlapping sets of publications: the first being mono-university research affiliated with i; and the second being multi-university research affiliated with each institutional pair ij. Each set of publications is useful for calculating a measure of research area diversity by way of the Herfindahl-Hirschman index (HHI), . In the first case, we use defined by mono-university research to calculate the disciplinary diversity of a particular institution, denoted by . And in the second case, we use to calculate the disciplinary diversity of the research co-produced by universities i and j, denoted by . The minimum value d^SC = 0 corresponds to a maximally concentrated distribution dominated by a single SC, connoting an extremely specialized institution; and the maximum value corresponds to a uniform distribution of SC more representative of a traditional multi-disciplinary RU.

To further explore how institutional similarity moderates RIS integration, we define the pairwise institutional alignment

(2)

calculated using each institution’s mono-university publications. Institutions with little overlap in their research area profiles will generate small values, with indicating no overlap at all. Two institutions that are maximally concentrated in the same single SC will generate the maximum value . And institutions with mixed research area profiles will generate intermediate values of , which empirically tend to cluster around when the institutions i and j are both traditional research universities (i.e. offering undergraduate and graduate education programs across a multi-disciplinary array of fields). The average and standard deviation of A_ij is with (min, max) values of (0.053, 0.95).

Research co-production model specification

In order to systematically evaluate the relative contributions of the four institutional assortativity channels on the structure and dynamics of institutional research co-production (quantified by J_ij,t), we estimate the coefficients of the following linear regression model,

(3)

We implemented the estimation using STATA 13 “reg” including robust standard errors. The full set of parameter estimates are shown in the model (7) column in Table 1; see the SI Appendix for complete model variable descriptive statistics.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 1. Research co-production model – full set of parameter estimates.

We implemented the estimation using STATA 13 including year fixed-effects and robust standard errors; see Eq (3) for the model specification. The dependent variable in each model is the research co-production J_ij,t between institutions i and j in year t calculated for publications in the 21-year period 2000-2020. We incorporate the alignment with a 1-year lag, ⋅ , to account for inter-annual variation in research area profiles ; note that research area profiles are calculated using mono-university (denoted by M) publications of institution i, whereas J_ij,t are calculated for co-produced publications. Below each point estimate is the associated p-value. See S3 Fig. for the corresponding descriptive statistics and covariance matrix. See Fig 5C for a plot of the interaction coefficients included in model (8) to identify the temporal trend associated with institutional homophily. See Fig 5D for a plot of the interaction coefficients generated by model (8) to identify the temporal trend associated with institutional prestige involving two premier universities (Prem_ij = 2).

https://doi.org/10.1371/journal.pcsy.0000088.t001

This model specification accounts for factors such as distance and relative size of the entities as in the traditional gravity model (see for example [5,7]), while also accounting for each of the four assortative channels. The main distinction from the gravity model is that we do not assume a multiplicate relationship between the dependent variables, which is implied when the dependent variable enters as a logarithm. Second, because N_ij,t and N_i,t are extensive variables that are susceptible to temporal trends, we focus on the intensive variable J_ij,t that appropriately standardizes the nominal integration measure N_ij,t by the pairwise subsample size (N_i,t  +  N_j,t − N_ij,t). The coefficients in the resulting model measure the degree to which shifts in J_ij,t are attributable to time-invariant (e.g. spatial variables) and time-dependent co-variates (e.g. institutional sizes). For the latter variable type, we account for potential causal relationships by implementing 1-year lags in the variables denoted by R_ij,t−1 and A_ij,t−1.

Considering the role of each co-variate more specifically, we start with the spatial factor variable , which classifies the institutional pair according to three non-overlapping categories denoted by the categorical variable G_ij. The first category is G_ij = Metro, corresponding to institutions that are co-located within a greater metropolitan area (e.g. UTD, UTA, UTSWMCD and SMU); the second is G_ij = WRIS, corresponding to institutions within the same state but extending across metropolitan areas; and the third is G_ij = XRIS, corresponding to institutions spanning across state boundaries. In what follows, we employ the second within-RIS group as the baseline category.

We measure institutional homophily via the binary indicator variable , which represents institutional pairs where both institutions belong to a common MUS with the value 1, and 0 otherwise. We measure the role of institutional specialization as it manifests in the research area alignment of the two institutions, denoted by A_ij. Note that research area profiles are calculated using mono-university publications of institution i, whereas J_ij,t is based upon co-produced research. Moreover, we include an interaction between A_ij and MUS_ij to explore the moderating role of institutional homophily on the contributions attributable to the alignment of institutional specialization.

To account for institutional prestige we employ two measures that control for institutional reputation as well as relative size variation. The first is a categorical variable that measures the combined reputation among the pair ij by counting the number of premier institutions, denoted by Prem_ij. This variable has three categories corresponding to 0, 1, or 2 institutions, and generates a set of corresponding coefficients denoted by . In what follows, we employ the group with 0 premier institutions as the baseline category. The second quantity is the institutional size ratio , which facilitates estimating the propensity for institutions to sort according to relative differences in total research production. Values of represent institutions of roughly similar size, whereas controls for institutional size asymmetry. The average and standard deviation of R_ij is with (min, max) values of (1.0, 150). And finally, represents annual fixed effects, such that estimates are measured in excess of idiosyncratic temporal shocks.

Temporal interaction model: To explore the temporal trends in the MUS_ij and Prem_ij variables, we elaborate on the basic model by including temporal interactions,

(4)

The interaction MUS_ij × t facilitates exploring the temporal evolution of this factor over time, which offers insights into the sensitivity of the MUS backbone to financial resource constraints characteristic of financial shocks such as the 2007-08 financial crisis. Similarly, the interaction generates a set of corresponding coefficients . For both interaction terms we measure the temporal change relative to the baseline value in 2000. The full set of parameter estimates are shown in the model (8) column in Table 1, and are demonstrably robust with respect to model (7) which lacks the temporal interactions.

Visualizing the structure and dynamics of RIS integration

Given the relatively high density of connections among institutions, we present the ensemble of co-production intensities quantified by J_ij,t as an ordered matrix. This descriptive visualization strategy is sufficient to reveal the structure of RIS integration and also facilitates the identification of dynamical patterns. To this end, the two sequential J_ij,t matrices shown in Fig 2 illustrate the structure and dynamics of these two RU ecosystems, showing significant levels of within-RIS and across-RIS integration. Visual inspection suggests that within-RIS co-production is strongly mediated by both institutional homophily prioritizing within-MUS collaboration, as well as stratification according to institutional prestige.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 2. Structure and dynamics of within-RIS and across-RIS research co-production (RQ1).

(A,B) The matrix J_ij measures the fraction of research output co-produced by universities i and j by way of the Jaccard similarity index. We identify university clusters using a modularity maximizing algorithm [97], as indicated by the gray-scale border segments along the upper border; within each cluster, universities are ordered according to their research productivity, N_i. Comparison of J_ij,t tabulated over two consecutive time periods indicates assortative regional integration mediated by spatial proximity, institutional prestige and biomedical & health science specialization. Each color-legend extends to the maximum value; the cyan segment begins at the value of the 10th-largest J_ij value to facilitate identifying the most prominent pairs. (C) Minimum spanning tree representation of J_ij,t shown in panel (B). (D) Slope-graph showing the rank-changes according to the weighted PageRank centrality calculated for the two matrices shown in (A,B). Universities with increasing centrality tend to specialize in biomedical and health sciences. See S1 GIF for a dynamic visualization of J_ij,t at the 1-year resolution from 1970-2020, and S1 Fig. for the PageRank centrality dynamics.

https://doi.org/10.1371/journal.pcsy.0000088.g002

To more objectively identify RU clusters in each J_ij,t matrix we employ a standard unsupervised (modularity maximizing) algorithm [97]. Results indicated along the border of each matrix confirm that clusters strongly correlate with spatial proximity largely corresponding to each RIS. The presence of notable community overlaps reflects the fact that J_ij,t are constructed by aggregating publication data across disciplinary boundaries (i.e., SC). While it is outside the scope of the present analysis, we anticipate that co-occurrence matrices constructed conditionally upon certain research areas would show more distinct communities.

Three commonalities among the most prominent J_ij,t values (highlighted by cyan) are: they feature strong alignment in research area specialization (e.g. UT Austin most frequently co-produces with other premier engineering schools at Caltech and UCB); indications of prestige sorting among the most premier institutions (e.g. UCLA features relatively high J_ij,t with UCSD, Stanford, UCB and UCSF); and the institutions are co-located within a single metropolis (e.g. UT Dallas and UTSW; UTMDACC and UTHealth; UCLA and USC). Across-RIS integration is most prevalent among the specialized UT health science centers, UCSF, and traditional multi-disciplinary research universities featuring prominent medical schools (e.g., Stanford, USC, UCLA, UCSD).

Comparison of J_ij,t clusters calculated for 2010-2015 and 2016-2020 indicates an increasing role of institutional specialization and homophily contributing to RIS integration. This contextual regularity is reproduced by the minimum spanning tree representation of J_ij,t shown in Fig 2C. This network representation indicates that the backbone of the RIS networks are universities with prominent medical schools and health science centers, and highlights the role of the most prominent hubs as mediators of both within- and across-RIS research co-production. In a similar vein, Fig 2D shows that institutions featuring the greatest cross-temporal increases in network centrality tend to be those specializing in biomedical and health sciences.

From a dynamic perspective, we analyze the information contained in the sequence of J_ij,t matrices to understand how the system responds to exogenous resource shocks, in particular the 2007-08 global financial crisis, which impacted federal and private spending on R&D [47,73–76], as well as university financials and academic labor markets [66,70–72]. To this end, the average value measures the characteristic level of pairwise integration, we note a dramatic decline at the onset of the financial crisis. Following a period of re-consolidation, the system features a second substantial negative shift from 2016-2020 – see Fig 3A. Thus, while it may be tempting to assume that RIS integration has increased by following secular trends of globalization [42], we find variation and departure from aggregate trends at the regional level.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 3. Structural dynamics of regional integration (RQ2).

(A) Mean value of the co-production matrix J_ij,t calculated from 2000-2020. (B) Two weighted network measures capturing the structural properties of J_ij,t. The weighted mean clustering coefficient measures the prevalence of prominent institutional triads [98], such that three institutions all feature relatively high co-production values, largely reflecting the emergence of modularity in the institutional ecosystem. The network assortativity measures the propensity for institutions to sort according to research co-production intensities, with negative values reflecting systems governed by resource constraints and zero-sum interactions [89]. Dashed lines indicate the mean value across each time series.

https://doi.org/10.1371/journal.pcsy.0000088.g003

Two complementary weighted network metrics yield additional insights into the dynamics of clustering and assortative mixing among institutions [41,89,90]. Treating J_ij,t as a weighted network, we calculate the mean clustering coefficient which quantifies the degree to which the strongest co-producing institutions of a given institution also feature relatively high levels of research co-production between themselves. Fig 3B shows that the strength of prominent institutional triads started to increase at the onset of the financial crisis indicating the emergence of structural modularity [98]. Instead, the network assortativity coefficient measures the propensity for institutions to sort according to the relative magnitude of neighboring J_ij,t values [89]. If institutions with relatively high (low) J_ij,t tend to pair with other institutions featuring relatively high (low) J_ij,t, then the J_ij,t configuration will generate positive values of network assortativity. Conversely, if institutions with relatively high (low) J_ij,t tend to pair with other institutions featuring relatively low (high) J_ij,t, then such a configuration will generate negative values of network assortativity. Results indicate that network assortativity is largely negative and tracks the trend observed for . These three metrics are consistent with a general shift towards regional collaborations orienting around resource sharing and less about prestige sorting during the 2007-08 financial crisis. Yet we also observe a general fragmentation of J_ij,t, with the recovery of structural integrity extending well into the mid 2010s – see S1 GIF for a dynamic visualization of J_ij,t at the 1-year resolution from 1970-2020. This finding is consistent with work studying the impact of this global financial shock on the research enterprise over the short and medium term [47,66].

Regional integration is mediated by the dichotomy of institutional diversity and specialization

We exploit the distinct multi-campus university system configurations in CA and TX to provide additional insights regarding the role of institutional specialization on regional integration. One the one hand, the UC features 9 campuses whose research profiles are variations on a multi-disciplinary theme. As such, researchers seeking to develop multi-university projects ranging from small collaborations to large consortia can strategically assemble expertise, access to equipment and other resources by coordinating within the system, as the organizational redundancy offers many options from which to choose. Contrariwise, if a large proportion of campuses are highly specialized and feature low redundancy, then there are relatively fewer within-MUS combinations that offer sufficient multi-disciplinary alignment. This latter scenario is more representative of the UT system, where roughly half of the institutions are biomedical and health science oriented, and the remainder are more traditional multi-disciplinary institutions. (Note that UT Austin was the only campus prior to 2016 with a medical school; the UTRGV and UTT medical schools launched very recently, in 2016 and 2021, respectively).

To explore the combinatorial implications of MUS composition – both at the institutional and system levels – we leverage the WOS research area categories (denoted by SC) to define a research area profile for a given institution over a particular time period. Fig 4 shows the disciplinary signature of each institution according to the relative frequencies of six primary SC categories, as indicated by . More specifically, we calculate two variants of according to two non-intersecting publication subsets. First, for each institution we calculate a research area profile based upon its mono-university research, denoted by . And second, for each institutional pair we also calculate a research area profile based upon research co-produced by institutions i and j (i.e., the subsample of size N_ij,t). Fig 4A and 4B show the frequency distributions and . The representations shown along the diagonal of each matrix indicate a wide range of research area distributions, both across and within each region and MUS. In the UC and UT, seven campuses feature the maximum observed d_i = 0.75 (UCB, UCSB, UCSC, UCM, UTAu, UTRGV and UTEP). Contrariwise, the specialized biomedical and health science centers feature relatively small diversity, d_i < 0.16.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 4. The composition and diversity of institutional research area profiles conditions the degree of regional integration (RQ3).

Research area composition and diversity for (A) California and (B) Texas, calculated for research published between 2016-2020. For each matrix, the pie charts comprising the upper diagonal matrix show the relative frequency of various WOS “Research Areas” across research co-produced by each university pair ij. Pie charts along the diagonal show the SC distribution tabulated using mono-university research over the same period. To measure SC diversity we calculate , where HHI is the Herfindahl-Hirschman index calculated across the six SC categories: small (large) d^SC values correspond to concentrated (diverse) SC profiles. Each d_ij value is shown in the cross-diagonal matrix element ji. University pairs with less than 50 co-publications are omitted from each matrix. (C) Below each matrix we show the interquartile range of d_ij values (purple) derived from co-produced research relative to the distribution of d_i derived from mono-university research (gray). The distribution of d_ij is shifted towards lower values, indicating that regional research co-production is mediated by university-level research area specialization. (D) Negative correlation between alignment of research areas between universities ( ⋅ ) and the diversity of co-produced research, d_ij. This relationship explains a significant portion of within-RIS variation in d_ij exhibited in panel (C). (E) Positive correlation between university alignment and pairwise integration, J_ij. Comparing the characteristic levels of J_ij between regions highlights the higher degree of ecosystem integration in CA versus TX. Callouts indicate highly localized university pairs, indicating the role of spatial proximity in addition to institutional similarity.

https://doi.org/10.1371/journal.pcsy.0000088.g004

Comparison of and profiles for a given i indicate that co-produced research is mediated by the particular specialization of each university, such that more specialized institutions (e.g. Caltech) tend to co-produce research with other universities that align with their principal research area (i.e., “Physical Sciences”). This pattern indicates that research co-production is mediated by research-area alignment rather than complementarity. Moreover, it also suggests that regions comprised of institutions with a rich variety of SC profiles will foster higher levels of integration. Interestingly, a bi-product of this coupling mechanism are lower levels observed for the co-produced research relative to distribution of values calculated for mono-university research. Hence, while regional integration is supported by alignment, the co-produced research outcomes tends to be more concentrated in specific research areas that are likely representative of institutional strengths – see Fig 4C.

Finally, comparison of d^SC distributions within and across regions demonstrate how institutional specialization conditions regional integration. The distributions of shown in Fig 4C are more narrowly distributed in the UT, which in turn constrains the variation in . These constraints represent hard limits on the combinatorial synergies that can be realized between institutions. Notably, a significant number of institutional pairs co-produce fewer than 50 publications, corresponding to empty cells in Fig 4A and 4B. These structural holes underscore the different levels of regional integration in CA versus TX. This result is only partly attributable to the distinct institution specialization in TX, as there are even notable weak links among the academic institutions (denoted by UT_A). Hence, one of our main findings is that maintaining a balance between institutional redundancy and variation is essential for creating a wide range of potential institutional synergies, and influences the degree to which regional ecosystems integrate.

We observe a negative relationship between and for both CA and TX – see Fig 4D. These trends exhibit the downside of redundancy. At the same time, they highlight the multidisciplinary advantage of regions featuring a diversity of institutional research area profiles. This latter point is reflected by the distribution of values, which is more continuous for CA and more modal for TX. At the same time, we observe a positive relationship between and J_ij, reinforcing the principle that institutional ecosystems integrate according alignment rather than complementarity, while also exhibiting a higher degree of integration in CA relative to TX – see Fig 4E. Notable J_ij outliers tend to be neighbors within the same metropolis, which points to the persistent advantages of co-location.

Multi-campus university systems promote regional integration

Research co-production affinities that persist over distance and time point to the factors that generate structural resiliency within innovation systems. In this regard, we exploit the annual variation in J_ij,t over the period 2000-2020 to evaluate the relative strength of assortative channels as they relate to regional integration. We employ a panel regression specified in Eq (3) to simultaneously measure the relative contributions of four assortativity channels to rates of research co-production. As an indication of goodness-of-fit, our full model generates an adjusted R² = 0.257. See Fig 5A for a visual summary of the focal variable estimates; and see Table 1 for the full list of point estimates and demonstration of model specification robustness.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 5. Sensitivity of multi-university research co-production to assortativity channels and exogenous socio-economic shocks (RQ4).

(A) Regression model point estimates. The impact of institutional co-location on research co-production is roughly 5× stronger than both the impact attributable to institutional prestige affinity () and the impact attributable to geo-political barriers affecting across-region collaboration (). Statistical significance levels: , , ; model adjusted R² = 0.27. (B) Marginal effect of institutional alignment conditional on MUS homophily, holding all other regression model covariates at their mean values – see Eq (3) for the model specification. Differentiating between ij pairs belonging to a MUS from those that do not (!MUS) shows that institutional homophily (MUS) moderates regional integration. The vertical dashed line corresponds to the mean value. (C) Plot of the temporal trend associated with institutional homophily, . Green data points indicate years in which the coefficient significantly deviates from the baseline value in 2000 at the p < 0.05 level. Note a general increase in up until the period of global financial crisis in 2007-08. (D) Plot of point estimates indicating the temporal trend associated with “binary star” co-production between two premier universities, . Red data points indicate years in which the coefficient significantly deviates from the baseline value in 2000 at the p < 0.05 level. The intensification of prestige sorting (2016-2020) follows the recovery period (2009-2012, during which the RU networks fragmented). See Table 1 for the full list of regression model point estimates.

https://doi.org/10.1371/journal.pcsy.0000088.g005

Whereas much of the research on global collaboration trends supports the ‘death of distance’ perspective [80,99], our results show that spatial proximity is still a dominant factor at the regional scale, as noted in other studies [42,53,100]. The coefficient measures the contribution from agglomeration density by denoting institutional pairs that are acutely proximal corresponding to a <2 hour driving distance within a greater metropolitan area. By way of example, four institutions in our sample are located within the greater Dallas-Fort Worth area. Measured relative to the baseline within-RIS category, the coefficient (p < 0.001; 95%CI = [0.012, 0.016]) quantifies the excess co-production attributable to co-location within the same metro area, which exceeds the characteristic co-production levels for many of the institutional pairs shown in Fig 2. Moreover, is roughly 5.5 times larger in magnitude than coefficient representing across-RIS pairs, (p < 0.001; 95%CI = [0.002, 0.003]), and is also 5 times larger than the prestige effect reflecting pairs where both i and j are premier institutions.

On of our main results is the relation between research area alignment and research co-production J_ij,t, and the degree to which it is moderated by institutional homophily. We operationalize this differential by measuring the coefficient associated with conditional on the two institutions ij belonging to the same MUS or not, denoted by the binary variable MUS_ij. Fig 5B shows that institutional pairs belonging to a common MUS feature a marginal effect of alignment that is 5 times stronger than the counterfactual: (p < 0.001; 95%CI = [0.006,0.011]) and (p < 0.001; 95%CI = [0.0009, 0.0025]). How consequential is this difference in terms of the net impact on research co-production levels? To assess the magnitude of this difference, we consider two institutions featuring the average level of alignment . At that level, the net differential − (p < 0.001; 95%CI = [0.004,0.090]) corresponds to a 50% increase in J_ij,t for MUS members relative to the counterfactual. This substantial difference reflects the advantages of access to common pool resources such as state and system-level funding initiatives, in addition to the relatively higher familiarity and mobility among scholars within multi-campus university systems that generate ecosystem network effects.

The degree to which institutions sort according to reputation is captured by the categorical variable Prem_ij, which counts the number of premier institutions among the pair ij. We do not identify a significant difference associated with institutional pairs involving 1 premier relative to the baseline of 0 premier institutions (; p = 0.08; 95%CI = [–0.0001, 0.0008])). However, we do identify a substantial increase in co-production attributable to “binary star” pairs featuring 2 premier institutions, (p < 0.001; 95%CI = [0.0023, 0.0033]). This result is indicative of the prestige hierarchies that foster the emergence of rich clubs in science [36,37,55].

The degree to which institutions sort according to their size prominence is captured by the continuous variable , which measures the ratio of the larger relative to the smaller institution size. A tendency for larger institutions to co-produce relatively more (relatively less) with smaller institutions corresponds to (respectively, ); and if there is no tendency for size-stratification, then . Additionally, this quantity controls for extensive variables associated with institutional size that generate larger N_i,t, such as the amount of research infrastructure and the researcher population. Results indicate a negative correlation, (p < 0.001; 95%CI = [–0.00011, –0.00009]), indicating a tendency for institutions to pair according to size. This results implies a comparative advantage among larger legacy institutions, as the preferential coupling may inadvertently generate barriers to entry for smaller regional counterparts.