Introduction

The socialization of young people in science through doctoral studies is one of the most important tasks of academic institutions. The number of doctoral graduates is constantly growing. While doctoral graduates used to represent a small elite in society, today they face intense competition in the labour market. This competition for jobs is strongest at universities and in the corporate sector. The number of high-skilled jobs in these sectors has not always risen at the same pace as the number of doctoral students. Despite this mismatch between the production and intake of doctorates, the training of doctorates is supported by governments in all developed countries given that doctoral graduates remain the most creative intellectual factor in meeting the challenges of modern knowledge-based societies. Finally, adults holding a doctorate or equivalent degree still boast the highest employment rates of any education level in the developed world. For example, in OECD countries, on average 93% of all 25–64 year olds holding a doctorate or equivalent degree are employed (OECD, 2022). Looking at the situation in EU member states, the number of doctoral students has also risen significantly over the past two decades (EUROSTAT, 2022). The same is true for Slovenia, one of the smallest member states of the EU.

While prior to 2000 it was difficult to speak of the strong (normative) comparability of Slovenian doctoral programmes (they were fragmented and non-standardized) with doctoral programmes in other European countries, the situation changed when Slovenia began to promote the Bologna higher education reforms. The Bologna Declaration was signed in 1999 by the ministers of higher education of 29 European countries and aimed to create a common degree structure, introduce a common credit system and quality assurance mechanism, and promote the mobility of students and academic staff between institutions and countries (Bologna Declaration, 1999; European Commission, 2018). In this way, (normative) frameworks have been created to harmonize European education programmes with a view to ensuring they become more comparable and coherent, even within national frameworks. These harmonization processes have also impacted the restructuring of doctoral education. Doctoral programmes represent the highest level of tertiary study and require students to contribute research skills through their doctoral work. In Slovenia, different public and private organizations are running a total of 103 doctoral programmes (Ministry of Higher Education, Science & Innovation, 2023).

The first students in Slovenia enrolled in the new Bologna doctoral programmes in 2005/2006. Their numbers grew early on: in 2011/2012, there were four times as many doctoral students than before the Bologna reforms were introduced (Romih et al., 2020). The biggest reasons for this radical change were the new Bologna study system (i.e., introduction of the 3-level Bachelor-Master-Doctorate system) and the new financial incentives of the state for doctoral students at that time. Since that year, the Slovenian Ministry of Science and Education has financed the tuition fees of a proportion of doctoral students. Given that doctoral studies in Slovenia still require the payment of tuition fees, it is necessary to distinguish three groups of doctoral students in terms of their funding sources. The first group contains doctoral students who rely on their own personal or family financial sources,Footnote 1 while the second group refers to the mentioned doctoral students for whom the Ministry has covered the tuition fee costs after 2012. The third group consists of doctoral students participating in the “Young Researchers programme”. The Young Researchers programme is a continuous measure provided by the Slovenian government in the last 40 years for financially supporting doctoral students. The two main goals of this programme are to revitalize the teaching staff at academic institutions and—much more importantly—to train highly qualified personnel to move into the non-academic sector, especially into industry (Mali, 1998). Doctoral students involved in this programme receive the most convenient and stable form of financial support during the time of their studies. They are admitted to the mentor academic institutions with the same employment rights (salary, life and pension insurance etc.) as other employees of that institution.

The process of supervising doctoral students in a micro-academic environment is still a relatively under-researched topic. This multifaceted and complex phenomenon (Stevens et al., 2021) receives less attention in expert literature than it deserves. Understanding the characteristics of mentoring collaborations is essential for developing successful higher education strategies to attract potential doctoral students. Therefore, our paper first explores what we know about the mentoring relationship, with an emphasis on how this relationship between mentors and mentees is established and maintained. The second issue addressed is whether the complex processes of doctoral mentorship in academic environments strengthen the collaboration between mentors and co-mentors themselves (in the case of collective mentorship of doctoral students). Our findings also provide insight into some less-investigated factors that play an important role in the education of doctoral students, as well as the building of new interdisciplinary academic esprit de corps during the education of doctoral students. The study can also help in the search for adequate national higher education and research strategies and policies to attract, educate and support doctorates in their further scientific careers.

Previous research

In our empirical analysis, the relationship between mentors and mentees, as well as between mentors and co-mentors, is operationalized through co-authored publications. Co-authored publications are, despite some criticism (e.g., Katz & Martin, 1997; Laudel, 2002), one of the most important indicators of successful collaboration among scientists and represent a growing trend in modern science. In the last few decades, there has been a tremendous increase in co-authorships across various scientific disciplines, sectors, and categories of researchers. As noted by many authors, research collaboration in the form of common publications continues to grow in academia to enhance scientific productivity, impact, knowledge acquisition, and interdisciplinary skills (de Miranda Grochocki & Cabello, 2023; Henriksen, 2016; Rodrigues et al., 2016). In the context of doctoral studies, a valuable indicator of good relationships between mentors and mentees is joint publication activity. Indeed, Luka Bulian and co-authors point out in their study on Croatian doctoral students, the mentor’s publication excellence strongly affects the later publication productivity of their mentees (Bulian et al., 2022). The Croatian case study showed that PhDs who had co-authored articles with their mentors published, on average, almost twice as much as those who did not during their doctoral studies, and more than twice as much after completing their studies.

For most doctoral students, completing the dissertation is not the end of their educational journey. Instead, it marks the beginning of a new stage in their subsequent professional careers, where expectations for their publication productivity and excellence increase. This makes it extremely important to foster a positive professional attitude towards publication activities during doctoral training (Amabile, 1996; Hemlin et al., 2004). Many sociologists of science have asserted that the process of the academic inculturation of young researchers through doctoral training, which involves common publishing activities, can be described as a form of craft (Gowing, 1974; Ravetz, 2020; Whitley, 1984). In certain aspects, doctoral training cannot follow the rigid and restrictive structures found in many other professions, such as hierarchy, formalized communication, and immediate employment status. The role of mentors is not determined by formal employment hierarchies but by their role in providing newcomers to the scientific community with the necessary skills. Social research in science provides a rich source of theoretical and empirical evidence on the important role of good mentor–mentee relationships in mentees’ subsequent successful scientific careers (Corsini et al., 2022; Delamont & Atkinson, 2001; Watson Todd & Louw, 2019). Robert Merton’s theory of the Matthew Effect also suggests that the initial advantages gained by mentees during the doctoral phase of their training may strengthen their professional status in later stages of their careers (Merton, 1973).

There are two basic modes with which doctoral students are socialized into research work. In the positional socialization mode, the role and status of doctoral students are fixed, resembling apprentices who gain greater freedom and autonomy as they progress. In the personal socialization mode, doctoral students work more independently, albeit they generally meet with their supervisors frequently. From the outset, they are treated as young colleagues rather than apprentices. Empirical studies have confirmed that the first model, the master–apprentice relationship, has slowly evolved into the second model, a more collaborative relationship and partnership between doctoral students and mentors (Bastalich, 2017; Revelo & Loui, 2016; Roach et al., 2019).

In modern doctoral education, there is a growing requirement that the preparation of the doctoral thesis be supervised by two or more peer reviewers. When doctoral students are guided by collective mentorship, they can capitalize on numerous advantages, even in cases where a PhD’s “everyday scientific life” is still determined by the rules of one domestic discipline (Abbott, 2010; Rafols et al., 2012). However, the rapidly changing academic environment requires doctoral students to engage in new forms of research work, including inter- and transdisciplinary work. Co-mentors from different disciplines who integrate their intellectual efforts into their mentees’ work are a good indicator of an academic environment’s ability to develop the esprit de corps of new scholarship for interdisciplinary collaboration in general (Holley, 2018; Kniffin & Hanks, 2017; Schmidt et al., 2012). Numerous empirical analyses have confirmed the advantages of such a new esprit de corps that is formed in “the mentor-co-mentor-doctoral student nexus”. For example, many studies have documented that collective supervision contributes to satisfactory PhDs and mentor support (Unda et al., 2020), performance accountabilities of PhDs (Khosa et al., 2020), and the reduction of doctoral students’ cognitive and social isolation (Hutchings, 2017).

Finally, it seems that despite numerous theoretical and empirical studies on various dimensions of doctoral training, more national case studies are needed. In particular, this is because documented evidence of various studies shows significant variations between countries. Even in EU member states, where a unitary policy model of doctoral training is formally accepted, practices vary considerably across countries. In Slovenia, general trends concerning the recruitment and training of new doctoral students are relatively well known. Nevertheless, there continue to be many ‘blind spots’ in this topic. Some analytical sociological and social network analyses were conducted on this topic in the past (Arzenšek et al., 2014; Kogovšek et al., 2011; Matelič et al., 2007). Based on analysis of the consequences of collaboration between mentors and mentees on the mentees’ subsequent career paths, and analysis of the quality of collaboration between mentors and co-mentors in the mentorship of doctoral students, our study provides new insights into this precarious issue of modern science and higher education.

Research questions

Two research questions are analysed in this paper:

RQ1:

How is collaboration between mentors and mentees established and maintained?

The doctoral period is a vital stage in the professional career of any scientist. Thus, this research question focuses on whether the mentor–mentee relationship is established just prior to the start of a doctoral programme, or is the continuation of an already existing relationship.

RQ2:

How is mentorship related to scientific collaboration between mentors?

We also aim to explain the characteristics of scientific collaboration between mentors who offer support to their mentees. One aspect of this investigated topic is the extent to which advanced practices of scientific collaboration between mentors with different disciplinary backgrounds are pronounced while providing support to mentees. Our previous studies, which concentrated on the analysis of different forms of collaboration among scientists in Slovenia, have shown that esprit de corps in science does not sufficiently follow the new principles of inter- and transdisciplinarity (Ferligoj et al., 2015; Groboljsek et al., 2014). Many scientists working in the academic environment in Slovenia still view the current processes of inter- and transdisciplinary collaboration with great scepticism. Even on the level of departments, not only on the level of faculties, teaching and research activities are sometimes extremely separated in disciplinary terms, as if academic staff are unaware that the main features of the new way of producing knowledge are not only the context of application, organizational heterogeneity, social accountability, and new forms of quality control, but above all interdisciplinary or even transdisciplinary collaboration.

In the following section, we describe the methodology used to address the research questions stated above. The data are then described in Sect. “Data “, and the results in Sect. “Results”. The latter sections are further arranged into subsections according to the research questions. Note that this research was approved by the Workplace Ethics Committee (801-2022-016/JG) at the Faculty of Social Sciences, University of Ljubljana.

Methodology

The same methodology was applied to address both research questions.

First, cluster analysis was used to reveal clusters of mentors and mentees with a similar collaboration pattern before and after completing a doctoral study (for the first research question), or clusters of pairs of mentors with similar collaboration patterns around the year of the first joint mentorship (for the second research question). Then, we applied linear discriminant analysis (Brown & Wicker, 2000; Klecka et al., 1980) to explain the clusters thereby obtained. In this study, collaboration is operationalized by co-authorship of any type of bibliographic unit according to the typology of documents/works for bibliography management in COBISS (see Online Resource 3 for a list of all types of bibliographic units) that is administered by the Institute of Information Science (Institute of Information Science, 2022).

To reveal the above-mentioned clusters, we applied hierarchical clustering of symbolic objects (Billard & Diday, 2006; Bock & Diday, 1999). Here, symbolic data are empirical probability distributions (of collaboration across years). Kejžar et al. (2021) proposed six dissimilarity measures to achieve meaningful cluster representatives. We used the \({\delta }_{3}\) dissimilarity measure with weighting since the empirical probability distributions contain peaks and zero-count frequencies (i.e., years with more publications and years without publications). The package»clamix« (Batagelj & Kejžar, 2019) for the R-programming language (R Core Team, 2008) was used.

Despite using the same statistical approaches to deal with both research questions, there are some methodological differences that are explained in the following subsections.

First research question: mentors–mentee collaboration

Unit of analysis The unit of analysis is a doctoral graduate.

Data considerations For each doctoral graduate, we calculated empirical probability distributions across years of: (i) co-authored publications with mentors; and (ii) other publications (i.e., solo-authored publications or publications published with authors who were not mentors).

Time frame An 8-year time frame before and after the year of publication of a doctoral dissertation was considered. The 8-year period before the finishing of a doctoral study was chosen based on an estimate of the typical duration of a doctoral study of 4 years. Another 4 years was added to capture the time before the start of a doctoral study. The 8-year period after finishing the doctoral study was chosen arbitrarily as a compromise so as not to consider a period that was too long (because this would reduce the number of analysed cases) or too short (because some doctoral students might still be involved in the research project after they finish the study).

Explanatory variables To explain the clusters obtained, the following variables were included:

  • Age of a doctoral graduate

    The age of a doctoral graduate was defined as the difference between the year of publishing the doctoral dissertation and the year of the first published professional or scientific bibliographic unit. Although the age of a doctoral graduate may not be directly related with their collaboration patterns with mentors, it can serve as an indicator for various nuanced factors not examined in this study. For instance, a notably young doctoral student might reflect a traditional educational path where students transition immediately from one academic level to the next. Such a trajectory could be associated with narrower collaboration networks. On the other hand, older doctoral students might possess more extensive scientific or professional backgrounds, and their motivations for undertaking doctoral research might differ (Bienkowska & Klofsten, 2012; Mangematin, 2000; Yang & Cai, 2022).

  • Age of a younger mentor

    The age of a mentor was defined as the difference between the year of publishing the doctoral candidate’s doctoral dissertation and the year of publishing a mentor’s doctoral dissertation (the year of the first scientific bibliographic unit was considered in cases where data about the doctoral thesis were unavailable). The smallest difference was considered in the case of several mentors). The age of mentors might influence the nature of their mentorship and the opportunities available to their mentees (Lu et al., 2021; Sheng et al., 2023; Wang et al., 2017). For instance, younger mentors may possess more resources to foster indirect collaboration with mentees, whereas older mentors could offer greater opportunities to expand their mentees’ collaborative networks with other researchers.

  • The Young Researcher programme

    Whether a doctoral candidate was included in the national funding programme for young researchers was accounted for. As outlined in earlier sections, the Young Researcher programme can provide consistent state funding for emerging scholars, as well as financial support for research materials. This could grant them additional time dedicated to research and foster a greater degree of research autonomy.

  • Gender homophily

    If the doctoral candidate and at least one mentor are of the same gender, the mentoring relationship is considered gender homophilous. Several studies identified gender as a important variable in understanding scientific collaboration patterns (DeJesus et al., 2021; Huang et al., 2020; Lerchenmueller et al., 2019; Schwartz et al., 2022).

  • One or more mentors

    Whether there is more than one mentor holding an ARRS research ID was taken into consideration. This control variable was introduced to account for the potential increase in mentee publication capacities when guided by more than one mentor. It is worth noting that there are very few instances of having more than two mentors.

  • Scientific field

    According to the ARRS classification scheme (Slovenian Research Agency, 2023b); this controlling variable was included since previous studies showed that field of research has an important impact on various aspects of scientific work (Cugmas et al., 2016; Kronegger et al., 2011), including motivation for pursuing doctoral studies (Tarvid, 2014).

  • Year of publishing a doctoral dissertation

    This is a controlling variable to capture differences in the occurrence of different types of collaboration patterns. Such differences might arise due to policy shifts, labour market fluctuations, or other external factors on the mezzo or macro social level.

Second research question: mentors’ collaboration

Unit of analysis The unit of analysis is a pair of mentors. When more than two mentors mentored a single doctoral candidate, all possible pairs of mentors were created and analysed independently.

Data considerations For all pairs, we calculated the number of publications for each year. On the assumption that the mentors have different publishing capacities, we calculated and analysed the share of common bibliographic units (i.e., the ratio between the number of joint bibliographic units and number of all bibliographic units) per year.

Time frame We considered a 10-year time frame before and after the first co-mentoring. This time frame is broader than the one chosen for examining mentor–mentee collaboration since the emphasis is on long-term scientific partnerships. Its duration exceeds the length of at least one research project (i.e., the typical duration of one ARRS research project is 4–5 years; this type of research project is among the most common (Cugmas et al., 2020)). Due to data limitations, we analysed only those pairs that co-mentored for the first time between and including 2000 until the end of 2011. For a given pair, it was considered that they had not yet co-mentored if the last time they co-mentored was before 1970.

Explanatory variables To explain the clusters obtained, we considered the following variables: gender (the same or a different gender); scientific discipline (the same or a different scientific discipline; scientific discipline homophily was considered instead of scientific field homophily due to the relatively low intra-field scientific collaboration among the mentors; note that disciplines are the subcategories of scientific fields and thus enable a deeper insight into the nature of collaboration) defined by the ARRS classification scheme (Slovenian Research Agency, 2023b); average scientific age (as scientific age, we considered the year of the mentor’s doctoral dissertation, or the year of the first scientific publication if the year of the doctoral dissertation was not available; this variable was selected to account for the average career stage of a mentoring pair); and year of the first co-mentoring (a controlling variable like with the first research question).

Data

The data source along with exclusion and inclusion criteria are described in the next subsection. The trends and patterns regarding the number of doctorates by years, scientific field and organization are then presented.

Data source and inclusion/exclusion criteria

The data sources are the Slovenian Current Research Information System (SICRIS) (maintained by the Institute of Information Science as well as ARRS) and the Co-operative Online Bibliographic System and Services (COBISS) (maintained by the Institute of Information Science). The data from SICRIS encompass information on Slovenian researchers, research organizations and research projects that are fully or partly financed by ARRS and other entities which submit their data voluntarily, while COBISS is a national bibliographic database containing data about bibliographic units such as authors, type of bibliographic unit, organization, and year.

Since the mentoring relationship is in the centre of the proposed research question, the exclusion criteria were based on the list of doctoral theses. Accordingly, for both research questions, the following doctorates were not included when:

  • The publication year of a doctoral thesis is not between and including 1991 until the end of 2020;

  • No data are provided about the mentors;

  • The author is from the field of Interdisciplinary research. The scientific field Interdisciplinary research was excluded as this is an administrative category in the ARRS classification scheme that does not reflect the actual development of the disciplines; and

  • There are more than two authors of a doctoral thesis, or the author has more than one doctorate. These were not analysed since it is reasonable to believe that they differ substantially from the rest. Still, these are very rare cases.

Specific additional excluding criteria apply to each research question. For the first research question, only doctorates published from 1999 to 2012 were considered (because the 8-year period before and after finishing the doctoral study was under analysis) and for the second research question only doctorates published between 2000 and 2011 are considered (because the 10-year period after co-mentoring the last doctoral candidate was being analysed). In addition, only those doctoral theses with more than one mentor were analysed as part of answering the second research question.

The number of doctoral theses after considering each exclusion criterion is given in Table 1.

Table 1 Number of doctoral theses after considering the exclusion criteria
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Basic description

The number of doctoral dissertations was rising linearly until 2012 (Fig. 1). In 2013, the number of doctoral dissertations increased in the fields of Natural sciences and mathematics, Engineering sciences and technologies and Biotechnical sciences, and in 2015 in all other scientific fields. The reason for this might be related to the renewal of study programmes. An important characteristic of the old study programmes was that the master level and doctoral level were joined within the same study programme. Students who had enrolled in the old study programmes had to finish it by 2015/2016, whereas after 2009/2010 students were only allowed to apply for the new study programmes.

Fig. 1
figure 1

Number of doctoral theses by years and scientific fields

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Considering the scientific field (note that the scientific field refers to researchers’ current scientific field, which might not be the same as the field a researcher was working in during their doctoral studies); no scientific field stands out in terms of the number of doctoral graduates (at the time the data were collected) (Fig. 1). The most common is Engineering sciences and technologies (27%) while the least common is Biotechnical sciences (8%).

The overall share of doctoral dissertations with more than one mentor is 39% (note that application of the exclusion criteria meant that only doctoral theses with at least one mentor holding a SICRIS ID were included but, among those, all mentors—including those without an ARRS ID—were counted). In Social sciences as well as Natural sciences and mathematics, the share was increasing until 2000. The share is more constant yet slightly increasing thereafter. The share of mentors was growing in the Humanities and Engineering sciences by 2010. A smaller share of doctoral theses with more than one mentor is evident after 2010 for these two fields. Biotechnical sciences is a very different field where the share is increasing throughout the analysed period (with a slight drop around 2000) (Fig. 2).

Fig. 2
figure 2

Share of doctoral dissertations with more than one mentor, by years (with loess)

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Table 2 shows the interdisciplinary collaboration between the authors and mentors while considering scientific fields and disciplines. Since scientific disciplines are subcategories of scientific fields, the percentages corresponding to scientific disciplines are generally higher.

Table 2 Interdisciplinary collaboration between authors and mentors
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The highest levels of interdisciplinary collaboration are mostly observed for doctoral dissertations from the authors’ fields of Social sciences, Medical sciences and Engineering sciences and technologies, and lower ones in the Humanities and Natural sciences and mathematics. Biotechnical sciences demonstrate a notable degree of inter-field collaboration.

However, when considering dissertations with at least two mentors from different fields, biotechnical sciences (25%) exhibit a lower percentage than fields like social sciences (35%), medical sciences (35%), and engineering sciences and technologies (38%). This indicates a more moderate level of collaboration in scenarios involving multiple mentors from diverse fields.

The number of doctorates funded as part of the Young Researchers programme between 1999 and 2012 (namely, the period analysed in this study) was around 2800. The highest number of such doctorates was seen in Engineering sciences and technologies along with Natural sciences and mathematics (together totalling around 1,600 doctorates). The proportion of doctorates funded by the Young Researchers programme was decreasing slightly in all scientific fields: between 1999 and 2003, it was around 62%, and between 2008 and 2012 around 53%.

Results

The research results are presented in the subsections below.

First research question: mentors–mentee collaboration

Clustering for symbolic data was used to reveal different patterns of collaboration (operationalized through the joint publishing of a bibliographic unit) with mentors and other researchers. Doctoral candidates who did not jointly publish any bibliographic unit with either mentors or other researchers (totalling 495 doctoral students) were excluded from the data. Clustering was applied to the remaining units and the excluded ones were returned as Cluster 1 and Cluster 4. Apart from these two clusters, four other clusters were identified (Fig. 3):

  • Cluster 1 (2%) and Cluster 2 (16%) (study-limited collaboration): These are groups of doctoral students whose collaboration was primarily concentrated in the time period before completing their doctoral studies. The difference between these two clusters is that students from Cluster 1 collaborated (as reflected in their bibliography) only with mentors, not also with other researchers as happened in Cluster 2. These two clusters have the lowest number of publications compared to the other clusters.

  • Cluster 3 (23%) and Cluster 4 (8%) (already established): The doctoral candidates in these two clusters had (before they began writing their thesis) already formed a network of collaborators beyond their doctoral study mentors. The difference between these two clusters is that there is no record of collaboration with mentors for those mentees from Cluster 4. Nevertheless, the doctoral candidates in both clusters show a large amount of collaboration with others.

  • Cluster 5 (35%) and Cluster 6 (17%) (born and raised): The researchers in these clusters had little or no collaboration 8 years before they finished their doctoral studies. However, during their studies they started to collaborate with both mentor(s) and other researchers. The difference between these two clusters is that the collaboration with mentor(s) was generally strongest in the period around the doctoral studies in Cluster 5, whereas in Cluster 6, collaboration with mentor(s) also continued after those studies were finished. Researchers in the latter cluster are the most productive in terms of number of published bibliographic units.

Fig. 3
figure 3

Average number of joint bibliographic units with mentors and with other researchers for any year before and after the year of completing the doctoral studies

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To further explain the clusters obtained, we performed linear discriminant analysis. The discriminant variable is calculated as the sum of weighted explanatory variables (see Sect. “Second research question: mentors’ collaboration” for a list of variables), such that the discriminant variable discriminates as much as possible between the clusters that emerged.

The result of the Box-M test was statistically significant (M-Box = 1700.7, \({\chi }^{2}\) = 1680.2, df = 257, p < 0.01), indicating that the population covariance matrices differ across the groups. However, note that the sample size is very large (Tabachnick & Fidel, 2013). Among all possible discriminant functions, only three were statistically significant at a 5% significance level (the centroids and the standardized discriminant function coefficients of the first three discriminant functions are visualized in Fig. 4; other relevant statistics regarding the discriminant analysis may be found in Online Resource 1):

  • The first discriminant function (Wilks’ \(\lambda\) = 0.75, F(55, 22,707) = 26.6, p < 0.01, \({R}_{c}^{2}\) = 19.7%) discriminates between already established clusters (especially Cluster 4) and other clusters. The clusters that were already established are more associated with natural and technical sciences and with older doctoral students. As expected, these clusters are less associated with the Young Researchers programme (given this programme is limited to younger individuals).

  • The second discriminant function (Wilks’ \(\lambda\) = 0.93, F(40, 18,604) = 8.6, p < 0.01 \({R}_{c}^{2}\) = 3.6%) discriminates between the born and raised clusters and the other clusters (especially study-limited collaboration clusters). Year of completing doctoral studies has the strongest effect: clusters born and raised are less associated with later years, compared to the study-limited collaboration clusters. Further, study-limited collaboration is more typical for older doctoral students and for STEM (i.e., Engineering sciences and technologies and Natural sciences and mathematics).

  • The last discriminant function (Wilks’ \(\lambda\) = 0.97, F(27, 14,331) = 5.9, p < 0.01, \({R}_{c}^{2}\) = 2.9%) mainly discriminates between Cluster 3 and Cluster 4. Students in these clusters were already very actively collaborating with other researchers. The difference in the clusters is that those in Cluster 3 had collaborated with their mentors yet those in Cluster 4 had not (or they had collaborated with mentors not holding an ARRS ID). Cluster 3 is more strongly associated with all natural-technical sciences (especially Medical sciences) and higher mentee age, while Cluster 4 is more associated with the Humanities.

Fig. 4
figure 4

Centroids of the first three discriminant functions with corresponding standardized discriminant coefficients

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Second research question: mentor’s collaboration

Before applying a clustering procedure, the mentorship pairs (i.e., units of the analysis) without any joint bibliographic units were extracted from the data set. The clustering algorithm was then applied to the remaining pairs. The extracted pairs were added to the partition obtained as an additional cluster labelled»No collaboration« because their mentors had not published any joint bibliographic unit within the 21-year period. In total, we analysed 1363 doctorates with at least two mentors, resulting in 1452 pairs of mentors.

Four clusters of pairs of mentors were identified according to the share of common publications. The empirical probability distributions (i.e., probabilities of publishing a joint paper for each year before or after finishing a doctoral study) are visualized in Fig. 5, and described below:

  • Cluster 1 (23%) (No collaboration): Mentors did not collaborate on any bibliographic unit (the doctoral dissertation is not included).

  • Cluster 2 (23%) (Short-term collaboration): The share of joint bibliographic units is low (compared to other clusters) and concentrated around the year of publishing a doctoral dissertation.

  • Cluster 3 (39%) (Before-defence collaboration): Collaboration between mentors mainly occurs in the year before publishing a doctoral dissertation. After that year, collaboration shrinks substantially. The average share of common bibliographic units between the mentors is mediocre compared to other clusters. This means that although the mentor pairs in this cluster collaborated relatively intensely, their collaboration did not continue after the mentee completed their doctoral studies.

  • Cluster 4 (15%) (Long-term collaboration): These are the most collaborative mentors. The average share of common bibliographic units is the highest for the whole period under analysis (compared to other clusters). This cluster stands out from other clusters by the higher average share of common bibliographic units after the doctoral dissertation was published compared to the years prior. This cluster is closest to the scenario in which mentoring acts as a bridge towards new scientific collaborations between researchers (i.e., mentors). Yet, note that the observed collaboration pattern could also emerge when an already existing pair of collaborative researchers invites a mentee to join their research project as a doctoral student. The latter scenario is revealed by the relatively high share of collaboration in earlier years after the doctoral dissertation was published. Accordingly, the available data do not allow us to confirm that the (co)mentoring of a doctoral student is a key element in the initiating of new scientific collaboration among mentors.

Fig. 5
figure 5

Average number of joint bibliographic units between mentors for any year before and after the year of the first co-mentoring, by clusters

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The result of the Box-M test was not statistically significant (M-Box = 37.5, \({\chi }^{2}\)=37.3, df = 30, p = 0.17), meaning that one cannot claim that that the population covariance matrices differ across the groups. Here, only the first discriminant function was statistically significant with a relatively small effect size (Wilks’ \(\lambda\) = 0.96, F(12, 3595) = 4.25, p < 0.01, \({R}_{c}^{2}\) = 3.3%) (see Online Resource 2 for the other discriminant analysis results).

The first discriminant function (Fig. 6) discriminates between Cluster 1 (No collaboration) and the other clusters. Considering the standardized discriminant coefficients, the absence of collaboration between mentors may be interpreted as more typical for mentors who work in different scientific disciplines. In addition, the pairs of mentors in this cluster are on average older than the pairs of mentors in the other clusters. Compared with other clusters, Cluster 1 (No collaboration) is also more common when the first co-mentoring occurred in recent years.

Fig. 6
figure 6

Centroids of the first two discriminant functions with corresponding standardized discriminant coefficients

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Although the second discriminant function is not statistically significant (Wilks’ \(\lambda\) = 0.99, F(6, 2720) = 0.91, p = 0.49, \({R}_{c}^{2}\) = 0.3%), long-term collaborations between mentors (after mentoring the first doctoral student) (i.e., Cluster 4) were shown to be more common for a higher mean age of mentors, when mentors come from the same scientific disciplines, and collaborations were engaged in longer ago than collaborations focused more on the time before the end of the first joint co-mentoring.

Discussion

The paper addresses two research questions concerned with the initialization and continuation of scientific collaboration in the context of doctoral studies. Scientific collaboration was operationalized through the co-authoring of any type of bibliographic unit (as defined by the typology of documents/works for bibliography management in COBISS). Patterns of collaboration were identified using a clustering of symbolic data approach and described using linear discriminant analysis. The empirical distributions of co-publications over time were used as symbolic objects and various variables related to different social levels were considered to explain the clusters observed.

The first research question concerns the mentoring relationship, how it is established and maintained. Here, six types of scientific collaboration (i.e., clusters) were identified, which can be grouped into three broader categories: study-limited collaboration, already established, and ‘born and raised’. The last one is the most stereotypical, characterized by students isolated from the scientific community (in terms of co-publishing) at the start of their studies who become well integrated into the scientific community and highly productive researchers after they have completed their doctoral studies.

‘Born and raised’ is the most common mentorship relationship type in Slovenia, indicating that organized forms of doctoral study are very important for doctorates continued success in their scientific careers. Organized forms of doctoral study revealed the importance of mentors’ good initial support for their mentees, which later becomes long-term collaboration between them and/or with other researchers. Namely, as shown by many previous studies, the ‘born and raised’ types of collaboration play a pivotal role in the success of doctorates’ subsequent professional career (Euacde, 2022).

The three discriminant functions were statistically significant with relatively low values of squared canonical correlations (except for the first discriminant function), indicating high cluster diversity, and the need for additional (perhaps more micro-level-oriented) explanatory variables.

The cluster with already established collaboration between other researchers prior to the start of a doctoral study but without any collaboration with mentors on one side and the cluster with exclusively study-limited collaborations on the other do not dominate in Slovenia. Still, they are the most distinguishable. On the contrary, the cluster with already established collaboration before the start of a doctoral study is characterized by older researchers working in the humanities and social sciences. In line with the age of researchers, this cluster has a small share of doctorates financed by the Young Researchers programme. This is understandable given that the requirements for a doctoral student to be included in the Young Researchers programme are relatively strict and rarely allow exceptions. The requirements define the maximum biological age of an applicant, the funds are allocated for a fixed term, (typically) up to a maximum of 4 years to complete and defend the doctoral thesis (Slovenian Research Agency, 2023a).

The occurrence of collaboration having been established previous to the start of a doctoral study may partly be explained by changes in the production of knowledge (Kitchin, 2014); namely, moving from individualistic and isolated knowledge production to a form that includes a far wider platform of theoretical and empirical resources (these changes are particularly relevant for the humanities and social sciences). Therefore, the new role of supervisors is to establish contact with talented students early on to enable them to discover the personally meaningful framework of their later doctoral study and possible professional career as a scientist. The fact that doctoral study, which includes all elements of research work, is not a linear process—but more sifting through data while seeking valid interpretations and linked back to published literature and finally transformed into new scientific understanding—might encourage supervisors to look for talented students in the earlier phases of their study to motivate them to develop their interest in scientific work. These earlier forms of collaboration can also be reflected in common publishing activities.

The year of thesis defence and scientific field discriminate the ‘born and raised’ from other (especially study-limited collaboration) clusters. The study-limited collaborations appear to be more common in later years and a relatively high proportion of them originate in technical and natural sciences. Two possible explanations may be discussed here. The first holds a positive connotation in terms of the high employability of doctorands in the technical and natural studies, who after defending their thesis soon continue their career in a non-academic environment in which publication activity is not of major importance. As already noted, one of the goals at least of the government-supported Young Researchers programme is to facilitate the transfer of doctorands into the non-academic sector, mainly into industry. The second possible explanation (with a negative connotation) is the problem of bending to the system’s requirements in terms of meeting the minimum criteria to obtain the degree and possible relegation to the scientific system’s periphery, with limited prospects of moving up the scientific ladder.

The last discriminant function reveals that established collaborations, with both mentors and other researchers, are more prevalent in the Medical sciences and among older mentees than in the other clusters, notably the cluster comprising established researchers who exclusively collaborate with mentors. Medical sciences stand out from other fields in various respects, such as a higher level of specialization and a smaller scientific community. Mentees in these fields consequently have limited flexibility in selecting collaborative partners. When combined with the typically longer duration of their studies, this often leads to the forming of very close collaborations prior to the completion of their doctoral studies.

To summarize, we can confirm that one-quarter of mentor–mentee relationships are entered into before doctoral studies even commence. The type of mentor–mentee relationship that is limited to doctoral studies nevertheless seems to be becoming more common. This could suggest several phenomena, such as the saturation of doctors in academia, the good receptivity of the non-academic labour market (especially in STEM), and the pursuit of a doctoral study for pragmatic reasons like promotion. Nonetheless, major differences exist among scientific fields.

The second research question addresses mentorship as an opportunity to build new long-term scientific collaboration among mentors. Clustering analysis revealed that no clusters would indicate this. On the contrary, the most common pattern is one whereby the scientific collaboration between the mentors was established before they started co-mentoring the first mentee. Also very common is the scenario in which mentors collaborate only during the mentoring period or the scenario where they do not collaborate at all during and (some years) after the mentoring period. The smallest cluster is characterized by very intensive and longer (compared to other clusters) collaboration, yet even here the collaboration seems to have been established prior to the commencement of the first co-mentoring and begins to weaken in the 10 years following their joint work on the mentee’s doctoral study.

The selected explanatory variables make it hard to discriminate between the patterns of collaboration that emerged (only the first discriminant function is statistically significant with a very low value of a squared canonical correlation). The cluster of co-mentors without publishing collaboration is closer to older mentors from different scientific disciplines.

The key takeaway appears to be that cross-disciplinary publication collaboration between mentors from different research fields is seemingly negligible. Scientific collaboration between mentors does not typically continue after the co-mentoring ends. This may suggest that the decision on co-mentoring is quite pragmatic. In this regard, the situation in Slovenia partially varies from the situation in some other European countries where “the collective institutional responsibility” (McAlpine, 2013, p. 267) in higher education processes is more strongly stressed. For example, in Nordic countries quite pragmatic decisions concerning selected doctoral co-supervision have mostly been replaced by dyadic forms of doctoral supervision, even supervision panels (Hutchings, 2017; Nordentoft et al., 2013). In Sweden, the official regulations state that a doctoral student should have (at least) two supervisors (Brodin, 2018).

While further studies are needed to explain the collaboration dynamic among mentors, one could speculate that the results we obtained are linked to several phenomena, such as where a co-mentor is invited to collaborate on the dissertation when particular knowledge is needed, e.g., methodological or statistical support, or the phenomenon of formal mentors, where the formal mentor engages very little in the mentoring (instead, the mentee works with their co-mentor).

Although various explanatory variables were selected to explain the clusters that emerged, the selection is still very limited to those available in the national administrative databases from which the data were acquired. Further controlling explanatory variables could reveal additional interpretations. Therefore, the study will continue with cognitive network analysis to locate every researcher in the ‘cognitive space’, determined by considering the content of their publications, in-depth interviews with the mentor and mentees and, finally, a survey used to test the holistic model of knowledge production that the mentoring relationship forms part of.

Conclusion

The study has examined the nature of establishing and preserving scientific collaborations between mentors and mentees, as well as among mentors.

It was confirmed that mentors and mentees often leverage their doctoral studies to establish new scientific collaborations. Still, collaborations confined to the duration of a doctoral study, although less common, are on the rise. Such partnerships are more characteristic of natural and technical sciences and for those engaged in the Young Researchers programme. This trend may suggest the favourable integration of doctorates into the non-academic labour market.

The professional development trajectories in which doctoral students build their collaborative scientific networks throughout their studies (and often become more autonomous from their mentors) remains the most prevalent one, underscoring the profound influence of the mentor–mentee relationship on academic socialization.

Another type of collaboration revealed by the study is one where the mentee already has well-established networks of collaborators even before they start their doctoral studies. The sub-type with a low level of collaboration with mentors is associated more with the humanities. A possible explanation is that the perception of mentoring is different in this scientific field in the sense that doctoral students are more often perceived as independent thinkers while their mentors might see themselves more as advisors or editors, rather than mentors. The sub-type with a high level of collaboration with mentors as well as with other researchers is more typical for medical sciences and older mentees, possibly due to the field’s specialized nature.

Co-mentoring a doctoral student does not typically pave the way for long-term collaboration between the mentors. This brings into question the role of a co-mentor, who might be more frequently regarded as an ‘external supervisor’ than an integral member of the research team.

Although there is a relatively high level of unexplained differences among the obtained types of scientific collaboration between the mentors and mentees, the variables related to the macro and mezzo levels seem to have a considerable effect on the type of scientific collaboration. Interestingly, mentors’ age, the presence of a commentor and gender homophily were not proven to affect the patterns of collaboration, despite studies showing the association between gender and the dynamic of mentorship relationship (Schwartz et al., 2022) and the way that researchers formulate and publish their research results (DeJesus et al., 2021; Huang et al., 2020; Lerchenmueller et al., 2019). Pezzoni et al. (2016) confirmed that gender homophily (between mentor and mentee) is related with the number and the quality (operationalized by their impact factor) of co-authored papers.

It should be noted that the present study is based on register data which offer a comprehensive insight into the publication activities of researchers but miss important contextual information with respect to the group and individual perceptions, values, and culture.

Overall, the conclusions of this study support the widely held view in sociological and social network theories of higher education that the relationship between mentors and mentees, i.e., the central point of any form of scholarly socialization, even if one focuses only on analysing their co-publication activities, has some general features in all scientific communities. These general features refer to the still important role of disciplinary differences in science, the nature of doctoral supervision (e.g., collective or individual), and—last but not least—the nature of recruitment of talented young people in the process of scientific socialization. Even though in many respects these experiences from Slovenia could be generalized to many other (national) systems of recruitment, socialization and further professional support for doctoral students in the EU member states, the results of this study suggest one should be very cautious about imposing any radical changes to the existing (Bologna) model of doctoral education.