Mathematical modelling and numerical bifurcation analysis of inbreeding and interdisciplinarity dynamics in academia

Abstract

We address a mathematical model to approximate in a coarse qualitative the interaction between inbreeding-lobbying and interdisciplinarity in academia and perform a one and two-parameter numerical bifurcation analysis to analyse its dynamics. Disciplinary diversity is a necessary condition for the development of interdisciplinarity, which is being recognized today as the key to establish a vibrant academic environment with bigger potential for breakthroughs/innovation in research and technology. However, the interaction of several factors including institutional policies, and behavioural attitudes put significant barriers on advancing interdisciplinarity. A “cognitive rigidity” may rise due to reactive academic lobby behaviours favouring inbreeding. The proposed model consists of four coupled non-linear Ordinary Differential Equations simulating the interaction between certain types of academic behaviour and the rate of knowledge advancement which is related to the level of disciplinary diversity. The effect of a control policy that inhibits inbreeding-lobbying is also investigated. The numerical bifurcation analysis reveals a rich nonlinear behaviour including multistability, sustained oscillations, limit points of limit cycles, homoclinic bifurcations as well as codimension-two bifurcations and in particular Bogdanov–Takens and Bautin bifurcations.

Introduction

The challenging complex problems that we are facing today, the ones with important social, health and environmental impacts (such as the climate change, the (re)emergence and the spread of infectious diseases and the mapping of the human brain connectome) are beyond the potential of any single scientific discipline to confront by itself. Their solution requires the synergy and integration of knowledge and efforts from diverse scientific disciplines. Thus, the role and importance of disciplinary diversity and its efficient integration is recognized today as a key to unlocking the potential to achieve breakthroughs in science and technology [1], [2], [3], [4], [5], [6], [7], [8]. Recall the example of computational neuroscience, a prototypical example of an interdisciplinary subject that was born around the early 70 s fertilized by the pioneering work of Ian Hodgkin and Andrew Huxley (Nobel Prize laureates in Medicine in 1963). The need to understand the complexity of brain development and functioning led to the integration of different traditional disciplines ranging from medicine and biology to physical sciences, social sciences, mathematics, and computer science.

Over the last decades, interdisciplinarity has been emerged in two ways [9]: (a) internally through the interaction and osmosis of different disciplines themselves (such as the case of the birth of computational neuroscience [10], and (b) externally-driven policies that increase and allocate public science funding. For example, the US government took the decision in 1988 to allocate a $3.8 billion (through its completion in 2003-$5.6 billion in 2010) funding the “Human Genome Project” with the objective of determining the DNA sequence of the entire euchromatic human genome within 15 years. According to studies, the benefit from this initiative added around $1 trillion to US economy [11], [12].

Today, many universities, government agencies and institutions acknowledge the importance of fostering multi- and interdisciplinary interactions both in research and teaching programs [3], [6], [7], [8]. However, this process is neither monotonic nor easy to establish. Several factors including structural and behavioural aspects, conflict of interests (especially in funding) raise significant barriers towards this aim [8], [13], [14]. All in all, what is recognized as the main barrier is the resistance to change [15]. These barriers establish a “cognitive rigidity” that favours the conduction of both research and teaching within rigid boundaries of disciplines [14]. Policies and practices for the allocation of research grants, recruitment, tenure and career advancement are some of the structural barriers hindering interdisciplinarity [8], [13], [16]. This structural “rigidity” coupled with professional friendships and academic lobbying behaviours make established/reactive practices harder to change [8]. As in any social system, people are connected to others that share common practices that are more familiar to them. In academia, this “familiarity” is expressed both in the advancement of careers and faculty recruitment. [17] defined “academic inbreeding” as the recruitment practice of departments/institutions to hire their own graduates as faculty directly after doctoral graduation (see also [18], [19], [20]).

In the past, this practice was likely to be beneficial in terms of fast production of research results as it fosters research team cohesion and continuity and diminishes recruitment risks [21]. However, it has been widely accepted [22] that academic inbreeding enforces the closeness of universities by favouring internal over external academic information exchange, thus leading to intellectual and organizational inertia [23]. Furthermore, academic inbreeding is criticized as a non-meritocratic practice hindering academic productivity, research quality and innovation [19], [21], [24], [25], [26].

On the other hand, it has been recognized that the challenges of today demand openness and disciplinary diversity to innovation [7], [8]. Thus, many countries, among them the USA, UK and Germany have established recruitment policies against academic inbreeding in order to facilitate dynamic interaction among academics with the aim of enhancing cross-disciplinary research [18], [27], [28].

Nowadays, it has been argued that the concept of academic inbreeding needs to be re-examined beyond its traditional “institutional” definition to include also “intellectual inbreeding” and “social”-related inbreeding: inbreeding has been associated with the re-production of learned knowledge, research activities, hiring practices, and a consolidation of social structures [29], [30]. In other studies, academic inbreeding is defined as the promotion of academic practices (hiring process, promotion of careers) on the basis of social/personal relationships (most often between senior faculty and former students), rather than on the basis of academic merits [19], [27], all in all what is called lobbying. Furthermore, inbreeding solidifies hierarchical relationships within departments, enhances the power of senior faculty members [19], consequently decreases disciplinarity diversity, thus leading to a vicious circle.

At this point we should note that there is no general consensus about what causes inbreeding and academic lobbying. Several reasons have been suggested including weak national academic labour markets, traditions of immobility in both employment and society, hiring mechanisms that involve personal/social ties and national language policies [19]. Interestingly, in most countries where inbreeding prevails, experts stress the importance of social ties (see for example the discussion in [19]).

Regarding scientific productivity, many studies have shown the negative effect of inbreeding in scientific productivity [21], [31], [32] and world’s research output in terms of innovation [19], [24], [32], [33]. However, as also noted in several studies [17], [19], [21], [34], the consequences of inbreeding are less harmful in “leading” universities, as their graduates are well above the average in terms of academic achievements and are well integrated into the international academic community.

Here, based on the above concepts, we construct and analyse a nonlinear ODE model that attempts to approximate qualitatively some features of inbreeding dynamics and its interplay with disciplinary diversity and the advancement of innovation. Our model (see Fig. 1 for a conceptual scheme) contains three types of individuals (adopting terms which are used in the literature [21], [27], [31], [35]: those that favour (are proponents to) academic inbreeding (lobbying), thus hindering cross-disciplinary research (we call them “Inbreds”), those that do not favour academic inbreeding and favour the advancement of disciplinary diversity (we call them “Outbreds”) and the “Neutrals”.

Because there is extensive literature on academic inbreeding, we will use the propensity to practice inbreeding as a proxy for being a proponent of disciplinary diversity. We recognize that these two concepts are slightly different, as inbreeding involves hiring graduates of the same university while disciplinary diversity means working with people from different research disciplines, but we suggest they are related as we also discussed above, thus adopting a more general concept/meaning of the above terms (also given in other studies (see e.g. [19], [36], [37]), than that usually given in the literature. For example the term “Inbreds” is most often used to characterize faculty who perform research and teaching in the university in which they had received all or any part of their training [17], [34], [38]. Similarly, the term “Outbreds” (or non-Inbreds) is most-often used to characterize the faculty [sic] “working in an university other than the one where the doctoral degree was awarded and worked on several universities during their academic career” [19], [27]. However, as discussed in other studies (see for example in [19], [36], [37]), the term “Inbreds“ is used in a more broader sense not limited to the fore-mentioned “geographical” mobility definition; it is rather used to characterize the faculty that favours inbreeding [sic] “based on personal relationships rather than the standardized evaluation of applications or the thorough analysis of individual skills” [36].

In our model, as reported in several studies (see e.g. [21], [27], Inbreds/Lobbyists show a clear tendency to work more within their sectorial/disciplinary expertise rather than on new ideas outside their discipline, i.e. on ideas that require interdisciplinary research. On the other hand, “Outbreds” refer to the individual researchers that do not favour inbreeding, and foster interdisciplinarity. So, individuals belonging to this category have an interest and tendency to work across traditional disciplinary boundaries. In fact, this attitude has been explicitly recognized as a transdisciplinary orientation characterizing researchers with higher production of interdisciplinary research articles [5]. Their interactions and relative dominance create the scientific-cultural environment affecting the capability of the system to achieve breakthroughs in knowledge and innovation (see e.g. the discussion in [24]). These two opposite behaviours objectively produce feedbacks on the diversity levels of the academic scenario, with the Inbreds/Lobbyists and Outbreds to decrease and increase, respectively in the long term, the rate of knowledge innovation. Neutral individuals represent those researchers that may not provide strong contribution to knowledge breakthroughs, but at the same time do not actively favour inbreeding. However, these individuals may change their status either joining the Inbreds/Lobbyists or the Outbreds. Such a decision is influenced (in an analogy to the concept of “cultural attractors”) by two opposing factors: the “power” of Inbreds and the level of attractiveness of interdisciplinarity fostered by the Outbreds, respectively [39], [40]. We also address a fourth variable (the potential for breakthroughs/innovation, $B$), representing the effect of the level of knowledge integration from different fields due to disciplinary diversity. By definition, $B$ is enhanced by Outbreds and inhibited by Inbreds/Lobbyists, as disruptive technologies and/or breakthrough concepts most likely rise from cross-border interactions rather than from data accumulation within an established field (see the discussion in [7], [8]).

We then perform a numerical bifurcation analysis to detect the critical points that mark the onset of phase changes in the academic structure and the related capability of innovation. Within this context, the bifurcation diagrams were constructed in the one and two-dimensional parametric space with respect to parameters related to the “influence” of Inbreds/Lobbyists and the external policy intensity aiming at establishing disciplinary diversity. The one-parameter numerical bifurcation analysis reveals a complex dynamical behaviour including multistability of equilibria, sustained oscillations, limit points of limit cycles and homoclinic bifurcations. The two-parameter numerical bifurcation analysis revealed the existence of Bogdanov–Takens and Bautin (Generalized Hopf) bifurcations.

Finally, we discuss some (loose) connections between our model and phase transitions observed in interdisciplinary research in biology reported from 1989 to 2000 due to the flow of Russian scientists in the USA, the Human Genome Project and the Internet diffusion.