# On the social and cognitive dimensions of wicked environmental problems
characterized by conceptual and solution uncertainty

Felber J. Arroyavea Department of Management of Complex Systems, Ernest and
Julio Gallo Management Program,
School of Engineering, University of California, Merced, California 95343, USA
Oscar Yandy Romero Goyenechea Utrecht University Centre for Global Challenges,
the Netherlands  Meredith Gore  Department of Geographical Sciences,
University of Maryland, College Park, MD, 20742 USA  Gaston Heimeriks
Copernicus Institute of Sustainable Development, Utrecht University, the
Netherlands  Jeffrey Jenkins  Department of Management of Complex Systems,
Ernest and Julio Gallo Management Program,
School of Engineering, University of California, Merced, California 95343, USA
Alexander M. Petersen  Department of Management of Complex Systems, Ernest and
Julio Gallo Management Program,
School of Engineering, University of California, Merced, California 95343, USA

11footnotetext:  a These authors contributed equally. Send correspondence to:
<EMAIL_ADDRESS>or<EMAIL_ADDRESS>
We develop a quantitative framework for understanding the class of wicked
problems that emerge at the intersections of natural, social, and
technological complex systems. Wicked problems reflect our incomplete
understanding of interdependent global systems and the systemic risk they
pose; such problems escape solutions because they are often ill-defined, and
thus mis-identified and under-appreciated by communities of problem-solvers.
While there are well-documented benefits to tackling boundary-crossing
problems from various viewpoints, the integration of diverse approaches can
nevertheless contribute confusion around the collective understanding of the
core concepts and feasible solutions. We explore this paradox by analyzing the
development of both scholarly (social) and topical (cognitive) communities –
two facets of knowledge production studies here that contribute towards the
evolution of knowledge in and around a problem, termed a knowledge trajectory
– associated with three wicked problems: deforestation, invasive species, and
wildlife trade. We posit that saturation in the dynamics of social and
cognitive diversity growth is an indicator of reduced uncertainty in the
evolution of the comprehensive knowledge trajectory emerging around each
wicked problem. Informed by comprehensive bibliometric data capturing both
social and cognitive dimensions of each problem domain, we thereby develop a
framework that assesses the stability of knowledge trajectory dynamics as an
indicator of wickedness associated with conceptual and solution uncertainty.
As such, our results identify wildlife trade as a wicked problem that may be
difficult to address given recent instability in its knowledge trajectory.

Scientific knowledge production is a necessary input for better responding to
the direct consequences, downstream impacts, and systemic risk associated with
complex problems bettencourt_evolution_2011 ; bloomfield_politics_2020 ;
defries_ecosystem_2017 ; helbing2013globally ; patterson_exploring_2017 .
Environmental problems in particular, such as climate change or biodiversity
loss, happen at the multidisciplinary intersection of ecological, social and
technological systems, and are therefore inherently complex
ramirez2020fostering ; smith2008social . Managing such challenging boundary-
spanning problems calls on the convergence of knowledge and expertise across
disciplines and inter-sectoral organizations petersen_grand_2021 . Although
different studies have addressed how knowledge is produced and integrated
within well-stablished disciplinary domains (e.g., astronomy), little is known
regarding scientific knowledge production about emerging environmental
problems within the broad envelope of sustainability science (e.g.,
bettencourt_evolution_2011, ).

In particular, we are motivated by _wicked problems_ , typified as untamed,
dynamically complex, and ill-structured problems, that lack clear-cut
conceptual and solution definition rittel_dilemmas_1973 ; alford_wicked_2017 ;
camillus_strategy_2008 ; head_wicked_2008 . Note that not all problems suffer
the same degree and type of ill-definition, or are equally ‘wicked’, as we
further discuss. These known but largely unattended problems wucker_gray_2016
are elusive given the multiple interdependencies and the absence of a
’correct’ view batie_wicked_2008 .

In order to fully appreciate the nature and implications of wicked problems,
communities of problem-solvers are needed in convergence to bridge knowledge
across disciplines, thereby triggering a common vision regarding the
properties of the core problems, and the means to address and manage them
alford_wicked_2017 . Such knowledge integration depends upon blending existing
concepts and social structures (e.g., formal communities of researchers) that
collectively and intentionally delineate an encompassing _knowledge
trajectory_ that defines the scope of knowledge around a given domain
heimeriks_how_2016 . Knowledge trajectories are thus defined as the
characteristic dynamical pathway followed by a domain in both its cognitive
(i.e., ideas and concepts) and social dimensions boschma_scientific_2014 ;
heimeriks_how_2016 ; wagner_network_2005 ; bonaccorsi2008search . Although the
study of knowledge trajectories has advanced towards identifying how knowledge
converge, diverge and eventually stabilize (e.g., bonaccorsi2008search, ;
bettencourt_scientific_2009, ; bettencourt_evolution_2011, ;
boschma_scientific_2014, ; heimeriks_how_2016, ), few studies have explored
how knowledge trajectories emerge within the scope of ill-defined or wicked
problems, where paradoxically, the multiple approaches can nevertheless
contribute confusion around the collective understanding of the core concepts
and feasible solutions.

Against this backdrop, we seek to provide a better understanding of knowledge
production around wicked problems starting with the question: _do knowledge
trajectories emerging around wicked environmental problems differ according to
their cognitive and social dimensions?_ As such, for a given problem domain,
we seek to elaborate on the association between the emergence and
stabilization of its knowledge trajectory, as it relates to the overall
wickedness of the underlying problem.

We develop this framework by constructing a representation of the knowledge
trajectory for each of three environmental problems – Deforestation, Invasive
Species, and Wildlife trade. These three problem domains were selected due to
the great risks for negative ecological and societal impact they pose, owing
to manifest systemic-risk associated with interdependent natural, social and
technological systems defries_ecosystem_2017 ; helbing2013globally ;
stirling_keep_2010 ; challender2021mis ; folke2007interdependent .
Specifically, a common criterion for selecting these three problems is the
lack of technically well-posed objectives, as multiple disciplinary lenses
might prioritize different components of the system and therefore the ways to
address the problem. We argue that these three environmental problems lack
certainty regarding the core concepts and possible solutions, and that such
flaws are sufficient to give rise to instability in the knowledge trajectory
dynamics which manifests in exacerbating conceptual and solution uncertainty.

This work contributes to the literature on the emergence and dynamics of
collective knowledge productionbettencourt_evolution_2011 ;
bettencourt_scientific_2009 ; boschma_proximity_2005 ; dolfsma_lock-and_2009 ;
heimeriks_how_2016 ; rafols_diversity_2010 ; sun_social_2013 ;
petersen_multiscale_2018 . To assess the emergence and stability of the
knowledge trajectory for each problem domain, we develop an empirical data-
driven framework focusing on the diversity of topics, disciplines,
collaboration, and geographic coordination. We associate each empirical facet
with either (a) cognitive dimension or (b) the social dimension. By
simultaneously comparing networks representing (a) and (b), in a similar vein
to prior research characterizing knowledge domains shiffrin_mapping_2004 ;
heimeriks_emerging_2012 ; petersen_grand_2021 , we seek to identify patterns
of scientific knowledge production related to wicked problems.

The remainder of this paper is structured as follows in Section I we describe
the relationship between cognitive and social dimensions of a knowledge
trajectory, in the particular context of wicked problems. Sections II
introduces the data and methodological framework for assessing the proposed
relationships. Section III presents our analysis on the cognitive and social
dimensions of knowledge trajectories. Finally, we conclude by discussing how
observed (in)stability in the social and cognitive dimensions relates to the
3-level typology of wicked problems developed by Heifetz & Heifetz
heifetz_leadership_1994 .

##  I Conceptual Background

### Defining the characteristics of wicked problems

’ Wicked’ is a concept that emerged from public policy research (also
frequently used in studies of science dynamics) referring to particular
characteristics of a knowledge domain alford_wicked_2017 ;
heifetz_leadership_1994 . However, we are unaware of literature exploring the
relationship between ‘wickedness’ and its implications on scientific knowledge
production. Hence, we seek to develop statistical methods for measuring,
evaluating and better understanding wicked problems.

Problems can be defined, among other notions, by the degree to which related
clear-cut concepts and solutions are identifiable. Heifetz & Heifetz
heifetz_leadership_1994  propose that in respect to the baseline of tame
problems (Type I), wicked problems can be divided between those with well-
defined conceptual definitions but with ill-defined solutions (Type II); and
those lacking both well-defined conceptual definitions and solutions. (Type
III).

In essence, not all wicked problems have the same degree of wickedness. On the
one hand, Type II wicked problems are conceptually clear but appear ‘fuzzy’ to
problem solvers, as they lack a single exact solution, or alternatively, are
faced with multiple solution pathways characterized by uncertainty
casals_fuzzy_1986 ; defries_ecosystem_2017 ; head_wicked_2008 ; head2019forty
. On the other hand, Type III wicked problems are inherently resistant to
clear and unique definitions alford_wicked_2017 ; camillus_strategy_2008 ;
defries_ecosystem_2017 , and are characterized by definition and solution
uncertainty (see, batie_wicked_2008, ; head_wicked_2008, ;
heifetz_leadership_1994, ; light_wicked_2020, ). In contrast to tame problems,
wicked problems result in thorny issues for which common top-down expert-
driven approaches can be insufficient to cope with their complexity
defries_ecosystem_2017 ; heifetz_leadership_1994 ; funtowicz_risk_1992 ;
schot2018deep ; rittel_dilemmas_1973 . In the present context, we acknowledge
that environmental problems aren’t simply differentiated as tame or wicked,
but given their tendency to be situated at the nexus of interdependent complex
systems, they are distributed in a spectrum of ill-definition or wickedness
alford_wicked_2017 ; head_wicked_2008 ; head2019forty .

Beyond the issues of ill-defined concepts and solutions, and the multiplicity
of conceptual and solution approaches, wicked problems are also exacerbated by
social factors. Indeed, problems derived from anthropogenic drivers are
socially situated alford_wicked_2017 ; camillus_strategy_2008 . Hence,
addressing wicked problems facing society and planet requires convergent
research spanning traditional disciplinary boundaries that leverages cross-
sectoral integration of expertise bammer_expertise_2020 ;
council_convergence_2014 ; light_wicked_2020 ; linkov_scientific_2014 ;
petersen_grand_2021 ; stirling_keep_2010 . Consequently, the variety of
stakeholders, interests, and objectives engaged in the social context may
involve a large collection of opinions and ideas about the problem itself and
its causes that can hinder consensus formation around a shared vision
alford_wicked_2017 ; batie_wicked_2008 ; camillus_strategy_2008 ;
defries_ecosystem_2017 ; funtowicz_risk_1992 ; rittel_dilemmas_1973 . For this
reason, it is commonly appreciated that the greater the disagreement among
stakeholders, the more wicked the problem is likely to be. Confusion, discord,
and lack of progress are telltale signs that an issue might be wicked
camillus_strategy_2008 . However, different studies (e.g.,
bettencourt_scientific_2009, ; petersen2015quanti, ; wagner_network_2005, ;
wagner2011approaches, ) also indicate that long term social interactions
between stakeholders is critical to the consequential diffusion of knowledge,
second-order learning and co-production of stable agreements schot_three_2018
; stirling_general_2007 ; schot2018deep . And while some scholars argue that
the multiplicity of stakeholders is the primary factor contributing to wicked
problems, we argue that such multiplicity is not a sole determinant. Instead,
we posit that social and cognitive integration plays a dominant role in
fostering the consolidation of knowledge domains, policy agendas, and shared
vision, which together can reduce conceptual and solution uncertainties
bettencourt_evolution_2011 ; defries_ecosystem_2017 ; guo_mixed-
indicators_2011 ; heimeriks_how_2016 ; rafols_diversity_2010 ;
stirling_general_2007 .

We seek to provide clarity around this point by analyzing cognitive and social
dimensions of knowledge trajectories rafols_diversity_2010 . Regarding the
first dimension, we posit that cognitive factors are most likely to obfuscate
the clarity of problem definitions. Such lack of agreement around concepts and
their relationships is characteristic of endeavors calling on multi-
disciplinary problem-solving. Consequently, wicked problems may fail to
consolidate into stable trajectories because new efforts fail to
constructively leverage and contribute to existing knowledge
boschma_scientific_2014 ; heimeriks_how_2016 .

Regarding the second dimension, social factors tend to contribute uncertainty
concerning the set of solution pathways. We posit that the benefits of
collaboration are less potent in research communities lacking clearly
delineated pathways forward, and conversely, that problems lacking
identifiable pathways forward are less likely to elicit stable community
formation. Indeed, establishing and sustaining consequential leadership may be
untenable in wicked scenarios if there is a failure to alert, activate,
orient, and incentivize the vast field of candidate problem solvers
rittel_dilemmas_1973 . Ideally, critical scientific agendas become
institutionalized as ’ Grand Challenges’ that serve as a lighthouse beacon to
guide trajectories toward a clearly identifiable objective helbing2013globally
; petersen_grand_2021 . Another important consideration is that wicked
problems are by definition intractable, thereby lacking a single ’closed-form’
solution; hence, ’ better’ solutions are converged upon instead of a unique
’correct’ one. Such a process is typically feasible when stakeholders
iteratively converge in agreement on how to institutionalize agendas that best
address the problem alford_wicked_2017 ; batie_wicked_2008 ;
camillus_strategy_2008 ; funtowicz_risk_1992 ; funtowicz_uncertainty_1994 ;
stirling_keep_2010 . As such, wicked problems are commonly managed, as opposed
to being solved, giving rise to a situation that requires long-standing
agreements between stakeholders, robust research agendas, and inter- and
trans-disciplinary approaches – e.g., as Masterson masterson_malaria_2014
shows for the case of managing the malaria crisis in global tropical and
subtropical zones.

### The relation between problems and knowledge trajectories

Various studies have addressed the knowledge trajectories for well-stablished
domains (e.g., astrophysics; organic chemistry) identifying that they
eventually reach stable trajectories reflecting the steady-state accumulation
of intellectual development (e.g., bonaccorsi2008search, ; heimeriks_how_2016,
; heimeriks_emerging_2012, ; wagner2011approaches, ). Such stability emerges
from the incremental addition of coherent knowledge; in other words, knowledge
based upon the preexisting. Although emerging fields (e.g., computer sciences)
show a more turbulent pattern characterized by fluctuations owing to
disruptive innovations, and therefore less related knowledge. Such fields
nevertheless eventually achieve stability in their richness, e.g. proxied by
descriptors like the rate of new keywords used – e.g., see Bonaccorsi
bonaccorsi2008search . Similarly, research on social dimensions (e.g.,
bettencourt_population_2008, ; bettencourt_evolution_2011, ;
petersen_multiscale_2018, ) show that social cohesion manifesting as
consolidated collaboration is a common characteristic of synergistic cross-
disciplinary integration; alternatively, if persistent collaboration is
lacking, then it is less likely that consequential blending of concepts and
methods will succeed.

A common theme in knowledge trajectory research is what role relatedness plays
in knowledge diversification boschma_scientific_2014 ; dolfsma_lock-and_2009 ;
heimeriks_emerging_2012 ; heimeriks_how_2016 . Implied in this definition of
relatedness is the strong path dependency regarding the entry and exit of
knowledge building-blocks accumulated in the system heimeriks_how_2016 . We
argue that cognitive relatedness thus captures to the permanence, continuity,
and integration (with the preexisting) of concepts and ideas.

Similar to cognitive relatedness, social relatedness refers to the permanence
and reinforcement of pre-existing associations between partners. Long-term
collaborations underly established process of academic debate
grauwin_mapping_2011 ; wagner_network_2005  that assists in consolidating
agendas, enables deep learning within and across academic communities
bettencourt_evolution_2011 ; granovetter_economic_1985 ; reinders_role_2011 ,
is associated with higher-impact research outcomes petersen2015quanti . Stable
collaboration is therefore an indicator of social consolidation of knowledge
trajectories bettencourt_evolution_2011 .

Cognitive and social networks provide a well-established framework for
defining synthetic indices for analyzing the structure and dynamic of
scientific knowledge production (e.g., bettencourt_evolution_2011, ;
bettencourt_scientific_2009, ; boschma_proximity_2005, ; calero-
medina_combining_2008, ; fagerberg_innovation_2009, ; frenken_spatial_2009, ;
funk_dynamic_2017, ; grauwin_mapping_2011, ; grauwin_mapping_2011, ;
rafols_diversity_2010, ; stirling_general_2007, ; uzzi_atypical_2013, ;
petersen_grand_2021, ). Building up on these efforts, here we focus our
analysis around the dynamics of two complementary characteristics – the
_diversity_ and the _relatedness_ of the entities comprising the aggregate
knowledge trajectory. This approach is similar to previous research using
diversity measures to characterize knowledge trajectories and relatedness
boschma_scientific_2014 ; heimeriks_how_2016 ; heimeriks_emerging_2012 ;
rafols_diversity_2010 ; stirling_general_2007 .

To distinguish our approach to measuring diversity, we first define diversity
using the typology proposed by Harrison & Klein harrison_whats_2007 , which
differentiates between three alternative perspectives: variety, separation,
and disparity. Unlike previous studies, here we seek to evaluate the emergence
of diversity in problem-solving approaches by measuring disparity, as opposed
to variety (also referred to as richness) or separation. To be specific, while
variety refers to counting the total number of varieties of entities (or
richness of a system), and separation measures the characteristic differences
between expressed values (differentiation), here we choose a measure of
disparity because it directly measures the dominance of one or few varieties
over the remaining varieties (i.e., heterogeneity in concentrations of
varieties). We posit that saturation to a problem-specific diversity level is
a robust indicator of whether or not a knowledge trajectory is confounded by
conceptual and/or solution uncertainty.

To develop this assessment framework, we systematically analyze disparity
levels for three research areas – Deforestation, Invasive Species, and
Wildlife trade – motivated by the following postulations:

  * P1.

Invasive Species. Given the clear task and conceptual definition of what is an
invasive species, we anticipate stable knowledge trajectory dynamics for both
cognitive and social dimensions (i.e., closer to a tame problem).

  * P2.

Deforestation. While the definitions regarding deforestation are clear, this
problem suffers from a lack of effective solutions, in part owing to multiple
global stakeholders, despite being a problem that is highly localized. Hence,
this problem suffers primarily from solution uncertainty (i.e., Type II wicked
problem). As such, we expect such conditions to generate unstable or turbulent
collaboration patterns.

  * P3.

Wildlife Trade. In contradistinction to P1 and P2, we suspect that instability
in both cognitive and social dynamics results from relatively high conceptual
and solution uncertainty (i.e., typical of a Type III wicked problem).

Figure 1:  Disciplinary composition of three environmental
problems.Disciplinary composition of the three environmental problems domains:
(a) Deforestation; (b) Invasive Species; (c) Wildlife Trade. Shown are the top
20 most frequent WoS categories associated with each. Data point colors
indicate physical sciences (green) and social sciences and humanities (blue).

##  II Methods

We analyze knowledge trajectory change by assessing structural changes in
diversity (disparity) among the constituent components of the research corpus
in and around each problem domain bettencourt_evolution_2011 ;
fagerberg_innovation_2009 ; heimeriks_how_2016 . In what follows we first
detail the environmental problems addressed and then we describe our proposal
for assessing structural changes in a given research domain, which is
sufficiently general to be applied beyond the three case studies explored in
this work.

### Environmental problems

Grand environmental challenges involve high degrees of uncertainty in
cognitive, social, and technical dimensions. By way of example, a conservation
biologist may have to make decisions or recommendations about ecosystem
management before a complete theoretical, empirical or methodological
foundation have been established alford_wicked_2017 ; head_wicked_2008 ;
head2019forty ; soule_what_1985 ; soule_what_1998 . Therefore, tolerating
epistemic uncertainty in terms of what the best available knowledge may be an
unavoidable component of environmental science defries_ecosystem_2017 ;
stirling_keep_2010 .

#### Three environmental problem examples

We focus on three environmental problems of global extent (Deforestation,
Invasive species, Wildlife trade) with origins in human development
van_uhm_social_2018 . Since the late 1970s several studies have suggested that
the three problems are both drivers and symptoms of global change,
biodiversity loss and the asymmetric relationship between the global North and
South barney_global_2011 ; scheffers2019global ; willcox_history_1974 . These
problems are therefore incorporated into political actions through
international conventions and accords that deal with the interconnected nature
and boundary crossing aspects of the phenomena at hand; examples include the
Convention on International Trade in Endangered Species of Wild Flora and
Fauna (CITES) of 1973, the Convention on Biological Diversity (CBD) of 1992,
and the Reducing Emissions from Deforestation and Forest Degradation (REDD) of
2008.

The first problem studied is Deforestation, which refers to the intentional
reduction of forest cover in both legal and illegal contexts. Deforestation
has been tied to the expansion of commercial and subsistence agriculture
frontier, legal and illegal logging for paper and industrial hardwood,
urbanization, desertification, and climate change barbier_trade_1994 ;
malhi_climate_2008 ; willcox_history_1974 . The impacts of deforestation on
vulnerable populations can be wide ranging and degrade human wellbeing
barbier_trade_1994 ; carrasco_2017 . Figure 1a shows the disciplinary
composition of the scientific research on deforestation, illustrating a
background context involving both the natural sciences (in the endeavor to
assess land cover change and its impacts), as well as the social sciences
(relating to forest/agriculture management, as well as efforts to understand
the sociocultural and economic impacts of deforestation).

The second problem studied is Invasive Species, which refers to biological
invasions or the unnatural demographic growth of species. Invasive species are
frequently nonnative species introduced to an ecosystem either intentionally
(e.g., in an active, deliberate manner) or unintentionally (e.g., in passive,
accidental manner), though some native species can also become invasive
cassey_global_2004 ; hulme_trade_2009 . The mechanisms and consequences of
biological invasions differ across species, organisms, and economic settings
hulme_trade_2009 . The economic impacts of controlling or coping with
existing, or preventing new, invasions are significant, frequently exceeding
hundreds of billion dollars per year mooney_evolutionary_2001 . Biological
invasions are mostly human driven, though ecologically shaped and filtered
which reflect the disciplinary composition of the research in this problem
that is notably focused on biological sciences, in particular zoology Fig.1b.
From a disciplinary perspective, biological invasion is mostly addressed
through the lenses of natural sciences, with little social sciences imprint
despite the known consequences of invasive species in the livelihoods and
economy of the inhabitants of the recipient ecosystems shackleton_role_2019 .

Finally, the third environmental problem is Wildlife Trade, or alternatively
wildlife trafficking, which refers to the legal and extralegal
commercialization and use of wild fauna and flora, as well as their derived
products. Both legal and illegal wildlife trade frequently suffer from fuzzy
boundaries that are highly debated in academia and practice challender2021mis
. Wildlife trade spans through local and international scales encompassing
complex social networks that supply the increasing demand for medicines,
souvenirs, pet markets, wild meats, and cultural customs
arroyave_multiplex_2020 ; scheffers2019global ; van_uhm_social_2018 . One
aspect of the problem frequently highlighted is its profound ecological and
social impacts arroyave_multiplex_2020  such as biodiversity loss, corruption,
and violence. In contrast to the previous two problem domains, Wildlife Trade
has prominent research streams in the social sciences. More specifically,
Fig.1c shows that besides biological sciences, this problem is co-dominated by
human sciences such as criminology and government.

### Data

Multiple scientific repositories have been widely used for understanding
scientific dynamics. We use Web of Science (WoS), one of the most prominent
sources of indexed literature leydesdorff_global_2013 , to collect the
scientific literature associated with each one of the environmental problems
here studied. The information was downloaded in November 2020 using general
queries designed to capture each problem (see Supplementary Note 1 -SN.1-).
For each publication we extracted various metadata fields, including journal
(SO), authors (AU), keywords (DE), year of publication, country of authors’
affiliation (CU) and, WoS research subject category (SC, similar to WoS
disciplinary category (WC), both of which are journal-specific ontologies).
Furthermore, for each source we also tally two co-occurrence measures, one for
co-author (C-AU) and another for co-keyword (C-DE), in which we tally the
frequency of dyads, i.e. the number of publications featuring author
(alternatively keywords) A & B.

#### Data refinement using co-bibliography networks

Scientific repositories systematically compile, store, and make accessible
vast quantities of information regarding scientific productivity. However,
these information search and retrieval engines might be sensitive to
misidentifications and synonyms. To avoid including unrelated publications
within our analysis we focus on publications cognitively related with at least
part of the core literature associated with each problem domain. We identified
such publications by reconstructing the corresponding co-bibliography network
grauwin_mapping_2011 ; ramirez_mobilizing_2018 ; velden2017comparison .

Figure 2:  General characteristics of the source sets defining the 3 case
studies. Deforestation (orange), Invasive species (brown), wildlife trade
(purple). (a) Cumulative number of sources including data for Ecology (green)
for benchmarking purposes. (b) Cumulative number of knowledge communities
emerging through a given year, reported as the proportion of the total in 2020
to better facilitate comparison. (c) Author productivity distribution,
indicating common scaling despite underlying differences in research domain
size.

Co-bibliography networks (CBN) synthetize the association of a pool of
publications through the literature they cited. CBN are composed by nodes
(publications) connected by links that indicate the bibliographic similarity
or bibliographic coupling between them. Publications with high similarity
share a large proportion of bibliographic references, thus they are expected
to address similar problems, or use similar frameworks crane_invisible_1973 ;
palacios2018developmental . Therefore, links in CBNs represent cognitive
proximity between publications. As such, clusters of densely connected
publications in a CBN represent groups of topic-specific publications. Note
that we consider publications within these groups as consolidated knowledge
since it underlies communities of researchers where the knowledge is discussed
and diffused crane_invisible_1973 ; fagerberg_innovation_2009 ;
latour2013laboratory . While there are other extant methods for mapping
publication topics, we choose CBN being that it produces maps similar to other
methods velden2017comparison  and it is amenable to including recent
literature that has not yet had sufficient time to be itself cited
grauwin_mapping_2011 .

We assess the bibliographic coupling between pairs of publications by using
the bibliographic coupling distance2 22footnotetext:  Bibliographic coupling
similarity $w_{ij}$ is defined by $\frac{|R_{i}\cap
R_{j}|}{\sqrt{|R_{i}||R_{j}|}}$, where $R$ represents the list of references.
Hence the distance between publications $i$ and $j$ is calculated as the
intersection of their references, normalized by the length of both reference
lists. proposed by Kesser kessler1963bibliographic  and implemented by Grauwin
& Jensen grauwin_mapping_2011 , which defines the coupling as the normalized
intersection of the cited references, varying from 0 (no coupling) to 1
(identical bibliographies). Following Ramirez et al. ramirez_mobilizing_2018 ,
we exclude from the analysis those links that represent low cognitive
proximity between papers (i.e., small coupling) by defining a threshold that
maximizes the formation of highly cohesive clusters of papers (i.e., network’s
modularity). We use the Louvain algorithm to identify these clusters
grauwin_mapping_2011 , which we term knowledge communities (KC). The threshold
is defined by iteratively removing the links weighted lesser than a given
value, and then measuring general properties of the resulting network such as
the resulting modularity, as described in S.N.2. By removing weak links, we
seek to retain the maximum of information (i.e., nodes and links) while
exposing the structure defined by strong links granovetter_economic_1985 ;
petersen2015quanti  defined here as communities forming around high cognitive
proximity. Consequently, several nodes might become disconnected and form
small components corresponding to tangential research. Note that studies using
networks frequently rely on analyzing the giant component of the network and
excluding the smaller components (e.g., newman2018networks, ). Here we include
communities larger than an arbitrary threshold of 10 nodes, which maintains
our ability to capture emerging topics ramirez_mobilizing_2018 . As such, we
include nascent frameworks and ideas, but exclude inconsistent, non-related,
and isolated publications.

#### Data characteristics

Using threshold values of 0.167 (Deforestation), 0.177 (Invasive Species), and
0.181 (Wildlife Trade), we obtain core CBN networks comprised of: 12,674
publications for Deforestation; 15,947 for Invasive Species; and 650 for
Wildlife Trade. The resulting networks are highly modular (0.88 for
Deforestation, 0.95 for Invasive species, and 0.85 for Wildlife trade)
indicating that the communities identified are highly cohesive and well-
defined.

Importantly, we note differences in the onset of knowledge consolidation for
each problem domain, indicated by the year of the first publication and the
time to reach half maximum, as illustrated in Fig.2a and Fig.2b. Note that we
refer to consolidated knowledge (or strongly connected CBN) rather that
publications in general. Although the three problems are relatively
contemporary (the earliest observation is in the 1960-70’s for the three
cases), consolidated knowledge for Deforestation and Invasive species emerges
in the early 1980’s, whereas for Wildlife Trade it emerges in the late 1990’s.
In Fig. S1(a,b,c) we provide additional network visualizations showing the
emergence of select knowledge communities. For each case we observe a
sigmoidal curve, similar to other studies of collaboration networks
(Bettencourt et al., 2008), here indicating the onset of knowledge
diversification since each community represents a collection of research
articles that are highly coupled in terms of their knowledge inputs (see also
Fig.3).

To assess the numerosity and productivity of researchers in each problem
domain, we applied a simple name disambiguation method by collecting articles
authored by common surname and first initial, an approach that is remarkably
robust in studies of this scope milojevic_accuracy_2013 . As well documented
in the literature bettencourt_population_2008 ; petersen_inequality_2014 ;
sun_social_2013 ; wagner_network_2005 , we observe an extremely right-skewed
productivity distribution Fig.2c), indicating that each problem supports just
few highly productive authors, whereas the vast majority of scholars publish
just few research articles. Despite the differences in the publications
abundance for each problem, estimation of the skew using the single-parameter
power law distribution model $P(x=\textrm{sources per author})=x^{a}$,
indicates similar scaling exponents ($a=$ 2.495 for Deforestation; $a=$ 2.494
for Invasive species; $a=$ 2.246 for Wildlife trade). In summary, we show that
the 3 case studies are not markedly different in their general
characteristics, thus we argue that differences are defining features of the
problem domains, as opposed to idiosyncratic differences associated with
variation in sample size and scholar productivity.

### Analytical approach

In this section we distinguish research article metadata categories used as
proxies for either cognitive or social dimensions. For the cognitive dimension
we include the size of knowledge communities (KC), the frequency of keywords
(DE), keywords co-occurrence or dyads (C-DE), subject categories (SC), and
journals (SO). For the social dimension we include the frequency of authors
(AU), coauthors dyads (C-AU) and countries (CU). Then for each variable we
measure the disparity, using two measures that both correspond to greater
disparity the smaller the value: Shannon Evenness index mccune_analysis_2002
and the Complementary Gini index (or simply $1-G$, where $G$ is the
traditional Gini index). We measure the diversity over the publications
retained in the CBN.

In more detail, Shannon evenness3 33footnotetext: The Shannon evenness $E$ is
represented by $-log(m)^{-1}\sum_{i=1}^{m}log(p_{i})p_{i}$, and is a bounded
version of the traditional Shannon entropy, normalized by the maximum entropy
$log(m)$ associated with equally frequent ($m$) varieties; where $m$ is the
total number of distinct varieties or types. is a normalized version of the
Shannon entropy which measures the average level of information contained in
the variable mccune_analysis_2002 . Alternatively, the Gini index4
44footnotetext: The Gini inequality index $G$ is calculated by
$(2n^{2}\overline{x})^{-1}\sum_{i=1}^{n}\sum_{j=1}^{n}|x_{i}-x_{j}|$,
evaluates the mean absolute difference between all pairs of values ($x$),
where $n$ is the total number of data values. is an inequality coefficient
that measures the pairwise difference between all the data values in the
sample normalized by the value expected of this quantify for a uniform
distribution. We use the complementary Gini (1- Gini) to simplify the
comparison with Shannon. In general, these two indices measure diversity
according to the disparity within the distribution of distinct varieties. Low
diversity (corresponding to high disparity) is associated with a system
dominated by few varieties or high homogeneity; while high diversity (low
disparity) represents high heterogeneity in the system since varieties are
uniformly distributed a no one dominates. Both metrics vary from 0
(representing homogeneity, low diversity, high disparity, high concentration)
to 1 (heterogeneity, high diversity, low disparity, low concentration).

We evaluate the temporal changes in the diversity in two ways – intra-annually
and inter-annually. In the first case we calculate the intra-annual diversity
using just the varieties that exist in each given year. Changes in intra-
annual diversity indicate whether the disparity varied in a particular non-
overlapping time-frame. For instance, a decrease in intra-annual authorship
diversity indicates that the publications in a given year increasingly
concentrated on just a few productive authors. Note that successive intra-
annual diversity values might be the same, indicating for instance certain
degree of concentration in a particular author, but the disparity can be
produced by different varieties (e.g., author $a$ dominates in year 1 and
author $b$ in year 2).

We complement the intra-annual perspective with a second cumulative
perspective on diversity change, calculated by accumulating varieties from the
beginning of the data up through the specific year being analyzed. In this
way, an increase in the inter-annual diversity indicates that varieties
included in year $t$ were marginally represented in the past, and possibly
non-existent. We argue that this inter-annual perspective accounts for the
temporal change in path-dependent or relatedness of the varieties existing up
through year $t$, since variations depend upon the intra-annual diversity of a
given year and the previously existing varieties. In other words, the inter-
annual diversity evaluates how varieties in time $t$ fit into the existing
trajectory funk_dynamic_2017 .

Finally, we assess the degree to which a given disparity value could arise
from random configurations of the same empirical varieties, calculated by
estimating the average diversity values obtained through a random null model.
In this way, the null model captures patterns representing a baseline for a
particular problem, where the variables of interest have no effect (see,
swenson2014functional, ). Our null model is comprised of 5000 random
ensembles, where each ensemble of varieties is obtained by shuffling the
publication years (i.e., intertemporal resampling), followed by the
calculation of the intra- and inter-annual diversities. We then represent the
estimated null diversities as the mean diversity across 5000 realizations
along with the corresponding inter-quartile range. In this way, we conserve
the number of research articles analyzed in a given year, but allow for
variation in their other covariates. The objective of this comparative
baseline is to assess to what degree temporal patterns can be explained by
phenomena in excess of the intrinsic fluctuation level associated with the
entry and exit of varieties, as well as their frequency dynamics.

Note that in cases where there is little difference between the empirical
intra-annual diversity and the null model suggests that the diversity is a
product of the number of varieties included, but not of their distribution.
Moreover, small differences between the empirical inter-annual diversity and
the null model indicates the absence of temporal sorting and sporadic bursts
in the underlying data. If the temporal distribution of varieties has some
order (e.g., some prolific author only published in early years and then were
replace by new prolific authors) it is unlikely that the null model captures
such order. Note also that in the last year of evaluation differences in the
inter-annual diversity between the null model and the empiric data are not
expected since the distribution of varieties in the last year is the same for
both. All the calculations were made in R 3.6 team2013r  using the package
igraph csardi2006igraph .

Figure 3:  Cognitive composition of the three environmental problems. Co-
bibliography networks showing knowledge communities (groups of publications
represented by circles) connected by links conveying their cognitive relation
(see Supplementary Note 2). We manually labeled several communities according
to the topics addressed by the group. The size of the circle represents the
number of publications, and the thickness of links is proportional to the
number of connected publications

##  III Results

In the previous sections we document the similarities in growth rate, author
productivity distribution, and modularity of the co-bibliography networks
(CBN) shown in Fig.2. In what follows, we first further describe the CBNs for
each of the three environmental problems, and then we assess the disparity
dynamics, used as proxies for the temporal structure of the cognitive and
social dimension of the overall knowledge trajectory. Importantly, the
observed dynamics are consistent regardless of the diversity measure used, as
indicated by comparing calculations using Shannon Evenness (Fig.S2-S5) and
Complementary Gini indices (Fig. S6-S9). Thus, we choose to focus the
remainder of our analysis on the results obtained using the complementary Gini
index.

Figure 4:  Temporal variation in parity in cognitive dimension. Temporal
parity measured as the complementary Gini index (1-Gini) in knowledge
community sizes for three problem domain areas: Deforestation (orange),
invasive species (brown), and wildlife trade (purple). (a) Intra-annual
variation. (b) Cumulative (inter-annual) variation. Larger (smaller) parity
values (reported as 1-Gini Index) correspond to lower (higher) concentration
levels. Shaded intervals denote the interquartile range for data generated by
randomized null model, applied to each domain separately; dashed lines
indicate the mean null model realization value

Knowledge communities (KC) are natural elements for analyzing the structure of
CBNs, given their co-bibliographic construction. In Fig.3 we show a simplified
representation of each CBN (for detailed networks see Fig. S1) in which nodes
represent KC and links between them represent the number of articles connected
(representing bibliographic coupling) between the papers included in each pair
of KCs. Note that the number of KC between each problem analyzed vary.
Differences in the sizes of KC (number of papers included) within each problem
are evident, showing that the BCNs are composed of a few very large
communities and a (relatively) large collection of small communities, some of
which are disconnected from the network’s fully connected (giant) component.

As mentioned, KC are clusters of publications cognitively proximal research
publications. Such clusters represent conceptual and methodological
frameworks, developed by scholarly communities incrementally over time for the
purpose of forming a coherent scientific discourse calero-
medina_combining_2008 ; grauwin_mapping_2011 ; rafols_diversity_2010 ;
ramirez_mobilizing_2018 . By manual assessment of titles and abstracts we can
identify the topics covered in each KC. For example, we find that
Deforestation KC encompass a variety of topics such as the relation between
land cover and water quality, fragmentation and habitat use, human impacts on
habitat integrity, the role of forest in economic growth and equity, and the
relationship between production of sustainable energies and deforestation,
among other topics (see Fig.1a, Fig. S1a). KC topics for Invasive Species
include the genetic structure of invasive populations, comparative biology
between invasive and non-invasive species, management of invasions, dispersion
and spatial structure of invasion, and invasions in human-dominated ecosystems
(Fig.1b, Fig S1b). Finally, Wildlife Trade is characterized by KC topics
associated with criminology, invasive species derived from wildlife trade,
epidemiology and public health, the relationship between wildlife trade and
social media, law enforcement and policy, among other topics (Fig.1c, Fig.
S1c). Note that the collection of topics included in each problem reflect the
multiple views that researchers develop. Although many views can be
complementary, it is likely each one emphasizes specific elements (concepts)
of the problem, and therefore also addressing possible solution pathways.

### Cognitive Dimension

We analyze the cognitive dimension of each knowledge trajectory by assessing
the changes in the disparity – for both intra and inter-annual levels. First,
Fig.4a shows the intra-annual variation for knowledge community sizes, which
indicates a sustained increase in diversity (increasing parity) across all
problem domains. However, we note for Invasive Species and Wildlife Trade that
the trajectories are only slightly greater that the expected values yielded by
the null model. This suggests that the intra-annual diversity for these two
problems is consistent with the random expectation and the changes in the
diversity are the product of the increase in the volume of publications. In
contrast, the KC diversity for Deforestation prior 2008 can’t be explained by
the abundance of publications, suggesting the existence of some internal
process associated with the temporal distribution of efforts across multiple
KC that lead such high initial diversity.

On the other hand, analysis of inter-annual variation, which better accounts
for inter-temporal correlations manifesting in burstiness, shows a rapid
increase in the diversity with large deviations from the null model,
especially during early periods (Fig.4b). However, Wildlife Trade, and also
Deforestation to a lesser degree, feature prominent decreases in diversity
corresponding to higher concentration levels (i.e., smaller Complementary Gini
index values). Additionally, complementary Gini index values for Wildlife
trade are consistently smaller than the rest of the problems, indicating in
general a lower baseline diversity, which is indicative of higher
concentration of knowledge within certain KC. We posit that both saturation
around a stable value, as well as higher concentration levels, can be
associated with higher relatedness. In such a case, as more recent
publications are incorporated, they tend to disproportionality contribute to
the growth of a few existing KC, as opposed to creating new KC or being
homogeneously distributed across existing KC. As such, results for KC indicate
that topical diversity emerges through diversification of varieties which tend
to grow equitably towards a stable saturation point at which point the system
of knowledge is coherently related, as it is the case of Invasive Species.

In addition to KC, we also computed the disparity time series for several
other cognitive dimension variables (Fig.5a-b), including subject category
(SC), journal (SO), keywords (DE), and keywords dyads (C-DE); for simplicity
we present only a subset of these results, and the rest are presented in Figs.
S2-S9. Results for intra- and inter-annual variation in the diversity of the
mentioned variables indicate that the variables are mostly indistinguishable
from the null expectation at the intra-annual level; the inter-annual
variables follow a generic increase in diversity that coincides the null
expectation, except for Deforestation which features a relatively high initial
diversity (Fig.5a-b); Wildlife Trade features relatively high concentration
levels for inter-annual dynamics (Fig.5a-b, Figs S2-S9). As such, we
corroborate that the main differences in the cognitive dimension between the
problem domains is in the analysis of KC disparities (Fig.4a-b).

Figure 5:  Temporal variation in parity in cognitive and social
dimensions.Cumulative (inter-annual) parity calculated for three problem
domain areas – deforestation (red), invasive species (blue), wildlife trade
(purple) – and 4 different types of cognitive and social networks: (a) WoS
Subject categories; (b) co-keywords dyads, (c) co-authors dyads, and (d)
author affiliation country. Shaded intervals denote the interquartile range
for data generated by randomized null model, applied to each domain
separately; dashed lines indicate the mean null model realization value. For
comparison, intra-annual analysis is provided in the SM.

### Social dimension

In order to analyze the social dimension of each knowledge trajectory, we
present results for co-author and country disparity, as indicators of the
relatedness of social communities (see Fig. S2-S9 for results derived from
other social dimension variables). In particular, we focus on results
corresponding to inter-annual diversity.

Figure Fig.5c shows the results for C-AU (which are nearly identical to the
results obtained for the authorship variable), which indicate that
collaboration is a variable that largely differs from the expectations of the
null model for Deforestation and Invasive Species, but less so for Wildlife
Trade. Although we identify prolific authors (Fig.3c) in the research domain
of Wildlife Trade, their impact is diminished in the case of inter-annual
variation where we account for their temporal ordering. Interestingly, for
Wildlife Trade and Deforestation we note a reversal towards higher
concentration during the past decade, indicating an increase in the social
relatedness possibly owing to a greater exploitation of existing
collaborations. This suggests, at least for Deforestation, that the research
activity has recently concentrated in a subset of authors and their
collaborators.

Analysis of author affiliation country data provides a proxy for diversity in
organizational (e.g., Universities, Research centers, NGOs) and institutional
factors (e.g., national science funding). Results reported in Fig.5d show that
empirical diversity calculated for Deforestation and Invasive Species feature
early excess parity with respect to null model levels. Over time these
differences reduced as parity levels stabilized around steady values,
indicating high geographic parity. Wildlife Trade features little deviation
from random expectation, and parity has steadily increased over time,
corresponding to a decreased concentration of geographic leadership. To
further support these results, we also calculated productivity diversity
between the global South and North (Figs. S5i-S9i) and also observe
inequalities in the production of knowledge generally decreasing over the long
run.

In summary, we identified important differences across the three environmental
problems evaluated. Invasive Species is characterized by an increasing
diversity in both cognitive and collaboration trajectories that saturates in
recent times. Such a pattern describes homogenous growth across the different
topics embodied, and the community of researchers as well as their supporting
organizations, in addition to growth supported by preexisting structures
(i.e., topics and researchers) fostering the recent stabilization of both
cognitive and social dimensions.

Similarly, Deforestation is also characterized by high diversity levels, for
both cognitive and social dimensions, and featuring an approach to a stable
diversity level. However, for some cognitive (KC) and collaboration (CU, C-AU)
variables, we observe a slight reduction in the diversity indicative of recent
increase in concentration in some varieties (e.g., topics, authors). These
suggest changes in the scope of the research in this problem either by
increased emphasis or paucity in some topics and researchers. We also observe
reduced productivity inequalities between the global North and South.

Finally, Wildlife Trade represents the most distinct problem of the three,
showing important changes in cognitive (KC) and collaboration trajectories
(C-AU) characterized by strong reduction in the diversity after periods of
sustained increased. Observed parity values are typically less than those
observed for other problems and are indistinguishable from the null
expectation in many circumstances (DE, C-DE, AU, C-AU, CU). These results
indicate that the knowledge about this problem has grown disproportionally
within a few building blocks (e.g., topics, countries), thereby reducing the
development potential for this wicked problem domain. Moreover, comparison of
intra- and inter-annual dynamics shows heterogeneous growth, indicating that
the knowledge trajectory is not consolidating into a stable core of research
topics or research leaders (neither individual nor geographic).

##  IV Discussion

We analyzed the social and cognitive dimensions of knowledge trajectories
emerging around three environmental problems – Deforestation, Invasive
Species, and Wildlife Trade. Despite the common backdrop of sustainable
development and conservation, we observe differences across the different
problem domains that we attribute to the role of uncertainty associated with
problem and solution identification. First, we note different time periods
when these problems first emerged (Fig.2b) along with different subsequent
total knowledge production as indicated by publication volumes in each problem
domain (Fig.2a). Together, these observations illustrate how problem
prioritization ciarli_relation_2017  reinforces the role of path-dependency in
the evolution of knowledge production, and consequently also affects the time
required for building a common understanding and agenda.

Second, we observe a broad spectrum of topical approaches (Fig.3), which may
indicate contested spaces where assumptions and knowledge are debated
bettencourt_evolution_2011 ; boschma_scientific_2014 ; funk_dynamic_2017 . In
particular, Deforestation and Wildlife Trade exhibit a prominent period of
decreasing parity across knowledge communities (Fig.4b). Third, we do not
observe any indication that Wildlife Trade will achieve stability in the
social dimension based upon the prominent decrease in parity observed in
Fig.5c. Yet it remains to be seen if stability in the cognitive dimension of
Wildlife Trade will spread into the social dimension, which is a potential
avenue for change bammer_expertise_2020 ; calero-medina_combining_2008 .
However, stability in the social dimension may exacerbate solution uncertainty
by reinforcing echo chambers in which a few highly productive authors (or
collectives) dominate the discourse. Such a situation could limit the
development of alternative leading roles, hampering the cross-fertilization
between researchers and organizations, and reducing progress towards second-
order ‘deep learning’ ramirez_mobilizing_2018 ; ramirez2020fostering ;
schot_three_2018 .

We posit that variability in knowledge trajectory dynamics indicate different
wickedness characteristics heifetz_leadership_1994 . When comparing our
results with those previously reported for more well-stablished domains
bettencourt_scientific_2009 ; bettencourt_population_2008 ;
bettencourt_evolution_2011 ; bonaccorsi2008search ; boschma_scientific_2014 ;
heimeriks_emerging_2012  we identify some marked differences in the three
domains evaluated here, which we associate with the characteristic ill-
definition of each problem.

First, in contrast with our initial expectation, we found Invasive Species to
more closely correspond to a Type II wicked problem (i.e., conceptually
definable but without clear-cut solution) since cognitive dimensions stabilize
in parity, whereas social dimensions are still changing. Until such a stable
community forms, it will be challenging to settle disagreements concerning
candidate solutions. Second, our initial expectations for Deforestation were
also short, as this problem appears to be closer to a Type III wicked problem
when considering the instability of both cognitive and social dimensions. And
finally, in the case of Wildlife Trade, our analysis confirms our initial
expectation of a Type III wicked problems. As such, these two Type III
problems suffer from disparities that negatively affect the development of an
integrated research domain.

We acknowledge that our approximation to capturing the evolution of these
problem domains is incomplete. For example, our focus on disparity measures
does not provide insights into knowledge relatedness through the lens of
separation diversity, as reported in other work (e.g.,
boschma_scientific_2014, ; heimeriks_how_2016, ; leydesdorff_global_2013, ).
In addition, while our operational framework illuminates the structure of
research producing fundamental changes in each problem, it does not provide
any additional indication as to how the particular pathways connecting
cognitive and leadership micro-changes translate into macro-level knowledge
trajectories. A better understanding of the causal channels through which
these dynamics operate will be critical to steering wicked problem domains
away from unconsolidated, unactionable and eventually neglected research
traps.

To address these extant challenges, we developed a generalizable framework
that compares the intra-annual to the inter-annual parity dynamics, as a way
to illustrate the nuances associated with the growth and saturation of
diversity. In particular, our analysis of inter-annual parity indicates that
growth and stability are not mutually exclusive. Indeed, cognitive
trajectories often follow a process of diversification followed by
consolidation and increased relatedness heimeriks_how_2016 ;
rafols_diversity_2010 , capturing the process by which multiple voices and
meld and trigger a shared vision for moving forward funtowicz_uncertainty_1994
; bammer_expertise_2020 ; calero-medina_combining_2008 ;
heimeriks_emerging_2012 ; granovetter_economic_1985 ; reinders_role_2011 ;
stirling_general_2007 . Contrariwise, locked-in or highly concentrated
trajectories, as exhibited in the case of Wildlife Trade, can inhibit
integrative, holistic, and post-normal approaches and instead may promote the
emergence of conceptual echo chambers in which disproportionally few topics
are mainly discussed by a reduced subset of voices defries_ecosystem_2017 ;
dolfsma_lock-and_2009 ; funtowicz_risk_1992 ; funtowicz_uncertainty_1994 ;
soule_what_1985 .

As such, environmental wicked problems appear to necessitate integrated
diversification bammer_expertise_2020 ; calero-medina_combining_2008 ;
linkov_scientific_2014  in which multiple voices and approaches can be
included while consolidation of existing research agendas and communities of
expertise takes place ramirez2020fostering . Balancing the tension associated
with this paradox of cross-disciplinary integration will help distribute
efforts and capabilities toward specific solutions that iterate towards
addressing the underling complexity alford_wicked_2017 ;
defries_ecosystem_2017 ; light_wicked_2020 . Failing to address the tension
may give rise to untenable or unactionable solutions that hinder the
translation of science-based solutions into societal action, particularly at
the academic-industry-government interface leydesdorff_emergence_1996 , or
neglected problems as in the case of some diseases sachs_end_2005 ;
savard_insomnia_2001 . Indeed, extremely wicked problems are likely to suffer
from a broader societal disregard for pursuing further action owing to the
lack of or insufficient clarity or completeness regarding problem definitions
and solutions.

### Supplementary Material

All supplementary materials will be available upon publication at (Link).
Supplementary materials include Supplementary Note 1: Search queries; Supp.
Note 2: Co-bibliography Networks construction; Fig S1: Co-bibliography
networks for the 3 problem domains; Figs S2-S5: Dynamics of knowledge
trajectories measured as Shannon Evenness; and Figs S6-S9: Dynamics of
knowledge trajectories measured according to the Complementary Gini index.

### Data and code availability

Data can be accessed through Web of Science web page and the search equations
in SN.1. Code will be available in the same link that the supplementary
materials and upon request to the correspondence authors.

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