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Suicide Life Threat Behav. 2020;00:1–12.
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1wileyonlinelibrary.com/journal/sltb
DOI : 10.1111 /sltb .12676
SPECIAL ISSUE
A network perspective on suicidal behavior: Understanding
suicidality as a complex system
Derek de Beurs1,2 | Claudi Bockting3 | Ad Kerkhof2 | Floortje Scheepers4 |
Rory O’Connor5 | Brenda Penninx6 | Ingrid van de Leemput7
This is an op en access article u nder the terms of the Creative Commons Att ribution License, which per mits use, distrib ution and reproduction in any medium,
provide d the origi nal work is properly cited.
© 2020 The Authors. Suicide and Life-Threatening Behavior published by Wiley Periodicals LLC on b ehalf of American A ssociation of Suicidology
1Trimbos Institute (Netherlands Institute of
Mental Health), Utrecht, The Netherlands
2Depar tment of Clinical, N euro and
Developmental Psychology, Amsterdam
Public Health Research Institute, Vrije
Universiteit Ams terdam, A msterdam, The
Netherlands
3Department of Psychiatry, Amsterdam
University Medical Centers (location AMC),
University of Ams terdam, Amsterdam, The
Netherlands
4Departement of Psychiatry, University
Medical Center Utrecht, Utrecht, The
Netherlands
5Suicidal Behaviour Research Laboratory,
Glasgow University, Glasgow, UK
6Department of Psychiatry, Amsterdam
Public Health Research Institute, Vrije
Universiteit Ams terdam, A msterdam, The
Netherlands
7Depar tment of Aq uatic Ecology and
Water Quality Management, Wageningen
University, Wageningen, The Netherlands
Correspondence
Derek de B eurs, Trimbos Instit ute
(Netherlands Institute of Mental Health),
Utrecht, The Netherlands.
Email: dbeurs@trimbos.nl
Abstract
Background: Suicidal behavior is the result of complex interactions between many
different factors that change over time. A network perspective may improve our un-
derstanding of these complex dynamics. Within the network perspective, psychopa-
thology is considered to be a consequence of symptoms that directly interact with
one another in a network structure. To view suicidal behavior as the result of such
a complex system is a good starting point to facilitate moving away from traditional
linear thinking.
Objective: To review the existing paradigms and theories and their application to
suicidal behavior.
Methods: In the first part of this paper, we introduce the relevant concepts within
network analysis such as network density and centrality. Where possible, we refer
to studies that have applied these concepts within the field of suicide prevention. In
the second part, we move one step further, by understanding the network perspec-
tive as an initial step toward complex system theory. The latter is a branch of science
that models interacting variables in order to understand the dynamics of complex
systems, such as tipping points and hysteresis.
Results: Few studies have applied network analysis to study suicidal behavior. The
studies that do highlight the complexity of suicidality. Complexity science offers
potential useful concepts such as alternative stable states and resilience to study
psychopathology and suicidal behavior, as demonstrated within the field of depres-
sion. To date, one innovative study has applied concepts from complexity science to
better understand suicidal behavior. Complexity science and its application to human
behavior are in its infancy, and it requires more collaboration between complexity
scientists and behavioral scientists.
Conclusions: Clinicians and scientists are increasingly conceptualizing suicidal behav-
ior as the result of the complex interaction between many different biological, social,
and psychological risk and protective factors. Novel statistical techniques such as
network analysis can help the field to better understand this complexity. The ap-
plication of concepts from complexity science to the field of psychopathology and
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1 | INTRODUCTION
Suicidal behavior poses a major public health problem, with a
global estimated 800,000 suicide deaths each year (World Health
Organization, 2014). It is estimated that suicide attempts are at least
20 times more common. Different international mental health sur-
veys have found that each year around 3% of the general population
experi ences a period of at le ast two weeks in wh ich they have felt that
life was not wor th living (Nock et al., 2009; Ten Have et al., 20 09).
Over recent decades, there has been a general consensus that sui-
cidal behavior is the end result of the complex interaction between
many different risk factors. Whereas earlier theories focused on a
single risk factor for suicidal behavior, such as entrapment (Williams
2001), escape from self (Baumeister, 1990), or a specific domain of
risk such as cognition, the integrated motivational–volitional (IMV)
model is one such approach that combines key factors from predom-
inant theories into a single complex model (Figure 1: O’Connor, 2011;
O’Connor & Kirtley, 2018).
The IMV model implicates many different risk and protective
factors as determinants of suicide risk across three phrases. In
the first phrase, the premotivational phase, the context in which
suicidal thinking or behavior may emerge is described. However,
within the motivational phase, suicide ideation is posited to result
from feelings of defeat and entrapment, which are, in turn, mod-
erated by feelings of thwarted belongingness and a lack of social
support. The final phase, the volitional phase, is hypothesized to
govern behavioral enac tion, such that a suicide attempt is argued
to be the result of the interaction between additional risk fac-
tors such as impulsivity or fearlessness about death and suicidal
thought s. Although different studies have confirmed the central
assumptions outlined with the IMV model (see also below), these
tenets have not yet to be tested within a dynamical model.
2 | A NETWORK THEORY OF MENTAL
DISORDERS
The proposal that suicidal behavior results from the interaction of
many diff erent variables is co nsistent with a broa der movement in psy-
chiatry, called the network perspective (Borsboom & Cramer, 2013;
Cramer et al., 2010). The central idea behind this school of thought is
that a mental disorder such as major depression (MDD) is the potential
consequence of symptoms that direc tly interact with one another in
a network structure (Figure 2). That is, symptoms of MDD such as in-
somnia, rumination, and anhedonia do not covar y because they share
an underlying cause (e.g., a brain dysfunc tion; Borsboom, Cramer &
Kalis, 2019) (see Figure 2a) but, rather, because they directly influence
one another: e.g., insomnia > rumination>anhedonia (see Figure 2b).
This is fundamentally different from the traditional medical model of
causality, where there is a specific cause, such as a tumor, that leads to
symptoms such as coughing up blood.
The application of this approach to psychopathology has proved
fruitful in generating novel hypotheses and/or understanding known
empirical phenomena across multiple disorders (see Robinaugh,
suicide research offers exciting and promising possibilities for our understanding and
prevention of suicide.
FIGURE 1 The integrated motivational–volitional (IMV) model of suicidal behavior
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Hoekstra, Toner, & Borsboom, 2019 for a review). When translated
to the field of suicide prevention, this approach allows us to inves-
tigate the interaction between factors that are related to suicidal
thought s and suicidal behavior, rather than a latent construct called
suicidality (de Beurs, 2017). In the first part of this paper, we intro-
duce the relevant concepts within network analysis such as network
density and centrality. Where possible, we refer to studies that have
applied these concepts within the field of suicide prevention. As an
introduction for further studies, in the Appendix S1, we offer an
overview of relevant online tutorials per method.
In the second part, we move one step further toward complex
system theory, which is a branch of mathematics that describes the
complex behavior of systems. Such an approach sees behavior as a
result of the interaction between all kinds of different processes.
The understanding of network interactions and feedback loops may,
for instance, help to explain how tipping points, chaos, or cycles
arise. Complex system theor y has been applied to understanding a
wide range of phenomena, such as the weather, financial systems,
biology, but also to health care and more recently to psychiatry
(Bringmann & Eronen, 2018; Cramer et al., 2016; van de Leemput
et al., 2014; Leemput et al., 2014; Wichers & Groot, 2016). It offers
useful concepts to better model the complex interactions between
variables that can result in suicidal behavior. For example, in a US
study Bryan and Rudd (2018) found that change in suicidal ideation
among active duty U.S. army soldiers who had a history of multiple
suicide attempts was characterized by a bimodal distribution in sui-
cide ideation. Such a distribution suggests that, for some at least,
suicidal ideation alternates between stable states and tipping points
(Bryan & Rudd, 2018). In the present paper, we introduce the con-
cepts of alternative stable states, tipping points, and resilience in
the context of suicidal risk, and refer to introductory papers.
3 | PART ONE: NETWORK ANALYSIS
3.1 | What is a network?
A typical network consists of edges and nodes. One well-known
network that comes to mind is a social network (Barabasi, 2014). In
a social net work, the nodes represent people or groups of people,
and the edges are a quantification of their relationships, for example
how many mutual friends they have. This is different from networks
within the field of psychopathology. Nodes do not refer to actual
physical representations, but to psychological phenomena including
symptomatology that are assessed by, for example, questionnaires or
clinical interviews. Whereas the edges in social networks represent
actual relationships that can be counted, the edges in psychological
research generally refer to the estimated st atistical relationship or
correlation between two nodes.
An often used method to estimate networks in psychiatr y is
a so-called Pairwise Markov Random Field (PMRF: Epskamp &
Fried, 2016). In a PMRF, nodes are connected by undirected edges
(i.e., edges with no arrowhead). When nodes are connected, they
are stated to be conditionally dependent: The two nodes are related
even after controlling for all other nodes in the network. An edge
between two nodes can occur for several reasons. The most com-
mon scenario is a true causal relationship (e.g., entrapment ↔ suicide
ideation), but the direc tion of the causal link cannot be inferred only
from the observed relation. Alternatively, an unmeasured third node
(entrapment ← cognitive reactivity → suicide ideation) could result
in an edge, where cognitive reactivity is the unmeasured third node.
Likewise, the absence of an edge can have several explanations, the
two most common being the absence of a causal relationship, or the
study has insufficient power to detect a small causal ef fect. Networks
can include continuous items/scales, binary/categorical items, or a
mixture of both. As psychological items and scales are often highly
correlated, networks are usually regularized, omitting small edges
(Epskamp & Fried, 2016). This means that a conser vative network is
estimated, resulting in the most sparse network. Most networks in
the extant literature are based on cross-sectional data. The nodes
typically represent the score of a single item of a psychological ques-
tionnaire such as the Beck scale for suicide ideation, and the edges
between two nodes represent the partial correlation between the
two nodes, which can be either positive or negative. Figure 3 pres-
ents an example of a network of the 19 items of the Beck scale for
suicide ideation (de Beurs, van Borkulo, & O’Connor, 2017). The items
were answered at one moment in time by a group of 366 patients
who were admitted to a hospital following a suicide attempt.
FIGURE 2 (a) Depression as a common cause of symptoms. (b) Depression emerges as a result of the interaction between symptoms
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3.2 | Network density
The network perspective hypothesizes that each individual
has their own individual network structure (see, e.g., Cramer
et al., 2016). Specifically, it is hypothesized that rather than focus-
ing on the symptoms themselves attending to the strength of con-
nections between symptoms can better inform us about whether
someone will develop future psychopathology or not. If one as-
sumes that edges represent positive causal interactions, an indi-
vidual with a strongly connected symptom network is reasoned
to be at higher risk of future psychopathology. For example, after
losing their job, an individual may experience high levels of defeat
that results in strong feelings of entrapment, which in turn lead
to feelings of suicide ideation. This activation of symptoms can
result in a reinforcing feedback loop: entrapment → suicide idea-
tion → defeat →entrapment (Figure 4a). As is explained in part
2 of this paper, this may play an important role in the transition
from being relatively low in risk to high in risk of suicidal behav-
ior. On the other hand, someone else may feel defeated after their
job loss, but defeat and entrapment are less strongly connected in
FIGURE 3 A network of the 19 separate items of the Beck scale for suicide ideation. Thicker edges present stronger associations/
correlations. arr, arrangements after death; att, attitude toward suicidal behavior; cea, concealment about ideation; con, control over action;
cou, courage for actual behavior; cry, cry for help versus cry for pain; des, desire to harm myself; det, deterrents of attempt; die, wish to
die; dur, duration of suicide ideation; exp, expectancy of actual attempt; fre, frequency of suicide ideation; liv, wish to live; met, availability
of methods; not, suicide note; pas, passive desire; pla, actual planning; pre, actual preparation; rea, reasons for living. See also de Beurs
et al., 2017. See the Appendix S1 for code and data used
FIGURE 4 The hypothetical networks (a) and (b). Str, stress; Def, defeat; Ent, entrapment; SI, suicide ideation. A green line indicates a
positive relationship between t wo symptoms. The thicker the line, the stronger the association. Str: stressor such as a job loss, Def: defeat,
Ent: entrapment: SI: suicide ideation
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BEURS Et a l.
their net work so they feel less entrapped. Also, in the latter net-
work, defeat and entrapment are not related to suicide ideation,
meaning suicidal ideation is less likely to emerge even in the pres-
ence of high levels of defeat (Figure 4b).
At a group level, in a prospective study of psychiatric patients, those
with more densely connected networks at baseline were more likely
to experience another depressive episode at follow-up compared to
those with less densely connected networks (van Borkulo et al., 2015).
However, this finding was not replicated in a different sample (Schweren,
van Borkulo, Fried, & Goodyer, 2018). A user-friendly method to com-
pare the structure of groups is via the NetworkComparisontest package
developed by Dr van Borkulo (Van Borkulo, Epskamp, & Milner, 2016). It
uses per mutation test s to investigate whet her all network st ructures are
identical (null hypotheses) or whether the null hypothesis must be re-
jected. A tutorial can be found online (https://cvbor kulo.files.wordp ress.
com/2017/06/ncttu torial.pdf). A more recent package called BGGM
uses Bayesian statistics to compare the structure between groups
(Williams & Mulder, 2019). (https://cran.r-proje ct.org/web/packa ges/
BGGM/vigne ttes/ppc1.html).
3.3 | Centrality
Among the most popular metric s in network analysis are centrality
estimates (Opsahl, Agneessens, & Skvoretz, 2010). There are several
centrality measures, but they all relate to the inter-connectedness of
a node within a network. The most often used metric is the strength
of a node, calculated by summing the size of all its edges. However,
as edges can both be positive and negative, an additional expected
influence metric has been developed, which takes negative edges
into account when calculating centrality (Robinaugh, Millner, &
McNally, 2016). Other popular centrality metrics are betweenness,
which is the number of times a node lies on the shortest path be-
tween nodes, and closeness, which is inversely proportional to the
mean shortest distance from the node to all the other nodes in the
network.
As is evident in Figure 5, the item “I have a desire to harm
myself” was by far the most central item from the Beck scale for
suicide ideation. Initially, within network theory, the most central
item was deemed the most relevant for clinical intervention. As
this item has the strongest relationship with all other items, inter-
vention on this node will most effectively influence the network.
It is impor tant to note, however, that the direction of the relation-
ship between nodes is not clear in an undirected network (i.e., a
network without arrows). Targeting a central node is only useful
when the central node influences the connected symptoms, and
not the other way around (Borsboom & Cramer 2013). In addi-
tion, most studies that repor t centrality measures are based on
between participants dat a, and we do not know how these group
centrality measures translate to the individual. The only way to
validate this is to conduct experimental studies where networks
before and after a manipulation of a central node are compared.
However, in psychiatry, it is almost impossible to target only one
node in a net work, as all interventions are likely to influence other
nodes as well. This prompted some authors to suggest that it may
beneficial to drop the concept of centrality, which centers around
a single variable and move toward the complexity of networks
(Bringmann et al., 2019).
FIGURE 5 Centralit y plot of the strength of each of the 19 separate items of the Beck scale for suicide ideation within the network. X-
axis represents standardized centrality coefficients. arr, arrangements after death; att, attitude toward suicidal behavior; cea, concealment
about ideation; con, control over action; cou, courage for actual behavior; cry, cry for help versus cry for pain; des, desire to harm myself;
det, deterrents of at tempt; die, wish to die; dur, duration of suicide ideation; exp, expectancy of ac tual attempt; fre, frequency of suicide
ideation; liv, wish to live; met, availabilit y of methods; not, suicide note; pas, passive desire; pla, actual planning; pre, actual preparation; rea,
reasons for living dying
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3.4 | Network stability and accuracy
There is not yet a clear standard for calculating the required sample
size to reliably estimate the strengths of the edges in a network. As a
rule of thumb, one needs at least as many observations as parameters
(n + n * (n − 1)/2 possi ble pairwise interactions, wi th n rep resenting th e
number of nodes). When you have a network of 10 nodes, this trans-
lates into a minimum of 55 participants. For 20 nodes, the minimum
number of participants is becomes 210, and for 30 nodes, one needs
46 participants. It has also become standard to test the stability and
accuracy of a network (Epskamp et al., 2018). A link to a tutorial on
how to estimate stability and accuracy is of fered in the Appendix S1.
3.5 | The utility of network analysis to test theory
Network analysis has largely been used as an explorator y tool, using
variables that have been selected because of their availability rather
than being driven by theory (e.g., De Beurs et al., 2017; Bringmann,
Lemmens, Huibers, Borsboom, & Tuerlinckx, 2015; Fried et al., 2018).
In 2019, Beurs et al. published a study with the explicit aim of under-
standing suicidal ideation from a network perspec tive by selecting
variables based on psychological theor y. In this study, the authors
used network analysis to compare the central tenets of two differ-
ent theories; the interpersonal theory of suicidal behavior (IPT: Van
Orden et al., 2010) and the earlier mentioned IMV model. According
to the IPT, suicide ideation emerges from the interaction of perceived
burdensomeness and thwarted belongingness, whereas in the IMV
model, entrapment is hypothesized to play a key role. The rationale
was simple, if the data would suppor t the IPT, then perceived bur-
densomeness and thwarted belongingness would be most strongly
related to suicide ideation compared to any other variable. If on the
other hand, the data would support the IMV model, then entrap-
ment would be most strongly associated with suicidal ideation. When
comparing the core construct s of both models, both perceived bur-
densomeness and internal entrapment were most strongly related
to suicide ideation. Thwarted belongingness and defeat were mainly
indirectly related to suicide ideation as posited by the IMV model.
The authors also estimated a net work using 20 different mo-
tivational and volitional risk factors (from IMV model). Twelve of
the 20 were directly related to suicide ideation after controlling
for all other variables, and none of the risk factors was isolated
within the network (de Beurs et al., 2019). This highlights the
complex relationships between different risk factors and suicide
ideation. The move from exploratory convenience networks to
network analysis with a strong theoretical foundation is an im-
portant step for ward in advancing our understanding. Another
innovative study translated existing psychological theory and re-
search on recurrent panic attacks into equations that explicitly
define the relationships among the different symptoms in a net-
work (Robinaugh, Haslbeck, et al., 2019). In a more theoretically
oriented paper, the impor tance of formal theory in psychiatry was
stressed, and it also offers ideas about how the network approach
can inform theory (Haslbeck, Oisín, Robinaugh, Waldorp, &
Borsboom, 2019).
3.6 | Inferring network interactions from time-
series data
Although psychology is concerned with the subjective experiences
of an individual, most psychological studies rely on group-level data
(Barlow & Nock, 2009). Historically, one important reason for this was
that it was technically not feasible to collect large amounts of data
within one person. It is only relatively recently that we have been able
to conduct studies using mobile telephone technology to collect time-
series data within suicidal individuals. Initial results showed that suicide
ideation fluctuates considerably over time, as do common risk factors
such as hopelessness and perceived burdensomeness (Hallensleben
et al., 2018; Kleiman et al., 2017). Time-series network analysis can be
conducted on a group level and on an individual level. In a recent study,
ecological momentary data in depressed inpatients were collected 10
times a day, over a period of 6 days (Rath et al., 2019). In addition to
suicide ideation, depressive feelings, anxiety, positive affect, perceived
burdensomeness, thwarted belongingness, and hopelessness were also
assessed. All variables demonstrated moment-to-moment variability,
and subst antial within person variance (Forkmann et al., 2018). Perhaps
unsurprisingly, over an assessment period of about 1.5 hr, suicide idea-
tion was mainly predicted by suicide ideation by the previous assess-
ment of suicide ideation (at lag 1). Other risk factors did not appear
to affect suicide ideation within this time span. When inspecting the
network of symptoms at the same assessment (the contemporaneous
network), the expected associations between, for example, hopeless-
ness and suicide ideation were present. These results indicate that the
temporal relationship between suicide ideation and risk factors may be
faster than 1.5 hr, and perhaps occur nearly simultaneously.
The collection of data via a mobile phone offers novel ways of
studying an individual's own dynamic network, and might be useful
during treatment. An early case study in which a patient discussed
their net work of symptoms related to depression with a clinician
indicated that it might be a feasible tool for use in clinical practice
if proven to be ef fective (Kroeze et al., 2017). Currently, there are
several ongoing studies (Stikkelbroek, Naut a, Bockting, 2019, Nuij
et al., 2018) that are collecting data using mobile phones to inves-
tigate, for instance, whether an individual with a more densely
connected network is indeed at higher risk of suicidal behavior and
depression and anxiety compared to someone with a less dense net-
work. Time-series data also have the potential to detect an upcom-
ing crisis before it takes place, as outlined below.
4 | PART TWO: SUICIDAL BEHAVIOR AS A
COMPLEX SYSTEM
One of the leading experts in network science, Professor Barabási
from the Northeastern University in Boston, has stated that
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“networks are only the skeleton of complexity, the highways for vari-
ous processes that make the world hum” (Barabasi, 2014). Complex
systems are everywhere in nature, from the processes within a sin-
gle cell to the climate on ear th (Schef fer, 2009). A system (which is
simply something concrete or abstract that is being studied) is called
complex when it consist s of a number of interacting elements that
show some form of behavior that cannot be explained by the dynam-
ics of the individual elements. Complex systems are nonlinear, mean-
ing that the input in the system is not proportional to the output. For
example, depression has been considered to be a complex system,
since a small change in mood can have a large ef fect on the state
someone is in. This is due to the occurrence of feedback loops in the
system (e.g., low mood may lead to sleep problems or reduced social
interactions, which may lead to an even worse mood). In this par t
of the paper, we introduce the idea that suicidal behavior can also
be understood as a complex system: complex, because many clini-
cians and researchers argue that suicidal behavior is the end result
of the interaction between many different risk factors, and cannot
be explained by one single factor ( Van Hemert, Kerkhof, de Keijser, &
Verwey, 2012; O’Connor & Nock, 2014); and a system, because the
risk factors are considered par t of a system such as that proposed
by the integrated motivational volitional model of suicidal behavior
(O’Connor & Kirtley, 2018a).
To understand the nonlinear dynamics of complex systems, it
can be helpful to understand the behavior of dynamical systems.
Dynamical systems are mathematical models that describe the time
dependence of one or more variables. They can have different types
of attractors, such as cycles, chaos, or stable states. A common at-
tractor is a stable state (Figure 6). If such a system is perturbed away
from the equilibrium, it eventually moves back to the stable state,
due to stabilizing mechanisms. For example, one can imagine that
a person's stable st ate is when there is no risk for suicidal behavior.
Mood or other elements of a person's emotion regulation system are
continuously fluctuating over time, so the ball in Figure 6 is kicked
around. Still, the system is organized such that an increase in de-
pressed feelings, for instance, because of some bad news, will be
followed by a decrease in depressed feelings, for instance, because
of a night's good sleep, or some physical activit y.
Some systems have alternative stable states (multiple values in
the stability landscape). Alternative stable states are different stable
states in which a system can be under the same conditions. Due to
extern al stressors, o r even normal fluct uations within a net work over
time, a system can move from one stable state to another alternative
state (Figure 7). Take, for example, a population of animals that will
get into trouble if their number become too low to find a mate and
reproduce (Scheffer et al., 2009). A large disturbance, such as a dis-
ease, could push the population below a critical level, such that the
system tips from the survival state to the extinction state, and is not
able to recover. Also, if the resilience of the sur vival state is already
low, for instance, because of anthropogenic pressure, small natural
fluctuations could already trigger a tipping point to an alternative
state. Translated to psychopathology, a patient could shift from a
state with no risk for suicidal behavior to an alternative state with
elevated risk for suicidal behavior.
The shape of the stability landscape (e.g., Figure 7) will largely
depend on the strength of positive and negative feedback loops in
the system (Scheffer et al., 2009). It is impor tant to note that the
terms “positive” or “negative” are value-free. They refer to the net
sign of the overall effec t of the feedback. Positive feedback loops
reinforce the effect of a perturbation in the network, and thereby
create an unstable intermediate state. An example of a positive
feedback loop within the IMV model would be: increases in feelings
of defeat → stronger feelings of entrapment → more suicide ide-
ation → stronger feelings of defeat etc (Figure 8).
Negative feedback loops have a stabilizing effect, because they
dampen a perturbation. A negative feedback loop might be: sui-
cide ideation → more social support → less suicide ideation. When
the resilience of a person erodes, stabilizing mechanisms generally
weaken, while reinforcing mechanisms strengthen. As a result, it
becomes easier to push a system out of its stable state, such that
the valley in Figure 7 becomes more flat. Knowing when a tipping
point is approaching, or in other words when resilience is decreasing,
might prove to be important from an intervention perspective.
4.1 | Cusp catastrophe model
The influence of stress on complex systems or networks in systems
with positive feedback loops can be understood in the context of
the cusp catastrophe model (Scheffer 2009). The cusp catastrophe
model is a mathematical model that can explain why relatively small
changes in a parameter (in our example, small changes in stress) can
result in catastrophic changes in the state of a system (in our ex-
ample, a shift from the motivational to volitional phase). The main
FIGURE 6 An conceptual representation of a stable state FIGURE 7 Some systems can have multiple stable states
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idea of the cusp model is that the stronger the positive feedback(s),
the more discontinuous the network will behave under stress. In
Figure 9a–c, three different kinds of hypothetical interactions be-
tween (external) stress and suicide risk are shown (Schef fer 2009).
In Figure 9a, an increase in stress results in a stable increase in risk of
suicide, as a patient moves in a linear way from low risk to high risk.
Importantly, after stress has increased, the patient can easily go back
from being at a high risk to being at a low risk when stress decreases
again to a relatively normal level.
In Figure 9b, it is hypothesized that across certain ranges of
stress, a patient's risk of suicide does not change very much, but
when a specific stress threshold is reached, a patient will respond
relatively strongly. When a positive feedback loop is really strong,
it could even be that low suicidal risk and high suicidal risk repre-
sent two separate states (Figure 9c), separated by an unstable state
(dashe d).
When a patient is in the lower branch of the curve (at low risk),
they may become at higher risk with increasing stress, but this
FIGURE 8 Example of a positive feedback loop (left-hand) and a negative feedback loop (right-hand)
FIGURE 9 (a) Linear relationship bet ween stress and risk of suicidal behavior. (b) Sigmoidal relation bet ween stress and risk for suicidal
behavior. (c) The relationship between stress and suicide risk as a cusp catastrophe model
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effect may go unnoticed. However, when a cer tain threshold level
of stress is reached, a “catastrophic” transition from low to high
risk occurs (at F1). From a clinical perspective, this is important be-
cause a ver y small change in stress (or any other risk parameter)
would result in a very large increase in risk for suicidal behavior.
When a patient suddenly becomes suicidal, we tend to look for
major changes that caused the transition, but for some patients, it
might be that the system was slowly getting less and less resilient,
and that the sudden collapse can be explained by an already fragile
system rather than a novel stressor. As visualized in Figure 10, as
stress increases, the basis of attraction changes, making it more
easy for the ball to reach the other st able state even after a small
perturbation.
Another important aspect from a clinic al perspective is that in
order to get back from a high- to a low-risk phase, it is not sufficient
to restore stress levels to the level before the collapse. The stress
level needs to go all the way back to the tipping point F2. This de-
pendence of the current state of the system on the previous state
is called hysteresis. The application of cusp catastrophe modeling
within the field of suicide prevention has been elegantly demon-
strated by Bryan and Rudd (2018). Within a sample of 76 active
duty U.S. army soldiers, they showed that over time, those with a
multiple attempt history displayed two stable states, corresponding
to a high-risk state and a low-risk state for suicidal behavior. As de-
picted in Figure 9c, when a participant was in one of the states, they
were more likely to stay in that state, until a new tipping point was
reached. Within those soldiers who had only thought about suicide
or who had a history of one suicide attempt, suicide risk tended to
change in a more linear fashion, as depicted in Figure 9a. This study
represents an important step forward in terms of studying nonlinear
change in suicidality, especially when combined with the concept of
critical slowing down (see below).
4.2 | Critical slowing down
Importantly, there can be detectable warning signals before a system
reaches a tipping point (Scheffer et al., 2009). Normally, if a person
experiences, for example, a higher level of hopelessness, the level
of hopelessness also goes down again after a short period of time.
Indeed, recent studies using data collected via mobile phones have
found that the level of well-known risk factors such as hopelessness
fluctuate heavily over time. However, when one gets near a tipping
point, this fluctuation tends to slow down. If this person experiences
a higher level of hopelessness compared to earlier assessments, it
will take them longer to return to their normal levels. This phenom-
enon has been called critical slowing down (CSD: Dakos et al., 2012;
Scheffer et al., 2009). A loss of resilience could be detected with per-
turbation experiments or by analyzing natural fluctuations around
an equilibrium. If a system slows down, one could detect this as an
increase in autocorrelation and variance in the time series. EMA data
seem to be good candidate to investigate such changes, see, for in-
stance, Van de Leemput et al. (2014) Wichers et al. (2016); however,
these dat a are still rare, which makes the analysis more complicated.
As summarized in the Appendix S1, many freely available tutorials
exist. We do however advise to always collaborate with a methodo-
logical expert and not to use the tools as a “black box.” Also, as the
field of analysis of time-series data in human behavior is relative new,
there is no preferred method of analysis for this kind of data. In an
innovative study, 12 prominent EMA teams were challenged to ana-
lyze the same data from one individual patient's time-series data. The
different teams chose different analytical approaches, resulting in
different outcomes (Bastiaansen et al., 2019). Many conceptual and
methodological issues still need to be resolved in this field of work.
4.3 | Critique of the network perspective
One of the main critiques reviewers often provide when evaluat-
ing the net work perspective is that it is nothing more than a visu-
alization of a correlation matrix or factor loadings. Indeed, a paper
on this topic (Kruis & Maris, 2016) has shown that latent variable
models and network models are statistically equivalent. So, what
is the difference? First of all, network analysis offers insights into
the relationships between all variables, not only into the rela-
tionships between the dependent variables and the independent
variable. This provides novel insights, and it can create additional
hypotheses. The visualization offers a much more intuitive way to
understand data compared to a t able of regression coefficients.
FIGURE 10 Increased stress results in loss of resilience, making
the transition from one state (valley) to the other more likely.
Bottom plane follows the curve of Figure 9c (Schef fer et al 2001)
10
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BEURS Et al.
However, it is impor tant not to use the network graphs as modern
Rorschach tests, in which the interpretation is in the eye of the
beholder. The nodes in a network should be interpreted with cau-
tion as they depend on the software settings. The visualization is
merely a useful tool to derive new hypotheses, it should not be
used as a confirmatory tool. As stated in the second part of this
paper, conceptualizing psychopathology as a network of symp-
toms offers a new set of tools derived from complexity theory that
may help us better understand complex dynamic phenomena such
as psychiatric illness and suicide risk.
It is also important to highlight that even when dif ferent scientific
models have similar statistica l properties , this does not necess arily mean
that they are theoretically similar (https://psych -netwo rks.com/meani
ng-model -equiv alenc e-netwo rk-model s-laten t-varia bles-theor etica
l-space/). Network theory of fers a completely dif ferent way of thinking
about psychopathology when compared to latent modeling. In the latent
model, making a change to a single symptom would not directly af fect
the other symptoms. However, from a network perspective, changing
one variable may have consequences for the whole network, at the very
least for the nodes directly related to the targeted node.
Many technical challenges remain. As noted above, when applying
networks, the st ate of the science is to estimate regulated networks
using LASSO regularization. However, it has been found that under cer-
tain circumstances, the specificity is lower than expected ( Williams &
Rast, 2019). This insight has resulted in an update in the qgraph package,
offering novel ways to estimate a network. Another technical critique re-
lates to the replicability of networks. Networks require large sample sizes
to be stable, and many researchers do not check the robustness of the
network. The limited replicability has also been the topic of a recent de-
bate (Borsboom et al., 2017; Forbes, Wright, Markon, & Krueger, 2017a,
2017b). Another challenge is that when a factor is stable, it cannot cor-
relate strongly with other variables. For example, if we study risk factors
within a highly suicidal group of patients, it might be that suicide ideation
will not be connected strongly to other nodes within the network, be-
cause all participants will score high on suicide ideation. The variance of
suicide ideation is then much smaller compared to the variance of other
items, resulting in small connections with the other items ( Terluin, De
Boer, & De Vet, 2016). Although beyond the scope of this paper, it is im-
portant to acknowledge that there are measurement issues around the
assessment of psychological factors and associated sc ales more widely.
Often, scales are not well validated, or they seem to measure something
different from what they purpor t to measure. There are at least 280
scales to measure depression, and sometimes different scales lead to dif-
ferent outcomes. The variety of scales used and the limited validit y of the
scales make replication of results difficult (Flake & Fried, 2019).
Another critique is that most net work studies are based on
cross-sectional data, and provide insight into static relations be-
tween symptoms at a group level. Cross-sectional networks do not
allow us to study the individual dynamic interactions between symp-
toms, as a result, time-series analyses are therefore a logical way
forward. However, time-series analyses within the field of network
analysis is in its early stage, leaving open fundamental questions
about how best to estimate a network over time.
4.4 | Future directions
One of the key questions within suicide prevention is why a minorit y
of people eventually act on their suicidal thoughts, while the over-
whelming majority do not. Future studies using ecological momen-
tary data such as from the CASPAR study offer the opportunity to
test whether an individual with a strongly connected network of risk
factors for suicidal behavior is indeed more at risk of suicidal behav-
ior over time when compared to an individual with a more weakly
connected network. These data may also allow us to come to for-
mal and quantified theories, as proposed by Haslbeck et al. (2019).
Formal theories are needed to really improve our understanding of
mental disorders, and to be able to provide better treatment. These
formal theories then inform novel data collec tion, yielding findings
that can be used to improve the initial formal theory.
Although we have focused on networks of psychological symp-
toms, complexity theory applies to all t ypes of information including
genetic, metabolic, social, and environmental data. The field of sui-
cide research and prevention should aim to gather such information
routinely as we move forward in the decades to come. To this end,
the University of Amsterdam has established a multidisciplinary re-
search institute that focuses on all of the different levels of influence
on mental health, ranging from the genes to the urban living envi-
ronment (https://www.uva.nl/en/share d-conte nt/zwaar tepun ten/
en/urban -menta l-healt h/urban -menta l-health.html). The future of
suicide prevention is interdisciplinary, with geneticists, experimental
psychologists, applied psychologists, psychiatrists, people with lived
experience, ecologists, computer scientists, policymakers, sociolo-
gists, and colleagues from other disciplines all working together to
advance our understanding of the complexity of suicidal behavior.
5 | CONCLUSION
Clinicians and scientists more and more conceptualize suicidal be-
havior as a result of the complex interac tion between many dif fer-
ent variables. Novel statistical techniques such as network analysis
can help us to better study this complexity. Network analysis can
be seen as a starting point to move from traditional linear thinking
toward a dynamical model of a complex system. Only recently have
researchers started in earnest to apply concept s from complex sys-
tems thinking to the field of psychopathology and suicidology. Such
a collaborative approach offers exiting and promising possibilities
for our understanding of suicidal behavior.
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SUPPORTING INFORMATION
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How to cite this article: de Beurs D., Bockting C., Kerkhof A .,
et al. A network perspective on suicidal behavior:
Understanding suicidalit y as a complex system. Suicide Life
Threat Behav. 2020;00:1–12. https://doi.org /10.1111 /
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