Visualization of causation in social-ecological systems

In social-ecological systems (SES), where social and ecological processes are intertwined, phenomena are usually complex and involve multiple interdependent causes. Figuring out causal relationships is thus challenging but needed to better understand and then affect or manage such systems. One important and widely used tool to identify and communicate causal relationships is visualization. Here, we present several common visualization types: diagrams of objects and arrows, X-Y plots, and X-Y-Z plots, and discuss them in view of the particular challenges of visualizing causation in complex systems such as SES. We use a simple demonstration model to create and compare exemplary visualizations and add more elaborate examples from the literature. This highlights implicit strengths and limitations of widely used visualization types and facilitates adequate choices when visualizing causation in SES. Thereupon, we recommend further suitable ways to account for complex causation, such as figures with multiple panels, or merging different visualization types in one figure. This provides caveats against oversimplifications. Yet, any single figure can rarely capture all relevant causal relationships in an SES. We therefore need to focus on specific questions, phenomena, or subsystems, and often also on specific causes and effects that shall be visualized. Our recommendations allow for selecting and combining visualizations such that they complement each other, support comprehensive understanding, and do justice to the existing complexity in SES. This lets visualizations realize their potential and play an important role in identifying and communicating causation.


INTRODUCTION
Science seeks to understand how systems are organized and function. A key element of such understanding is identifying the relationships between causes and effects, also referred to as causation (Woodward 2016, Pearl andMackenzie 2018). Claiming causal relationships is so commonplace in everyday life that scientists rarely ask themselves what causation actually means and on what basis we make causal claims. The word "because" is omnipresent: we have day and night "because" of the earth's rotation; the plant will not grow "because" it does not get enough water. Such causal claims are simple and direct, and such simple claims are hardwired into our language and thinking.
For explaining phenomena in complex systems, however, simple claims are often not sufficient (Meyfroidt 2016). This is the case for social-ecological systems (SES), which are composed of decision-making interacting agents, such as humans and organisms, and their environment (Ostrom 2009, Ferraro et al. 2018. The key building blocks of these systems, the agents, often behave in elusive ways. Causal relationships between variables in these systems are often nonlinear and can involve more than two variables. Moreover, in SES, social and ecological processes are intertwined. All this leads to complex systems in which single causal relationships are difficult, if not impossible, to disentangle (Schlüter et al. 2019).
The consequences for trying to understand and, thereupon, influence or manage such systems can be dire. Decisions based on erroneously understood causal relationships, or too simple or narrow mental models, can lead to unintended consequences and potentially disasters (Merton 1936, Sterman 2006, Levin et al. 2013. This happened, for example, during the 2008 global financial crisis and the collapse of Atlantic cod stocks (e.g., Frank et al. 2016, Sguotti et al. 2019. Factors complicating the construction of useful models of causation in SES include the diversity of their building blocks, adaptive behavior, positive and negative feedback loops, indirect, delayed or path-dependent effects, stochasticity, and the interaction of processes on different spatial, temporal, and organizational scales (e.g., Meyfroidt 2019, Elsawah et al. 2020. Being aware that simple causal claims and single, linear causal chains are often insufficient to understand what happens in SES, researchers have sought to identify and communicate more elaborate causal relationships. As the primary sense of humans is the visual one, visualizations play a key role in this endeavor. Their main purpose is to represent complex systems and phenomena with different foci, from different angles, and at different levels of detail. By decomposing and depicting parts of the system and their relationships, visualizations are used to elucidate how these systems function or how the phenomena emerge. This may happen at different stages throughout the research process, from visualizing initial hypotheses to eventually consolidated causal findings (Sheredos et al. 2013). Thus, visualizations are widely used to comprehend and to communicate causal relationships in SES. However, visualizations may also constrain our ability to capture causation, in particular in complex and intertwined systems such as SES. As graphical representations of structures and dynamics, they translate into mental models that may often suggest a level of simplicity in causal relationships that does not mirror reality. Likewise, even if we have better understood complex causation, using, for example, statistical analyses or mechanistic simulation models, our visualizations might not be able to adequately represent this understanding. Table 1. Assessment of the presented visualization types according to the six visualization challenges. o Cannot meet the challenge. ✓ Can partly meet the challenge, requires specific adjustments. ✓✓ Broadly meets the challenge. ✓✓✓ Is especially suited to meet the challenge. The strengths and weaknesses of each visualization type are discussed in the main text. See also  (4) is especially suited to meet the challenge ( Table 1). The assignment to these categories is explained below and supported by a detailed consideration of how the different aspects of each challenge can be addressed by the different visualization types (Table A1.1, Append. 1). For illustrative purposes, we use a hypothetical SES as a main example (Box 1) and add examples from the literature where appropriate. It should also be noted that many visualizations mix these main types of visualization of causation and also may contain additional elements that do not fit into any of these types. We refer to examples of such combinations in below in the section "Visualizing Complex Causation in SES Research."

Box 1:
DemoViz: a model of a hypothetical SES. To create exemplary visualizations, we generated data for a hypothetical system with an individual-based simulation model. Here, we provide a short summary of the model. A detailed description following the ODD (overview, design concepts, and details) protocol for standardized descriptions of individual-based and agent-based models (Grimm et al. 2006(Grimm et al. , 2020 is given in Append. 2. The assumed SES comprises a fish population in a river affected by river pollution, temperature, and fishing. Each fish individual is characterized by its body condition and location along the river. Both body condition and location change in time. The individuals' body condition is affected by the environmental variables river pollution level and river temperature, and differs among individuals. The individuals' locations are affected by river temperature only (representing movement to follow shifts of regions with favorable temperature along the river).
The population-level dynamics emerge from stochastic simulations of the individual-level processes according to the individuals' current attributes in each time step (corresponding to 1 year). The ecological processes comprise mortality, which is affected by body condition, and reproduction of individuals, which is affected by body condition and location. Besides natural mortality, the individuals can die through fishing. The social part of the SES is represented in a very simple form via the option to reduce river pollution, and via adapting the fishing pressure to the fish population size. Only above a certain threshold is fishing carried out, and approximately 20% of the individuals are caught randomly. The simulation is run for 200 time steps, but the population may go extinct before.

Objects and Arrows
One of the most common ways of visualizing and explaining causation in complex systems is a diagram consisting of objects and arrows connecting them (e.g., Fig. 1). It visually represents a phenomenon in a system by its organized parts and relationships, proposing how these interact to bring about the phenomenon (Sheredos et al. 2013). When used for representing causal relationships, an arrow from object A to object B depicts that a change of A causes a change of B. If there is another opposite arrow from B to A (or the arrow is double-headed), the causation is reciprocal: there is a feedback between A and B, as a change of B also causes a change of A. These meanings of objects and arrows are very general and flexible. Yet they require a conceptualization of the system for which the causal relationships are visualized. In particular, the objects must be defined. They can be entities in the system (e.g., agents or other components), but also state variables or processes. It is also possible to connect different kinds of objects in one diagram.
The selection of objects and arrows to be included has important implicit consequences. The objects already determine which claims about causal relationships in the system are possible based on the diagram. The arrows depict which of these relationships are actually considered. Any further causal relationships the objects might be involved in, and any further objects not shown, are ignored. All details within an object are usually ignored too, i.e., the higher-resolution objects it is composed of and the causal relationships between them. This simplified representation of the real complex system (e.g., Fig. 1A) helps to focus only on elements and relationships that are considered essential for a given question (Starfield 1990, Grimm andRailsback 2005). But it is crucial to be aware of these decisions, and they should be made clear. Often they are not explicitly stated, but taken for granted with the diagram of objects and arrows. However, they guide and constrain all subsequent efforts based on this visualization. The diagram represents, so to speak, a certain worldview and leaves out elements that might in fact be important but are ignored in this worldview. This is not only a decision of where to draw the https://www.ecologyandsociety.org/vol27/iss1/art31/ boundaries and how to choose the resolution of the SES representation. Also, what kind of objects are depicted in a diagram matters. In ecology, a good example is whether ecosystems are perceived either as being composed of organisms or of compartments containing energy and nutrients. This decision strongly influences for which real-world phenomena a causal understanding can be achieved . Conceptual diagram broadly visualizing causal relationships in the SES. Humans affect fish by polluting the river and by fishing. They also cause the change of climate, which in turn affects fish via river temperature. The arrows have different meanings, such as processes (e.g., fishing) or mediators (e.g., river temperature), which is expressed by the different arrow labels. The bottom arrow shows two relationships (two labels).
The direction of effect of relationships is not specified (e.g., whether high or low temperature is better for the fish). One may interpret that the dashed arrow means that the causal relationship between humans and climate is not part of the analysis. However, this is not explicitly defined and should be explained in the figure caption. (B) Diagram of a causal chain that illustrates how river pollution by humans is mediated to eventually affect the fish population. Note that river pollution, which was a label for the arrow between objects (the relationship between entities) in A, is now an entity itself, as the causal relationship is visualized at a higher resolution.
Potential. This visualization type can represent multiple causes by several arrows leading to an object. Thus, it can also indicate that a phenomenon emerges from the influence and interaction of these multiple causes. The visualization can also represent multiple effects by several arrows starting from an object. In addition to direct feedback between two objects (cf. above), indirect loops of causal relationships involving more than two objects can be visualized. An arrow starting from and looping back to an object can represent internal feedback. The causal relationship indicated by an arrow can be used to represent temporal order (i.e., termination of object 1 causes the start of object 2; e.g., in flowcharts). It can also represent flows of energy, matter, or information. The direction and strength of causal relationships can be visualized by using different widths or styles of arrows, or by labeling them. In any case, the absence of an arrow allows for a clear and even quantitative statement: there is no direct causal relationship between objects 1 and 2.
Limitations. Due to their versatility, visualizations with objects and arrows are used in many ways. This freedom can also be a drawback leading to confusion. Any intended meaning of specific shapes and styles of objects and arrows (e.g., Fig. 1A) should therefore be well explained in the figure captions. The meaning of arrows can remain unclear as they do not necessarily represent causal relationships. If they do, the possibilities of expressing different characteristics of these relationships are clearly limited. Even if the specific appearance of arrows can be varied to show differences, all these specifications are not inherent to the visualization. They might root implicitly in a presupposed common understanding of their meaning in the visualized context, for instance because this is established in a specific scientific discipline or methodological community. Preferably, they should be explicitly communicated in addition to the diagram, in particular with regard to the fact that SES research is interdisciplinary. Moreover, a single arrow does not specify the underlying mechanism(s) of causation. Additional objects involved in such mechanisms and any details within objects are not visualized according to the selected resolution or worldview. They are therefore also ignored. However, for showing these detailed objects and their relationships, such as causal chains, the same form of objects and arrows can be used too (e.g., Fig. 1B). This offers an important option for understanding and visualizing causal mechanisms.
Three subtypes of diagrams with objects and arrows are particularly relevant for causation in SES: conceptual diagrams, causal diagrams, and network diagrams.

Conceptual diagrams
Visualization by objects and arrows is very popular for conceptual diagrams, which are highly generic and flexible. They are ubiquitous in use for SES representations, visualizing conceptual models of the systems, but also frameworks and approaches to study them. Conceptual diagrams do not require strict formal rules. They may contain just a few objects and arrows (e.g., Fig.  1A) or many. To take into account the complexity of SES, different kinds of arrows, different kinds of objects (e.g., representing factors, actors, other system components, processes), multiple colors, layers, labels or pictures can be included, and diagrams can be nested (e.g., Fig. A3.1, Append. 3). However, to be used meaningfully and unambiguously, these differences require careful explanation. Moreover, although very helpful for visualizing multiple causes and discriminating causal from non-causal relationships, the high flexibility comes at the cost of lower potential for conveying more specific or quantitative information, for instance on the shape, strength, or temporal changes of causal relationships (Table 1). As the numbers of objects and arrows increase, it can become difficult to grasp which causal relationships are indicated, and it becomes likely that only selected relationships will be grasped, ignoring how they are embedded and interact with additional system elements. Attempts to reflect the actual complexity of an SES can lead to a conceptual diagram containing plenty of objects and arrows in an almost arbitrary manner (i.e., everything is linked to everything). Although each object and link in such a diagram may be justified and have a meaning, the visualization is then of limited use for specifying and disentangling complex causal relationships. Nonetheless, it can be useful for demonstrating this complexity, showing that phenomena are intertwined and that simple, mono-

Fig. 2.
Visualizations of causal relationships based on the example model DemoViz (Box 1) by causal diagrams. (A) Causal diagram of the system in dot and arrow format as it is represented in the simulation model. Each node depicts a specific state variable or process rate, each arrow depicts a causal relationship. The diagram includes instances of mediators (e.g., an indirect path from river pollution to fish mortality via fish body condition, which thus mediates the effect), multiple causes (e.g., two arrows leading to fish body condition), multiple effects (e.g., two arrows from river temperature), and reciprocal relationships (a direct loop between fish reproduction and population visualizing density dependence; an indirect loop involving fishing, fish mortality, and the fish population). This causal diagram is particularly useful for discriminating causal from non-causal relationships. For example, one might think that the fish location affects body condition, and also find them to be correlated. However, the diagram shows that there is no direct causal relationship between them (no arrow), but both are affected by temperature, which is therefore a confounding variable. (B) Causal loop diagram of a part of the system. Two state variable names (fish body condition, fish location) have been converted into clearly interpretable descriptions consistent with the "+" and "-" labeling scheme. This example combines stocks (e.g., fish population) and flows (e.g., fishing), and the loops are additive. The left loop is a balancing loop (one negative sign along the loop), whereas the right loop is a reinforcing loop (no negative sign).

Formal causal diagrams
Certain diagrams of objects and arrows follow a more specific formalism to represent causal relationships, for instance the dot and arrow format (e.g., Fig. 2A). Using such causal diagrams to visualize what we assume (or know) about the causal relationships in an SES makes these assumptions about the system more explicit and transparent, and allows inferences about their consequences. Causal diagrams in the dot and arrow format, with dots representing variables and the additional restriction that only unidirectional arrows and no cycles are allowed, can be used as tools for causal inference Mackenzie 2018, Lederer et al. 2019). To this end, the paths between dots can be traced, and common challenges for causal inference can be identified because they go along with characteristic structures in causal diagrams. For example, for a given arrow between two variables, a backdoor path is a path that leads to both of them from a third variable, which is therefore a confounder of the relationship. An indirect path connects the two variables in the same direction as the direct arrow, but via a third variable, which is therefore a mediator (Textor et al. 2016, Lederer et al. 2019. Such paths can be embedded in relationships involving many more than just three variables. Detecting them, as well as more complicated generic structures with specific meaning for causal analysis, is greatly facilitated by causal diagrams. Thus, the visualization serves as a robust and powerful tool that provides the basis for well-justified decisions whether certain variables must or must not be controlled for in causal inference. Without visualization, this would soon become much more difficult with an increasing number of variables and causal relationships between them (Pearl and Mackenzie 2018).
Although causal diagrams can be used for depicting stochastic causal relationships, the stochasticity itself is not visualized (Table  1). This means that it is not clear whether an arrow indicates, for example, that changes in one variable will sometimes, often, or always lead to changes in another variable that is linked by an arrow. Or an arrow connecting two events need not mean that the first event always causes the second. It may just modify the chances for the second event to occur.
Causal diagrams are also used to visualize structural equation models (SEM), a popular method for analyzing statistical associations between variables that then serve for causal interpretation (Shipley 2000, Grace 2006, Asah 2008, Fan et al. 2016. In these diagrams, in addition to arrows showing the direction, path coefficients indicate the strength and sign of relationships between variables (e.g., ; Fig.  A3.3, Append. 3). When applying SEM, the relationships that are included (i.e., the structure of the diagram) can be varied to test different models and select the preferred one based on fitting to data. Thus, the causal relationships that form the underlying conceptual model of the system would not be determined a priori but as a result of the system analysis (Eisenhauer et al. 2015). However, it is important to notice that the causal relationships cannot be derived from the associations between variables alone. Rather, these relationships need to be provided to the SEM as causal assumptions, and subsequent findings rely on careful interpretation (Bollen and Pearl 2013).
Causal loop diagrams are another popular type of visualizing causal relationships (e.g., Fig. 2B). They are a key tool in systems dynamics approaches to SES research (Elsawah et al. 2017. In these diagrams, arrows are labeled with "+" or "-" signs to indicate positive or negative relationships between the connected variables, respectively. The particular focus Ecology and Society 27(1): 31 https://www.ecologyandsociety.org/vol27/iss1/art31/ of the diagrams is on closed loops involving two or more variables. If the number of negative signs along a loop is even, the loop is reinforcing, meaning that increases (decreases) in one variable feed back positively through the loop and further increase (decrease) that variable. If the number of negative signs along the loop is odd, the loop is balancing, meaning that increases (decreases) in one variable feed back negatively through the loop and decrease (increase) the variable. These features make causal loop diagrams highly suitable to visualize and characterize reciprocal causal relationships (Table 1).
However, when combining stocks and flows (as variables) in a causal loop diagram, the visualization is prone to misinterpretation because the "+" and "-" labels can have two different meanings: additive or proportional change. An additive arrow denotes that the first variable adds to the second variable (or, for the negative sign, subtracts from that variable). But two variables linked by a positive arrow do not necessarily change in the same direction (and vice versa for a negative arrow). For instance, fish reproduction adds to the fish population ( Fig. 2B), but it is possible that fish reproduction decreases whereas the fish population increases (e.g., when the population approaches its maximum capacity). For proportional arrows, the two variables do always change in the same (or opposite) direction and thus are positively (or negatively) correlated (see Richardson 1997, Lane 2008 for details on this ambiguity of causal loop diagrams). Hence, thorough reflection and clarification of these meanings is strongly advocated when using causal loop diagrams.

Network diagrams
Network diagrams visualize objects and their pairwise relations as networks of nodes (objects) and edges (lines linking objects) between them (e.g., Fig. 3). The networks (also called graphs) can be used as abstract descriptions of structural aspects of studied systems, including SES (Borgatti et al. 2009, Dale 2017, Will et al. 2020. The nodes and edges can have flexible meaning. For instance, nodes may represent specific organizational units, such as individuals, populations, species, or spatial areas. Although nodes typically represent elements of the same type, this need not always be the case. For example, actor-network theory focuses on associations between different types of elements to investigate, among other things, how social processes influence a studied phenomenon (Latour 2005, Langley andTsoukas 2016). Edges in network diagrams may represent proximity, flows, (potential) interactions or any other kind of associations between the elements. They can be undirected (edges only) or directed (edges with arrows), and they can have weights that, for example, express the distance between objects or costs, durations, or intensities of flows or interactions. This flexibility can lead to ambiguity. For example, when visualizing foodwebs with network diagrams, arrows can be used to represent predation (directed from predator to prey), flows of biomass (from prey to predator), or reciprocal causation between predator and prey abundance (bidirectional arrows). Edges without arrows are also common, which can represent any of these options.
Network representations of SES focus on structural aspects of the systems and thereby implicitly assume that interaction structure plays a key role in the systems' causations (Borgatti et al. 2009, Scott 2011, Levine et al. 2017. To analyze this structure, graph theory provides a variety of tools and metrics to assess, among others, the spatial or functional connectance, density, nestedness, vulnerability, or node centrality of networks (Bollobas 1998, Butts 2009, Thébault and Fontaine 2010. The structure that is visualized in a network diagram often determines the framework for identifying causal relationships, for example, the potential interactions. But it is not equivalent to the actual processes operating in an SES, for example, the realized interactions. Fig. 3. Visualization of the spatial connectedness of fish individuals at two points in time by network diagrams. Snapshots from a run of the example model DemoViz. A random subgroup of the fish population is shown, with dots representing individuals. Their number differs because individuals may die, and new ones get born in each time step. Two dots are connected if the two individuals' locations are within a neighborhood (defined by a maximum distance). In the diagrams, dots are placed arbitrarily such that the resulting networks are well displayed. They visualize that individuals are much closer to each other and thus more connected at time step 121 (A) than at time step 122 (B). The underlying, yet invisible cause is that temperature increased between these time steps and affected the individuals' locations (cf. Box 1, Append. 2).
Networks can be used in two ways for deciphering causation in an SES. On the one hand, the structure has certain causes, that is, properties and dynamics of the system elements that led to the structure. On the other hand, the structure also has consequences as it enables, facilitates, or constrains processes in the system. In both cases, the network structure and its metrics can be regarded as patterns, and these patterns hint at the system's causal relationships (Bodin et al. 2019). However, such causal implications of the network structure are not conveyed by the visualization itself. They require interpretation and additional analyses and explanations. Nonetheless, the causal understanding is considerably supported by network diagrams, and its derivation can be straightforward. A network diagram of a foodweb implies that an abundant predator population causes a pressure on its prey population. A weighted network diagram of trading routes makes visible that closing a certain route could cause higher costs for trading partners using that route and higher usage of alternative routes. Here, the weights also serve to characterize the causal relationships.

X-Y Plots
This very common visualization type comprises two-dimensional line, point, bar, or similar plots relating two variables X and Y (e. g., Fig. 4). In this way, an X-Y plot reduces system complexity to just two chosen factors. The plot displays how different values of X are associated with different values of Y. Given that Y is not constant, this means that changes in X are related to changes in Y. Very often, this visualization type is interpreted as indicating causation, meaning that changes in X cause changes in Y. This suggested causal relationship is mirrored by a common terminology, calling X the independent and Y the dependent variable. X-Y plots are appealing as they convey a simple message, which is easy to grasp and memorize. However, they also strongly evoke mono-causal thinking, ignoring complexity and context. X-Y plots often suggest a simplicity and generality that do not exist in reality. . This number drops to zero during several periods. The (invisible) cause is that fishing is adaptive and stops when the population size falls below a threshold (cf. Box 1). (B) Bar plot comparing the total amount of fished individuals over the whole simulation period for two different scenarios. The visualization suggests that the intervention (reduced river pollution) is the cause for the higher amount of fishing, which is correct. (C) Point plots of the body condition of fish both at the individual and the population level (cf. legend) vs. river pollution. The visualization suggests a causal relationship from river pollution to body condition. This relationship exists, but is not that simple as pollution is not the only factor affecting body condition (cf. Fig. 2A). (D) Point plot of population growth vs. population size of the previous time step. It makes the causal relationship visible that large population sizes do not allow for high reproduction. However, for small population sizes reproduction can also be low, driven by different causes that are not shown.
There are exceptions of X-Y plots for which the visualized relationship is clearly not meant to indicate causation. The independent variable may be a mere criterion for discriminating different cases, such as the names of different agents or places, or the ranks of different items according to their associated Y value (e.g., species rank-abundance plots, ; Fig. A3.4, Append. 3). Also time series, plots in which time is the independent variable on the X axis (e.g., Fig. 4A), do not imply that time is the direct cause for change of the dependent variable (although time is usually involved in such change).
Potential. This visualization type is standard and extremely useful for depicting the relationship between one potential cause and one effect. In X-Y plots, the detailed characteristics of such a relationship can be made visible right away, such as its direction, strength, nonlinearity, or non-monotony, and also critical thresholds (Table 1). The relationship can be shown at high resolution of the variables' values. Variations, uncertainty, or confidence can be incorporated, for instance by individual values underlying a mean (Fig. 4C), error bars, intervals around the plotted curve, or symbols and labels for the results of statistical tests (e.g., tests whether data from different treatments have a common mean). In time series, the time points/periods of occurrence of events/treatments/interventions can be highlighted. This facilitates inspection whether those changes, which are not plotted themselves, are related to changes in the plotted Y variable. For the same purpose, one can plot two time series, one for the (potential) causal and one for the effect variable, or even more to consider multiple effects. Generally, using multiple lines/points/ bars differing in style or color can overcome the restriction to only one Y variable (sometimes also using two different Y axes). This strategy can be used to visualize different instances of an additional variable (cf. "Multiple Plots of the Same Visualization Type" below). But within one plot, these potentially dependent Y variables all need to be related to the same independent X variable.
Limitations. Apart from depicting the relationship to only one (potential) cause, the most important limitation of X-Y plots is that it is not possible to visually discriminate causation from mere covariance (Table 1). For instance, two variables might show a strong relationship not because X is the cause of Y, but because both are affected by a common cause C that confounds their relationship but is not shown. This is crucial and makes the plot amenable to mis-or over-interpretation. It adds to the problem that depicted relationships, even if they are causal, can be modified in complex systems by additional factors. Information about such factors and context, as well as mechanistic interpretations of causation behind depicted relationships, is not conveyed by the plot itself. These aspects require additional explanation. The same is true for underlying statistical models and assumptions, if uncertainty is included in the visualization.
It is also possible to plot the values of an independent variable X together with the change of that variable (dX/dt as Y variable). This allows visualizing the feedback of a variable X on itself (e. g., Fig. 4D). However, it also separates this self-feedback from its context and suggests ignoring the additional causes for changes of the X variable.
To visualize the reciprocal relationships between two variables, phase space plots can be used. These X-Y plots show the trajectories of combinations of two state variables (value pairs of X and Y), denoting changes over time in the phase space of possible states of a system (e.g., Fig. 5A). They usually imply that X and Y are causally related in both directions. In addition to visualizing possible combinations of X and Y, a trajectory also shows that for a given value of one variable, various values of the other variable are possible. from 1875 to 1906. The two populations are prey and predator and thus involved in a reciprocal causal relationship. However, the visualization does not allow clearly discriminating whether this predator-prey relationship, an alternative relationship of disease transmitted from hare to lynx, the relationship between hare and its food, or the relationship from human hunters to both populations is the major cause for the system dynamics. Source and further details: Gilpin (1973). showing hysteresis in a hypothetical dynamic ecosystem with alternative stable states (Y axis). Arrows visualize the temporal development, including abrupt changes (catastrophic shift or restoration) when the environmental conditions (X axis) cross a tipping point (black dots). Ecosystem states between the solid black curves are not stable, they cannot be maintained over time. The dashed curve separates unstable states from which the ecosystem would return to the upper "conserved" stable state (blue area above the dashed curve) and states from which it would return to the lower "degraded" stable state (area below the dashed curve). The blue arrow depicts a disturbance. Source and further details: van den Elsen et al. (2020). When X depicts an environmental driver and Y depicts a state variable, the effect that the driver has on the system state can depend on the current state of that system (e.g., Fig. 5B). Thus, both X and Y have an effect on changes in Y, leading to alternative stable states for the same value of the driver variable X. There may also be tipping points (Milkoreit et al. 2018), which means that the state variable changes abruptly when the driver exceeds a certain threshold. Even if the driver variable changes back, potentially very far from the threshold, the state variable does not reach the same values as before. It is possible that two tipping points exist, meaning that the state variable changes back (abruptly) only if the driver exceeds another threshold. This phenomenon of path-dependence causing alternative stable states (hysteresis) is common for SES, and X-Y plots are popular for visualizing it (May 1977, Scheffer et al. 2001, Hughes et al. 2013, Sguotti et al. 2019. Typically, the trajectories of the different stable states are connected with dashed or dotted lines to visualize that the corresponding combinations of X and Y values belong to unstable states (cf. Fig. 5B).

X-Y-Z Plots
This visualization type includes three variables. Here, X and Y are two independent variables, and Z is the dependent variable shown for different combinations of values of X and Y (e.g., Fig.  6). This is realized, for example, by two-dimensional contour or raster plots, or by three-dimensional surface or point plots. Thus, two potential causes and their effects on Z can be visualized together. This is an important step toward visualizing complex relationships in the system represented. The downside of this added complexity is that the plots can be more difficult to grasp compared with X-Y plots. And similar to X-Y plots, there remains the pitfall of perceiving depicted relationships as causal even though this may not be the case (Table 1).  . color bar). The background raster plot visualizes the trends of body condition increasing with decreasing river pollution and with increasing temperature. The colored points reveal that the single points approximately follow this trend, but also show considerable deviations. Some deviations are easier to discern than in plot (A) due to the color differences.
Potential. The visualization of two independent variables enables inspecting and presenting effects that emerge from their interaction. The characteristics of their relationship to the dependent variable get visible, including nonlinearity or critical thresholds. Even highly multifaceted relationships can be quantitatively shown. Similar values of Z for different combinations of X and Y values show that different regimes are similar in terms of their associated effect on Z. This can point to trade-offs between two causes and to options for buffering or compensating for negative effects of one factor by changing a second factor. In particular, the second factor can be a moderator or a variable representing the context and, thus, the dependence of the relationship between X and Z on this second factor Y is visualized. If time is the Y variable, changes of a relationship over time are depicted, although time is not considered a direct cause Fig. 7. Visualizations of a conceptualization of SES by objects and arrows, illustrating an analytical framework for analyzing emergent social-ecological phenomena. (A) The collapse of a fishery (top object) emerges from and affects "action situations" in which policy makers, fishers, and fish populations interact (middle objects). These diverse action situations affect each other (arrows between middle objects) and they each involve a different network of actors and system components (exemplified by bottom objects). (B) More abstract and generic visualization of the framework, highlighting how an SES phenomenon emerges from and again influences social, social-ecological, and ecological action situations (AS, middle objects). The AS also influence and emerge from their effects on each other (arrows between them). Each of these AS objects involves several instances of participating actors (A) and/or ecological entities (EE) (arrows from bottom objects). An example network of interactions between these A and EE is visualized by lines connecting them. The figure uses different kinds of objects, arrows, colors, labels, layers, and photographs to convey different types of entities and causal relationships that let the SES phenomenon emerge. Frames around the diagrams show that all this is considered in its context of social and ecological conditions. Source and further details: Schlüter et al. (2019). for changes of the dependent variable (cf. above). X-Y-Z plots can also be used to visualize the possible combinations of three variables that describe a system state and may all affect each other (e.g., ; Fig. A3.5, Append. 3). Or, comparable to X-Y plots (Fig. 5B), they can visualize that and how the relationship between two variables changes from bistability to a single stable state depending on the value of a third variable (the "cusp" model in catastrophe theory, e.g., Dudgeon 2016, Sguotti et al. 2019; Fig. A3.6, Append. 3).
Limitations. Also in X-Y-Z plots, causation cannot be visually discriminated from mere covariance. Moreover, it can be difficult to accurately discern the characteristics of relationships. Transferring visual differences of colors into quantitative differences of Z values is susceptible to errors (Fig. 6B). Exactly determining the positions of points or a surface in a threedimensional space, which must nevertheless be plotted as a twodimensional figure, is not always possible (Fig. 6A). Visualizing uncertainty about relationships is difficult and usually requires an additional plot, for example of the variation of Z values for different combinations of X and Y values. If time is chosen as the second independent variable Y, the benefit of showing the temporal development of the relationship between X and Z comes at the cost of not showing the interaction with a second potential cause.

VISUALIZING COMPLEX CAUSATION IN SES RESEARCH
The presented characteristics, potentials, and limitations of the different visualization types provide a sound basis for choosing the appropriate visualization of causation in an SES depending on the intended purpose. Nonetheless, this means that a decision needs to be taken as to which-often substantial-aspects of the complexity of the SES will be disregarded and which aspects will be brought into focus. For example, recent advances developed ways to visualize multiple and complex causal relationships that bring about an emergent phenomenon of interest in an SES, such as a fisheries collapse, through elaborate conceptual diagrams with objects and arrows (Fig. 7). A distinctive feature here is that Fig. 8. Visualizations of a network of action situations that lead to an emergent SES phenomenon by objects and arrows. The diagram follows the approach described by Schlüter et al. (2019, cf. Fig . 7) for the hypothetical SES used in the DemoViz model. The social-ecological (dark blue) and ecological (light blue) action situations can lead to the collapse of the fish population. (Purely social action situations are not included in this example, cf. Box 1.) The action situation "Fish life" comprises fish movement, changes in fish body condition, and fish deaths through natural mortality (cf. Append. 2 for details). How emergent outcomes of one action situation affect another action situation is visualized by labeled arrows between them. For instance, the fish movement in response to the river temperature affects the individuals' locations and, thus, their spatial connectedness (cf. Fig. 3), which affects fish reproduction. Temperature is an external driver of the action situation "Fish life", visualized by a gray dashed arrow.
several levels of organization are visualized: from single actors and ecological entities over the action situations they participate in as well as networks of action situations, to the overall emergent phenomenon. Implicitly, such a figure also communicates that (and why) the phenomenon is complex as it is produced by multiple interacting processes. The approach to visualize networks of action situations can be applied to a specific case, for example the hypothetical SES used for the DemoViz model (Fig.  8, cf. Box 1). Based on such visualizations, the analytical framework can be used to develop hypotheses about causal mechanisms that generate SES phenomena (Schlüter et al. 2019, Orach and. These possible explanations can then be further examined through empirical research or modeling. If the focus of a visualization, however, lies in supporting causal inference of relationships between variables in an SES, more formal causal diagrams are often the appropriate choice (Fig. 2). On the other hand, the focus may also lie in presenting specific causal relationships, ignoring the wider SES context they are embedded in for the sake of visualizing the particular shape, tipping points, or reciprocity of a relationship in an X-Y plot (Figs. 4,5) or, for instance, interactions of two causal variables in an X-Y-Z plot (Fig. 6).

Multiple Plots of the Same Visualization Type
An important option for widening the focus and visualizing complex causation is bringing together several plots of the same type in one figure. This allows increasing the number of causes to be shown, the number of effects, or both. For example, multiple X-Y plots in one figure depicting the same relationship between one causal and one effect variable for different instances of a second cause (i.e., different contexts) can show how two causes interact (Fig. 9, different columns). At the same time, the precise quantitative visualization of the depicted relationship provided by X-Y plots is maintained. Moreover, depicting the relationships between one causal and several effect variables in multiple X-Y plots further adds complementary information to these relationships, respectively (Fig. 9, different rows). This may, for instance, visualize trade-offs between different effects of changing one cause. The principle of multiple X-Y plots can be extended, for example, by using the X axes, different columns, different rows, and different line colors to show the effects and interactions of four different causal variables (e.g., Banitz 2019; Fig. A3.7, Append. 3). However, it needs to be mentioned that the data needed for such comprehensive visualizations of an effect variable for all combinations of relevant values of the causal variables are rarely available, except for computational models of SES, where conditions can easily be controlled and resulting system state variables obtained (Schulze et al. 2017, Schlüter et al. 2019. The same principle of multiple plots can also be used with other visualization types. With X-Y-Z plots that already show the interaction of two causes, a third cause or context can be added (Fig. 10). Similarly, this can be achieved by nested rows and Fig. 9. Visualization of complex causation for a modeled generic agricultural SES by multiple X-Y plots. Rural farmers invest a certain percentage of their assets in individual household activities (X axes) and give the remaining percentage to the community. The single plots show how these investment decisions affect the household-and community-level assets (Y axes) and, thus, poverty. Different columns are used to visualize the effects of a second cause or context, namely the operating poverty trap (column titles). These poverty traps result from mechanisms that involve several additional causes, which are not shown in the figure. Different rows are used to discriminate between two effects. They visualize how farmers' decisions and the operating poverty trap affect the assets of the whole community (top) and of individual households (bottom). Note that, in the single plots, different values of assets are possible for the same values of investments as the modeled dynamical system has multiple stable equilibria (attractors, red line plots). Source and further details: Radosavljevic et al. (2021).  The single plots show how the two causal variables "fishing cooperatives' loyalty" (X axes) and "variation of the fishers' reliability" (Y axes) affect the proportion of all fishers that do not directly contract with a fish buyer, but instead become members in a cooperative (visualized by color, cf. color bar). The two causes are varied in three discrete categories (three steps on the X and Y axes). Thus, broad effects are clearly shown, but detailed shapes of the relationships are not in focus. Different columns are used to visualize the effects of a third cause, namely fluctuations in environmental conditions (column titles). Source and further details: Lindkvist et al. (2017).

Combining Visualization Types
Combining different visualization types in one plot is another common and useful option for visualizing complex causation in SES. This strategy allows benefiting from the respective strengths of each visualization type (cf. "Types of Visualization of Causation" above). For example, X-Y plots showing the temporal development of an SES state and of underlying causal variables can be amended by objects and arrows diagrams showing the internal SES organization for different points in time (Fig. 11). Thus, the state of system entities and the causal relationships between them are integrated into the visualization and support causal understanding of the depicted temporal developments. Vice versa, X-Y plots can be inserted in a diagram of objects and arrows to illustrate the specific shape of the visualized relationships between different system variables (e.g., Banitz et al. 2020; Fig. A3.10, Append. 3). In another example from the SES literature, the combination of X-Y plots with objects and arrows visualizes causal relationships between trophic groups in a Fig. 11. Visualization of complex causation in a modeled fisheries SES in the Baltic Sea by combining an X-Y plot and network diagrams. The time series show the temporal development of several environmental variables (labeled black areas) and an index aggregating them (dashed line). Although the environmental conditions are similar in the first and third period shown, the ecosystem state (straight line) is very different. This is explained by network diagrams that show the biomass of different species populations (white node sizes, Ccod, S -herring, P, A -zooplankton species Pseudocalanus acuspes and Acartia spp.), the extent of fishing pressure (black node size), and the direction and strength of causal relationships between these SES entities (black arrows). Through the network diagrams, the figure aims to visualize that the changing environmental conditions during the second period have (together with fishing pressure) caused a transition to a different system state, which is difficult to reverse despite favorable environmental conditions. Source and further details: Möllmann et al. (2009). It is also possible to combine different X-Y-Z plots and thus visualize the interaction of two causes both in three dimensions and-in a more precise quantitative manner-in two dimensions (Fig. 12). However, a disadvantage of such nonstandard multifaceted visualizations is that they may easily get very complicated. They require extensive explanation, and grasping the depicted causal relationships is not always intuitive. If used, readers should therefore always be guided through the visualizations in order to fully explain the intended causal claims.
The visualizations presented so far can also be combined with additional types. One example are set diagrams that visualize sets by closed areas (e.g., circles). Set diagrams are widely and flexibly used, for instance, to visualize an SES conceptualization for studying poverty traps, according to which economy is part of a society, and this society is part of the biosphere (e.g., ; Fig. A3.12, Append. 3; see also Folke et al. 2016). In Venn   Fig. 12. Visualization of complex causation in a fisheries SES in the North Atlantic by combining different X-Y-Z plots. The three-dimensional surface plot depicts the effects of two causal variables (fishing mortality and sea surface temperature) on cod biomass according to a theoretical "cusp" model. The "cusp" shape of the surface visualizes the interaction of both causes: depending on temperature, the relationship between fishing and cod biomass is either continuous or discontinuous (hysteresis, cf. surface edges). Dots on the surface depict particular empirical values of cod biomass over time, whereby dot size is used to visualize biomass and dot color to separate two periods (cf. legend). The plot is mapped onto an X-Y plane (bottom), and a section of it visualized by a two-dimensional plot (left). This is again an X-Y-Z plot with the two causal variables on the axes and their effects on cod biomass visualized by the position and size of the dots. The dots are connected to visualize their sequence in time. The background blue area depicts the combinations of values of the two causal variables for which the model is discontinuous, as visualized in the surface plot. Source and further details: Sguotti et al. (2019). diagrams, overlap of two areas represents overlap of sets, that is, elements that belong to both sets. The same principle works for more than two sets. Integrating a Venn diagram in an objects and arrows visualization can be used to illustrate complex causation in an SES, for instance, the contribution of different causes to an effect. A typical situation is that different factors alone are insufficient to cause an effect. However, they necessarily belong to a particular combination of factors that causes the effect. As this combination is not the only way to bring about the effect, it is sufficient but unnecessary (e.g., Fig. 13A). Such "insufficient but necessary parts of unnecessary but sufficient" (INUS) conditions were defined by Mackie (1965) and are employed to disentangle complex causation in social and social-ecological research (Mahoney 2008, Morgan 2013, Meyfroidt 2016, Carlson et al. 2018. The combination of a Venn diagram with a network diagram can also be used to integrate visualizing subsets of  potential factors that are included in an analysis and visualizing causal relationships between these factors (e.g., Fig. 13B).

CONCLUSION
We have highlighted that visualizing causation in SES poses significant challenges, but there are promising ways to overcome them. A prerequisite for using visualizations to present and explain complex SES phenomena is to be aware of the key visualization challenges ("Challenges for Visualizations of Complex Causal Relationships" above) and the strengths and weaknesses of the different types ("Types of Visualization of Causation" above). In summary, the high flexibility of diagrams of objects and arrows is excellent for visualizing complex causation, but can easily lead to ambiguities, so consistency and explanation are critical. Moreover, the biggest limitations of these diagrams are their poor capability to show the characteristics of singular causal relationships and to visualize temporal dynamics and uncertainty. X-Y plots and X-Y-Z plots are more suitable for these challenges, but strongly limited in discriminating causal from noncausal relationships and visualizing multiple causes (Tablea 1, A1.1). Our assessment enables the informed selection of the appropriate visualization type depending on the research question, the purpose (e.g., visualizing assumptions, visualizing results, or visualizing a conceptual framework of a causal analysis), the knowledge about causal relationships in the SES, and the properties and part(s) of the system that shall be the focus of a figure (cf. specific exemplary recommendations at the beginning of "Visualizing Complex Causation in SES Research" above).
Ideally, figures speak for themselves and their messages are straightforward and fully comprehensible. But a correct and complete understanding of a figure may also rely on certain implicit assumptions. These may be familiar to researchers with a common scientific background. However, tacitly assuming specific knowledge and interpretation along with a visualization risks confusing readers who are unfamiliar with them, even more so because SES research is highly interdisciplinary. For these reasons, information that is needed to correctly understand a figure, or that is needed to communicate an aspect of causal analysis not conveyed by the figure, should be explicitly added with explanatory text. The respective caption should aim at clearly guiding readers through a figure, almost as one would do in presentations. This guidance can be critical to get the meaning and causal implications of a visualization unambiguously understood. One practical option to support this is to use https://www.ecologyandsociety.org/vol27/iss1/art31/ numbered labels and, in the figure caption, make readers grasp the figure sequentially by "walking" from element to element (e. g. ; Fig. A3.1, Append. 3).
For diagrams of objects and arrows, such guidance can also help readers to mentally animate visualizations and, thereby, comprehend how an SES phenomenon is caused by the operation of several processes. This works particularly well for sequential processes. But also in the case of simultaneous processes that let a complex phenomenon emerge, the visual summary of these processes can support causal reasoning and provide a sound basis for the design of analytical tools such as computational models (Jones andWolkenhauer 2012, Sheredos et al. 2013).
Besides relying on mental animation, a recent additional option is to create actual animations of visualizations (e.g., Anderson 2013, Grossman et al. 2016). Similar to their use during a presentation, animations can be used to visually tell a story about how an SES is organized and functions, in other words, to develop a causal narrative (cf. Shepherd and Suddaby 2017). This option can be appropriate for all three main types of visualization presented. Applied to X-Y and X-Y-Z plots, animations can also be used to visualize the changes of relationships over time, overcoming the challenge of visualizing temporal dynamics while retaining other strengths, such as the precise characterization of relationships (cf. Table 1). Most journals allow for animated visualizations in the supplement, whereas including them in the main manuscript is rarely possible. However, there are attempts to encourage the latter and keep the manuscript still comprehensible when printed on paper (e.g., with additional static figures as placeholders; Grossman et al. 2016).
Most visualizations used in science aim for simplicity so that the key message of a figure is easy to grasp and memorize. For complex causation, however, this design principle can be counterproductive as it suggests a level of simplicity that plainly does not exist. We therefore see a particularly promising way for overcoming the challenges of visualizing complex causation in SES ("Challenges for Visualizations of Complex Causal Relationships" above) in the combination of multiple visualizations in one figure.
Multiple plots of the same visualization type ("Multiple plots of the same visualization type" above) can be used to show specific causal relationships between variables in different contexts or for different values of additional variables. Thus, they visualize interactions and common emergent effects of multiple causes. The approach can also be used to visualize multiple effects of the same cause(s) within one figure (e.g., Fig. 9). As this principle of adding causes and effects by multiple instances of the same visualization works for all types, their specific potential for visualizing different aspects of complex causation in SES can nonetheless be exploited.
An alternative way to exploit this potential are well-designed combinations of different visualization types in one plot ("Combining visualization types" above). If one is careful not to overcomplicate these combinations, they can provide otherwise impossible comprehensive pictures that simultaneously tackle several of the presented visualization challenges. This considerably helps to disclose the complexity of SES phenomena and prevents unduly simple causal interpretations. However, especially when using creative and less common ways of combining different visualization types, careful and consistent design and thorough guidance in accompanying captions are crucial. Otherwise, they risk being of little value: although containing a large amount of heterogeneous information, they do not serve their main purpose of conveying causal insights to a broad interdisciplinary readership.
Thus, we assert that visualizing causation in complex SES remains an often difficult task and simultaneously addressing many, let alone all, of the identified challenges is virtually unfeasible. A single figure will not capture and characterize all causal relationships that are relevant for the fate and functioning of an SES. Simple figures remain important and useful, for example when putting the visualization focus on subsystems, on specific aspects of complex phenomena, on selected causes and effects. But they should be complemented by figures with combinations of visualizations to remind ourselves that causation in SES is more complex than our common way of thinking in terms of simple causal relationships and linear causal chains-and more complex than common visualization types may suggest. By being aware of this pitfall, and of the strengths and weaknesses of the different types of visualization, we will be well equipped to use visualizations to do justice to the complexity of SES and support a better and more comprehensive causal understanding.
Responses to this article can be read online at: https://www.ecologyandsociety.org/issues/responses. php/13030

Acknowledgments:
This research was supported by the Swedish Research Council (grant No 2018-06139).

Data Availability:
Data/code sharing is not applicable to this article because no data/ code were analyzed in this study.  Table on visualization challenges   Table A1.1. Details supporting the assessment of visualization types according to the specific aspects of the challenges presented and explained in Section 2 in the main text. No entries denote that the visualization type is, to our knowledge, typically not used to address the respective aspect of the challenge. Categories for overall assessment: o Cannot meet the challenge. ✓ Can partly meet the challenge, requires specific adjustments.

LITERATURE CITED
✓✓ Broadly meets the challenge. ✓✓✓ Is especially suited to meet the challenge (cf. Table 1).

Conceptual diagrams
Causal The following model description complies with the ODD (Overview, Design concepts, and Details) protocol for standardized descriptions of individual-based and agent-based models (Grimm et al. 2006(Grimm et al. , 2020.
1 Purpose The purpose of the DemoViz model is to create example visualizations of causation in a hypothetical SES. The hypothetical research purpose of the model could be to predict the effects of different pollution, fishing or climate scenarios on the dynamics of a river fish population and the catch from this population, and to understand causal mechanisms that lead to these dynamics.

Entities, state variables and scales
The model environment comprises a river of 60 km length and individuals belonging to a fish population within this river. The river is characterized by its state variables pollution level P, 3 Process overview and scheduling Each time step includes the following processes: fish movement, fish reproduction, fish mortality, fishing. After fish movement, the remaining processes are scheduled synchronously.
This means that new born individuals cannot die in the same time step. If both mortality and fishing happen to cause death of the same individual, the information is stored and at the end of the time step half of these death events are assigned to mortality and to fishing, respectively.
The rationale for this is to approximate synchronous dynamics since the temporal order of events within one time step is not explicitly modeled.

4 Design concepts
Emergence. All process rules and the individuals' state variables' responses to environmental conditions are imposed. The population abundance and the fishing catch emerge from the interplay of all modeled processes.
Adaptation. Fishing is adaptive to the fish population abundance. Only if the abundance was above a certain threshold (here set to 150 individuals) in the previous time step, fishing is carried out (cf. 7 Submodels -Fishing).
Objectives. The objective of adaptive fishing is not to exert additional pressure on the fish population when it has a low abundance, thus reducing the risk of extinction.
Sensing. The model uses one overall temperature value for the whole river (cf. 2 Entities, state variables and scales). However, we assume that in reality the local temperature actually varies along the river, the individuals sense this local temperature and move to a location with their preferred temperature range. This is implicitly considered in a simple manner as the fish individuals change their location in response to the overall river temperature (cf. 7 Submodels -Fish movement).
Interaction. Fish individuals' competition for resources is modeled implicitly via limiting the maximum population abundance to the capacity of the river. Humans, who are not explicitly modeled, interact with the fish via altering the level of river pollution and via fishing.
Stochasticity. The creation of environmental input data contains stochastic elements. The individuals' state variable's responses to environmental conditions are partly stochastic. The model processes contain stochastic elements, i.e. random movement, random death and reproduction events, and random fishing mortality (cf. 7 Submodels). These stochastic elements represent variability that is potentially essential for the modeled dynamics, but without explicitly including the causes of this variability.
Observation. The fish population abundance and the fishing catch rate over time are the main observations. Each state variable of the individuals as well as emergent process variables (e.g. population mortality rate, population reproduction rate) can be observed (Fig. A2.1).

Initialization
The fish population is initialized with 350 individuals. Their state variable values are not initialized separately as they depend on current environmental conditions in each time step and, thus, get assigned during the submodels Fish movement and Fish mortality (cf. 7 Submodels).
6 Input data The model uses input data to represent time series of river pollution level, temperature and capacity over the simulation time of 200 years ( Fig. A2.1A-C). These hypothetical input data were randomly generated to represent reasonable variability in the environmental conditions.  Fish movement. Changes in river temperature T cause the fish to change their locations. The rationale for this relationship is that we assume that the real temperature varies along the river (decreasing from position 0 to position 60 km). This means that when the whole river gets warmer (colder), areas with the temperature range preferred by the fish shift to higher (lower) positions along the river. We additionally assumed that these areas get larger when the overall river temperature T increases. Thus, we implicitly take the movement of fish in response to local   of objects and arrows with X-Y-plots. The objects and arrows visualize causal relationships between disturbances D, biodiversity B and ecosystem functioning F (biodiversity is shown twice to illustrate that its relationship to ecosystem functioning is often studied separately from disturbances). The X-Y-plots inserted visualize observable relationships between variables representing the connected objects, respectively (axis labels). These emergent DBF relationships are affected by the underlying causal relationship between these variables, and by additional variables (either shown or not shown). For example, the relationship between the effective number of species and the multifunctionality index (bottom X-Y-plot) is confounded by the disturbance frequency which is causally related to both variables (visually detectable by a backdoor path between them, cf. Section 3.2.1 in the main text). Source and further details: Banitz et al. (2020).   Fig. A3.11. Visualization of complex trophic relationships between different species in a marine ecosystem model by combining X-Y-plots with diagrams of objects and arrows. The two bar plots (X-Y-plots) visualize frequency distributions of body length (X-axes) of two fish species (the predator cod and the prey sprat, cf. Y-axes, also visualized by icons). They show that the populations are structured in cohorts. In these bar plots, arrows between cohorts visually indicate the model processes growth (black arrows), reproduction (gray arrows) and mortality (dashed gray arrows). Another line plot (X-Y-plot) visualizes the switching of cod prey preference throughout its life-stages. Additional prey species are visualized by icons (zooplankton at the bottom, benthic organisms in the middle), and thin arrows represent biomass flows from these prey species to the different life-stages of the two fish species. Similarly, the gray areas visualize the predatorprey relationship between the two fish species, but here the dotted area shows the size range of predators that can feed on a prey individual of a certain size (11 cm), and the shaded area shows the size range of prey a predator individual of a certain size (35 cm) can feed on. The figure requires detailed explanation, but helps understanding the model rules and processes that let the population dynamics emerge in simulations. Source and further details: van Leeuwen et al. (2013).