Agent-based modeling of environment-migration linkages : a review

Environmental change can lead to human migration and vice versa. Agent-based models (ABMs) are valuable tools to study these linkages because they can represent individual migration decisions of human actors. Indeed, there is an increasing, yet small, number of ABMs that consider the natural environment in rural migration processes. Therefore, we reviewed 15 ABMs of environment-migration linkages in rural contexts to synthesize the current state of the art. The reviewed ABMs are mostly applied in tropical contexts, serve a wide range of purposes, and cover diverse scales and types of environmental factors, migration processes, and social-ecological feedbacks. We identified potential for future model development with respect to the (1) complexity of environmental influence factors, (2) representation of relevant migration flows, and (3) type of social-ecological couplings. We found that existing models tend to not include fully integrated feedbacks and provide recommendations for the further development of ABMs to contribute to an understanding of the environment-migration-nexus in the future.


INTRODUCTION
Environmental change puts tremendous pressure on socialecological systems.This applies in particular to contexts in which humans both depend on natural resources and affect them.Changes in precipitation patterns, including occurrences of droughts, floods, and sea level rise, pose some of the biggest challenges of environmental change for societies.In addition, the pressure on social-ecological systems is potentially exacerbated by demographic and economic dynamics, such as a growing population or changing market prices.One strategy to deal with these challenges is human migration, including rural-to-urban as well as rural-to-rural migration.The latter is of particular importance in developing countries (Bilsborrow 2002, Zimmerer 2004) where an increasing demand for labor during harvest times pulls people to rural areas.
Besides being triggered by environmental change, migration can also have environmental consequences, including deforestation and degradation of natural resources (Bilsborrow 2002, Carr 2009, Lambin and Meyfroidt 2011).For example, in a global-scale study, Neumann-Hermans et al. (2016) found the strongest forest resource degradation in those villages that were characterized by immigration.In addition to the impacts on the destination, the place of origin can experience environmental consequences of out-migration, for example through changes in land use practices such as a lack of maintenance of terraces causing soil erosion (Collins 1986), reduced intensification through population decline (Preston 1998), or remittances impacting the use of forest resources (Hecht et al. 2015).In summary, indications exist that environmental change, combined with a bundle of socioeconomic factors, can lead to migration which, in turn, can trigger additional environmental change (de Sherbinin et al. 2008, Foresight 2011).
There is a growing body of literature on environment-migration linkages based on an emerging number of case studies, and major strides were made with respect to theory development (e.g., Black et al. 2011, McLeman 2013a, 2017, Hunter et al. 2015).Still, considerable research gaps exist regarding the interplay of environmental and nonenvironmental migration determinants as well as regarding the social-ecological impacts of environmentally induced migration at both the migrant's destination and the place of origin (Hunter et al. 2015).Overall, there is a lack of understanding on how environmental changes and migration mutually reinforce each other.
Simulation models have the potential to address these gaps (McLeman 2013b, Neumann andHilderink 2015).They can explicitly include feedbacks between the social and the ecological system and enable the simulation of future trajectories under different scenarios.Aggregated modeling approaches include the work of Krol and Bronstert (2007) who simulated linkages between climate change, water availability, agricultural economy, and migration for northeast Brazil.The authors conclude that migration is largely driven by mean municipality income being a function of climate change, water availability, and agricultural yields.In a recent study, Rigaud et al. (2018) integrated the shared socioeconomic pathway (SSP) narratives in a gravity model to estimate flows of people who left their home because of sea level rise, water availability, and crop productivity decline.Modeling results show that by 2050, approximately 140 million people across sub-Saharan Africa, Latin America, and South Asia could be forced to move within their own countries as consequence of climate change.
Together, these studies represent a valuable contribution to the exploration of possible future trajectories of climate induced migration by covering large regions.Yet, they tend to disregard that migration emerges from the complex decision making of heterogeneous individuals and their interactions.It is this importance of individual behavior that brings our attention to agent-based modeling.Agent-based models (ABMs) with their ability to depict how individual decision processes lead to changes at the population level are valuable tools in the discipline of The overall system consists of subsystems (A and B).For simplicity reasons we refer to two subsystems; in principle each subsystem can represent more than one origin or destination system.In both subsystems, humans interact with the natural environment.In terms of migration flows, subsystems are characterized by out-migration from subsystem A to subsystem B and/or return-migration from subsystem B to subsystem A. Furthermore, persons can enter subsystems (migration into the system) and/or leave them (migration out of the system).In modeling terms, this process implies that agents are newly initialized or deleted in the course of the simulation.In other words, a person that sends remittances or information to its place of origin does not migrate out of the system but stays within the system.

Box 1:
To represent the interactions within the subsystems we adapted Parker et al. (2008) and differentiate between one-way linkages, partly integrated linkages, and fully integrated two-way linkages: . For one-way linkages, agents are influenced by the environment but do not influence it vice versa.
. In the case of partly integrated linkages, agents make natural resource-use decisions and are in turn influenced by them in their migration decision.For example, agents harvest natural resources in and are influenced in their migration decision via the harvest success.Importantly, the agents' decisions have no lasting impact on the environment; hence, there is no closed-loop feedback between the environmental and the human system.
. Fully integrated two-way linkages imply that environmental consequences of natural resource use and migration decisions are considered within the model, e.g., resource depletion or soil degradation.
The different types of linkages have been included in well-known stylized ABMs of social-ecological systems.Both partly integrated and fully integrated linkages are present in different versions of the Sugarscape model (Epstein and Axtell 1996).In Sugarscape, the landscape comprises cells with various amounts of sugar.In each time step, agents stay put or move to an unoccupied cell and then consume all the sugar available on their current location.In the version with immediate grow back, the sugar completely regrows to its maximum in the next time step, thus forms a partly integrated linkage.A fully integrated two-way linkage is present in gradual grow back because the amount of sugar increases only incrementally in each time step.Thus, agents have an impact on the availability of natural resources of the following time steps.According to our knowledge, no well-known one-way integrated version of Sugarscape exists, but could be imagined in a way that agents are attracted by different amounts of sugar, but do not actually consume it.https://www.ecologyandsociety.org/vol23/iss2/art41/The purpose of this framework is to enable us to describe and compare ABMs on environmentally induced migration with regard to the linkages within and between the subsystems.Therefore, our framework is complementary to generic standards for describing ABMs such as the ODD+D framework (Müller et al. 2013).The ODD+D framework addresses modeling choices such as temporal and spatial scales, various model design concepts, and details of human decision making.However, because of this broad scope, the ODD+D framework does not consider specific aspects that need to be addressed in ABMs for environmentally induced migration such as types of migration flows.While focusing on describing and comparing ABMs, our framework does not provide guidelines for model testing and analysis.For this, frameworks such as the TRACE (TRAnsparent and Comprehensive model Evaludation) framework (Schmolke et al. 2010, Grimm et al. 2014) for documenting the development and testing of models represent valuable complements to our framework.

Paper selection
In March 2017, we performed a Web of Science topic search to obtain a systematic and unbiased literature selection.For this purpose, we adapted the search term proposed by Klabunde and Willekens (2016) to include a wide range of synonyms used for the method of ABMs (see Table 1).We did not restrict our search to a certain period of publication.From the resulting 508 articles we extracted those publications describing ABMs in which migration decisions in rural contexts are influenced by at least one environmental factor, e.g., rainfall.We excluded urban-urban migration as well as constantly moving societies including pastoralists, hunter and gatherers.This led to 14 publications.
We complemented this set by considering the non-ISI listed Journal of Land Use Science, which is an important outlet for ABMs.This step resulted in one additional publication.Furthermore, we included four relevant papers identified by Klabunde and Willekens (2016) and within our own network.Additionally, we added two non-ISI-listed technical reports as additional references for two of the identified publications because they provided a more detailed model description than the respective ISI-listed publication.Finally, we checked all publications that cited the review of Klabunde and Willekens (2016) and performed a Web of Science topic search using "microsimulation" instead of "agent-based model" and "mobility" and "movement" instead of "migration."Both steps did not result in additional ABMs fulfilling our consideration criteria described above.As a result, 21 publications describing 15 ABMs were considered for this review.

Model categorization
We reviewed the identified 15 ABMs according to the conceptual framework described above and according to the categories listed in Table 2.We developed a standardized protocol for categorizing the models and investigating how rural migration is modeled.
Based on the conceptual diagram we additionally drafted diagrams for each ABM to visualize the considered processes; the diagrams for each of the ABMs can be found in the Appendix 1.Each ABM was categorized by two authors of this article and we subsequently sent our results to the developer of the ABM for an additional cross-check.This final step enabled us to eradicate possible misinterpretations; the response rate was 87%.
The following definitions were used for classifying the ABMs: Context-specific conceptual model: In a context-specific ABM, model processes are based on data or expert knowledge specific to a case study, represented in a stylized model; however, it is not based on a specific geographic region or spatially explicit data (based on Groeneveld et al. 2017).
Migration flows: Systems can be characterized by out-migration from subsystem A to subsystem B and return-migration from subsystem B to subsystem A. In the latter case, agents can move directly back to the origin (direct return) or do so via multiple stops (indirect return).Furthermore, humans can in-migrate from outside the two subsystems into subsystem A and/or B and humans can out-migrate from subsystem A and/or B to somewhere outside the overall system.Migration was only classified as "out of system" for agents that had no opportunity of returning within the model setup and did not interact with their origin system by sending information or remittances.
Duration of migration (seasonal/permanent): We differentiate between seasonal and permanent migration.Seasonal migration is characterized by short-term absence, i.e., less than a year, from the place of origin.In the context of natural resource use, this type of migration is often aligned to harvest cycles.In the case of permanent migration, migrants leave with the intention to stay for long-term periods.However, it is not precluded that they move on or return after a short-term because of changing conditions.
Properties of the destination system known: This indicates whether the agents consider properties of the destination system, e.g., availability of natural resources or market prices in the destination system, in their decision to migrate there.
Direct/indirect environmental influence factors: We assessed whether environmental influence factors are conceptualized as direct, e.g., agents consider amount of precipitation when deciding to migrate or not, or indirect drivers, e.g., rainfall affects income, which agents consider when deciding whether to migrate or not.
Abiotic/biotic: Abiotic are all environmental factors that are not influenced by living organism, e.g., climate, atmosphere, temperature, light.Biotic are all environmental factors that are influenced by living organisms, e.g., plant growth, soil quality.
Social network: Social networks are explicitly modeled social linkages, e.g., through remittance, information exchange, dependents.If agents compare their own situation with that of others or consider the impact a decision has on others, it is not considered a network effect.Social-ecological feedbacks (one-way linkages/partly integrated linkages/fully integrated two-way linkages): We assessed the models following the classification introduced with our conceptual framework.
Migration decision (probability function/decision theory/ heuristics/optimization): We assessed the approach used for simulating a migration decision.A "probability function" can be any function that includes a stochastic factor to determine the migration decision, e.g., random destination, logistic regression function.Models that are based on "decision theory" use an existing decision theory from economics, psychology, or other fields, e.g., Theory of Planned Behavior."Heuristics" are simple decision rules or rules of thumb, e.g., the if-then rule."Optimization" includes any form of maximization of a certain indicator, e.g., income, fitness, happiness.

Overview
The number of ABMs that resulted from our literature search is substantially lower than the 27 ABMs reviewed by Klabunde and Willekens (2016) who analyzed migration ABMs in general.This indicates that a substantial share of ABMs in the field of migration does not consider environmental factors.
Table 3 provides an overview of the 15 reviewed models.All considered ABMs are used for gaining system understanding, which is in line with other fields of ABMs (e.g.land use ABMs reviewed by Groeneveld et al. 2017).Four ABMs are used within participatory contexts (e.g.Naivinit et al. 2010, Wu et al. 2011), three to provide decision support (e.g.Smajgl and Bohensky 2013) and three for predicting numbers of migrants (e.g.Berman et al. 2004, Hassani-Mahmooei andParris 2012).
The temporal scales of the reviewed models range from small, e.g., three years in daily time steps in Naqvi and Rehm (2014), to large, e.g., 10,000 years in yearly time steps in Janssen (2010).Numerous models applied different time steps for simulating different processes and, thereby, tackle the challenge of subsystems operating at different temporal scales as discussed by Martin and Schlüter (2015).For example, Smajgl and Bohensky (2013) use daily time steps for capturing environmental processes and weekly time steps for household-level processes such as migration.In this case, migration processes are modeled with a coarser temporal resolution than the remaining model processes.
The spatial scales cover a wide range from local (e.g., Naivinit et al. 2010) to national extent (e.g., Kniveton et al. 2011).The majority of reviewed ABMs consider a specific case study (Table 3).The locations of the case studies are distributed across the tropics with a focus in Southeast Asia (Fig. 2).This might indicate that environmental factors or natural resources are linked with human migration especially in this climate zone.We grouped the environmental factors considered in the reviewed models (rightmost column in Table 3) into two types: the availability of (1) natural resources, i.e., provisioning services such as resource availability and (2) influencing environmental factors, i.e., mostly factors of environmental change such as rainfall.This distinction is illustrated in the diagram with the tree symbol (natural resources) and the rain cloud symbol (influencing environmental factor).Figure 3 shows that influencing environmental factors determine the availability of natural resources in a large number of models, e.g., soil quality affects crop yields in Janssen ( 2010).Both natural resources and influencing environmental factors may influence human agents in their decision to migrate.Furthermore, human agents frequently influence the availability of natural resources, e.g., consumption of resources in Hadzibeganovic and Xia (2016)).In contrast, human agents affecting influencing environmental factors is rarely included in the models, e.g., pollution affecting glacier processes in Magallanes et al. (2014).

Types of migration processes
Figure 3 shows that most reviewed ABMs consider out-migration from one subsystem with the option to return in the course of the simulation (e.g., Berman et al. 2004, Rogers et al. 2011).Two ABMs include migration out of the system (Rogers 2011, Smajgl et al. 2013) and one ABM allows for in-migration from outside Table 4. Environmental factors considered in the reviewed agent-based models.
the overall system (Hadzibeganovic and Xia 2016).The neglect of migration into and out of the system can be considered a particular strong simplification because, in reality, humans often leave and enter systems such as a country or a region (United Nations 2013).According to our definition, "migration out of system" does not include agents who leave their home and send remittances.Finally, the majority of reviewed ABMs consider permanent migration (see Appendix 1).In contrast, especially in rural areas in the tropics, seasonal migration during the lean season often plays an important role (Henry et al. 2004, Rademacher-Schulz et al. 2014) and there seems to be a lack of ABMs studying this crucial agricultural labor migration.

Factors influencing migration decisions
In eight ABMs, the properties of the destination system, also referred to as pull factors, are influencing the migration decision (indicated at the top left corner of subsystem B in Fig. 3).The number of environmental factors (being push or pull factors, or both) represented per ABM ranges from one to five (  (Berman et al. 2004, Naivinit et al. 2010, Kniveton et al. 2011, Smith 2014).This rather limited representation might partly be due to our strict definition of social networks, but also reflects the complexity associated with modeling social networks.The most frequently considered economic influence factors are distance (to the nearest road, market, or the destination), assets (either on individual, household, or village level, e.g., land, TV, water pump), and income.Among the social influence factors, age, influence by peers (e.g., number of neighbors, fitness of neighbors, behaviors of neighbors, migration of others), gender, population size, migration experience, social ties (e.g., dependent at home), and education are most frequently accounted for.These influence factors are frequently discussed as migration drivers identified in empirical and conceptual studies on environment-migration linkages (e.g., Black et al. 2011, Morrissey 2013, Neumann and Hermans 2017).Interestingly, political influence factors, including discrimination, persecution, conflict, which are known to drive significant migration flows are underrepresented in ABMs, probably because data on how such factors shape individual decisions is scarce.

Coupling of the social-ecological system
We categorized the reviewed ABMs into one-way, partly integrated and fully integrated social-ecological feedbacks (cf.Parker et al. 2008).Table 5 shows the social-ecological feedback included in each of the 15 reviewed ABMs.In five ABMs we found Flooding, fish scarcity, timber scarcity -> (Forest economy ->) Migration decisions -> Fish scarcity, timber scarcity Smajgl et al. 2015a Weather variability, floods, fish catch, brackish water and water availability -> Migration decisions -> Fish catch, brackish water, water availability one-way linkages, i.e., agents are influenced in their migration decision by the environment but do not influence it in turn.Four models include partly integrated linkages, e.g., agents alter land use and are in turn influenced by harvest success (Mena et al. 2011).Six ABMs implement fully integrated linkages and as such consider environmental change as both a cause and consequence of migration decisions, e.g., soil degradation in Janssen (2010).
Six out of 15 models consider fully integrated linkages; although the representation of these feedbacks between social and ecological systems is a strong advantage of ABMs (e.g., Matthews et al. 2007, Schlüter et al. 2012, Filatova et al. 2013) and is advocated in several scientific fields, such as land use modeling (Parker et al. 2008).Interactions between the social and environmental subsystem can either amplify or weaken a regime shift (Filatova et al. 2016), thus, omitting critical interactions could lead to missing or overemphasizing such regime shifts.Of course, it needs to be acknowledged that the incorporation of fully integrated linkages is not necessary in every case; if the system under study does not depend on social-ecological feedbacks, a one-way or partly integrated model can be sufficient, or even better suited, to answer the posed research questions.The important challenge in this respect is to identify crucial linkages, especially because they might occur across different scales and involve indirect feedbacks (Parker et al. 2008).If in doubt, including linkages in a model would allow modelers to check their importance in a sensitivity analysis.
Should fully integrated social-ecological feedbacks be required, implementing them most likely implies increasing the model complexity, possibly leading to reduced transparency (Müller et al. 2014) or difficulties regarding parameterization (Smajgl et al. 2011) and model analysis (Lee et al. 2015).A fully integrated model will be more difficult to understand, to parameterize, and to validate against real world data.This increased difficulty in model development and analysis is also indicated by our result that fully integrated ABMs contain a slightly higher number of environmental factors than one-way or partly integrated models.Yet, this insight is based on a limited number of models and therefore can only be seen as an indication rather than as statistically robust result.

The challenge of matching the conceptual framework
As visualized in Figure 3, some elements of our conceptual framework receive more attention than others.The number of considered framework elements per ABM is on average 6.4 out of the 20 framework elements.Here, we aim to shed light on the reasons for the limited number of framework elements per ABM and discuss how various model parts relate to each other.As such, we are particularly interested in how the representation of socialecological feedbacks is associated with the number of environmental factors or the representation of migration flows and migration decisions.
The number of environmental factors being included in the reviewed models is slightly higher for ABMs with fully integrated two-way linkages (Fig. 4) than for one-way and partly integrated ABMs.For example, Magallanes et al. (2014) implemented a fully integrated coupling that represents the complex biophysical process of water availability being affected by the interplay of human action and glacier processes (see Table 5).In Janssen (2010), the fully coupled process of humans affecting agricultural harvest levels via soil depletion is reflected in the larger number of environmental variables compared to the number of considered environmental factors in the other reviewed ABMs.
In contrast, fully integrated models with low numbers of environmental factors also exist.For example, Rogers et al. (2011) present a fully integrated ABM with only one environmental factor.We identified a relationship between the type of coupling and the decision rules used to model migration decisions: decision models based on probability functions or decision theories are exclusively used in ABMs with one-way or partly integrated linkages (Fig. 5).
For example, the one-way integrated models by Kniveton et al. (2011) and Smith (2014) use the Theory of Planned Behavior to model migration decisions (Ajzen 1985(Ajzen , 1991)).In contrast, all ABMs with fully integrated linkages solely contain heuristics, i.e., simple decision rules or rules of thumb such as if-then rules.For example, in the fully integrated models by Smajgl et al. (2015a) and Smajgl and Bohensky (2013) migration decisions are based on Boolean variables, which were derived from interviews and households and indicate whether an agent would migrate in a particular situation, e.g., if fish scarcity exceeds a certain level.This relationship between type of coupling and the representation of migration decisions might hint at the challenges for combining complex decision rules with complex social-ecological feedbacks for model development.Here, the goal to model human decisions in general and migration decisions in particular in a comprehensive way in ABMs seems to challenge considering fully integrated feedbacks.Modeling human decisions to study social-ecological systems is of increasing importance (Groeneveld et al. 2017).
Although progress such as the use of decision theories is being made (Schlüter et al. 2017), the flexibility and complexity of human decisions still represent major challenges for modeling.
All reviewed ABMs with one-way or partly integrated linkages consider out-migration together with an either direct or indirect return of migrants (Fig. 5).Yet, migration into or out of the system is solely included in fully integrated two-way integrated ABMs.This indicates that modelers seem to focus either on representing human decision making in as detailed a manner as possible, e.g., by using decision theories, see Groeneveld et al. 2017) or on representing fully integrated social-ecological feedbacks (see Filatova et al. 2013) and considering all possible migration flows.
One reason for this observation might be missing data and understanding of the complex environment-migration context.Bilsborrow and Henry (2012) state that, very seldom does sufficient data on both environmental factors and migration exist from the same region and the same time.The lack of input data has also been identified for ABMs in general (Schulze et al. 2017).For example, data on individual decision making would improve the representation of decision making in ABMs (Filatova et al. 2013).
A second reason for the focus on specific model parts are challenges associated with analyzing complex models (Sun et al. 2016).The discussion of difficulties and strategies for analyzing complex ABMs has been gaining more and more attention recently (e.

Methodological considerations
Categorizing ABMs based on provided model descriptions is always prone to subjective biases.To limit such biases and to mitigate possible misinterpretation, we did a cross-check within our author team as well as with the authors of the reviewed models.
Advancing the practice of describing models by using standard protocols is a crucial step in tackling the challenge of model communication (e.g., Müller et al. 2013Müller et al. , 2014)).
Categorizing ABMs requires the use of consistent definitions.Hence, the conclusions drawn from our review depend on the applied definitions.For example, our strict definition of social networks and of migration out of the system has contributed to the small numbers of ABMs in these categories.Similarly, in order to cover all relevant ABMs we applied a broad definition of environmental factors.For example, we categorized "crop yields" as natural resource, which could also be seen as an economic factor.
Finally, as we focused our review on ABMs of the environmentmigration-nexus in rural contexts of natural resource use, we applied a rigorous procedure of eliminating ABMs, including urban-urban migration and residential mobility.This led to a limited number of ABMs to review, which hampers a statistical analysis of the results.

CONCLUSION
In this study, we reviewed 15 ABMs of environment-migration linkages to synthesize the current practice in this field and to further advance the model development.We provide a conceptual https://www.ecologyandsociety.org/vol23/iss2/art41/framework for social-ecological systems connected through human migration, which can be used for describing and comparing ABMs.In summary, we found that ABMs considering environment-migration linkages are still scarce.Given the importance of environment-migration linkages, we call for further developing ABMs of environment-migration linkages and would like to highlight promising ways forward in advancing this field.This also implies intensifying interdisciplinary work between social and natural scientists, modelers, and empiricists to appropriately depict human decision making in such ABMs and to understand and represent linkages of social and ecological systems.
Most reviewed ABMs represent case studies in the tropics, serve a wide range of model purposes, and cover diverse spatiotemporal scales.Based on our analysis, we identified major gaps with respect to modeling environment-migration linkages.First, important migration flows such as migration into and out of the system as well as temporary migration processes currently receive little attention in ABMs of environment-migration linkages.Furthermore, 9 out of 15 models lack fully integrated socialecological feedbacks.Exploiting the potential of social-ecological models by implementing more fully coupled systems is essential for exploring whether environmental changes and migration mutually reinforce each other, although drawbacks such as increasing model complexity exist.
To close these gaps, standards for developing and analyzing ABMs are needed.These standards should include the development and realization of strategies for sharing and reusing social-ecological ABMs, the provision of methodological guidelines for analyzing complex social-ecological ABMs such as the TRACE framework (Schmolke et al. 2010, Grimm et al. 2014) and the further propagation of using standard protocols for documenting ABMs such as the ODD+D protocol (Müller et al. 2013).Specifically for the ABM development in the field of environment-migration linkages, we propose our conceptual framework for assisting model development.Together with standards for supporting a good practice of model development, documentation, and analysis, this will help to advance agentbased modeling of environment-migration linkages and thereby foster an understanding of the environment-migration-nexus in the future.
__________ [1] In the remainder of the article we use the term "rural migration" to refer to rural-rural as well as to rural-urban migration.
Responses to this article can be read online at: http://www.ecologyandsociety.org/issues/responses.php/10200

Berman et al. 2004
Fig. A1.1 Diagram drafted for the ABM described by Berman et al. (2004) Table A1.1 Standardized protocol for the ABM described by Berman et al. (2004) Hadzibeganovic & Xia (2016); the model includes two types of migration decision ("reproduction-based" and "payoff-based") of which one is with knowledge of the destination system (i.e.emptiness of a node) and one is not; the case with knowledge of the destination system is illustrated here     2011); agents do not make explicit return decisions, but migrate from region to region and can thereby visit a region again at some point in the future; migration out of the system is possible from all subsystems, but for simplicity reasons it is only visualized for the origin system; the situation in the destination system does not influence the migration decision, but as agents interact with the environment in all visited systems these factors are visualized   Fig. A1.12 Diagram drafted for the ABM described by Smajgl et al. (2013;2015a;2015b) Table A1.12Standardized protocol for the ABM described by Smajgl et al. (2013;2015a;2015b) Walsh et al. (2013) and Entwisle et al. (2008;2016) Table A1.14Standardized protocol for the ABM described by Walsh et al. (2013) and Entwisle et al. (2008;2016)

Fig. 1 .
Fig. 1.Conceptual framework of coupled social-ecological systems connected through migration.Tree and rain cloud represent the natural environment and the stick man represents the human actor; each of the subsystems can represent more than one origin or destination system.

Figure 3
Figure3gives an overview of the framework's elements considered within the reviewed ABMs by counting the occurrences of the framework's elements.Hereby, framework elements are the interlinkages between the environmental factors and the agents, the various migration flows, as well as the origin and destination system.

Fig. 3 .
Fig. 3. Conceptual diagram with the numbers beside the lines indicating the number of agent-based models considering the respective element; the tree represents the availability of natural resources, the rain cloud represents the influencing environmental factors, and the stick man represents the human agent

Fig. 4 .
Fig. 4. Type of social-ecological coupling and the number of environmental factors included in the agent-based model.The white dot indicates the median; the bold bar indicates the first and the third quartiles.

Fig. 5 .
Fig. 5. Type of social-ecological coupling and the decision rule used to model migration decisions (left) and the migration flow considered within the agent-based model (right).
Fig. A1.3 Diagram drafted for the ABM described by Hassani-Mahmooei & Parris (2012); agents do not make explicit return decisions, but migrate from region to region and can thereby visit a region again at some point in the future Fig. A1.10 Diagram drafted for the ABM described by Rogers et al. (2011); agents do not

Table 1 .
Search terms used for the Web of Science topic search.

Table 2 .
Categories to classify the reviewed agent-based models.The † marks terms that are explained in the text.
† Probability function, decision theory, heuristics, optimization Other decision processes besides migration decision Cropping, livestock, hunting, others, none Others Indicate which other decision processes are included

Table 3 .
Summary of the reviewed agent-based models; the full categorization of each model can be found in the Appendix 1.

Table 3
Black et al. (2011)ironmental factors are considered as indirect drivers (see Appendix 1).This is in line withBlack et al. (2011)who conceptualized the indirect role of environmental influence factors in migration processes.In Table 4, we categorize environmental influence factors by the two types "influencing environmental factors" and "availability of natural resources."Most of the 15 ABMs include both economic and social factors next to environmental factors and a few focus on either economic or social factors next to environmental factors.Four ABMs explicitly model social networks

Table 5 .
Causal chains representing the social-ecological feedbacks within the reviewed agent-based models (ABM); italic terms represent actions taken by the agents; the term in brackets applies only for parts of the causal chain, i.e., forest economy is affected by timber scarcity.

Table A1 .
15 Standardized protocol for the ABM described byWu et al. (2011)Wu, J., R. Mohamed, and Z. Wang.2011.Agent-based simulation of the spatial evolution of the historical population in China.Journal of Historical Geography 37:12-21.