Identifying leverage points in climate change migration systems through expert mental models

As the impacts of climate change increase, the Intergovernmental Panel on Climate Change advises that global migration will also increase. A deeper understanding of the factors and interactions that influence the migration decision-making of climate-affected populations is needed to more accurately predict migration estimates and adequately inform and prepare future receiving cities. In this study, we survey thirty-two experts in the field of climate migration to explore how demographic, economic, environmental, political, and social factors interact to lead to climate (im)mobility and how these interactions change within sea level rise, drought, flooding, and erosion contexts. We use system mapping and network analysis to determine which factors should be targeted as leverage points for policy makers and their resulting effects within each hazard context. Our findings identify physical infrastructure, social services, social capital, and political stability as places to intervene to increase resiliency in drought, flooding, and erosion climate migration systems. Using hazard context and community consultation, we recommend selecting target factors with direct relationships to other highly influential factors (livelihoods, food security, and financial capital) to elicit the most positive cascading effects through the whole system, leading to changes in migration. We also highlight the sea level rise climate migration system as highly complex in comparison to the other contexts examined and the need for multi-factored interventions in this context to create more resilient migration systems. Our findings contribute to the growing body of work which seeks to better understand the interactions between factors influencing climate migration.


Introduction
Migration is set to accelerate due to climate change, with an estimated 216 million total internal climate migrants by 2050 (Clement et al. 2021). However, the estimation of climate migrants is often a controversial topic as some experts argue the difficulty in pinning climate change as the primary cause of migration (Black et al. 2011;Curtis et al. 2015). Unlike migration estimates based on mono-causal hazard exposure modelling (Kam et al. 2021;Myers 2002;Robinson et al. 2020), current research incorporates a complex array of direct and indirect non-climatic factors that influence how migration decisions are made (Maretti et al. 2019;McLeman 2013;Menjívar et al. 2019;Pei et al. 2016). We use the term climate migration to describe scenarios of migration that have been directly or indirectly affected by climate change. This shorthand is used to differentiate between other types of migration (e.g. economically motivated), but does not prescribe a linear relationship between climate change and migration (Kabir et al. 2018). In this study, we aim to further the discourse on the multi-faceted nature of climate migration by examining how principal influencing factors interact to lead to climate migration.
Although researchers work to identify the relationships between climate, socio-economic and political factors, and migration (Parrish et al. 2020), these connections are often not realised by climate-affected individuals themselves (Mortreux and Barnett 2009). Studies have found that when directly asked, many climate-affected individuals rarely state climate change or related environmental hazards as reasons for migration (Kelman et al. 2019;Speelman et al. 2017;van der Geest et al. 2020). Although climate-affected individuals recognise the impacts of climate change on their health, livelihoods, and other aspects of their daily lives (van der Geest et al. 2020), climate is not often cited as reason for movement. The lack of recognition of relationships between climate change, socio-economic and political factors, and migration points to a need to draw the underlying connections more explicitly. In this study, we employ a systems approach to address gaps in understanding the relationships and feedback mechanisms between demographic, economic, environmental, political, and social factors and migration (Black et al. 2011;Jokisch et al. 2019;Sakdapolrak et al. 2016;Schwerdtle et al. 2021;Willett and Sears 2020). The delineation of underlying and often unintuitive relationships is needed for policy makers when identifying key climate resiliency and adaptation policy strategies, whether to support migration or in situ adaptation.
To this end, we build from factors identified in literature as influencing migration decision-making and look to place them within the larger context of the climate migration system through a survey of experts. We present climate migration systems as multidimensional, interconnected, and dynamic interactions of macro-, meso-, and micro-level factors, exacerbated by climate change impacts, that lead to (im)mobility. While there exists a global climate migration system, culminating from decisions and movements worldwide, we build from Mabogunje (1970, p. 3) who states, "a system with its environment constitutes the universe of phenomena which is of interest in a given context" and contend for the existence of localised climate migration systems broken down by unique characteristics (i.e. geographic location, group ethnicity, hazard type).
We surveyed experts from a wide range of backgrounds to better understand these localised climate migration systems. We positioned that the best way to capture realistic representations of these systems is to draw on multi-disciplinary knowledge and expertise. Through the collection of insights from our survey of experts, we brought together diverse understandings to form a well-rounded portrayal of climate migration systems. To this end, our first research question asks [RQ1]: What are the relationships between factors that influence climate change migration? As used in this study, factors reference decisionmaking influences that climate-affected individuals and households weigh when deciding whether to migrate. Factors are also often called "drivers" of migration (Black et al. 2011). While conceptually the same, we chose "factors" of climate migration to reinforce the decision-making power of the climate-affected individuals and households in choosing to migrate or not. From the relationships of factors, we were able to build a system map to conceptualise how each factor affects others while using additional analysis techniques to determine key relationships.
When analysing climate migration, the nexus of natural hazards, cultures, and geographies shape decision-making of climate-affected individuals (Kabir et al. 2018). The Intergovernmental Panel on Climate Change (IPCC) warns that as the global temperature rises, we can expect an increase in the frequency or severity in a range of natural hazards (IPCC 2018). Each hazard type (e.g. drought, sea level rise) will exploit different vulnerabilities within climate-affected communities; thus, approaches to resiliency and adaptation should be likewise tailored. With this in mind, our second research question [RQ2] asks: What are the differences in casual relationships between migration factors for different hazards influenced by climate change? Through the comparison of causal relationships in multiple natural hazard contexts, we aim to determine how specific factors and their relationships shift in importance and roles with migration systems. This leads us to the identification of leverage points for policy and migration planners looking to support climate-affected populations.

Background
Literature on the topic of migration relating to climate change has risen remarkably in the past decade (Piguet, 2022). This uptick can be at least partially attributed to the publication of major works such the Foresight (2011) and Groundswell (Riguad et al. 2018) reports, following the landmark Cancun Adaptation Framework (2010), which formalised our understanding of migration, displacement, and relocation. Although growing, the field of climate migration studies is still relatively nascent and in contention on various terminology and concepts.
One such point of debate is whether migration should be encouraged as a means of adaptation (Adger and Adams 2013;McLeman and Smit 2006;Morrissey 2012) or viewed as a last resort policy (Ingham et al. 2019). For many climate-affected communities, there is a high preference for remaining in place (Campbell 2014;Kartiki 2011). The decision to prioritise safe migration or in situ adaptation will significantly change the climate strategies employed. For instance, seawalls (Tomlinson and Jackson 2019) and climate-adaptive livelihoods (Akhtar et al. 2022;Cooper and Wheeler 2015) are common adaptation measures that local and regional governments encourage to help residents combat the impacts of climate change and remain in place. Meanwhile, governments focused on encouraging migration as adaptation may promote education or livelihood opportunities elsewhere, such as Kiribati's "Migrate with Dignity" labour migration scheme (McNamara 2015). Whether policy makers intend to encourage migration as adaptation or support in situ adaptation strategies to improve climate resiliency in place, we aim to uncover critical relationships to inform policy implementation. To better understand the holistic effects of such strategies on the climate migration system, we employ systems thinking to evaluate their potential impacts on migration.

Conceptualising the complexities of climate migration
The complexities of climate migration are evident in the deeply interwoven relationships between factors influencing decision-making. A central point to the idea of migration is agency retention-the ability affected populations to make their own decisions. In this way, we differentiate migration from displacement, a mobility reaction linked more often to rapid-onset hazards (Black et al. 2013).
Our study draws from the conceptual climate migration framework put forward by Foresight (2011). The Foresight framework identifies five key categories of drivers (factors) that influence climate migration: environmental, political, demographic, economic, and social, while climate change acts as an external force that exacerbates existing vulnerabilities within the five categories. Rather than climate change acting as the sole driver, it is more accurate to say that climate migration is caused by the compounded effects of the other socio-economic and political factors, aggravated by climate change until affected populations no longer find it in their best interest to stay (McLeman et al. 2021). Previous works can be referenced to see how others have sought to identify the factors in an effort to better understand their relationships to climate change and migration, such as Cai el al.'s (2016) analysis of agriculture's role in climate migration and Whitley et al.'s (2018) exploration of individuals' mental models to explore climate migration decision-making processes.
The Foresight climate migration conceptual model is theoretically grounded in a combination of neoclassical and push-pull theory, among others (de Sherbinin et al. 2022). Neoclassical migration theory states that movement is predominantly driven by labour demand differentials between geographic locations, thus leading to migration in search of wages (Massey et al. 1993). This framework has largely been overtaken by the New Economics of Labor Migration (NELM) which accounts for more diverse household economic needs when migrating (de Sherbinin et al. 2022;Fussell et al. 2014). While aspirations for economic gains in tandem with climate change impacts makes it difficult to differentiate between climate migrants and economically motivated migrants, economic factors are nonetheless an important aspect in climate-affected individuals' decision-making (Oliver-Smith 2012), making NELM an appropriate stepping stone in our understanding of climate migration. We also draw largely from the push-pull theory in this research which incorporates NELM in identifying economic factors (e.g., low wages) and other non-economic factors (e.g. persecution) that repel individuals from an area and attract them to another location (e.g. job opportunities) (Khalid and Urbański 2021). We focus specifically on push factors and how they relate to migration, as well as to other push factors.

Mental models
While our development and analysis of this research is framed from the Foresight framework, others may understand and conceptualise climate migration through a different lens. de Sherbinin et al. (2022) note the potential pitfall of restricting focus on singular framework, stating that the utilisation of one theory or framework can lead to oversight in other critical relationships. To avoid the potential omission of important aspects in climate migration systems, we propose an aggregation of viewpoints from multiple experts with experience in climate migration research. By aggregating multiple perceptions, bringing inter-disciplinary experience and knowledge, we offer a well-rounded conceptualisation of the climate migration system (Boumans and Martini 2014). We present these expertinformed climate migration systems to address current gaps in literature stemming from discipline and framework siloed understanding and analysis.
Central to this effort of combining multiple viewpoints is the utilisation of experts' mental models. As Jones et al. (2011) succinctly states, "Mental models are cognitive representations of external reality". Mental models are how processes and phenomena are simplified in our minds to be later called back or applied to similar experiences. Mental models are widely used in system dynamics for their ability to represent cause and effect dynamics (Doyle & Ford 1998) and specifically have been previously used to inform climate migration (Whitley et al. 2018). Mental models are moulded and informed through lived experiences, and we contend that by aggregating experts' perceptions, we can avoid the pitfalls that result from conceptualising the climate migration system from a singular viewpoint. In this study, gathering the mental models of experts allows us to build a combined understanding of how the climate migration system unfolds (Moray 1998).

Methods
This study used expert perceptions of the causal relationships between factors influencing climate migration as the primary source of data. These perceptions-or mental modelswere elicited using an online survey. The survey aimed to identify key migration factors and explore how causal relationships and overall system structures differ between natural hazard context (sea level rise, drought, flooding, and erosion). In Fig. 1, we provide an overview of the method sequence used in this study before discussing each in more detail below.

Data collection
We collected data through a survey of experts conducted from December 2021 to January 2022. As mental models are informed and developed through experience, understanding the background of expert contributors provides meaningful context for how factor relationships were evaluated. Experts were identified from a previous systematic literature review where climate migration factors were synthesised (Nabong et al. 2022), using authorship on one or more peer-reviewed journal publications on the topic of climate migration indexed in the Scopus database as the criteria for expertise. We also used snowball sampling to allow survey participants to nominate others with expertise in the field of climate migration. Nominated experts were reviewed by the research team to determine inclusion criteria were met (publication on a climate migration topic) before being invited to participate. Seven additional experts were contacted from peer recommendations. In total, surveys were sent out to a total of 590 participants of which we received 32 responses (5%).
Within the survey, the experts were asked to share perceptions of relationships between a given list of factors influencing climate migration decision-making. These factors were identified from (Nabong et al. 2022) which produced a list of 21 factors and interactions found as influencing decision-making in climate migration literature. The factors identified in the systematic literature review were termed according to causal loop diagramming best practice which recommends using factor names that consistently convey positive or neutral concepts (e.g. Food Security vs. Food Insecurity) (Sterman 2000, p. 153). In this way, negative concepts are determined by the causal relationship polarity rather than by the terms themselves. For example, loss ( −) of livelihoods leading to less ( −) food security is conceptually the same as increasing food insecurity.
To keep the length of the survey compact, we ranked the factors identified in literature by eigenvector centrality scores and used only the top 10, shown in Table 1. Eigenvector centrality values of the factors were calculated from their frequency in coded pairwise relationships in literature. Eigenvector centrality is a metric to measure the connectedness of each factor to other central factors in the system (Knoke and Yang 2008). This centrality metric was used to prioritise climate migration factors based on their level of interconnectivity, so that factor importance and top causal relationships could be explored in greater depth.
We began our survey by collecting basic demographic information including institutional affiliation and position, years of experience, country of residence, and geographic focus of research. Additionally, prior to beginning their responses on factor relationships, participants were asked to choose the climatic hazard that they had the most experience with and respond to the factor relationships with that specific hazard context in mind. In this way, experts could keep a consistent context in mind throughout the survey allowing us to analyse structural differences in factor relationships between hazards. The top four hazards chosen by the experts (sea level rise, drought, flooding, and erosion) were used in our comparative analysis along with the generalised climate migration system ("aggregate"). Through the disaggregation of survey data by hazard, we recommend targeted policies for specific hazard contexts.
Experts were asked to evaluate the polarity and strength of factors links using pairwise comparisons. In this way, we attempted to mitigate potential response bias or error that may have arisen from evaluating too many factor relationships at one time (Saaty 2008). The definitions of each factor were provided to respondents to maintain consistency for response comparison with the option to provide feedback or their own definitions. Polarity of factor interactions was gauged by having participants fill in the blank of "Factor A ______ Factor B" with either increases/improves, decreases/degrades, both increases and decreases, or no relationship. Polarity allows us to infer shifts in factor strength over time, whether increasing as another factor increases in strength or prominence ( +) or decreasing when another factor increases in strength or prominence ( −). The strength of that relationship was then evaluated using a 5-point Likert scale of unclear, very weak, weak, strong, and very strong. For example, one might choose to say that livelihoods increase health with a strong relationship. The systematic elicitation of expert perceptions on pairwise factor relationships allowed us to reveal their mental models on the climate migration system for particular hazard contexts.
Through the aggregation of the thirty-two experts' mental models, we developed a collective representation of a generalised climate migration system. We also develop hazardspecific climate migration systems by disaggregating the survey responses from experts' selected hazard experience. The responses from experts of each hazard context resulted in impact matrices containing strength values for all possible relationships. Scholars point to the need to account for particular nuances (e.g. geography, culture) to fully understand migration decision-making (Kabir et al. 2018;McLeman and Smit 2006). By comparing the hazard-specific climate migration systems, we can better understand contextual climate migration decision-making.

Data analysis
To compare and contrast climate migration systems between hazard contexts, we used three complimentary structural and network analysis techniques: systems maps, eigenvector centrality, and influence mapping which were used to evaluate factors' interconnections, interconnectedness, and role characterisation, respectively. Below we describe these analyses in more detail.

Systems maps-evaluating factor relationships
We begin our exploration of the "aggregate" climate migration system through system mapping. System mapping is a tool used to visualise relationships and feedback loops between factors in a system (Ford 1999). System mapping is useful in interconnected systems by showing not only linear cause and effects, but also pathways and dynamic interactions between factors (Cradock-Henry et al. 2020; Kunze et al. 2016). System mapping is used in this way in a variety of related fields, such as climate change (Cradock-Henry et al. 2020) and sustainable livelihoods (Banson et al. 2015). The system maps in our study resulted from the separate hazard impact matrices and visually represent the mental models of study experts for the aggregate climate migration system as well as each hazard context. We used the online platform Kumu to create and analyse these system maps (Kumu 2022).
The inputs of the systems maps were based on the factor relationships' polarity and strength data from the survey of experts. The mode of the relationship polarity was used as a consensus measure to reflect the general perceptions of the experts. The strength of each factor relationship was taken as the weighted sum of expert responses where unclear, very weak, weak, strong, and very strong were weighted as 0, 1, 2, 3, and 4, respectively. Using the weighted sum of relationships' strength allowed us to compare and contrast each relationship's strength with more granularity and is an acceptable approach for evaluating non-parametric Likert data (Jamieson 2004). We calculated the summed strength for each pairwise factor relationship for experts (n = 32) as: where n is the total number of experts in each hazard context and n i , n j , n k , n l , and n m are the number of responses for unclear, very weak, weak, strong, and very strong, respectively. Although system maps are typically non-weighted, in this study, we follow Murphy and Jones's (2021) methodology called leverage analysis. With this technique, we combine the dynamic insights of system mapping with the quantitative analysis offered through network analysis. This approach is similarly used in fuzzy cognitive mapping which also allows for quantitative weights to be given to causal relationships (Voinov et al. 2018). By assigning weights to each factor in the system map, we identify leverage points from both a dynamic and structural standpoint. Strength n = Unclear n i × 0 + VeryWeak n j × 1 + Weak n k × 2 + Strong n l × 3 + (VeryStrong n m × 4) Through the system maps, we show a visual representation of the factors' connectedness; both direct links between two factors and pathways between multiple factors. Experts were asked about the relationship between each of the 10 factors bi-directionally, for a total of 90 pairwise relationships. Relationships were excluded from the system maps if the resulting polarity mode was "no relationship".
The data within the hazard impact matrices was additionally filtered to only strong and very strong relationships. Strong and very strong relationships, as perceived by experts, are indicative of stable causal relationships within the climate migration system. We performed a network density analysis of these filtered relationships to compare how the drivers of climate migration vary between systems. Network density was calculated by counting the number of strong and very strong relationships perceived in each climate migration system and dividing by the total potential relationships (90 potential relationships).

Eigenvector centrality-evaluating and ranking factor connectedness
While system mapping allows for the visualisation of key relationships through link strength, a quantitative comparison is useful for finding key factors. We calculated the weighted and directed eigenvector centrality score of each factor based on the weighted sum strength score described in the previous section, input into the "igraph" package in R (Csardi and Nepusz 2006). Eigenvector was selected as a metric for measuring factors' centrality for its usefulness in identifying high leverage factors in a system Murphy and Jones 2021). Other centrality metrics, such as (in/ out) degree, simply count the number of incoming or outgoing connections, while eigenvector centrality measures a factor's connection to other highly connected factors. By evaluating each factor on their connectedness to other important factors (as measured by the eigenvector score), we can highlight factors that potentially drive climate migration system outcomes.

Influence maps-characterising factor roles
Once key factors were identified through weighted eigenvector centrality scores, we further characterised their roles in each system with an approach from Godet (1994) called "influence maps". Using the matrices of weighted sum values for the relationships''strengths, the influence and dependence scores for each factor were calculated, normalised, and then plotted on a two-dimensional influence vs. dependence chart. Factor influence is calculated as the sum of influence (arrows) from one factor on the other factors, while factor dependence is the sum of influences from all the factors on a particular factor (Arcade et al. 1999). Factor influence and dependence are plotted on an influence map, which was broken into four quadrants to help categorise the roles of each factor, described in Fig. 2. The plotted position, along with the quadrant characteristics, helps us to understand the role of the factors in the climate migration system.
While eigenvector centrality scores measure overall connectedness, influence maps allow us to distinguish whether a factor's relationship role is more dependent or influential. Factors plotted in quadrants I and II are of particular interest when evaluating factor roles due to their high levels of influence. This means that perturbations to these factors would cause rippling effects throughout the system. When developing policy strategies, factors should be targeted from quadrant I. A low dependence score is preferable when seeking to identify which factors might serve as system leverage points, given their lower vulnerability to influence from other factors, and any unintended consequences that could result. Mapping of factor dependence and influence has been used in similar contexts, such as natural resource management (del Mar Delgado-Serrano et al. 2016) and rural water systems (Walters et al., 2017;Valcourt et al. 2020;Walters et al. 2022), where researchers look to classify factors' roles in a system.

Results and discussion
Our survey solicitation generated 32 responses from experts in the field of climate migration. The majority (n = 29) of experts self-described their roles as researchers at academic or research institutions. Other experts self-reported roles in non-governmental organisations (NGO) (n = 3), government (n = 1), and multi-lateral organisations (n = 1). Two experts selected that they were both engaged at an academic or research institution as well as in the NGO sector. The experience of the experts varied from 20 + years (n = 10), 10-14 years (n = 9), 5-9 years (n = 8), 15-19 years (n = 3), and 1-4 years (n = 2). Collectively, the 32 experts who participated in the survey have published 1,298 journal articles which have been cited 49,658 times, according to Scopus data. Accounting for the range of experience, the median number of articles published by the surveyed experts was 16 with a median citation count of 272. Although the survey was sent to a geographically diverse group, the experts who responded were from high-income countries, with only one individual who was from a middle-income country. Many experts selected having a global focus in their research (n = 9). Bangladesh (n = 9) and the USA (n = 5) had the highest rates of respondents reporting country-specific research expertise. Experts noted that their primary hazard experience related to sea level rise (n = 9), drought (n = 6), flooding (n = 6), coastal and river erosion (n = 5), land and forest degradation (n = 3), salinisation (n = 2), or heat waves (n = 1). The results of the survey capture experts' mental models of causal relationships between factors influencing climate change migration [RQ1]. Here we present aggregated results (n = 32) for all experts while highlighting the four most prevalent hazard experiences among surveyed experts: sea level rise, drought, flooding, and erosion. The remaining hazards were still included in the aggregated results, but not highlighted due to low response numbers. By disaggregating the data by hazard experience, we sought to understand differences in generalised (aggregated) conceptualisations and hazard-specific factor relationships [RQ2]. In the following sections, we discuss how system mapping, factor ranking, and factor characterisation help us to understand the leverage points in each climate migration system.

Systems maps-evaluating factor relationships
We begin our analysis of the survey results by visualising the factor relationships in system maps. System maps were created for the aggregate system of climate migration from all experts' mental models and four climate migration systems specifically reflecting scenarios of sea level rise, drought, flooding, and erosion. In these maps, we identify how factors affect each other and at what strength, as indicated by polarity notation and link width. We present a system map in Fig. 3 of the aggregate climate migration system showing the factor relationships as perceived by all the surveyed experts. This map shows general trends of how each factor is perceived to impact the others in the system. In Fig. 3, the polarity is denoted by " + " or "-" symbols at the end of each link, as well as blue and red colouring, respectively. Positive ( +) links show relationships where the factor at the tail leads to an increase or improvement in the secondary factor. Negative ( −) links show relationships where the first factor leads to decreases or degradation of the secondary factor. Link polarity offers insight into how factors might change over time. Relationships that experts perceived as being capable of both increases AND decreases are coloured grey.
In the analysis of relationships, the mode of all experts' responses was used to assign a polarity to each relationship. Of all the responses relating to relationship polarity, more than 60% were in agreement with the polarity choice as identified by the mode. In general, 61% of the polarities selected by experts were ( +) positive, 8% were ( −) negative, 17% were "increases and decreases", and 14% were "no relationship".
One main takeaway from Fig. 3 is the polarity of the factors' relationships towards migration. With the exceptions of financial capital and social capital, all other factors have a negative relationship with migration. This implies that the increased presence of livelihood, health, physical infrastructure, food security, political stability, resource security, and social services potentially leads to decreases in migration. This point is supported by one participant who stated, "If people have secure livelihoods they are more likely to withstand climate change impacts and will not leave their place of origin (reduce migration). Most people want to remain (and adapt) in place". Another expert commented, "…In a resource dependent island community, there will be linkages between resources and livelihoods, health etc. People would be reluctant to move away from resources (eg. proximity to fishing grounds)…" In contrast, the system map shows a positive relationship between financial capital and migration (i.e. increases in financial capital lead to an increase in migration). While this positive relationship ( +) was selected by the plurality of experts (n = 14), a significant number (n = 10) felt that this relationship could lead to either increases or decreases in migration. This contention on the influence of financial capital on migration reflects current discourse in literature. While some studies show that liquidity constraints lead to immobility (Bell et al. 2021) and improved financial capacity supports the ability to move (Cai et al. 2016;Grecequet et al. 2017;Benveniste et al. 2022;Kartiki 2011), others highlight that improved financial capacity may also lead to "mooring" (Bell et al. 2021) where affected populations use their funds to invest and stay in their home locations rather than moving. This is especially seen in cases of mixed family mobility where one member may migrate and later send remittances to provide stability against future climate shocks (Das Sharma et al. 2020;Shi et al. 2019). While "mooring" illustrates a chosen immobility, another relatively new topic of research explores cases specifically where individuals are motivated to migration, but lack the resources to do so, leading to "trapped populations" (Nawrotzki & DeWaard 2018;Suckall et al. 2017). This point is further supported by a comment from one expert who shared, "Contrary to popular belief, greater economic resources and opportunities facilitate migration. Many of the poor hunker down in response to adversity and, when they do, it is out of desperation". Similar to financial capital, the presence of strong social capital helps to increased migration by offering a continuation of kinship ties and transitionary assistance (Nawrotzki et al. 2013;Smith 2007;van der Geest et al. 2020). However, one expert also argued that, "Social capital levels [strength] may be less important than the configuration of networks. Dense but closed networks (as in tribal societies) have a different impact than more diffuse '-1 tie' networks (as in modern civil societies)". Prioritising community togetherness rather than strengthening diasporic ties is an important point for policy makers looking to strengthen social capital in climate-affected communities.
After disaggregating the survey data by hazard type and filtering to only include strong and very strong relationships, we compared the network density between the four hazard systems. A higher density within these systems points to higher interconnectedness and complexity, adding difficulty in determining the best intervention points for policy. The densest system of strong relationships was erosion (77%), followed by flooding (49%), drought (30%), and sea level rise (23%). A possibility for these density differences is that experts with experience in sea level rise and drought were more capable discerning nuance in their selection of strength due to higher experience in and understanding of the system. All expert respondents who contributed to the sea level rise system had over 10 years of experience, with the majority over 15 years. In contrast, the majority of the experts contributing to the erosion system had less than 10 years of experience.

Eigenvector centrality-evaluating and ranking factor connectivity
In our system maps, we can visually compare the interaction between factors for different hazard contexts. With eigenvector centrality scores, we can systematically and quantitatively identify which factors are the most highly connected. In Fig. 4, we show the ranking of the factors' connectedness within their respective systems based on their weighted eigenvector centrality scores. In this figure, the initial colour gradient was set from the factor rankings in the aggregate system, and factor colours were carried through to the other climate migration system contexts to show a comparison on how ranking shifts. Figure 4 shows that livelihoods, health, and food security are consistently among the most connected factors throughout all five climate migration systems. Other notable factors are social capital, financial capital, migration, and political stability which increase in connectivity depending on the hazard context. Social capital ranked as seventh in the aggregated scores and hovers around this position in drought, flooding, and erosion contexts. In scenarios of sea level rise, however, social capital has an upward shift in rank to fourth. From literature and expert comments, it is unclear why social capital is more highly connected in this hazard context and is perhaps an avenue for future studies. Financial capital shows highest centrality in the context of drought. Much research centred on migration relating to drought has a strong focus on the impacts to agriculture and other water sensitive livelihoods likely explaining this shift (Missirian and Schlenker 2017; Nawrotzki et al. 2013;van der Geest et al. 2020). Lastly, we found that political stability shows a high interconnectivity in the context of flooding. This shows that experts perceive political stability as a more central factor to affecting (im)mobility in scenarios of flooding than other hazards. As a factor, migration is ranked highest in the context of erosion meaning it is highly connected within that system. Migration's high connectivity has two possible explanations: (1) that singular factors are more likely to catalyse migration compared to other hazards that may require multiple compounding factors to reach a migration tipping point or (2) migration is likely to cause direct impacts.

Influence maps-characterising factor roles
To better understand the connectivity scores and characterise factors' roles, we mapped their relative dependence and influence in each climate migration system. Weighted summations of pairwise strength, as perceived by the surveyed experts, were used to generate normalised dependence and influence scores which were plotted as circles on an influence map. Starting with the aggregated data for each factor (circle outlined in black), we can see how the factors' dependence and influence shift per hazard context (Fig. 5).
In this map, we show the top five factors as ranked by the eigenvector centrality scores in the aggregated climate migration system results. These factors and their respective eigenvector centrality scores were livelihoods (1.00), health (0.98), food security (0.93), financial capital (0.87), and migration (0.79). Beginning with the aggregated climate migration system, we can see that three of the top factors are contained within the top right quadrant (quadrant II). These factors display high levels of dependence and influence in the system, meaning that they may be easily perturbed and influenced by other factors, in turn causing significant ripples across the other factors in the system. This makes these factors highly dynamic and potentially volatile. In contrast, migration and health are located in quadrant III and can be thought of as outcome factors. This implies that changes in other factors greatly affect whether an individual may migrate, but migration does not have a significant effect on how the other factors change after migration. We note that it is unclear whether this is a true representation or an indication that there is not a strong research focus on the consequences of climate migration.
The dependence of health on other factors is well noted in literature, such as the relationship of food security on health (Carney and Krause 2020;Rakib et al. 2019). Experts also shared examples of health's high dependency saying, "The social gradient of health means that people with better financial capital/higher SES have better health. The opposite is also true-low SES generally associated with poorer health", and "Social capital is considered a social determinant of health. As social capital increases, generally, so does health". However, there is relatively little mention of how changes in health affect other factors in climate migration literature nor is there any strong influencing relationships identified by experts.  Figure 5 is also a useful visualisation to consider how the role of factors shifts in different hazard contexts. For example, we see that in the context of drought, livelihoods become less volatile and more of an outcome factor. We also see financial capital become less dependent and more stable in all hazards except drought. Migration experiences a similar shift in decreased dependency in all hazards except erosion. Evaluating the shifts in factor roles is an important strategy for determining prioritisation of interventions between different hazard contexts.
As these examples show, a highly connected factor may not necessarily be an ideal leverage point for policy makers looking to affect the climate migration system. To find factors suitable for adjustments, we look to quadrant I in the upper-left of the map. As shared in Fig. 2, factors located in quadrant I display high influence over other factors in the system with minimal influence from other factors. These qualities make them ideal for policy makers looking to make changes to the system. In Fig. 6, we present the leverage points (from quadrant I) for each hazard system and tie together our results. Using the system maps of each hazard, we highlight the leverage factors that policy makers should target in each system. We also highlight the pathways leading to and from the leverage points to determine which factors would be next affected if leverage factors were targeted. We see that physical infrastructure is identified as a leverage point in many of the systems, as well as social services, social capital, and political stability. Notably, the sea level rise climate migration system did not produce any leverage points. The lack of leverage points does not indicate the absence of potential interventions but rather that interventions should reflect a constellation of policy actions, targeting multiple factors in tandem. As a highly complex system, there is a need for deeper understanding into the interactions between factors in the context of sea level rise.
We additionally recommend prioritising leverage points with pathways leading to highly influential factors (top two quadrants in Fig. 5) so that we can create the greatest impact on migration (outcome variable in Fig. 5). For example, in the context of erosion, we see that social services can lead to increases in livelihoods, leading to an increase in food security and a decrease in migration. Practically, this can be seen in real cases such as the Philippine government's distribution of rice seedlings to increase agricultural livelihoods and thus food security (Gomez 2022). While realistically food security does not prevent migration, it creates a lower likelihood than situations of food insecurity.
In each climate migration system, all leverage points have a positive ( +) causal relationship with effected factors and each are linked with at least one highly influential factor to create widespread impact through the system. We posit that these characteristics make physical infrastructure, social services, social capital, and political stability appropriate targets for policy interventions.

Implications and limitations
Our findings in this study expand the current knowledge of causal relationships within climate migration without suggesting their preferred use in either encouraging migration or supporting in situ adaptation. Policy planning for climate-affected populations should always be made in consultation with those affected. We recognise the view of climate migration as an adaptation strategy and present these leverage points as strategies that governments can pursue to ease the transition of movement. For example, investments in the leverage point, physical infrastructure, in destination locations, is a critical need as population sizes grow (Kelman et al. 2019). Many scholars share cases of the inability of infrastructure in destination locations to support incoming flows leading to housing crises (McLeman 2018) and Fig. 6 System maps with highlighted leverage points and relationships per hazard deleterious health outcomes (Haque et al. 2020;Schwerdtle et al. 2021), among other consequences. Likewise, increasing social services such as government agriculture assistance during drought has been found to affect the amount of migrants (Whitley et al. 2018).
On the other hand, we also acknowledge that continued habitation of home and ancestral lands is often a preferred option for climate-affect populations (Constable 2017;Dreier and Sow 2015;Zickgraf 2019), and the encouragement of migration as adaptation unjustly shifts the burden of adapting to climate change on individuals rather than the government actors at fault (Baldwin 2014;Bettini 2014;Sakdapolrak et al. 2016). These leverage points can also be adapted to in situ adaptation strategies such as investing in physical infrastructure to mitigate the effects of climate change. Efforts to build social cohesion and community may also increase climate resiliency, as demonstrated in previous research that shows increased intergroup cooperation and generosity during hazards (De Juan and Hänze 2021).
While providing valuable insights into the causal relationships with climate migration systems, we acknowledge several limitations. While our survey responses reached a variety of experts, a large number of perspectives are still missing. To develop the truest representation of a climate migration system, the ideal contributors would be from a diverse range of technical and geographical expertise. Researchers from high-income countries benefit from a well-acknowledged publication bias (Piguet et al. 2018). As such, the majority of our invited experts were likewise affiliated with high-income countries. This disproportionality was even greater still among the participants of whose mental models the climate migration systems produced in this study were built. However, while our study would benefit from an increase in perspectives from low-and middle-income country participants, we believe that those sampled in this survey are well representative of the geographic spread of researchers in the field of climate mobility studies. In the future, perspectives from low-and middleincome countries should be intentionally sought to strengthen the climate systems models' accuracy. In addition to online surveys, we recommend in person consensus building workshops and focus groups specifically targeted in low-and middle-income countries.
Similarly, we also recommend future work to not only expand the number and diversity of participants, but also the number of factors considered in the climate migration system. In this study, the number of factors included was necessarily bounded by practicality in survey implementation. Thus, we recommend future works use these results as a baseline map of top factors to create a more detailed and rigorous view of climate migration systems. We additionally highlight the need to better understand the dynamics of the systems by analysing feedback loops that drive changes over time.
We also acknowledge the limitations associated with insights produced from generalised climate migration systems. Even with the disaggregation of expert responses by hazard experience, we still lack the nuance that geography and culture add to each unique climateaffected community. While the most reliable method for ascertaining the truest representation of an area's climate migration system is through a detailed case study specific to that site, we posit that there is still a theory-building benefit to a generalised view of the collective climate migration system and hazard-specific climate migration systems.

Conclusion
In this study, we answer the questions of how climate migration factors interact (RQ1) and how these interactions change in different hazard contexts (RQ2). While system mapping, eigenvector ranking, and dependence and influence maps show factors' relationship to climate migration, it is the use of all three methods in tandem that best inform understanding of complex systems. Working together, we used the system mapping to visualise causal relationships through individual linkages and as an entire system, the eigenvector centrality rankings to determine the most connected factors, and the influence maps to characterise the roles of factors in hazard-specific climate migration systems.
Our findings identify physical infrastructure, social services, social capital, and political stability as intervention points when looking to increase resiliency in drought, flooding, and erosion climate migration systems. These recommended target factors have positive causal relationships with livelihoods, health, and food security, factors which were found to be the most highly connected with the aggregated climate migration system. As such, targeting the identified leverage points will elicit positive cascading effects through the whole system. These effects can be forecasted through the causal relationships shown in our system maps (Fig. 6). We also highlight the sea level rise climate migration system as highly complex and interconnected where further research is needed to determine best strategies for intervention. However, while the results of our study suggest differences between the climate hazard context, additional statistical tests with a larger study size are needed to draw more definitive conclusions. Instead, we offer these results as an exploratory steppingstone for future research in digging deeper into the relationships that affect climate migration.
By presenting results formed from the combination of multiple experts' mental models of climate migration systems, we capture a more accurate representation of reality than could be created through the lens of an individual expert. Our findings, rooted in systems thinking approaches, contribute to the growing body of work which seek to better understand the dynamic interactions between factors influencing climate migration. as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.