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Dynamical systems modeling (DSM) explores how a system evolves in time when its elements and the relationships between them are known. The basic idea is that the structure of a dynamical system, expressed by coupled differential or difference equations, determines attractors of the system and, in turn, its behavior. This leads to structural understanding that can provide insights into qualitative properties of real systems, including ecological and social-ecological systems (SES). DSM generally does not aim to make specific quantitative predictions or explain singular events, but to investigate consequences of different assumptions about a system's structure. SES dynamics and possible causal relationships in SES get revealed through manipulation of individual interactions and observation of their consequences. Structural understanding is therefore particularly valuable for assessing and anticipating the consequences of interventions or shocks and managing transformation toward sustainability. Taking into account social and ecological dynamics, recognizing that SES may operate on different time scales simultaneously and that achieving an attractor might not be possible or relevant, opens up possibilities for DSM setup and analysis. This also highlights the importance of assumptions and research questions for model results and calls for closer connection between modeling and empirics. Understanding the potential and limitations of DSM in SES research is important because the well-developed and established framework of DSM provides a common language and helps break down barriers to shared understanding and dialog within multidisciplinary teams. In this primer we introduce the basic concepts, methods, and possible insights from DSM. Our target audience are both beginners in DSM and modelers who use other model types, both in ecology and SES research.

Dynamical systems modeling (DSM) explores how a system evolves in time when its elements and the relationships between them are known. The basic idea is that the structure of a dynamical system, expressed by coupled differential or difference equations, determines attractors of the system and, in turn, its behavior. This leads to structural understanding that can provide insights into qualitative properties of real systems, including ecological and social-ecological systems (SES). DSM generally does not aim to make specific quantitative predictions or explain singular events, but to investigate consequences of different assumptions about a system's structure. SES dynamics and possible causal relationships in SES get revealed through manipulation of individual interactions and observation of their consequences. Structural understanding is therefore particularly valuable for assessing and anticipating the consequences of interventions or shocks and managing transformation toward sustainability. Taking into account social and ecological dynamics, recognizing that SES may operate on different time scales simultaneously and that achieving an attractor might not be possible or relevant, opens up possibilities for DSM setup and analysis. This also highlights the importance of assumptions and research questions for model results and calls for closer connection between modeling and empirics. Understanding the potential and limitations of DSM in SES research is important because the well-developed and established framework of DSM provides a common language and helps break down barriers to shared understanding and dialog within multidisciplinary teams. In this primer we introduce the basic concepts, methods, and possible insights from DSM. Our target audience are both beginners in DSM and modelers who use other model types, both in ecology and SES research., Funding Agencies|Swedish Research Council [2018-06139]; European Research Council (ERC) under the European Union [682472]

Models are widely used for investigating cause-effect relationships in complex systems. However, often different models yield diverging causal claims about specific phenomena. Therefore, critical reflection is needed on causal insights derived from modeling. As an example, we here compare ecological models dealing with the dynamics and collapse of cod in the Baltic Sea. The models addressed different specific questions, but also vary widely in system conceptualization and complexity. With each model, certain ecological factors and mechanisms were analyzed in detail, while others were included but remained unchanged, or were excluded. Model-based causal analyses of the same system are thus inherently constrained by diverse implicit assumptions about possible determinants of causation. In developing recommendations for human action, awareness is needed of this strong context dependence of causal claims, which is often not entirely clear. Model comparisons can be supplemented by integrating findings from multiple models and confronting models with multiple observed patterns.

Both climate change and land use regimes affect the viability of populations, but they are often studied separately. Moreover, population viability analyses (PVAs) often ignore the effects of large environmental gradients and use temporal resolutions that are too coarse to take into account that different stages of a population's life cycle may be affected differently by climate change. Here, we present the High-resolution Large Environmental Gradient (HiLEG) model and apply it in a PVA with daily resolution based on daily climate projections for Northwest Germany. We used the large marsh grasshopper (LMG) as the target species and investigated (1) the effects of climate change on the viability and spatial distribution of the species, (2) the influence of the timing of grassland mowing on the species and (3) the interaction between the effects of climate change and grassland mowing. The stage- and cohort-based model was run for the spatially differentiated environmental conditions temperature and soil moisture across the whole study region. We implemented three climate change scenarios and analyzed the population dynamics for four consecutive 20-year periods. Climate change alone would lead to an expansion of the regions suitable for the LMG, as warming accelerates development and due to reduced drought stress. However, in combination with land use, the timing of mowing was crucial, as this disturbance causes a high mortality rate in the aboveground life stages. Assuming the same date of mowing throughout the region, the impact on viability varied greatly between regions due to the different climate conditions. The regional negative effects of the mowing date can be divided into five phases: (1) In early spring, the populations were largely unaffected in all the regions; (2) between late spring and early summer, they were severely affected only in warm regions; (3) in summer, all the populations were severely affected so that they could hardly survive; (4) between l

Functional stability of microbial ecosystems subjected to disturbances is essential for maintaining microbial ecosystem services such as the biodegradation of organic contaminants in terrestrial environments. Functional responses to disturbances are thus an important aspect which is, however, not well understood yet. Here, we present a microbial simulation model to investigate key processes for the recovery of biodegradation. We simulated single disturbances with different spatiotemporal characteristics and monitored subsequent recovery of the biodegradation dynamics. After less intense disturbance events local regrowth governs biodegradation recovery. After highly intense disturbance events the disturbance pattern's spatial configuration is decisive and processes governing local functional recovery vary depending on habitat location with respect to the spatial disturbance pattern. Local regrowth may be unimportant when bacterial dispersal from undisturbed habitats is high. Hence, our results suggest that spatial dynamics are crucial for the robust delivery of the ecosystem service biodegradation under disturbances in terrestrial environments.

Environmental change is expected to shift the geographic range of species and communities. To estimate the consequences of these shifts for the functioning and stability of ecosystems, reliable predictions of alterations in species distributions are needed. Projections with correlative species distribution models, which correlate species’ distributions to the abiotic environment, have become a standard approach. Criticism of this approach centres around the omission of relevant biotic feedbacks and triggered the search for alternatives. A new generation of mechanistic process-based species distribution models aims at implementing formulations of relevant biotic processes to cover species’ life histories, physiology, dispersal abilities, evolution, and both intra- and interspecific interactions. Although this step towards more structural realism is considered important, it remains unclear whether the resulting projections are more reliable. Structural realism has the advantage that geographic range shifting emerges from the interplay of relevant abiotic and biotic processes. Having implemented the relevant response mechanisms, structural realistic models should better tackle the challenge of generating projections of species responses to (non-analogous) environmental change. However, reliable projections of future species ranges demand ecological information that is currently only available for few species. In this opinion paper, we discuss how the discrepancy between demand for structural realism on the one hand and the related knowledge gaps on the other hand affects the reliability of mechanistic species distribution models. We argue that omission of relevant processes potentially impairs projection accuracy (proximity of the mean outcome to the true value), particularly if species range shifts emerge from species and community dynamics. Yet, insufficient knowledge that limits model specification and parameterization, as well as process complexity, increases proje

Ecological dynamics often show intricate variations in response to different spatial configurations of environmental conditions. For instance, efficient turnover of natural or anthropogenic compounds in soils strongly depends on the bioavailability of these compounds to metabolically active bacteria. Experimental and modelling studies have highlighted that fungal networks may considerably enhance bioavailability by facilitating bacterial dispersal. Therefore, such dispersal networks may play a key role in many soil processes, for example, in contaminant degradation. Particularly, simulation studies revealed that the spatial configurations of networks may be a crucial factor determining the bacterial access to contaminants. Since these spatial configurations are typically complex and not precisely known, suitable metrics describing them in an aggregated manner are required for assessing expected biodegradation benefits from different bacterial dispersal networks. Using a spatially explicit microbial model we randomly created various dispersal network configurations and simulated the resulting bacterial degradation of organic compounds. We investigated numerous spatial metrics for characterizing the manifold network configurations, and identified appropriate metrics based on nonparametric correlation measures. Our results show that single metrics can approximately indicate biodegradation performance, and that well-chosen combinations of two metrics offer very good assessments. Thus, our analysis provides characteristics to focus on when dealing with real fungal networks in future practical applications in environmental management. Moreover, the protocol we employed for deriving the appropriate metrics is suited to be adapted to other ecological studies of functional responses to spatial environmental characteristics, for instance, changes in ecosystem services or biodiversity aspects due to habitat loss and fragmentation.

Soil organic matter dynamics are essential for terrestrial ecosystem functions as they affect biogeochemical cycles and, thus, the provision of plant nutrients or the release of greenhouse gases to the atmosphere. Most of the involved processes are driven by microorganisms. To investigate and understand these processes, individual-based models allow analyzing complex microbial systems' behavior based on rules and conditions for individual entities within these systems, taking into account local interactions and individual variations. Here, we present a streamlined, user-friendly and open version of the individual-based model INDISIM-SOM, which describes the mineralization of soil carbon and nitrogen. It was implemented in NetLogo, a widely used and easily accessible software platform especially designed for individual-based simulation models. Including powerful means to observe the model behavior and a standardized documentation, this increases INDISIM-SOM's range of potential uses and users, and facilitates the exchange among soil scientists as well as between different modeling approaches.

Soil organic matter dynamics are essential for terrestrial ecosystem functions as they affect biogeochemical cycles and, thus, the provision of plant nutrients or the release of greenhouse gases to the atmosphere. Most of the involved processes are driven by microorganisms. To investigate and understand these processes, individual-based models allow analyzing complex microbial systems' behavior based on rules and conditions for individual entities within these systems, taking into account local interactions and individual variations., Postprint (author's final draft)

Successful biodegradation of organic soil pollutants depends on their bioavailability to catabolically active microorganisms. In particular, environmental heterogeneities often limit bacterial access to pollutants. Experimental and modelling studies revealed that fungal networks can facilitate bacterial dispersal and may thereby improve pollutant bioavailability. Here, we investigate the influence of such bacterial dispersal networks on biodegradation performance under spatially heterogeneous abiotic conditions using a process-based simulation model. To match typical situations in polluted soils, two types of abiotic conditions are studied: heterogeneous bacterial dispersal conditions and heterogeneous initial resource distributions. The model predicts that networks facilitating bacterial dispersal can enhance biodegradation performance for a wide range of these conditions. Additionally, the time horizon over which this performance is assessed and the network’s spatial configuration are key factors determining the degree of biodegradation improvement. Our results support the idea of stimulating the establishment of fungal mycelia for enhanced bioremediation of polluted soils.

The performance of biodegradation of organic pollutants in soil often depends on abiotic conditions and the bioavailability of these pollutants to degrading bacteria. In this context, bacterial dispersal is an essential aspect. Recent studies on the potential promotion of bacterial dispersal by fungal hyphae raised the idea of specifically applying fungal networks to accelerate bacterial degradation processes in situ. Our objective is to investigate these processes and their performance via simulation modelling and address the following questions: (1) Under what abiotic conditions can dispersal networks significantly improve bacterial degradation? and (2) To what extent does the spatial configuration of the networks influence the degradation performance? To answer these questions, we developed a spatially explicit bacterial colony model, which is applied to controlled laboratory experiments with Pseudomonas putida G7 organisms as a case study. Using this model, we analyzed degradation performance in response to different environmental scenarios and showed that conditions of limited bacterial dispersal also limit degradation performance. Under such conditions, dispersal networks have the highest potential for improving the bioavailability of pollutants to bacteria. We also found that degradation performance significantly varies with the spatial configuration of the dispersal networks applied and the time horizon over which performance is assessed. Regarding future practical applications, our results suggest that (1) fungal networks may dramatically improve initially adverse conditions for biodegradation of pollutants in soil, and (2) the network's spatial structure and accessibility are decisive for the success of such tasks.