DISCUSSION

Multispecies models have huge potential as tools for understanding and predicting the dynamics of interacting species, and helping to disentangle the effects of these interactions from other processes affecting population dynamics, such as climate change, habitat changes and harvesting (Kinzey & Punt 2009; Péron & Koons 2012; Swallowet al. 2016). Rapid progress is made towards fulfilling this potential, but important challenges remain. Currently, the greatest limitations to multispecies model development are data availability and model complexity, leading to difficulties in parameterization and large uncertainty.
Data availability is improving (McCallen et al. 2019), but data collection will always be burdened by logistical limitations. It is therefore important that the right types of data are collected to maximize their use for multispecies modelling, for instance by ensuring that data collection gives attention to species interactions and data are collected for multiple cohabiting species simultaneously (Trijouletet al. 2019). Still, collecting data on all components and processes is virtually impossible in most ecosystems. Therefore, it is important to consider grounded ecological knowledge about a system before making decisions regarding the community components that are sampled or omitted during data collection. This may be achieved by, for example, identifying community modules and impossible or missing links (Dormann & Strauss 2014; Terry & Lewis 2020). Additionally, prior assumptions about our knowledge of community functioning must be challenged, given that ecosystems are ever-changing and discrepancies between experts’ knowledge can have important impacts on the models (Picard et al. 2012; Terry & Lewis 2020). Evaluations of ongoing multispecies monitoring programs can help identify weaknesses in the data collection (e.g., poor sampling of a particular species or region), which, when addressed, could greatly benefit multispecies model performance (Carvalho et al. 2016; Zhang et al. 2020). In addition, it would be extremely beneficial to foster collaborations among researchers and improve organization of data collection. By increasing collaborations, researchers working on different species could coordinate sampling efforts in the same region, thereby producing data more useful to multispecies modelling without incurring additional costs. Finally, development of methods that promote more efficient use of limited data, such as data integration, have an important role to play in multispecies modelling development.
Model complexity is another major challenge for the development of multispecies models. Attempting to capture the inherent complexity of natural ecosystems in mathematical models causes issues related to computational and data requirements, model parameterization, number of potential error sources, and interpretability and transferability of model outputs. Assumptions and simplifications will continue to be necessary. For example, multispecies population dynamics models need to rely on the assumption that the subset of species and processes included in the models are sufficient to describe the dynamics of interest, and simplified community models must rely on the criteria chosen to group certain species or simplify species interactions. It is crucial that such simplifications are grounded on robust ecological knowledge, rather than on data limitations (Lafferty et al. 2008), and that they are transparently reported so that future studies can compare and assess the effects of different simplifying strategies on model outputs (Fultonet al. 2003).
The lack of adequate quantification and reporting of uncertainty currently represents a major challenge for the development of multispecies models. Uncertainty is inevitable in ecological modelling, and it is often accentuated in increasingly complex models. In multispecies models, uncertainty comes associated with many sources, which makes the quantification and propagation of individual sources of uncertainty more difficult. There is a great need for methods to assess uncertainty consistently so that models can be compared and evaluated. Although uncertainty is often viewed as a negative model characteristic with regard to practical applications (Pappenberger & Beven 2006), a model with unknown uncertainty is certainly less useful than a model with high, but reported, uncertainty (Keenan et al. 2011). In some cases, high uncertainty in multispecies models can be a positive outcome if it means that the model accounts for important external processes affecting the populations rather than regarding these as random variation, as single-species models would do (Hollowed et al. 2000; Kinzey & Punt 2009).
Ultimately, a promising way forward that maximizes data use is the combination of modelling approaches with contrasting strengths and weaknesses (Strauss et al. 2017). For example, Schmolke et al. (2019) built a hybrid model consisting of a food web simulation model for an aquatic system coupled with an IBM for a single species of interest (Fig. 3). For each time step, the food web model provided biomass estimates for different parts of the food web, based on environmental variables, estimates of vital rates, and expected interactions. Estimates of prey biomass from this model were then fed into the IBM, which modelled in detail the transfer of prey biomass to individuals of the focal species, and the resulting biomass estimate for the focal species was fed back into the food web model. While this model did not include stochastic effects and focused on a single species, the general approach of coupling more detailed population models with a system-wide community model could represent a promising method for incorporating species interaction effects into predictive models of population dynamics (Ernest et al. 2011). Other types of hybrid modelling frameworks have also been proposed, for example, by linking a spatially explicit dynamic model of a plant community to an IBM describing the behaviour of frugivorous birds to account for the effect of the birds on seed dispersal (Vincenot et al. 2011). As hybridizing models is a relatively new approach within ecology, and their development requires a diverse range of expertise, their potential and benefits remain largely unexplored, representing an exciting path moving forward (Kim et al. 2019).
In this review, we have identified common themes in relation to the challenges faced by different subfields of ecology aiming to model multispecies dynamics. Working together on shared challenges across subfields should promote faster and more fruitful progress towards a better understanding of multispecies dynamics. It has become customary for modelling studies to compile their developed models as readily available open-source software and code, which will undoubtedly promote development (Powers & Hampton 2019; Alston & Rick 2021). Moving forward, we emphasize that it is important that multispecies studies clearly outline the model objectives and assumptions. We also encourage increased communication across multispecies modelling disciplines, and hope that this leads to the development of new hybrid frameworks that successfully combine models with contrasting strengths and weaknesses, representing cost-effective ways to advance our understanding of multispecies dynamics (Gray & Wotherspoon 2015; Strauss et al.2017).

Acknowledgements

This study was funded by the Research Council of Norway through the Centre of Excellence Centre for Biodiversity Dynamics (project 223257) and research project SUSTAIN (244647). MVH was supported by the Norwegian Research Council (280715).

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Captions

Figure 1. Diagram illustrating four methods for reducing complexity of natural systems. Centre figure shows a hypothetical system with the true interactions and variables. Functional groups/trophospecies illustrates the idea of grouping species by trophic/functional similarity and treating each group as one component. Modules represent sub-groups of mostly mutually interacting species which can be modelled independently. Modules can also be linked to each other. General functions can define interactions between individuals based on traits (e.g., size), rather than between species. Latent variables are used to represent the variability caused by unknown factors (e.g., species or environmental variables).
Figure 2. Representation of potential sources of uncertainty. The thick/grey arrows on top illustrate the propagation of uncertainty through the modelling process. The red symbols highlight example causes for uncertainty, such as: (a) interactions taking place at night (represented by the moon symbol) or in difficult to observe/monitor places, (b) incorrect assumptions about the presence or absence of species interactions and, (c) uncertainty in estimated parameters. Lastly, model uncertainty can be reduced through increasing transparency.
Figure 3. Example of hybrid model that combines a food web model (brown) and individual based model (IBM; blue) to represent a focal species (S3) in more detail. For each model iteration, values of the food web model components influence responses of individuals in the IBM, like movement, metabolism, excretions, fecundity, growth or behaviour. In turn, total changes in the population of the focal species (S3) produced by the IBM feed back into the food web model, affecting the species that interact with the focal species in the following iteration (i.e., S1 and S5).

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