Scaling methods in ecological modelling

Abstract

Scaling is ubiquitous and persistent in ecology. Following the acclaimed concept of pattern and scale (Levin, 1992), patterns and processes at a certain spatial or temporal scale or organizational level emerge from patterns and processes at finer scales or levels and these, in turn, are influenced by the large-scale patterns (Figure 1, Lischke, Löffler, Thornton, & Zimmermann, 2007). Due to this, scaling, that is, changing from one scale to another, is not always straightforward, and sometimes can cause problems due to scale breaks, nonlinearities, feedbacks and heterogeneity in such patternprocess relationships (Snell et al., 2014). Additionally, scaling is sometimes not explicit, and confusion in terminology adds to scaling-related problems. Here, we (1) address scaling terminology; (2) define three categories of scaling approaches, (a) pre-model scaling, (b) in-model scaling and (c) post-model scaling; and (3) explore examples, problems, and, where available, potential solutions in each category. We also elaborate our main claim that modelling is often confronted with scaling challenges, because modelling-directly or indirectly-always implies scaling.

The ecology of plasmid-coded antibiotic resistance: a basic framework for experimental research and modeling

“…This is because any experimental design is guided by an implicit model, an imagination of the system under investigation, but which lacks a clear definition of assumptions and tests of consistency and logical consequences [90] . This represents a form of ’pre-model scaling’ [91] , a simplification or aggregation that is done prior to running ’a model’. Usually, people have an explicit model in mind, if they think of ’models’ or ’modeling’.…”

Spatio-temporal point processes as meta-models for population dynamics in heterogeneous landscapes

“…Ecosystem patterns and processes can cover a wide range of space and time, and they depend on multiple drivers acting over different scales (Fritsch et al, 2020). Problematic loss and the lack of information may arise in procedures of scaling-up or scaling-down when coupled with the complexity of the involved systems.…”

“…A solution to deal with this complexity could be the application of non-spatial analysis methods via spatial and temporal output aggregation (Gotelli, 2000;Webb, 2000;Fritsch et al, 2020). For example, Nathan et al…”

“…Analytical solutions can provide insight from different aggregation levels, but their construction and use are not always unequivocal (see Johst et al, 2013). Spatial statistic techniques are potential candidates of great interest and should be further explored (Fritsch et al, 2020). For example, Jia and Taflanidis (2013) present a systematic implementation and optimisation of kriging meta-models for hurricane wave and surge prediction maps based on high-dimensional outputs to reduce complexity while preserving spatial dimension.…”

“…Hence, dealing with ecological processes involves studying different spatial and temporal scales, since ecosystem patterns and processes cover various spatio-temporal ranges and may have multiple drivers acting across different extents (Fritsch et al, 2020). The characterisation of the spatial distribution of landscape features and individuals in response to such complex interplay of processes across scales belongs to the field of landscape ecology.…”