We simplified the model compared to Charisma 2.0 to reduce the number of parameters (47 species-specific parameters in Charisma 2.0) by excluding processes of i) carbonate limitation because the lakes we simulated were not carbonate limited and no proof was found for the process; ii) spatial processes like seed dispersal, which we assume not to limit occurrence of macrophytes within the regional context (Alahuhta et al., 2020); iii) water level fluctuation, because corresponding data are not available for all lake and because the macrophyte mappings correspond always to the actual water level; iv) interspecific competition and v) herbivory because both processes are not relevant for modelling the eco-physiological constraints on the potential distribution of species; and vi) vegetative reproduction because we focus on eco-physiological constraints rather than demographic or dispersal constraints. After that, MGM still includes 28 species-specific parameters. The detailed Overview, Design concepts, Detail (ODD) protocol (Grimm et al., 2006, 2010) for MGM (see Appendix S3) and the model code (see Appendix S4) is open access and available as Supporting Information and on GitHub.

Datasets

The available dataset from the German federal state of Bavaria consists of large lakes (>0.5 km² surface area). We selected all lakes of natural origin (without artificial influence on water level fluctuation and not of artificial origin) and with a minimal maximal depth of 9 m. Their locations are shown in Figure 1c. They are all carbonate-rich and stratified (formation of different thermal layers during summer), but provide a broad range of environmental conditions, e.g. from turbid to clear, or from cold to warm waters. Macrophyte occurrence in four water depths (0-1m; 1-2m; 2-4m; >4m) and monthly physical-chemical measurements (e.g. water temperature, Ptot, and Secchi depth) are recorded in all these large lakes for the EU-Water Framework Directive (WFD) monitoring and are publicly provided by the Bavarian State Office for the Environment underwww.gkd.bayern.de. Secchi depth, a measure for transparency of water, was converted to kD, the extinction coefficient of light in water (Holmes, 1970; Kirk, 1935). Data for irradiance are obtained from the nearest German Weather Service (DWD) weather station as daily mean (StMWi, 2019).
For each lake we selected the most recent macrophyte mapping data (2004-2017). We excluded all species that are sterile hybrids, emerged, with floating leaves, mosses, and are non-rooted. In addition, “indicator species” were selected, i.e. species that are oligotraphentic, mesotraphentic, or eutraphentic (Melzer, 1999).

Experimental design

Data preparation and analyses were done in R 4.0.5 (R Core Team, 2021). We defined parameter spaces for oligotraphentic, mesotraphentic, and eutraphentic functional types. We selected the parameter spaces based on parameters of reference species out of the groups for which some of the parameter values are known. Reference species were Chara aspera (Characeae) for oligotraphentic species, Myriophyllum spicatum (Haloragaceae) and Potamogeton perfoliatus (Potamogetonaceae) for mesotraphentic species as well as Potamogeton pectinatus (Potamogetonaceae), Elodea nuttallii (Hydrocharitaceae), andNajas intermedia (Hydrocharitaceae) for eutraphentic species. As the eco-physiological parameters of submerged macrophyte species are not known, we randomly select 300 parameter combinations for each of the three parameter spaces defined for oligotraphentic, mesotraphentic, and eutraphentic functional types respectively (Table 1). Each of the resulting 900 parameter combinations represent hypothetical, virtual species.
We select lake parameter values according to measured data within the 30 selected lakes from the available dataset (see description above). The lakes differ not just in their latitudes, but also in their maximal summer temperature, nutrient content, and turbidity. Based on these four parameters we classified the lakes into clear, medium, and turbid lakes by using a clustering method (hclust, “ward.D2”). All other lake parameters are identical across lakes and are given in the Supporting Information (Appendix 2; Table S2.1).
We run the model for all 900 virtual species within the 30 lakes at four depths (0.5m, 1.5m, 3m, 5m) for 10 years to reach equilibrium (Figure 1d). We select as potential growing species those that can establish a mean biomass of more than 1 g (per depth and in sum over depth) during summer (June-August). Those species that passed through the considered processes within MGM in the given lake conditions are denoted as “potential species”. Species that passed through all ecological processes (including demography, interaction, and dispersal) in nature will be called “observed species”.
Table 1: Parameter spaces for oligotraphentic, mesotraphentic, and eutraphentic functional types. Parameters are marked as bold if they are different for the functional types. The spaces were selected based on reference species from the groups. Reference species were Chara aspera for oligotraphentic species, Myriophyllum spicatum and Potamogeton perfoliatus for mesotraphentic species, Potamogeton pectinatus, Elodea nuttallii, and Najas intermedia for eutraphentic species.