Modeling approach

Huisman-Olff-Fresco models were fitted in the R statistical program (v. 3.3.1; R Developmental Core Team [23]) using the package “eHOF” (Jansen and Oksanen [10], version 3.2.2). To improve modeling results even for small data sets, the stability of model choice was double-checked by (1) bootstrapping (100 samplings, default package setting) to ensure model robustness, and (2) the Akaike information criterion corrected for small data sets (AICc, Burnham and Anderson [24], default setting). In case the two procedures differed in their choice for the best model type, the bootstrapping model was preferred. A minimum number of 10 presences and absences in the data set was set as a pre-condition for modeling in the package.

HOF models were applied to 14 different training combinations of presence and frequency constructed by random sampling from the original data set (Table 1). With a constant number of presences, the frequency was changed by varying the number of absences. These are hereinafter referred to as Pre10, Pre25, Pre50, Pre100 and Fre0.068, Fre0.116, Fre0.5, Fre0.714, respectively, and cover a wide range of situations that can be found in ecological studies, from very rare to very common species in small and big data sets. In total 105 species from the original data set met the pre-condition of a minimum of 50 occurrences within the data set to be used in the analysis of scenarios Pre10, Pre25 and Pre50, whereas only 72 species could be used for scenario Pre100 requiring a minimum of 100 occurrences. The scenario Pre100:Fre0.068 could not be modeled due to data shortage of the original data set (1470 plots would have been needed), whereas the scenario Pre10:Fre0.714 did not meet the pre-condition of the “eHOF” package. For the number of presences and frequencies of the species in the original data set, see S2 Table.

Four different presence scenarios (number of randomly selected presences being 10, 25, 50 or 100) combined with four different frequency scenarios (by varying the number of absences) were modeled. Two combinations could not be applied due to model restrictions or data paucity.

For each data combination (14) and each species (105/72), model fitting was repeated 100 times, resulting in a total number of 137,100 HOF models. From the 100 repetitions, mean niche parameters, a model stability index and the probability of getting a certain niche parameter were calculated for every species—data combination. Moreover, differences in model choice (which model types were chosen) were evaluated visually.