*2.3. Model Building*

In order to illustrate the niche-biotope dualism (known as Hutchison's duality [27]) the fact that the two invasive fish species can occupy ecological niches in different biotopes that have different combination of bioclimatic variables and make an ecological niche modelling (ENM), we used niche clustering ('ntbox' package in R [25]), which provides

the opportunity to perform k-means clustering and project the results in the geographic and environmental spaces in a form of a world's map. The map shows the world's areas where the two fish species were found in biotopes that differ from those within their home range (different combinations of variables in places of species findings are market with differently colored circles).

Species distribution modelling (creation of standard distribution models or SDMs) was used to determine the potential change of distribution ranges of invasive alien species in new environments with time (MaxEnt [28] with 35 replicates, DivaGis (version 7.5; using CliMond dataset of current and predicted variables)). The Maxent software (version 3.4.4, [28,29]) was utilized for modelling, using the default settings. Maxent, unlike other distributional modelling techniques, uses only presence (registration points) data instead of presence and absence data. The SDMs were shown as maps where the areas of the highest habitat suitability (r > 0.3–0.5) are colored in red and areas of the lowest (r < 0.2)—in blue when visualized in SagaGis (System for Automated Geoscientific Analyses, version 7.6.0). The evaluation metrics for the obtained SDMs (performance) included: Partial receiver operating characteristic (ROC) [29], binomial tests [30], and the confusion matrix [31]. The ROC area under the receiver-operator curve (AUC) was used for assessing the discriminatory capacity of the models: AUC > 0.9 is considered excellent. The true skills statistics (TSS) was used to make a post-modelling check of obtained SDMs based on the standard confusion matrix that represents matches and mismatches between real observations of species (collected data) and predicted theoretical points within areas of high habitat suitability according to the created SDMs [26]. Binomial test mentioned earlier, as one of standard ways for evaluating obtained SDMs' quality, allowed to determine whether test points (from obtained SDMs' .acs files) fall into regions of predicted presence more often than expected by chance, given the proportion of map pixels predicted present by the model and showed on the world's map) [30]. This also helped to visualize the difference in predicted world areas occupied by the two fish species. GIS-modelling was accomplished using visualization in SagaGis, DivaGis, QGIS (version 3.16.9) [26]. Statistical processing of the obtained data was carried out using Statistica for Windows v.10.

#### **3. Results**
