2.4. Distance‐based Redundancy Analysis—db‐RDA

We performed distance‐based redundancy analysis (db‐RDA) to unravel the variables explaining the genetic differentiation of J. lineata among localities. To do so, we adapted the db‐RDA script published by Jardim de Queiroz et al. (2017). We used the pairwise‐FST matrix as the response variable in the db‐RDA. To test the effect of regional and environmental variables in genetic distance, we used the following explanatory variables:

The geographical distance between each pair of sampling sites (to test for isolation by distance, IBD): For this analysis, we used the geographical distance calculated by considering the course of the rivers instead of using the Euclidean distance extracted from the geographical coordinates. To transform the matrix of geographical distance into vectors, we applied a Principal Coordinates of Neighbour Matrices (PCNM) by using the package PCNM (Legendre et al., 2013) and its function “PCNM,” following the methodology described in Borcard and Legendre (2002). In our analyses, the first six axes (out of a total of 10) were found to have positive eigenvalues and were kept for the db‐RDA.

Basin type (representing possible isolation by barrier, IBB): We incorporated a dummy variable in the model according to the type of basin of each sampling site: The sites were categorized either as “0” if exorheic basins—have connection with the main La Plata Basin or the sea—(localities: 1, 2, 3, 5, 6, 9, 14, 15, 16, 19, 20), or “1” if endorheic basins—without connection—(localities: 4, 7, 8, 10, 11, 12, 13, 17, 18).

Hydrographic system (representing possible IBB): The sampling sites were classified in 8 systems: (a) Mar Chiquita, (b) La Plata, (c) Río Quinto, (d) Salar Ambargasta, (e) Río Colorado‐Negro, (f) Salar de Pipanaco, (g) Sierras de San Luis, and (i) Este Uruguay; these were taken as factors since it was necessary to give them a numerical value for the analysis.

Altitude (representing isolation by environment, IBE): As J. lineata is present from lowlands to up to 2,300 MASL, we used altitude data inferred for each sampling site in our model. Values were taken from Google Earth Pro. However, contrary to the haplotype network reconstruction where we classify the localities into groups of altitudes, in which we used five categories of altitude (i.e., (a) group 1 from 0 to 99 MASL, (b) group 2 from 100 to 299 MASL, (c) group 3 from 300 to 499 MASL, (d) group 4 from 500 to 699 MASL, and (e) group 5 from 700 MASL), for the db‐RDA we used this variable as a continuous variable.

Elevational gradients may be challenging for most species and can be considered as IBE for many reasons: (a) The number of species increases downstream with a marked difference in species' richness between upland and lowland areas (Bistoni & Hued, 2002). Studies of the changes resulting from the correlation of altitude with biodiversity have included a wide range of organisms, including vertebrates, invertebrates, and plants from many different geographic regions (Tobes et al., 2016). (b) The water flow is different between lowlands and uplands. In uplands, the headwaters of the rivers are fast flowing due to more pronounced slopes, which leads to a strong erosive power that affects the physicochemical properties of the water: high oxygen, low conductivity, and low levels of nutrients. (c) The area covered by a basin is larger in lowlands. (d) The physical and chemical conditions influence the distribution of fish in aquatic ecosystems (Buisson et al., 2008). In addition, physiological and morphological adaptations (hydrodynamic shapes), as well as low metabolic rates, are conditions necessary for fish survival (Beitingera et al., 2000; Taniguchi & Nakano, 2000; Winemiller et al., 2008).

Latitude (representing IBE): For J. lineata, each sampling site has a coordinate measured in decimals, both for latitude and longitude. For this analysis, we only took into account the list of latitudinal coordinates for each location.

The gradients across latitudes in the La Plata Basin imply changes in community composition and climatic variation. Therefore, we added latitude in our model as a proxy for environmental heterogeneity. This variable was included in the model as decimals, measured according to the geographical coordinates of each site's south latitude. The latitudinal gradients of species richness for fishes generally corroborated the paradigm of latitudinal diversity gradient (LDG) (Willig et al., 2003), which encompasses the tendency of biological diversity to concentrate in tropical regions. This LGD is ultimately dependent on historical, geographic, biotic, abiotic, and stochastic forces (Schemske, 2002), which affect the geometry, internal structure, and location of species ranges in ecological or evolutionary time. Specifically, latitude is a surrogate for a number of primary environmental gradients (e.g., temperature, insolation, seasonality) that interact and are correlated to each other. With regard to the species' richness of fishes, it is considered that it increases with decreased latitude throughout the world for marine and freshwater taxa as well as for assemblages in lentic and lotic habitats (Barbour & Brown, 1974; Hof et al., 2008; Willig et al., 2003).

Before starting the analyses, we performed a Pearson test (for the quantitative) and a chi‐square (for the qualitative) variables to test for the independence of the variables. Then, to identify the variables that explain part of the genetic structure, we first ran a db‐RDA on the full model (including all investigated variables) using the function “capscale” of the package vegan (Oksanen et al., 2007). Then, we ran a db‐RDA on nested models to identify the best model based on Akaike information criterion (AIC). As db‐RDA does not provide information on the relative contribution of each variable of the model, we performed a variance partitioning analysis on the variables present in the best model to identify their relative contribution. For that, we used the function “varpart” of the package vegan in the R environment (Peres‐Neto et al., 2006).