2.4.2 Water effects on the patterns of dominant and subordinate visitation to the plants
To evaluate the role of water availability in the overlap of dominant and subordinate ant species visiting the plants with EFNs, we used the networks in which we had access to ant species identity (N = 37). In three networks, no subordinate ant species interacted with the plants. These networks were excluded from all the analyses focusing on the subordinate species (N = 34 networks) but maintained in the analyses focusing on the dominant ant species (N = 37 networks). For each network, we calculated the proportion of dominant ant species. Additionally, we calculated three metrics to explore the patterns of plant use by dominant and subordinate ant species interaction: the Connectance, the Resource range (RR), and the Jaccard Index. These metrics are commonly used to describe the trophic specialization of species in the network (Jordano 1987, Poisot et al. 2012), which allowed us to evaluate the magnitude of dominant and subordinate trophic specialization and overlapping in the networks along the water gradients.
The connectance of each hierarchical group (\(C_{d}\)and \(C_{s}\)) described the proportion of all interactions reported in each network performed by dominant or subordinate ant species to the total possible interactions within the networks. We calculated \(C_{s}\ \)and \(C_{d}\)as a subset of the general network connectance as follows:
\(C_{d}=\frac{\ I_{d}}{PA_{d}}\), \(C_{s}=\frac{\ I_{s}}{PA_{s}}\) ,
where \(C_{d}\) and \(C_{s}\ \)is the connectance of dominant and subordinate ant species, respectively. \(I_{d}\) \({(I}_{s})\) is the number of interactions performed by dominant (subordinate) ant species,P is the number of plant species, and \(A_{d}\) \({(A}_{s})\) is the number of dominant (subordinate) ant species in each network. If the decline in water availability reduces dominant and subordinate overlap in using plants with EFNs, \(C_{d}\) and \(C_{s}\ \)values will decline when the mean precipitation rate also declines.
Resource Range (RR) is a binary metric resulting from the normalization of the total number of interactions realized by the species within the network (Poisot et al. 2012). In our case, it will describe the proportion of plant species used by dominant and subordinate ant species within each community. To calculate RR, we first counted the number of interactions performed by each ant species within the networks. Then, we estimated the mean RR of ants from each hierarchical group (\(RR_{d}\)and \(RR_{s}\)) as follows:
\(\text{RR}_{d}=\frac{1}{A_{d}}\sum_{i=1}^{A_{d}}\frac{P-\ k_{i}}{P-1}\),\(\text{RR}_{s}=\frac{1}{A_{s}}\sum_{j=1}^{A_{d}}\frac{P-\ k_{j}}{P-1}\)
In which \(k_{i}\left(k_{j}\right)\) is the number of interactions the species of dominant (subordinate) ant species i (j ). This metric ranges from 0 to 1, with 0 indicating the use of all plant species within the networks by ants from each group (i.e. complete generalization) and 1, the use of only one plant species by all ants from each group (i.e. complete specialization). Then, if decreasing in water availability increase the monopolization of more valuable plants by dominant ants and the competitive exclusion of the subordinate one to less valuable plants, we expect that the \(RR_{d}\) and \(RR_{s}\)values increase as the mean precipitation rate decreases.
Finally, we used the Jaccard Index (J ) as a proxy for the overlapping degree of dominant and subordinate ant species interacting with the plants in each network. To calculate it, we created P x 2 binary matrices describing the patterns of dominant and subordinate ant interaction with the plants in the networks. In this case, we were not interested in when each ant species from each group interacted with each plant species. Instead, we focused on when each plant species interacted with any dominant or subordinate ant in that specific community (1 when any dominant and/or subordinate ant species visited the plant and 0 otherwise). Once we built the matrices for each network, we calculated the Jaccard index, using the vegdist function at veganpackage in the R program. At vegdist , we used the method “jaccard” which estimates the dissimilarity between the patterns of dominant and subordinate ants with the plants. To make it more intuitive, we subtract one from the dissimilarity index (1 – dissimilarity) to obtain the Jaccard similarity index. Therefore, the lower the Jaccard similarity index for a network, the lower the overlap among the plant species used by dominant and subordinate ants. Therefore, if the decline in water availability improves the monopolization of the more valuable plants in the community by dominant ants and the displacement of subordinate ants to less valuable plants, we expect that the Jaccard index will decrease as the mean precipitation decreases.
2.5 Statistical analysis
Initially, we created a series of linear mixed regression models (LMM) to investigate all our predictions, assuming that the residuals of our data were normally distributed and heteroscedastic. However, once we ran the models, we observed that these assumptions were not true for almost all LMM models. Because of that, we built different models according to the nature of the dataset used for each analysis. For models that broke the normality assumption (see Supporting information), we fitted a GLMM (Generalized Linear Mixed Model), using the error distribution with the best fit to the data. If the LMM model broke the assumption of variance homogeneity (see Supporting information), we fitted a GLS (Generalized Least Square) regression. We used the GLS because it allowed us to adjust the residual variance while keeping the raw data, avoiding the use of non-parametric tests or data transformation (Zuur et al. 2009). In all models described below, we used the mean precipitation rate and the paper identity as predictors and random factors, respectively.
To evaluate if ant-plant interactions become more specialized and modular as drier the environment (hypothesis 1), we first evaluated the effects of the mean precipitation on the S of the networks. For that, we built a GLS model using the of 53 networks as our continuous response variable. Then, to evaluate the effects of the mean precipitation rate on the specialization and modularity of the networks, we built three models, one for each of the following response variables: connectance (C; N = 51 networks), zNODF (nestdness; N = 63), and zQ (modularity; N = 51). For the connectance model, we built a GLMM with a Gamma distribution. Because the connectance can be influenced by the size of the networks (Yodzis 1980, Blüthgen and Menzel 2006), we included the S of each network as a weight in this model. For the zNODF and zQ, we build GLS models using each metric as a response variable.
To investigate if the structure of the ant-plant networks along the water gradient will be driven by changes in the patterns of dominant and subordinate ant interaction with the plants with EFNs (hypothesis 2), we first evaluated the effects of the mean precipitation rate on the proportion of interactions performed by dominant and subordinate ants on the networks. For that, we used a GLMM with a Gamma distribution, including the proportion of dominant ant species in 37 networks as our response variables. To investigate if water availability affected the connectance of dominant and subordinate ant species in the networks, we built two GLMMs with Gamma distribution. For each model, we used the\(C_{d}\) (N = 37) and the \(C_{s}\) (N = 34) values as our response variables. To investigate if the mean precipitation rate affected the RR of dominant and subordinate ant species, we built two GLMs, including the mean RR of dominant (N = 37) and subordinate (N = 34) ants as our response variables in each model. To investigate the overlapping in the plants used by dominant and subordinate species, we used a GLS model including the Jaccard values of each network as our response variable (N = 34). We built and analyzed the GLMM and GLS models described above using the “nlme” (Bates and Pinheiro 2000) and the “lme4” package (Bates et al. 2015) in R software, respectively (R Core Team 2022).