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).