Is the hummingbird-mistletoe-marsupial mutualism a keystone interaction?
To test if the hummingbird-mistletoe-marsupial mutualism is a keystone interaction we compared network complexity, functional redundancy among generalist species, and the ecological importance of keystone interaction members between intact forest sites with and without the keystone interaction.
Network Complexity - Network structure is influenced by the number of motifs and their frequency (Simmons et al. 2018). Networks composed by a greater number of different motifs are more complex structures because they harbor more different direct and indirect ecological interactions (Milo et al. 2002; Simmonset al. 2018). Likewise, network complexity increases with the frequency of the largest motifs (those composed of six species; Fig. S1). To estimate network complexity, network structure was described using the frequencies of motifs containing between two and six species, resulting in 44 possible motif combinations. Motif frequencies were calculated for each pollination and seed dispersal network using the “bmotif” R package (Simmons et al. 2018). We then normalized motif counts to control for network size. We calculated motif frequency using the method “normalize_sum”, which expresses counts as the proportion of motifs in the network and considers whether species are more involved in smaller or larger motifs (Simmons et al. 2018).
To assess dissimilarity in motif frequencies between intact forest sites with or without the hummingbird-mistletoe-marsupial mutualism interaction, here after keystone treatments, we used a non-parametric permutational multivariate analysis of variance (PERMANOVA). This method allows comparing dissimilarity among and within groups using a pseudo F-statistic (Anderson 2001). We used Bray-Curtis dissimilarity to quantify differences among network structures because it is a robust measure of dissimilarity for multiple ecological properties, including motifs (Anderson 2001; Baker et al. 2015; Simmons et al.2019). We conducted a PERMANOVA test with keystone treatments as fixed factor and considered networks from different years built in the same site as replicates. We performed PERMANOVA with the adonis2 function of the vegan package (Oksanen et al. 2012) of R (R Core Team), and using 9999 permutations to generate the null distribution of test statics. Finally, we validated the results of PERMANOVA test by estimating dispersion in the data using the betadisp function of vegan package and testing with one-way ANOVA whether dispersion varied between treatments using lme4 package (Bates et al. 2015). We found no significant differences between dispersion values, which indicates that PERMANOVA results are not caused by heterogeneous dispersion of the data.
Functional redundancy among generalist species - In mutualistic networks, nestedness is associated with stability and robustness of species extinction (Memmot et al. 2004; Burgos et al.2007; Thébault & Fontaine 2010). In nested networks, a core of generalist plants and animals interacts with each other while specialist species interact only with generalist species, enhancing robustness to species extinction. In addition, functional redundancy among generalist species can increase stability by replacing the position of other generalist after its extinction and reducing the cascading effect on other species (Memmott et al. 2004; Kaiser-Bunbury et al.2010).
We estimated the functional redundancy of generalist species and compared between keystone treatments to assess community stability on pollination and seed dispersal networks. First, for each network we calculated the number of species that occupy generalist positions in motifs using bmotif package in R. When we disassemble a network in subnetworks, we obtain 148 different species positions across the 44 motifs (Fig. S1). For pollinator and seed disperser species, we selected the positions number 16 and 148, which represent generalist species, as these positions have the highest number of direct interactions with plants (four and five respectively; Fig. S2). For plants, we selected as generalist positions the number 17 and 47, with four and five interactions respectively (Fig. S2). Functional redundancy among generalist species will be higher when more species occupy these positions. Second, we built regression models for each generalist position (16, 17, 48, and 148) with number of species as the response variable to check differences of functional redundancy between keystone treatments. We selected keystone treatments as fixed factor and considered networks from different years built in the same site as replicates to test this difference. We used the Poisson distribution in our GLMs with a log link function because the response variable is positive and consists in count data (Zuur et al. 2009). Regression models were conducted using the lme4 package of R.
Ecological importance of the keystone interaction members - As a consequence of the constrained relationship among hummingbird-mistletoe-marsupial, the reduction in the abundance or alteration of behavior of any of them could have the potential to disrupt this keystone interaction. Therefore, we expect that the ecological importance of these species change between intact forests sites with and without the keystone interaction. Because motif positions represent different direct and indirect effects and have different ecological meanings (Stouffer et al. 2012; Baker et al.2015; Cirtwill & Stouffer 2015); hence, the greater the variety of positions a species occupies, the greater its ecological importance.
To assess the difference in the ecological importance of the mistletoe, hummingbird, and marsupial, we first calculated the number of positions occupied by these species using bmotif package in R. The mistletoe and hummingbird importance were calculated from pollination networks, while the importance of the marsupial was calculated from seed dispersal networks. We normalized the data using the method “sum” to control the tendency that nodes (e.g. species) with more interactions will occupy more positions than nodes with fewer interactions. This method expresses position counts as the proportion of total occurrences a node occurs at any position. Additionally, to check the difference between keystone treatments we built regression models for each species with number of positions as response variable and keystone treatments as fixed factor. We considered networks from different years built in the same site as replicates to test for this difference. We used the negative binomial family distribution because we found overdispersion in the data and this distribution is a good alternative to deal with it in count data (Zuuret al. 2009). Regression models were conducted using the R package lme4.