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.