Methods
Study Site and
System
We conducted fieldwork at Finca Irlanda (15°20’ N, 90°20’ W), a 300 ha,
privately owned shaded coffee farm in the Soconusco region of Chiapas,
Mexico with ~250 shade trees per ha. The farm is located
between 900-1100 m a.s.l. Between 2006-2011, the field site received an
average rainfall of 5726 mm per year with most rain falling during the
rainy season between May and October. The farm hosts ~50
species of shade trees that provide between 30-75% canopy cover to the
coffee bushes below. The farm has two distinct management areas – one
that is a traditional polyculture and the other that is a mixture of
commercial polyculture coffee and shade monoculture coffee according to
the classification system of (Moguel and Toledo 1999).
The arboreal twig-nesting ant community in coffee agroecosystems in
Mexico is diverse. There are ~40 species of arboreal
twig-nesting ants at the study site including Brachymyrmex (3
species), Camponotus (8), Cephalotes
(2), Crematogaster (5), Dolichoderus
(2), Myrmelachista (3), Nesomyrmex
(2), Procryptocerus (1), Pseudomyrmex (11),
and Technomyrmex (1) (Philpott and Foster 2005a ;
Livingston and Philpott 2010).
‘Real-estate’
experiments
We examined the relative competitive ability of twig-nesting ants by
constructing dominance hierarchies based on ‘real estate’ experiments
conducted in the lab. We collected ants during systematic field surveys
in 2007, 2009, 2011, and 2012 in the two different areas of the farm,
and then used ants in lab experiments. We first removed ants from
individual twigs, and then placed ants (workers, alates, and brood) from
two different species (one twig per species) into sealed plastic tubs
with one empty artificial nest. The artificial nest, or ‘real estate’,
consisted of a bamboo twig, 120 mm long with a 3-4 mm opening. After 24
hours, we opened the bamboo twigs to note which species had colonized
the twig. All ants collected were used in ‘real estate’ trials within
two days of collection, or were discarded.
We conducted trials between pairs of the ten most common ant species
encountered during surveys: Camponotus abditus , Camponotus
(Colobopsis ) sp. 1, Myrmelachista mexicana ,
Nesomyrmex echinatinodis , Procryptocerus scabriusculus,
Pseudomyrmex ejectus , Pseudomyrmex elongatus ,
Pseudomyrmex filiformis , Pseudomyrmex PSW-53, and
Pseudomyrmex simplex . We selected a priori to use the 10 most
common species. We intended to replicate trials for each pair (out of a
total of 45 two-species pairs) at least ten times. However, low
encounter rates for some species, and for pairs of species within two
days of one another precluded obtaining ideal sample sizes. We
replicated trials for each species pair on average 5.73 times; four
species pairs were replicated once, nine species pairs were replicated
twice, and 31 species pairs were replicated three or more times. Only
one species pair (M. mexicana and P. filiformis ) was not
tested. We conducted 42 trials in 2007, 105 trials in 2009, 82 trials in
2011, and 30 trials in 2012 for a total of 259 trials.
We used our ant dataset to infer a dominance hierarchy by simulating
interactions among individuals to estimate level of uncertainty and
steepness in the hierarchy. All simulations were conducted in R version
3.3.3 (R Core Development Team 2017). We used the R package “animDom”
version 0.1.2 to infer dominance hierarchies using the randomized
Elo-rating method (Sánchez‐Tójar et al. 2017). The R package ‘statnet’
was used to test triangle transitivity measures (Handcock et al. 2008).
We subsampled the observed data to determine if the population had been
adequately sampled to infer reliable dominance hierarchies. We
calculated the ratio of interactions to individuals to determine
sampling effort. An average sampling effort ranging from 10-20
interactions is sufficient to infer hierarchies in empirical
networks (McDonald and Shizuka 2013). Furthermore, we compared the
proportion of observed dyads to the expected proportion of dyads with
the probability of interactions of equal group size following a Poisson
distribution (Sánchez‐Tójar et al. 2017). We estimated the dominance
hierarchy using the random Elo-rating method in order to track ranking
dynamics over time. We converted the observation data and randomized the
order in which sequences of interactions occurred (n = 1000) such that
different individual Elo-ratings were calculated each time to obtain
mean rankings (Neumann et al. 2011; Strandburg-Peshkin et al. 2015). We
estimated uncertainty in the hierarchy by splitting our dataset into two
halves and estimated whether the hierarchy in one half of the matrix
correlated with the hierarchy of the other half in the
matrix (Sánchez‐Tójar et al. 2017).
In addition to examining the role of individual ant attributes and
levels of uncertainty in dominance hierarchies, we were interested in
assessing how the organization of linear dominance hierarchies emerged
at higher levels. While individual attributes of species serve as a good
predictor of dominance hierarchies among dyadic pairs, the pattern
becomes less clear when seeking to explain linear dominance hierarchies
at higher levels of species interactions (Chase and Seitz 2011).
Therefore, we examined the formation of dominance hierarchies using
motif analysis to identify network structures composed of transitive and
cyclical triads (Faust 2007). Motif analysis is commonly used in social
network analysis to detect emergent properties of the network structure
as an explanation for dominance hierarchies by comparing the relative
frequencies of motifs in the observed network to the expected value for
the null hypothesis of a random network (Holland and Leinhardt 1972;
Faust 2007). We carried out motif analysis with customized randomization
procedures (McDonald and Shizuka 2013) to compare the structure of our
network model against random network graphs. Species interaction data
were represented as a directional outcome matrix. The nodes in the
network represent individual ant species and the one-way directional
arrows of the edges represent dominant-subordinate relationships. In the
random networks, we maintained the same number of nodes and edges as in
the observed network, but the directionality and placement of edges were
generated randomly. Using the adjacency matrix, we calculated the triad
census (McDonald & Shizuka 2012). The triad census allows us to examine
directed species interactions (Pinter-Wollman et al. 2011). We
used the seven possible triad configurations fully composed of three
nodes that either have asymmetric or mutual edges (Holland and Leinhardt
1972). We used the network analysis packages ‘statnet’ (Handcock et al.
2008) and ‘Igraph’ (Csardi and Nepusz 2006) in R (R Core Development
Team 2017) to calculate the frequencies of triad configurations (total
triads = 220) and to compare the observed (N = 10) to the random network
graphs (N = 10).
To test for statistical significance between the observed and randomly
generated networks, we computed the triangle transitivity
(\(t_{\text{tri}}\)). Although the triad census consists of 8 different
triangle configurations, we focus our attention on the relative
frequencies of transitive triangles. The proportion of transitive
triangles P(t) in a dominance network is given by:
\(P\left(t\right)=\frac{N_{\text{transitive}}}{N_{\text{transitive}}+N_{\text{intransitive}}}\)
In this case, the expected probability of a transitive triangle in a
random network is P(t)=0.75. Using our expected value, we use a scaled
index \(T_{\text{tri}}\) ranging from 0 as the random expectation to 1
where all triangles are transitive in the network. In random networks
the expected frequency of transitive triangles is 0.75. For each
empirical network, we simulate 1000 random graphs and calculate
the \(T_{\text{tri}}\) each time. The P-value represents the number of
times the randomized \(T_{\text{tri}}\) is greater than the
\(T_{\text{tri}}\) value of the observed network (Shizuka and McDonald
2012).
Results