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