Data analysis

To assess population responses to edge effects along the forest-pasture gradient with a sufficient number of individuals, for each site we joined the number of individuals captured in the traps of the same distance (corresponding to the three transects) as a single sampling unit (SU). Differences among transects are minimal (see Results “Population responses to the edge”); however, these differences cannot be statistically verified because of the low number of transects, which limits the power of any analysis. Thus, for each site we retained seven SU (at −90, −60, −30, 0, 30, 60, and 90 m). We calculated the relative abundance of each dung beetle species at each SU as the number of individuals of the species divided by the total number of individuals.

First, to assess the completeness of dung beetle assemblage inventories for the 28 SUs (7 SUs × 4 sites) we calculated the sample coverage (Chao & Jost, 2012). Then, we calculated the following metrics: (a) species richness, (b) species diversity, (c) functional divergence (FDiv), (d) functional richness (FRic), (e) functional evenness (FEve), and (f) compositional dissimilarity. Species richness (S) was measured as the number of species observed at each site. Species diversity (D) was measured using the exponential of Shannon’s entropy, which is the true diversity of order q = 1 (sensu Jost, 2006).

We used three indices that measure complementary aspects of functional diversity (Villéger, Mason & Mouillot, 2008; Mouchet et al., 2010): FDiv describes how species’ abundance is spread within the functional trait space occupied by all species; FRic is the volume of functional space filled by the assemblage; and FEve is the regularity with which the functional space is filled by species, weighted by their abundance. These metrics were calculated in the FDiverstiy software (Casanoves et al., 2010) using four functional traits: food relocation behavior (species can be rollers, tunnelers or dwellers), activity period (diurnal or nocturnal), diet (strictly coprophagous or copro-necrophagous) and biomass (dry weight) (Table S1). Roller species shape the food source into a ball and roll it on the ground to another location for burial, tunneler species build their nests and bury portions of food in tunnels beneath the resource, while dwellers breed inside the dung itself (Hanski & Cambefort, 1991). For diet, coprophagous are those species that feed on dung, while copro-necrophagous are attracted to dung but also carrion. Functional traits of the species were obtained from specialized literature (Halffter & Edmonds, 1982; Hanski & Cambefort, 1991; Pineda et al., 2005; Navarrete & Halffter, 2008; Barragán et al., 2011). We calculated mean biomass of each beetle species as the dry weight of 50 randomly selected individuals per species. For species with sexual dimorphism we weighted 25 males and 25 females. To obtain dry weight we put individuals in an oven at 70 °C for 48 h. After that, we weighed beetles in a digital scale (Scientech ZSA 80, precision ± 0.001 g).

The response of compositional dissimilarity to the edge was measured with a dissimilarity index based on presence–absence (1-Jaccard similarity) and an abundance-based index (1-Morisita similarity). To get their values, we compared species composition of each SU with their two adjacent SU in the gradient and calculated average dissimilarity, except for the extreme SU (−90 and 90 m) where we took one dissimilarity value with the unique adjacent SU (−60 or 60 m, respectively). We expect the response of dissimilarity to edge effects to be clearer with the abundance-based index than with the presence–absence index.

The response of populations and assemblage parameters to the edge was analyzed using the procedure of Ewers & Didham (2006) modified by Zurita et al. (2012). Our population analyses were restricted to those species with more than 30 individuals captured on each forest type. We used five theoretical models that represent the three expected edge responses: (1) neutral (mean equation), (2) edge avoidance (linear, power or sigmoid), and (3) unimodal response. The mean model describes species that use both habitats equally and therefore exhibit no response to edges (generalist species). Regarding edge avoidance, the linear model would best describe circumstances where the response of species to edges extends beyond the sampled range on both sides of the ecotone; the power function may be useful for describing the incomplete coverage of the edge response of species in which an asymptote is reached on one side of the ecotone; and the sigmoid model describes circumstances in which species respond to edges either gradually or abruptly, and there is thus a discrete change in habitat suitability. Finally, the unimodal response fits edge preference, where species have the highest abundance at the middle of the gradient (Zurita et al., 2012). In this framework, the neutral response corresponds to “reflecting edges,” and edge preference to “absorbing edges” sensu Olson & Andow (2008). Our sampled distances (−90 to 90 m) could encompass the full extent of these edge effects (sigmoid and unimodal) showing a complete response, or edge effect could extend larger distances in both habitats (linear) or in one habitat (power) indicating an incomplete response. Basically, we used non-linear regression analyses to test for these models, using the relative abundance of species (the number of individuals of each species divided by the total number of individuals of each site) or the assemblage parameters as the dependent variables, and the distance to the nearest edge type as the independent variable. The full description and statistical procedures can be found in the proposal of Ewers & Didham (2006), Zurita et al. (2012) and Peyras et al. (2013).

To compare the best fit of each dependent variable (species relative abundance and assemblage parameters) to the five proposed models (neutral, linear, power, sigmoid, unimodal) we first calculated the Akaike’s information criteria for each model, with a correction for small sample sizes (AICc). Then, we selected the two most probable models (lower AICc) and calculated the Akaike weight between both models (−0.5 * ΔAIC). The Akaike weight represents the relative likelihood of a model (probability of being correct). Finally, we selected the model with more than 90% of probability of being correct. In cases were both models had more than 90% probability of being correct we keep both models as the most probable responses to the edge. In cases when a complete (sigmoid or unimodal) and an incomplete model (linear or power) showed similar fit the final response was considered undetermined.

Summarizing, the response of dung beetles could be (1) unimodal distribution of abundance with a peak near to the edge, (2) edge avoidance (linear, power or sigmoid) or (3) neutral response (mean model). The extent of the response can be incomplete if edge effects extend beyond the 90 m sampled distances (linear or power) or complete (sigmoid and unimodal). In cases when a complete and incomplete model showed similar fit, the response is considered undetermined. Finally, to compare the proportional number of species fitting to each model between localities, we performed a G-test.