INTRODUCTION
The study of the spatial pattern of soil biota and the factors by which they are governed is a key research area in understanding the structure and function of soil biodiversity and their relationships with above-ground processes (Ettema & Wardle Reference ETTEMA and WARDLE2002, Ettema et al. Reference ETTEMA, RATHBUN and COLEMAN2000). To date however, soil communities have been minimally considered in spatial ecology when compared with above-ground biota (Ettema & Wardle Reference ETTEMA and WARDLE2002). As an example, despite the early recognition of the fundamental role played by earthworms in soil processes (Darwin Reference DARWIN1881), the very first descriptions of their spatial distribution were published as late as the 1950s (Boyd Reference BOYD1957, Guild Reference GUILD1951). Earthworm spatial patterns are however likely to contribute to existing heterogeneity in soil resources and microhabitats, and to promote species co-existence through greater resource partitioning (Lavelle Reference LAVELLE1996, Reference LAVELLE2002; Wardle Reference WARDLE2002). In this sense earthworms could be keystone organisms in soil faunal communities (Lavelle et al. Reference LAVELLE, DECAËNS, AUBERT, BAROT, BLOUIN, BUREAU, MARGERIE, MORA and ROSSI2006).
In recent studies, spatial statistics have been used to describe the horizontal spatial patterning of earthworm assemblages at local scales (i.e. habitat surfaces of about 1 ha). In most cases, species are aggregated in patches over ranges of 20–50 m, each of them characterized by a dominant species assemblage that seems to be temporally stable for about 20 mo (Decaëns & Rossi Reference DECAËNS and ROSSI2001, Hernández et al. Reference HERNÁNDEZ, FERNÁNDEZ, NOVO, TRIGO and DÍAZ-COSÍN2007, Jiménez et al. Reference JIMÉNEZ, ROSSI and LAVELLE2001, Reference JIMÉNEZ, DECAËNS and ROSSI2006a; Margerie et al. Reference MARGERIE, DECAËNS, BUREAU and ALARD2001, Nuutinen et al. Reference NUUTINEN, PITKÄNEN, KUUSELA, WIDBOM and LOHILAHTI1998, Rossi Reference ROSSI2003, Rossi & Lavelle Reference ROSSI and LAVELLE1998). The determinants of these patterns are hardly identified as they probably imply both environmental and population or community factors operating and interacting at different scales (Barot et al. Reference BAROT, ROSSI and LAVELLE2007). For instance, species-assemblage patchiness may result from species responses to the heterogeneity in plant cover and soil properties (Margerie et al. Reference MARGERIE, DECAËNS, BUREAU and ALARD2001, Phillipson et al. Reference PHILLIPSON, ABEL, STEEL and WOODELL1976, Poier & Richter Reference POIER and RICHTER1992), intrinsic population processes such as reproduction rates and limited dispersal (Barot et al. Reference BAROT, ROSSI and LAVELLE2007, Jiménez et al. Reference JIMÉNEZ, ROSSI and LAVELLE2001, Rossi et al. Reference ROSSI, LAVELLE and ALBRECHT1997, Whalen & Costa Reference WHALEN and COSTA2003), or interspecific competition leading to spatial segregation between species pairs with high niche overlap (Jiménez & Rossi Reference JIMÉNEZ and ROSSI2006, Jiménez et al. Reference JIMÉNEZ, DECAËNS and ROSSI2006a).
The implication of interspecific interactions, in particular competition, in shaping the structure of natural communities has been reported for many animals and plants (Connell Reference CONNELL1983, Diamond Reference DIAMOND, Cody and Diamond1975, Goldberg & Barton Reference GOLDBERG and BARTON1992, Gotelli & McCabe Reference GOTELLI and McCABE2002, Schoener Reference SCHOENER1974, Wilson & Habiba Reference WILSON and HABIBA1995). According to the theoretical framework of interspecific competition, two basic predictions may be formulated (Gotelli & Ellison Reference GOTELLI and ELLISON2002): first, among a set of communities or species assemblages, species should co-occur less often than expected by chance (EBC) (Diamond Reference DIAMOND, Cody and Diamond1975, Pielou & Pielou Reference PIELOU and PIELOU1968); second, within a community or species assemblage, co-existing species should present a lower niche overlap than EBC (Schoener Reference SCHOENER1974). Classic examples of the latter include limitation of similarity in body size or in multi-trait morphology (Hutchinson Reference HUTCHINSON1959, MacArthur & Levins Reference MACARTHUR and LEVINS1967, Weiher & Keddy Reference WEIHER and KEDDY1995, Weiher et al. Reference WEIHER, CLARKE and KEDDY1998). Non-randomness in niche overlap and co-occurrence patterns is thus considered to reflect competition constraints on community assembly. Recently, null model analysis has emerged as an efficient tool to identify non-random community patterns (Gotelli Reference GOTELLI2001, Gotelli & Graves Reference GOTELLI and GRAVES1996). They are pattern-generating models that deliberately exclude a mechanism of interest (for instance competition), and allow testing of observed data against randomized null communities (Gotelli Reference GOTELLI2001, Gotelli & Graves Reference GOTELLI and GRAVES1996). They were successfully used to highlight and interpret, among others, non-random patterns in body-size distribution (Feeley Reference FEELEY2003, Gotelli & Ellison Reference GOTELLI and ELLISON2002) and niche overlap (Albrecht & Gotelli Reference ALBRECHT and GOTELLI2001, Hofer et al. Reference HOFER, BERSIER and BORCARD2004) in different animal assemblages.
In this paper, we re-analysed with null models the data collected in the course of different studies of the spatio-temporal distribution of earthworm assemblages in Colombian tropical grasslands (Decaëns Reference DECAËNS1999, Decaëns & Rossi Reference DECAËNS and ROSSI2001, Jiménez Reference JIMÉNEZ1999, Jiménez et al. Reference JIMÉNEZ, DECAËNS and ROSSI2006a). All these studies described a consistent horizontal patterning in alternated patches dominated by particular species assemblages. We hypothesized that these patches result from predictable assembly rules related to interspecific competition, i.e. are a consequence of spatial exclusion among competing species. If so, segregation should be most evident, based on the degree of niche overlap, at local scales (‘patch-level assemblages’, i.e. the list of dominant species characterizing a given patch), and less so at larger scales (‘plot-level assemblages’, i.e. the list of species present in a given grassland plot). We thus expected to observe two types of non-random patterns: (1) within-patch niche overlap should be lower than EBC and lower than plot-scale overlap (MacArthur & Levins Reference MACARTHUR and LEVINS1967, Weiher & Keddy Reference WEIHER and KEDDY1995); (2) morphometric distance (size ratio) between species co-existing in a given patch should be higher and more constant than EBC, and higher and more constant than at the plot level (Brown & Wilson Reference BROWN and WILSON1956, Dayan & Simberloff Reference DAYAN and SIMBERLOFF2005, Gotelli & Ellison Reference GOTELLI and ELLISON2002, Hutchinson Reference HUTCHINSON1959). We tested this hypothesis for different dimensions of the niche (seasonal activity, vertical distribution and multi-trait morphology) and by separately analysing different biometric traits.
An alternate hypothesis is that patchiness reflects environmental heterogeneity and that patch-level assemblages are composed of species sharing the adapted traits to the patch environment. In this case, dominating species of a given patch should present a higher niche overlap than EBC and than at the plot-scale (Keddy Reference KEDDY1992, Weiher & Keddy Reference WEIHER and KEDDY1995). Morphometric distance within a given patch should also be lower and less constant than EBC and lower and less constant than for plot-level assemblages.
STUDY SITE
A data set was compiled from two studies carried out at the CIAT-CORPOICA Carimagua Research Station, in the phytogeographic unit of the well-drained isohyperthermic savannas of eastern Colombia (4°37′N, 71°19′W, 175 m asl). Climate is subhumid tropical with a mean annual rainfall and temperature of 2280 mm and 26 °C, respectively (1972–1995, CIAT data). Study plots were located in an upland area with a well-drained silty clay Oxisol (Tropeptic Haplustox Isohyperthermic; USDA classification), characterized by its acidity (pH[H2O] = 4.5), a high Al saturation (>80%) and low values of exchangeable cations. All the study plots were located in the same area of the Research Station, with no more than 100 m between each other.
Sampling was carried out in three savanna plots and three sown pastures. Savanna plots (Savanna 1 to 3) were all devoid of any management, and had areas of 0.36 (Savanna 2 and 3) and 2.26 ha (Savanna 1). Vegetation was dominated by the Poaceae Andropogon bicornis L., Gymnopogon foliosus (Wild.) Nees, Panicum sp., Trachypogon sp. and Imperata brasiliensis Trin. Pasture 1 was a 1 ha and 18-y-old plot of Urochloa decumbens (Stapf) R.D. Webster (Poaceae) and Pueraria phaseoloides Benth. (Fabaceae), grazed by cattle at an average stocking rate of 1.75 Animal Unit (AU) ha−1 (1 AU = 250 kg). Pasture 2 was a 0.72 ha and 3-y-old plot of Urochloa humidicola (Rendle) Morrone & Zuloaga (Poaceae), Arachis pintoi Krap. & Greg (Fabaceae), Stylosanthes capitata Vog. (Fabaceae) and Centrosema acutifolium Benth. ‘Vichada’ (Fabaceae), grazed by cattle at an average stocking rate of 2 AU ha−1. Pasture 3 was a 0.72 ha and 1-y-old plot of Panicum maximum and A. pintoi, managed similarly to pasture 2.
METHODS
Earthworm sampling
In each plot, samples were taken on a regular grid of evenly spaced points. The dimension of the grids varied depending on plot size: 8 × 8 sampling points each 10 m in Pasture 1 and Savanna 1; 8 × 15 points each 5 m in Pastures 2 and 3; 4 × 15 points each 5 m in Savanna 2 and 3. Each plot was surveyed at different successive dates: November 1993, 1994 and May 1995 for Savanna 1; September 1993, October 1994 and June 1995 for Pasture 1; and every 2 mo from October 1995 to August 1997, with exception of December 1995 and July 1997, in the other plots. Thus, the total study period for each plot ranged from 21 to 22 mo.
At each point, a soil monolith of 40 × 40 cm (Savanna 1 and Pasture 1) or 25 × 25 cm (other plots) was dug out down to 30-cm depth and hand sorted in the field. Collected earthworms were identified, counted and replaced in the monolith point with the sorted soil. Prior to the monolith extraction, the density of the large species Martiodrilus sp. was estimated by counting its fresh casts at the surface of a 1-m2 square that was centred on the monolith (Jiménez et al. Reference JIMÉNEZ, MORENO, LAVELLE and DECAËNS1998a). Soil monoliths at subsequent dates were taken in points separated about 30–50 cm from the sample of the first date. This displacement in space was considered negligible at the scale of the plot, and sampling coordinates were taken as identical from one date to another.
As the characteristics of samples varied significantly among plots, we used non-parametric regression (using Ecosim software, Acquired Intelligence Inc. & Kesey-Bear, http://garyentsminger.com/ecosim.htm) to verify that differences in observed patterns were not a by-product of different sampling procedures. This procedure was run to test the effect of sampling grid size, distance between sampling points, sample sizes and sampling frequency (dependent variables) on patch spatial range (independent variable). Non-parametric regression fits a standard linear regression to the data set, and then uses randomization to test the null hypothesis that the slope, intercept or correlation coefficient equals 0. In all cases, slope, intercept and correlation coefficient were as EBC (r2 = 0.00; P = 0.457 for grid size, r2 = 0.58; P = 0.129 for distance effects, r2 = 0.58; P = 0.140 for sample size, r2 = 0.58; P = 0.147 for sampling frequency). The different sampling designs were thus assumed to address processes at similar spatial scales.
For niche overlap calculations, we used the data sets obtained by Jiménez (Reference JIMÉNEZ1999) from a stratified random sampling performed from April 1994 to September 1995 in the Savanna 1 and Pasture 1. In each plot, five monthly 1-m2 monoliths were dug out down to 50 cm and hand sorted in 10-cm increment layers. Two 20 × 20 × 20-cm soil cores were sampled 1 m distance from the monolith; the soil was then washed and sieved to collect small species that were not efficiently collected by hand sorting (Jiménez et al. Reference JIMÉNEZ, LAVELLE and DECAËNS2006b). Earthworms were fixed and stored in 4% formaldehyde, identified and counted in the laboratory to calculate mean population density for each sampling month and in each soil layer. Body length (mm), weight (g) and preclitellar diameter (mm) were measured on fixed specimens for all specimens that were complete. Voucher specimens of all species were deposited in the Universidad Tecnologica de Pereira (Colombia). For both the grassland and the savanna, we obtained three matrices describing species according to their temporal dynamics over a complete seasonal cycle (July 1994–June 1995), vertical distribution and biometric traits.
Partial triadic analyses and identification of patch-level assemblages
The partial triadic analysis (PTA) is used to analyse a chronological series of tables that describes the same objects with the same variables (Kroonenberg Reference KROONENBERG1989, Rossi Reference ROSSI2003, Thioulouse & Chessel Reference THIOULOUSE and CHESSEL1987). It allows extraction of the multivariate structure that is expressed through the different dates, and describes dominant patterns in its first axes while relegating the random noise to further axes that are not retained for interpretation (Rossi Reference ROSSI2003). For each plot, we used t matrices (t = number of sampling dates), each one describing n observations (sampling points) for p variables (species abundances). Each PTA consisted of two successive steps: (1) The interstructure analysis provided a global description of the sampling points as a function of the typology of the sampling dates. For each species and in each plot, spatial patterns that were stable over the study period were described by mapping the coordinates of the sampling points on the first interstructure axis on the sample grid. (2) The compromise analysis provided a description of sampling points as a function of the species typology. It was used for each plot to identify the species assemblages that characterized similar patches at different dates, to which we refer herein as the ‘patch-level assemblages’. On the first compromise axis, a patch-level assemblage was defined as a group of species displaying coordinates of the same sign. The maps of the coordinates of the sampling points on the first compromise axis thus described the spatio-temporal distribution of these patch-level assemblages.
All the computations and figures were processed with the module STATIS and other graphical modules of the software ADE-4 (Thioulouse et al. Reference THIOULOUSE, CHESSEL, DOLÉDEC and OLIVIER1997).
Moran's autocorrelogram
For each PTA, we tested the presence of spatial autocorrelation in species assemblages using Moran's correlograms (Legendre & Fortin Reference LEGENDRE and FORTIN1989, Sokal & Oden Reference SOKAL and ODEN1978) computed with the sample scores on the first compromise axis (Decaëns & Rossi Reference DECAËNS and ROSSI2001). The correlogram shows the changes of autocorrelation coefficients with increasing distance. It thus indicates the spatial range of the observed spatial patterns and provides a test of the significance for non-randomness (Sokal & Oden Reference SOKAL and ODEN1978). Data were allocated to nine (Pasture 1 and Savanna 1), 12 (Savannas 2 and 3) or 14 (Pasture 2 and 3) distance classes depending on the size of the analysed matrix. Moran's index was calculated using the ‘Autocorrélation 3.03’ module of the ‘R Package’ (Université de Montréal, Canada), and the normality of the data distribution was tested with a Kolmogorov–Smirnov test before computation with the ‘VerNorm 3.0’ module of the same software. When necessary, the Box-Cox transformation was used to reduce the asymmetry of the frequency distribution (Sokal & Rohlf Reference SOKAL and ROHLF1995).
Temporal and vertical niche overlap analysis
Niche overlap analysis was undertaken for the six plot-level assemblages and the twelve patch-level assemblages identified by the compromise analyses. For each of them, we built an individual matrix in which rows and columns represented species and niche categories, respectively, and we tested if niche overlap significantly differed from the corresponding value under the null hypothesis (i.e. random assemblage). We used Pianka's index (Pianka Reference PIANKA1973) and the Czechanowski index (Feinsinger et al. Reference FEINSINGER, SPEARS and POOLE1981). For species j and k, with resource utilizations pji and pki, Pianka's overlap index of species j on species k (Ojk) is given by the following formula:

For species j and k, with resource utilizations pji and pki, Czechanowski overlap index (Ojk) is:
The level of niche breadth was calculated with both indices for three distinct dimensions of resource utilization. (1) Although temporal partitioning may be relatively uncommon in animal communities (Schoener Reference SCHOENER1974), several examples involving invertebrates have been described to date (Gotelli & Graves Reference GOTELLI and GRAVES1996). We considered that time was of potential importance for earthworm assemblages because the high seasonal fluctuations of important resources, such as water and litter, may cause diet shifts according to the time of the year. For this analysis, we used the seasonal dynamics data. Each individual matrix was a table where rows and columns represented species and months respectively. Table entries were the average number of individuals collected for each species at a given month. (2) Niche partitioning according to species vertical distribution is a common feature in soil animal communities (Lavelle & Spain Reference LAVELLE and SPAIN2001, Wardle Reference WARDLE2002). When foraging at different depths, earthworm species may reduce competition by feeding on different types of organic resources (Bouché Reference BOUCHÉ, Lohm and Persson1977). Vertical niche partitioning among Carimagua's earthworms has been suggested by Jiménez & Decaëns (Reference JIMÉNEZ and DECAËNS2000), who found that the average living depth differed substantially among species. To quantify and test vertical niche overlap, we used individual matrices in which rows and columns represented species and soil strata, respectively, and where entries consisted of the mean number of individuals collected in each stratum over the total study period. As most species were not represented below 40 cm, we performed the analysis with the data of the first three 10-cm layers, and bulked the deeper layers into a single ‘<30 cm’ category. (3) In ecological communities, ecologically similar species that are also morphologically alike might not co-exist because of excessive overlap in their resource uses (Hutchinson Reference HUTCHINSON1959). Consequently, biometric traits have been widely used to quantify the influence of competition on community assembly (Dayan & Simberloff Reference DAYAN and SIMBERLOFF2005). Biometric niche overlap was calculated for individual matrices where rows and columns represented species and biometric traits, respectively, and where the entries consisted of the mean trait values measured for the collected individuals. Here, we used three traits (body length, weight and preclitellar diameter) that describe earthworm external morphology in a reliable way (Jiménez Reference JIMÉNEZ1999). To avoid any influence of the measurement units in the index calculation, data were previously standardized by dividing each value by the standard deviation of the corresponding column in the matrix.
Mean niche overlap was calculated for each patch- and plot-level assemblage and compared with a null model in which the observed data were randomized among species (10 000 iterations). If competitively structured, a given assemblage should present less niche overlap than EBC for the dimensions of the niche that are subject to competition. We used a randomization algorithm that retains the niche breadth of each species, but randomizes which particular resource states are utilized (RA3 in Albrecht & Gotelli Reference ALBRECHT and GOTELLI2001). It corresponds to a simple reshuffling of each row of the matrix that assumes all the different resource states to be equally abundant (or usable) by all species. Calculations and tests were done with the ‘Niche Overlap’ module of Ecosim.
Size distribution analysis
We tested if identified assemblages presented patterns that limit biometric similarity between co-existing species for the three morphometric traits that were used in the niche overlap analysis. For each trait, we calculated: (1) the minimum segment length (MSL), which is the smallest size difference found in all available pairs of species; (2) the variance in segment length (VarSL) that measures the overall tendency for the trait values to be evenly spaced. Both metrics were successively computed after log-transforming the data, which allowed analysing the size ratio of the considered trait (Gotelli & Ellison Reference GOTELLI and ELLISON2002). Observed values were calculated for all assemblages that comprised more than two species, and were compared with those obtained for 10 000 random assemblages. In a competitively structured community or assemblage, MSL and VarSL should be higher and lower than EBC, respectively (Gotelli & Ellison Reference GOTELLI and ELLISON2002). We used a null model algorithm which takes the largest and smallest species in the assemblage to set the minimum and maximum boundaries for the simulation. The remaining (n – 2) species were chosen from a random, uniform distribution within these limits. This null model assumes that in evolutionary time, any possible configuration of body sizes is equiprobable within the limits imposed by the largest and smallest species (Gotelli & Ellison Reference GOTELLI and ELLISON2002). Calculations and tests were done with the ‘Size Overlap’ module of Ecosim.
Data comparisons
For each index (Pianka's and Czechanowski Oik, MSL, VarSL), we calculated the standardised effect size (SES):
where Isim is the mean index of the simulated assemblages, Ssim is the standard deviation, and Iobs is the observed index (Gotelli & Graves Reference GOTELLI and GRAVES1996). For each type of assemblage (patch-level or plot-level) and each index, we further calculated the average values of the observed and simulated indices, and the average corresponding SES.
We used a permutation test to compare: (1) the average values of the observed indices with those of simulated assemblages; (2) the average observed values obtained in patch-level assemblages with those obtained for plot-level assemblages. A similar approach was used to test whether average SES values obtained for a given set of assemblages did differ from zero or not. Each test involved 10 000 iterations in which the data were reshuffled among the categories to determine how much variation was expected among the means. The null hypothesis was that the observed variation among the means of the groups was no greater than EBC. Calculations were performed using the ‘Anova’ module of Ecosim.
RESULTS
Earthworm assemblage composition
A total of six species, all still undescribed and all native from the study region, was identified in the six sampled plots (Jiménez Reference JIMÉNEZ1999). Apart from Andiorrhinus sp., which occurred only in Pasture 1 and Savanna 1, all species were present in all the plots (Tables 1 and 2). Mean total earthworm density and biomass respectively ranged from 16–25 ind. m−2 and 1.7–4.2 g fw m−2 in the savannas, and 45–97 ind. m−2 and 5.5–62.1 g fw m−2 in the pastures. Detailed studies of species assemblage composition in the different study plots have been published previously in Decaëns & Jiménez (Reference DECAËNS and JIMÉNEZ2002) and Jiménez et al. (Reference JIMÉNEZ, MORENO, DECAËNS, LAVELLE, FISHER and THOMAS1998b). The highest densities were recorded for Glossodrilus sp. and, in the pastures, Ocnerodrilidae sp. Depending on the plot, the highest contributions to biomass were recorded for Glossodrilus sp., Andiodrilus sp. or Martiodrilus sp., the latter being dominant in the three pastures.
Main features of the spatio-temporal distribution of earthworm communities in the six study plots as described by the partial triadic analyses. CPI1 = first axis of the interstructure analysis; CPC1 = first axis of the compromise analysis; Moran's P = significance level of the spatial patterns.

Composition of the species assemblages in the six study plots. For a given plot, species with the same letters belong to the same patch-level assemblage as identified by the first component of the compromise analysis (a = species with positive scores; b = species with negative scores). Species codes: And = Andiodrilus sp.; Anr = Andiorrhinus sp.; Aym = Aymara sp.; Glo = Glossodrilus sp.; Mar = Martiodrilus sp.; Ocn = Ocnerodrilidae.

Earthworm assemblage spatial patterns
The percentages of the total inertia explained by the first axes of the PTA's interstructure and compromise analyses are presented in Table 1. Values were always lower than 50%, indicating relatively little inertia in the data. Interstructure analyses described the patterns of population distribution that were stable across time. Most species were significantly aggregated, but high-density patches had sharper boundaries for endogeic species (e.g. Glossodrilus sp., Andiodrilus sp.), and were more diffuse for surface-dwelling species (Aymara sp. and Martiodrilus sp.) (Figure 1). Compromise analyses described the species assemblage patterns that were stable across time, and highlighted clusters of species that shared similar spatio-temporal distributions (similar relative position on the first axis) (Figure 2, Table 2). According to Moran's autocorrelograms, sample scores on the first compromise axis were significantly aggregated in space over ranges of 6 to 33 m (Table 1). In each sampled plot, earthworm assemblages thus presented non-random and statistically significant spatio-temporal structure consisting in a juxtaposition of patches characterized by dominant ‘patch-level assemblages’. As an example, the compromise analysis of Pasture 1 distinguished (P < 0.001, Table 2) a cluster composed of Martiodrilus sp., Andiodrilus sp. and Aymara sp. from another with Glossodrilus sp., Andiorrhinus sp. and Ocnerodrilidae sp. (Figure 2). The six PTAs thus identified 12 patch-level assemblages (Table 2) differentiated within the six plot-level assemblages (i.e. the complete species list occurring in a given plot).
Interstructure analysis of the species assemblage structure in pasture 1: ordination of sampling dates on the plan defined by the first two axes of the PCA on the interstructure matrix (a); maps of the factorial coordinates of the 64 sampling points on the first axis of the interstructure analysis for each of the six species identified in the pasture (b) (circles and squares represent positive and negative scores and the size is proportional to the corresponding value). Modified from Figure 1 in Jiménez et al. (Reference JIMÉNEZ, LAVELLE and DECAËNS2006) Acta Oecologica 30: 299–311. Copyright © by Elsevier. Reprinted with permission of the publisher.

Compromise analysis of the species assemblage structure in pasture 1: correlation circle showing the ordination of the variables (species) on the factorial plan defined by the first two axes of the PCA on the compromise matrix (a); maps of the factorial coordinates of the 64 sampling points on the first axis of the PCA on the compromise matrix (b) (circles and squares represent positive and negative scores respectively and the size is proportional to the corresponding value). Modified from Figure 2 in Jiménez et al. (Reference JIMÉNEZ, LAVELLE and DECAËNS2006) Acta Oecologica 30: 299–311. Copyright © by Elsevier. Reprinted with permission of the publisher.

Niche overlap patterns
Both the Pianka and Czechanowski indices provided very similar results and we thus decided to present only those obtained with the former. Temporal niche overlap was significantly higher than EBC for the majority of patch- and plot-level assemblages (Table 3) and average observed overlaps were unusually high (P = 0.050 and P = 0.002, respectively). Average SES was significantly higher than 0 at both scales, but was significantly lower in patch- as compared with plot-level assemblages (Table 3).
Results of the niche overlap analysis. For each niche axis, we analysed niche overlap patterns for both patch-level assemblages (species with same signs on the first compromise axis, but see Table 2) and plot-assemblages (species present in a given plot). ‘Lower tail’ and ‘Upper tail’ indicate the number of assemblages for which the observed Pianka Oik was respectively less than or greater than predicted by the null model. The number in parentheses indicates the number of assemblages with significant patterns (P < 0.05, one-tailed test). Different letters indicate significant differences between observed and EBC averages (P < 0.05, one-way ANOVA). The P values indicate the probability of accepting the null hypothesis that the standardized effect size (SES) differed from zero, and the P* values the probability of having no significant difference between SES calculated for patch-level and plot-assemblages (one-way ANOVA).

At both patch- and plot-levels, vertical niche overlap was almost always significantly higher than EBC, average observed Pianka's Ojk was higher than mean simulated value (P = 0.018 and P = 0.001, respectively), and the average SES was significantly higher than 0 (Table 3). Average SES was not significantly different between patch- and plot-level assemblages.
Biometric niche overlap was lower than EBC in a majority of patch assemblages, but the observed and EBC values were not significantly different, and the SES was not significantly lower than 0 (Table 3). Patterns were mainly random for plot-level assemblages and no significant difference was found when comparing average SES calculated for patch- and plot-level assemblages.
Size distribution patterns
Patch-level assemblages showed a consistent trend toward over and even spacing of body length (Table 4). MSL was higher than EBC in six of seven cases (with significant individual tests in two of them), average MSL tended to be higher than EBC (P = 0.026) and had a SES significantly higher than 0. Conversely, plot-level assemblages were characterized by random body length ratio patterns and, when compared with patch-level assemblages, lower average value of the SES calculated for MSL. The VarSL was lower than EBC in the majority of patch and plot assemblages (with two individually significant values for patch-level assemblages), showed an unusually small average (P = 0.011 for both patch- and plot-level assemblages), and a SES significantly lower than 0.
Results of body-size structure analysis. For each biometric trait, we analysed minimum segment length (MSL) and its variance (VarSL) for both patch-level assemblages and plot-assemblages. ‘Lower tail’ and ‘Upper tail’ indicate the number of assemblages for which the observed metric was respectively less than or greater than predicted by the null model. The number in parentheses indicates the number of assemblages with significant patterns (P < 0.05, one-tailed test). Different letters indicate significant differences between observed and expected by chance (EBC) averages (P < 0.05, one-way ANOVA). The P values indicate the probability of accepting the null hypothesis that the standardized effect size (SES) differed from zero, and the P* value the probability of having no significant difference between SES calculated for patch- and plot-assemblages (P < 0.05, one-way ANOVA).

Body weight tended to be over spaced in both patch- and plot-level assemblages (Table 4): although average observed values were not significantly higher than simulated ones, the corresponding SESs were significantly higher than 0. Average VarSL was also less than EBC (P = 0.001 and P = 0.009 for the patch- and plot-levels, respectively), with a SES lower than 0. These patterns should however be viewed with caution, as they were weakly supported by individual matrix analyses which on the whole did not differ from the null model (no significant individual test found for VarSL, and only a single instance found for MSL in Savanna 1). Differences among SES calculated at the patch and at the plot scales were not significant.
Size analysis of body diameter provided results similar with the analysis of body length (Table 4). In patch-level assemblages MSL was higher than EBC in six of seven cases (with significant individual tests in one of them), average MSL was significantly higher than EBC (P = 0.050) and SES was significantly higher than 0. An opposite trend was found in plot-level assemblages, where mean MSL was lower than EBC (P = 0.025), with an average SES significantly lower than 0 and lower than the SES calculated for patch-level assemblages. Although only a single significant individual value was detected, the VarSL was lower than EBC in nearly all of the patch and plot assemblages. For plot-level assemblages, the mean VarSL was significantly lower than expected by chance (P = 0.001), and the corresponding average SES was lower than 0. A similar, although not significant, pattern was found for patch-level assemblages.
DISCUSSION
The spatial organization of earthworm assemblages in alternating patches characterized by specific species assemblages has been found in both tropical and temperate soils (Margerie et al. Reference MARGERIE, DECAËNS, BUREAU and ALARD2001, Nuutinen et al. Reference NUUTINEN, PITKÄNEN, KUUSELA, WIDBOM and LOHILAHTI1998, Poier & Richter Reference POIER and RICHTER1992, Rossi Reference ROSSI2003). Except for savanna 1, the spatial extent of the patches found in our study (6–22 m) was in the lower range of what is reported in other studies (20–50 m) (Margerie et al. Reference MARGERIE, DECAËNS, BUREAU and ALARD2001, Rossi Reference ROSSI2003). This may be because assemblages were dominated by small and weakly mobile species (Glossodrilus sp., Ocnerodrilidae sp. and Andiodrilus sp.) that aggregate at small spatial ranges (Decaëns & Rossi Reference DECAËNS and ROSSI2001, Jiménez et al. Reference JIMÉNEZ, ROSSI and LAVELLE2001, Reference JIMÉNEZ, DECAËNS and ROSSI2006a). The spatial range of patches is thus likely to be context dependent, and aggregation at larger scales is often observed in assemblages with a higher contribution of large and more vagile species, such as in European grasslands (Margerie et al. Reference MARGERIE, DECAËNS, BUREAU and ALARD2001) or African savannas (Rossi Reference ROSSI2003).
The structured proportion of the spatio-temporal variability in earthworm assemblages remained low as indicated by the percentage of inertia associated with the first axes of both the interstructure and compromise analyses. This indicates a high residual variability from the analysis, which may result from different sources including species vagility (Decaëns & Rossi Reference DECAËNS and ROSSI2001), sampling error (Jiménez et al. Reference JIMÉNEZ, LAVELLE and DECAËNS2006b) and/or small-scale variability (below the minimum inter-sample distance) in species distribution (Rossi & Nuutinen Reference ROSSI and NUUTINEN2004). All these factors are likely to differ substantially among species, and thus to increase the residual noise in the data matrices. However, despite this residual variability, we observed non-random and statistically significant patterns in the six studied plots. This consistency suggests that the spatio-temporal arrangements of species assemblages are generated by deterministic assembly rules rather than by random events.
The reason why patch-level assemblages differed so much in composition among plots of the same habitat type is an interesting question that will require additional information to be elucidated. Differences between species assemblages of apparently similar habitats might be due to slight environmental differences that may confer a slight selective advantage to colonists of particular species (Diamond Reference DIAMOND, Cody and Diamond1975). In our case, however, the detailed study of the sampled plots provided no evidence that this mechanism may account for the observed differences in assemblage composition (Decaëns & Rossi Reference DECAËNS and ROSSI2001, Jiménez et al. Reference JIMÉNEZ, ROSSI and LAVELLE2001, Reference JIMÉNEZ, DECAËNS and ROSSI2006a). Alternatively, chance in the form of random historical events (e.g. chronological order in colonization events) might play a large role in building up non-identical assemblages that represent stable equilibria (Diamond Reference DIAMOND, Cody and Diamond1975). Any given patch-assemblage would thus represent one of many possible, alternative, stable assemblages that could be constructed on paper from the same species pool.
Despite the widely accepted idea that earthworm species show a high degree of niche partitioning with regards to vertical distribution (Bouché Reference BOUCHÉ, Lohm and Persson1977, Lavelle & Spain Reference LAVELLE and SPAIN2001), we reported a niche overlap according to this dimension higher than EBC. This is an unexpected result, as the local pool comprises species of different ecological guilds that are supposed to differ substantially in their yearly average vertical distribution. Similarly, we found a higher seasonal niche overlap than EBC, in accordance with the review of Schoener (Reference SCHOENER1974) who concluded that animals often segregate along food and habitat dimensions but rarely along temporal niche axes. These results suggest strong constraints on membership in assemblages (Weiher & Keddy Reference WEIHER and KEDDY1995). Ecological theory predicts that environmental conditions acting as strong habitat filters may induce an underdispersion of the traits associated with these pressures (Keddy Reference KEDDY1992, Keddy & Weiher Reference KEDDY, WEIHER, Weiher and Keddy1999, Weiher & Keddy Reference WEIHER and KEDDY1995). The low levels of organic matter, its concentration in the superficial soil layers and the high seasonality of rainfall may for example select earthworm species that display dormancy during the dry season, concentrate their activities during the rainy period and/or locate their foraging activities in the first 20 cm of the soil profile (Jiménez & Decaëns Reference JIMÉNEZ and DECAËNS2000, Jiménez et al. Reference JIMÉNEZ, BROWN, DECAËNS, FEIJOO and LAVELLE2000). Alternatively, niche overlap SES were on average significantly lower in patches than in plot-assemblages, which suggests that competition is reduced in patches by limiting ecological similarity between species that co-exist at this scale.
The idea that co-existing species should differ in morphology in order to reduce resource use overlap is supported by a great amount of empirical evidence (Dayan & Simberloff Reference DAYAN and SIMBERLOFF2005, Weiher & Keddy Reference WEIHER and KEDDY1995). For instance, patterns of limiting similarity, such as ecological and community-wide character displacements, have been reported for many groups of vertebrates but more rarely for invertebrates (see review by Dayan & Simberloff Reference DAYAN and SIMBERLOFF2005). Regular spacing of body size and morphometric overdispersion was however reported in assemblages of molluscs (Barker & Mayhill Reference BARKER and MAYHILL1999, Chiba Reference CHIBA2004, Grudemo & Johannesson Reference GRUDEMO and JOHANNESSON1999), crustaceans (Marchinko et al. Reference MARCHINKO, NISHIZAKI and BURNS2004), beetles (Brandl & Topp Reference BRANDL and TOPP1985, Satoh et al. Reference SATOH, UEDA, ENOKIDO and HORI2003, Sota et al. Reference SOTA, TAKAMI, KUBOTA, UJIIE and ISHIKAWA2000), and ants (Gotelli & Ellison Reference GOTELLI and ELLISON2002, Nipperess & Beattie Reference NIPPERESS and BEATTIE2004). The only case study dealing with earthworms, an example of ecological character displacement in sympatry between congeneric species in Mexico (Fragoso & Rojas Reference FRAGOSO and ROJAS1997), suggests that body shape is directly related to resource utilization. The relationship between species biometric features and life history strategies, and in particular resource uses, is also central in most eco-morphological classifications that are classically recognized in earthworm studies (Bouché Reference BOUCHÉ, Lohm and Persson1977, Lavelle Reference LAVELLE1997). Despite the non-significance of the results obtained for biometric niche overlap, our data support this idea by demonstrating that a minimum level of morphometric differentiation in body sizes is necessary to allow species to co-exist in a given patch-level assemblage.
Competition may however generate different patterns according to the spatial scale considered. We found that body weight was significantly overdispersed and constant among species at both the plot and patch scales, while body length shows a similar pattern at the patch scale only. This suggests that both attributes may be directly related to different features of species feeding habits. Body weight is, for example, known to reflect the quality of the resource ingested by geophagous species (Lavelle Reference LAVELLE1981): small species are often specialized for organic-rich substrates (e.g. litter, root exudates, vertebrate faeces, etc.), while larger ones usually ingest a variable proportion of soil with lower organic content. Although litter-feeding species may not fully match this model, most earthworms of Carimagua were described to feed at least partly on soil (Jiménez et al. Reference JIMÉNEZ, MORENO, DECAËNS, LAVELLE, FISHER and THOMAS1998b, Mariani et al. Reference MARIANI, BERNIER, JIMÉNEZ and DECAËNS2001), and different weights among species may thus reflect differences in the organic content of their food substrate. Alternatively, species body length was reported to reflect the size of the ingested soil particles, although no general pathway for this relationship has been pointed to date (Blanchart et al. Reference BLANCHART, LAVELLE, BRAUDEAU, LE BISSONNAIS and VALENTIN1997, Lowe & Butt Reference LOWE and BUTT2003). Differentiation of trophic niches according to both the organic content and particle size of the ingested material among earthworm species has been reported in a number of other studies (Curry & Schmidt Reference CURRY and SCHMIDT2007). Our results thus suggest that species may co-exist in a given plot thanks to a minimum level of niche partitioning with regards to the organic content of their feeding substrate. At a lower scale, assemblage patchiness would result from spatial segregation between species competing for similar particle size classes, and from within-patch complementarity between species of different body size. This last hypothesis was first proposed by Rossi (Reference ROSSI2003) for earthworm assemblages of savanna soils of Côte d'Ivoire, and is supported in our results by some conspicuous trends in pairwise relationships among species. For example, the large-sized Martiodrilus sp. is associated in four of six cases with the small Ocnerodrilidae sp., which feeds upon the large casts produced by the former species (Jiménez et al. Reference JIMÉNEZ, DECAËNS and ROSSI2006a). Conversely, Andiodrilus sp. and Glossodrilus sp., two potentially competing geophagous species with relatively similar biometric features, are segregated in different patches in four cases of six (Table 2). Although these patterns of coexistence/segregation are not strong, it is reasonable to interpret them as being consistent with the overall conclusion that the spatial structure of earthworm assemblages is non-random and mainly reflects competition versus complementarity interactions between species.
Our results broadly demonstrate that competition influences assemblage structure more strongly within patches than within plots, and therefore plays a significant role in the spatial patterning of earthworm assemblages below the plot scale. This supports the conclusions of a recent study that pointed to competition as the main assembly constraint in earthworm assemblages of north-western France (Decaëns et al. Reference DECAËNS, MARGERIE, HEDDE and BUREAU2008). The exact mechanisms involved in earthworm interspecific interactions are however still poorly known. Dalby et al. (Reference DALBY, BAKER and SMITH1998) found that competition among species may result from direct cocoon consumption. Such intra-guild predation has been reported for a number of other animals, e.g. birds (Hakkarainen & Korpimaeki Reference HAKKARAINEN and KORPIMAEKI1996, Spooner et al. Reference SPOONER, PRIBIL and PICMAN1996), fish (Garner Reference GARNER1996), salamanders (Roudebush & Taylor Reference ROUDEBUSH and TAYLOR1987) and scorpions (Polis & McCormick Reference POLIS and MCCORMICK1987). It is assumed to increase the competitiveness of the predating competitor through an enhanced nitrogen intake (Matsumura et al. Reference MATSUMURA, TRAFELET-SMITH, GRATTON, FINKE, FAGAN and DENNO2004). Additionally, earthworms are ecosystem engineers (sensu Jones et al. Reference JONES, LAWTON and SHACHAK1994) able to physically modify their environment, thus altering resource availability for other species. Soil engineering has been reported as a possible mechanism of interspecific competition among earthworm species or between earthworms and other groups of organisms. As an example, deep-burrowing species may deprive surface-dwellers of their habitat and trophic substrate when actively burying litter into the soil (Dalby et al. Reference DALBY, BAKER and SMITH1998, Hendrix et al. Reference HENDRIX, BAKER, CALLAHAM, DAMOFF, FRAGOSO, GONZALEZ, JAMES, LACHNICHT, WINSOME and ZOU2006). Geophagous species may also interact, either positively or negatively, with each other by modifying the size distribution of soil aggregates, and therefore their availability as a readily ingestible substrate for other species (Blanchart et al. Reference BLANCHART, LAVELLE, BRAUDEAU, LE BISSONNAIS and VALENTIN1997, Lowe & Butt Reference LOWE and BUTT2003). As proposed by Hastings et al. (Reference HASTINGS, BYERS, CROOKS, CUDDINGTON, JONES, LAMBRINOS, TALLEY and WILSON2007), more research should be undertaken to improve our comprehension and to quantify the role of earthworm engineering activities relative to other processes such as resource competition and trophic interactions.
In conclusion, our study supports the model of Weiher & Keddy (Reference WEIHER and KEDDY1995) that species traits associated with meeting the challenges of competition adversity (morphometric traits) are overdispersed, while those associated with environmental pressure (vertical and temporal distribution) are underdispersed. The assembly rules that emerge from our results are: (1) at the plot scale, body weights of co-existing earthworm species show a significant trend toward overdispersion and low variance of segment length, seasonal and vertical niche overlap are higher than EBC and species are aggregated in discrete patches; (2) at the scale of these patches, niche overlap is reduced when compared with the plot scale, and body length and diameter of co-existing species are overdispersed and display low variance in segment length.
ACKNOWLEDGEMENTS
We wish to thank all the persons who contributed to some extent in the achievement of this work. We are particularly grateful to the former team of the ‘Unidad Suelos y Nutrición de Plantas’ (CIAT): R. Thomas, E. Amézquita, G. Rippstein, I. Rao, R. Vera and D. K. Friesen for their valuable technical and scientific help, C. G. Meléndez, I. Corrales, J. Galvis, H. Alarcón, N. Betancourt, L. Soto and H. Unda for their participation to field sampling, J. García, G. Murcia, S. Rojas and J. Soto for their help and friendship in the field and the management staff of the Carimagua Research Station (CIAT-CORPOICA). Thanks to S. James (Kansas University) and K. R. Butt (University of Central Lancashire) for their comments and language corrections. Financial support was provided by the DIVERSITAS and the MAS, SWNM programmes.





