Spatial density dependence is associated with a positive relationship between host density and the proportion of parasitized hosts across patches. Therefore, in this study, using a spatially explicit approach, we aimed to quantify spatial density dependence between the bruchid Acanthoscelides schrankiae and its parasitoids occurring on a Mimosa bimucronata plant population. To answer this question we firstly used the Spatial Analysis by Distance Indices (SADIE) approach to investigate patterns of spatial distribution of bruchids and parasitism rates. Secondly, we used an extension of SADIE method (overall spatial association (X)) to compare coincidences of patch and gap cluster indices of host density and parasitism rate at each shared, spatially referenced point. Density dependence was evaluated at different sampling dates in order to understand temporal patterns of spatial density dependence. Fifty branches were selected on plants in the population and fruits were collected at 2-weekly intervals. Six and three collections were carried out on years 2006 and 2007, respectively. Each branch was mapped and positioned in a Cartesian plane with coordinates. After collection, fruits were individualized in small flasks and the number of emergent adult bruchids and parasitoids was recorded. The number of emergent bruchids and parasitoids was ascribed for each mapped branch. 

Results/Conclusions

We verified that spatially structured populations with patch (V^_i) and gap (V^_j) clusters were observed only during the year 2007 (V^_i = 1,629; P = 0,0238; V^_j = –1,560; P = 0,0370). However, we observed density independence, inverse density dependence, and direct density dependence at both years, but such patterns were dependent of the sampling date. At the first samples, when the host presented high densities, inverse density dependence and density independence were predominant (e.g. first sample (2006): X = –0,5922; P < 0,0001; Second sample (2006): X = –0,1851; P < 0,8826; Third sample (2006): X = 0,5412; P < 0,0001). Instead, at low host densities (last samples), direct density dependence was predominant for both years (e.g. Sixth sample (2006): X = 0,4260; P < 0,0018; Third sample (2007): X = 0,5022; P < 0,0009). Therefore, the parasitoids (Pteromalidae, Eulophidae, Braconidae, Encyrtidae, Eupelmidae, Eurytomidae, and Scelionidae) may be very efficient at finding bruchid larvae at low densities, raising the direct density dependence patterns observed. Our results also suggest that the methods used here were efficient to quantify spatial density dependence, showing that density dependence can be much more frequent in natural populations than previous studies suggest.