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Data from: Model selection analysis of temporal variation in benefit for an ant-tended treehopper


Morales, Manuel (2021), Data from: Model selection analysis of temporal variation in benefit for an ant-tended treehopper, Dryad, Dataset,


Recent studies of mutualism have emphasized both that the net benefit to participants depends on the ecological context and that the density‐dependent pattern of benefit is key to understanding the population dynamics of mutualism. Indeed, changes in the ecological context are likely to drive changes in both the magnitude of benefit and the density‐dependent pattern of benefit. Despite the close linkage between these two areas of research, however, few studies have addressed the factors underlying variation in the density‐dependent pattern of benefit. Here I use model selection to evaluate how variation in the benefits of a mutualism drives temporal variation in the density‐dependent pattern of net benefit for the ant‐tended treehopper Publilia concava. In the interaction between ants and treehoppers in the genus Publilia, ants collect the sugary excretions of treehoppers as a food resource, and treehoppers benefit both directly (e.g., by feeding facilitation) and indirectly (e.g., by predator protection). Results presented here show that temporal changes in the relative magnitude of direct and indirect benefit components of ant tending, especially the effectiveness of predator protection by ants, qualitatively change the overall pattern of density‐dependent benefit between years with maximum benefit shifting from treehoppers in small to large aggregations. These results emphasize the need for empirical studies that evaluate the long‐term dynamics of mutualism and theoretical studies that consider the population dynamics consequences of variation in the density‐dependent pattern of benefit.

Usage Notes

File Description
data.0304.csv Data in comma separated value format
data.0304.Rdata Data in R binary format
0304.nlme.analysis.R Script to generate 2003-04 results in Table 1
results.0304.nlme.R Script to generate results in Table 1, Figures 1-5, and Appendix A1
0304.nlme.analysis.[1-10].R Scripts called by results.0304.nlme.R that fit the models listed in the file models.csv for 10 different start values
models.csv Comma separated value file that contains the model name and number of parameters

For the underlying data in the data.* files, column labels are as follows:

census - Census interval: early (1 = censuses 1-2) or late (2 = censuses 2-3)

year - 2003 or 2004

census.year - unique combination of year and census

grid - blocking variable

plant - unique plant and year identifier

ant.trt - ant manipulation treatment: 0 = ant exclusion, 1 = control

T0 -  The number of the treehoppers at time t=0 (i.e. either census 1 or census 2)

T1  - The number of treehoppers at time t+1 (i.e. either census 2 or census 3)

ants - average number of ants observed on plant

species - ant species: Note that in Table 2, C.n. corresponds to c, F."f." to ff, F."n." to fl, F."p." to fs, M. to m, "P.i." to p and T.s. to t

p - Dummy variable associated with step function for ant-protection, redundant with ant.trt

dC - Dummy variable associated with census

dY - Dummy variable associated with year

apm - ants divided by T0