DOI: 10.5061/dryad.bk3j9kdb2
title: Data from: Model selection analysis of temporal variation in benefit for an ant-tended treehopper

description: 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.
description: <strong>File</strong>
 <strong>Description</strong> 
 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