DOI: 10.5061/dryad.gmsbcc2t1
title: Michener’s group-size paradox in cooperatively breeding birds

description: According to Michener's Paradox, most altruistic groups in nature
 should be small, and large groups should not exist. This is because per
 capita productivity is thought to decrease as groups get larger, meaning
 that the share of indirect fitness available to each group member
 declines, which favours dispersal. The empirical evidence for a decrease
 in per capita productivity is contradictory, however, and limited to the
 social Hymenoptera. I report that per capita reproductive success
 decreased with increasing group size across 26 cooperatively breeding bird
 species. Small groups comprising two or three individuals were the most
 common (79% of 16,101 groups) and these had the highest per capita
 reproductive success. This close fit between per capita reproductive
 success and the distribution of group sizes in nature suggests that it may
 indeed be difficult for large groups to evolve through indirect fitness
 benefits alone.
description: # Michener's group-size paradox in cooperatively breeding birds
 Author: Philip A. Downing Contact:
 [philip.downing@oulu.fi](mailto:philip.downing@oulu.fi) Number of
 supplementary items: seven 1\. MP_R_Code.R 2\. MP_Table_S1.csv 3\.
 MP_Table_S2.csv 4\. MP_Table_S3.csv 5\. MP_Data_Extraction.txt 6\.
 Cooperative_bird_literature.pdf 7\. MP_Supp_Methods_Figures.pdf ### File
 name: MP\_R\_Code.R This R script contains all the code needed to
 replicate the analyses (including packages and functions). Models cited in
 the manuscript are located in this code. The lettering in the code matches
 the lettering used in the methods section of the manuscript. \- Data
 manipulation (lines 25 to 100) \- Part A. Per capita and total
 reproductive success across group sizes (lines 106 to 256) \- Part B. Per
 capita and total reproductive success and the frequency of group sizes
 (lines 262 to 434) \- Part C. Study effort (lines 440 to 627) Note that
 the code includes two-stage models fit using restricted maximum likelihood
 in the metafor R package to investigate the sensitivity of the results to
 Bayesian methods (results reported in Table S3). See Viechtbauer, W.
 (2010)
 [https://www.metafor-project.org/doku.php/tips:two_stage_analysis](https://www.metafor-project.org/doku.php/tips:two_stage_analysis) ### File name: MP\_Table\_S1.csv This CSV document contains: \+ reproductive success estimates (annual number of fledglings) in different sizes groups for 26 species \+ the data are organised in a long format (137 rows) \+ read into R (some of the column headings will need changing to match the R code) \+ column descriptions: A. common name = English name of each species B. Latin binomial = scientific name of each species (matches the Jetz et al. nomenclature) C. measure = the metric used to measure annual reproductive success in each study D. mean = estimate of mean reproductive success E. standard_dev = standard deviation of the mean reproductive success estimate F. variance = variance of the mean reproductive success estimate G. N = sample size used to estimate mean reproductive success H. group_size = the group size pertaining to each mean reproductive success and % of groups estimate I. source = where the mean reproductive success estimates were extracted from in the study J. reference = study from which the mean reproductive success estimates were extracted K. % of groups = the frequency of each group size in nature L. N = sample size used to estimate % of groups M. source = where the % of group estimates were extracted from in the study N. reference = study from which % of groups estimates were extracted ### File name: MP\_Table\_S2.csv This CSV document contains: \+ the frequency of different group sizes in natural populations for 23 species \+ data are absent for three species in Table S1: chestnut-crowned babbler, toucan barbet, Pygmy Nuthatch \+ the data in columns D and E are entered in columns L and K in Table S1, but only for group size with reproductive success estimates \+ the data are organised in a long format (183 rows) \+ read into R (some of the column headings will need changing to match the R code) \+ column descriptions: A. common name = English name of each species B. Latin binomial = scientific name of each species (matches the Jetz et al. nomenclature) C. group_size = the group size pertaining to each % of the group estimate D. N = sample size used to estimate % of groups E. % of groups = the frequency of each group size in nature F. source = where the % of group estimates were extracted from in the study G. reference = study from which % of groups estimates were extracted ### File name: MP\_Table\_S3.csv This CSV document contains: \+ parameter estimates from statistical models (see MP_R_Code.R for further information) \+ 34 rows = output from 8 statistical models \+ includes results from the two-stage models (see MP_Supp_Methods_Figures.pdf) \+ variable names: beta = parameter estimate (slope) from the model lwr CI = lower 95% credible interval from the posterior distribution of the model upr CI = upper 95% credible interval from the posterior distribution of the model ### File name: MP\_Data\_Extraction.txt This plain text document contains details of the figures, tables, and text fragments from which data were obtained, and the calculations used to pool data, organised alphabetically by Latin name. ### File name: Cooperative\_bird\_literature.pdf A database of 879 studies on 182 species of cooperatively breeding birds, organised alphabetically by Latin name. Comprises all known studies (published research, MSc and PhD theses, monographs, and edited volumes) with data on the breeding biology and fitness parameters of cooperative birds. ### File name: MP\_Supp\_Methods\_Figures.pdf This PDF document contains further details on the methods used in the study (prior specification and model convergence, quadratic effects, and study effort) and supplementary figures S1 to S5.