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Diminishing returns drive altruists to help extended family


Altruism between close relatives can be easily explained. However, paradoxes arise when organisms divert altruism towards more distantly related recipients. In some social insects, workers drift extensively between colonies and help raise less related foreign brood, seemingly reducing inclusive fitness. Since being highlighted by W. D. Hamilton, three hypotheses (bet hedging, indirect reciprocity and diminishing returns to cooperation) have been proposed for this surprising behaviour. Here, using inclusive fitness theory, we show that bet hedging and indirect reciprocity could only drive cooperative drifting under improbable conditions. However, diminishing returns to cooperation create a simple context in which sharing workers is adaptive. Using a longitudinal dataset comprising over a quarter of a million nest cell observations, we quantify cooperative payoffs in the Neotropical wasp Polistes canadensis, for which drifting occurs at high levels. As the worker-to-brood ratio rises in a worker’s home colony, the predicted marginal benefit of a worker for expected colony productivity diminishes. Helping related colonies can allow effort to be focused on related brood that are more in need of care. Finally, we use simulations to show that cooperative drifting evolves under diminishing returns when dispersal is local, allowing altruists to focus their efforts on related recipients. Our results indicate the power of nonlinear fitness effects to shape social organization, and suggest that models of eusocial evolution should be extended to include neglected social interactions within colony networks.

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Fig. 1: Three adaptive hypotheses have been proposed for cooperative drifting.
Fig. 2: Brood development in the Neotropical paper wasp P. canadensis.
Fig. 3: Brood-rearing rates in P. canadensis.
Fig. 4: Evolution of cooperative drifting in a spatially explicit social haplodiploid simulation.

Data availability

The transitions data for P. canadensis are available in the Supplementary Information.

Code availability

The statistical code and individual-based simulation code are available in the Supplementary Information.


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P.K. was funded by a Smithsonian Tropical Research Institute (STRI) Short-Term Fellowship (hosted by W. Wcislo), the National Geographic Society (GEF-NE 145-15) and a European Research Council Grant to A.N.R. (award number 682253). S.S. was funded by the Natural Environmental Research Council (NE/M012913/2). A.D.H. was funded by the Natural Environment Research Council (NE/L011921/1). A.N.R. was funded by a European Research Council Consolidator Grant (award number 682253). Simulations were run on the University of Bristol’s high-performance computing facility, BlueCrystal. B. Wharam and A. C. Chadwick assisted with data entry. We are very grateful for the support of the Panamanian authorities for this project; data were collected in accordance with Panamanian law under a Ministerio del Ambiente research permit (SE/A-46-16) and Ministerio de Economía y Finanzas authorization for field site access (024-2016). We thank the generous support of STRI at Galeta Field Station.

Author information

Authors and Affiliations



P.K., S.S. and A.N.R. planned the field data collection. P.K. and P.B. collected the field data. P.K. and A.D.H. conducted the modelling. P.K., N.J.W. and A.N.R. conducted the statistical analysis. P.K., S.S. and A.N.R. interpreted the results. P.K. drafted the manuscript and all authors contributed to its development.

Corresponding author

Correspondence to P. Kennedy.

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Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Ecology & Evolution thanks Michael Cant, Petri Rautiala and Christina Riehl for their contribution to the peer review of this work. Peer reviewer reports are available.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Diminishing returns can allow the invasion of cooperative drifting.

a, The parameter T captures the level of diminishing returns in the model. b, Candidate equilibrium levels of drifting predicted by Eq. 3 of the main text, for illustrative values: d=0.5, x=0.75, ϕ=1, z=0.25.

Extended Data Fig. 2 Candidate equilibrium drifting levels from a colony with ϕ1=1.

We assume a monomorphic sex ratio \(\bar z\) and level of female helping \(\bar x\) common to all colonies. Diminishing returns become more likely drivers of cooperative drifting as the level of helping rises (top left corner). \(\bar m = 1\), ϕ1=1, d=d=0.5.

Extended Data Fig. 3 Repeat observations (n = 257,867) were made of all brood cells on 91 post-emergence colonies over a 56-day period, recording eight developmental states, empty cells, and death due to parasitism (sarcophagid flies and ichneumonid wasps).

Brood pass through a clear developmental sequence of changing size, colour, and mouthpart complexity, which allows categorisation of larvae into stereotyped morphological categories on their transition from egg to pupa. Image adapted with permission from J. Pickering (

Extended Data Fig. 4 Main effects on the probability of transitions in the Markov model of wasp development.

Transitions corresponding to steps through the Markov model states (represented in Fig. 2b of the main text) are shown along the horizontal axis. For instance, the first transition on the left is 1→3, and the effect is negative (below the dashed line): accordingly, the model fits a negative association (at a between-colony level) between nest emptiness (‘nest state effect’) and the probability that an individual egg (state 1) transitions to larval state 3 in a 5-day interval. Only main effects whose 95% credible intervals do not overlap zero are shown. In the main text, we focus on whether increased worker number and/or worker-to-brood ratio is associated with higher productivity. When considering between-colony variation (‘between-colony worker number effect’ in the figure), worker number increases brood development pace and reduces brood death. Higher worker-to-brood ratios (‘between-colony worker-to-brood ratio effect’ in the figure) increase brood developmental pace.

Extended Data Fig. 5 Posterior mean of the total residual deviance.

Deviance explained is the posterior mean of the total residual deviance of the fitted model as a percentage of the null posterior mean residual deviance (for an intercepts-only model). There are seven models, corresponding to the seven starting states.

Extended Data Fig. 6 Residual deviance against worker number.

Residual deviance contributions by each 5-day colony-observation, plotted against the predictor ‘worker number’ (xworkers).

Extended Data Fig. 7 Residual deviance against worker-to-brood ratio.

Residual deviance contributions by each 5-day colony-observation, plotted against the predictor ‘worker-to-brood ratio’ (xratio).

Extended Data Fig. 8 Residual deviance against brood number.

Residual deviance contributions by each 5-day colony-observation, plotted against the predictor ‘brood number’ (xbrood).

Extended Data Fig. 9 Proportion of cells that are empty.

Predictions for between-colony effects plotted in Fig. 3 in the main text take the mean proportion emptiness across colony-observations (dashed red line).

Supplementary information

Supplementary Information

Notation, supplementary information for the Taylor–Frank model and additional statistics information.

Reporting Summary

Peer Review File

Supplementary Data 1

Covariate data used in the model file.

Supplementary Data 2

Transition data used in the model file.

Supplementary Data 3

Example initial values of intercepts.

Supplementary Data 4

Mathematica file for the construction of Fig. 3.

Supplementary Data 5

Zip file containing MATLAB code for the individual-based model.

Supplementary Data 6

R script for MCMC.

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Kennedy, P., Sumner, S., Botha, P. et al. Diminishing returns drive altruists to help extended family. Nat Ecol Evol 5, 468–479 (2021).

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