Correction to: Scientific Reports https://doi.org/10.1038/s41598-019-41988-3, published online 02 April 2019

This Article contains an error in Reference 41.

Peña, J. Group size effects in social evolution. J. Theor. Biol. 457, 211–220 (2018).

should read:

Peña, J. & Nöldeke, G. Group size effects in social evolution. J. Theor. Biol. 457, 211–220 (2018).

As a result, in the Introduction section,

“Thus, Peña considered evolutionary models, finding that the outcome of general nonlinear public goods games depends not only on the average group size but also on the variance of the group-size distribution in case groups are heterogeneous40; also, he showed that larger group sizes can have negative effects (by reducing the amount of cooperation in some cases) and positive effects (by enlarging the basin of attraction of more cooperative outcomes) on the evolution of cooperation41.

should read:

“Thus, Peña considered evolutionary models, finding that the outcome of general nonlinear public goods games depends not only on the average group size but also on the variance of the group-size distribution in case groups are heterogeneous40; also, he and Nöldeke showed that larger group sizes can have negative effects (by reducing the amount of cooperation in some cases) and positive effects (by enlarging the basin of attraction of more cooperative outcomes) on the evolution of cooperation41.”