Correction to Supporting Information for Grunert et al., Evolutionarily stable strategies in stable and periodically fluctuating populations: The Rosenzweig–MacArthur predator–prey model

POPULATION BIOLOGY, APPLIED MATHEMATICS Correction to Supporting Information for “Evolutionarily stable strategies in stable and periodically fluctuating populations: The Rosenzweig–MacArthur predator–prey model,” by Katrin Grunert, Helge Holden, Espen R. Jakobsen, and Nils Chr. Stenseth, which published January 21, 2021; 10.1073/pnas.2017463118 (Proc. Natl. Acad. Sci. U.S.A. 118, e2017463118).

The authors note that, in the SI Appendix: “The argument leading to the proof of Lemma 9.8 was erroneous. The statement of Lemma 9.8 has been modified, and Lemma 5.3 in the main paper where this is used remains unchanged. We are grateful to Sebastian J. Schreiber (Department of Evolution and Ecology, University of California) whose feedback helped us realize the error.”

Additionally, in the SI Appendix, page 6, line 115, the equation

$$\widehat{\alpha }=\frac{1}{3}{\alpha }_0-\frac{2\widehat{x}}{3B\widehat{\beta }}\frac{B\widehat{\beta }}{{\displaystyle \frac{ak}{c\left(\widehat{\beta }\right)}}-1}\widehat{\alpha }=\frac{1}{3}{\alpha }_0-\frac{2}{3}\frac{1}{{\displaystyle \frac{ak}{c\left(\widehat{\beta }\right)}}-1}\widehat{\alpha }$$

should instead appear as

$$\widehat{\alpha }=\frac{1}{3}{\alpha }_0-\frac{2}{3B\widehat{\beta }}\frac{B\widehat{\beta }}{{\displaystyle \frac{ak}{c\left(\widehat{\beta }\right)}-1}}\widehat{\alpha }=\frac{1}{3}{\alpha }_0-\frac{2}{3}\frac{1}{{\displaystyle \frac{ak}{c\left(\widehat{\beta }\right)}-1}}\widehat{\alpha }$$

The authors also note that new ref. 4 has been added on page 8 of the SI Appendix. The SI Appendix has been corrected online.