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bioRxiv · 10.64898/2026.04.07.716994

Spectral requirements for cooperation

Pachter, L.
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Abstract

We introduce a spectral existence criterion for the evolution of cooperation in the form of the inequality{lambda} maxb > c, where{lambda} max is the leading eigenvalue of an interaction operator encoding population structure, and b and c represent benefit and cost tradeoffs, respectively. Nowaks five rules for the evolution of cooperation correspond to cases in which the cooperation condition reduces to a scalar assortment coefficient. These results follow from the Price equation, which sheds light on a long-standing debate on the role of inclusive fitness and evolutionary dynamics in explaining the evolution of cooperation.

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Pachter, L.. 2026-04-09. Spectral requirements for cooperation. https://doi.org/10.64898/2026.04.07.716994

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