Trait Heritability in Major Transitions

8 A crucial component of major transitions theory is that after the transition, adaptation 9 occurs primarily at the level of the new, higher-level unit. For collective-level adaptations 10 to occur, though, collective-level traits must be heritable. Since collective-level traits are 11 functions of lower-level traits, collective-level heritability is related to particle-level 12 heritability. However, the nature of this relationship has rarely been explored in the 13 context of major transitions. We examine relationships between particle-level heritability 14 and collective-level heritability for several functions that express collective-level traits in 15 terms of particle-level traits. When this relationship is linear, the heritability of a 16 collective-level trait is never less than that of the corresponding particle-level trait and is 17 higher under most conditions. For more complicated functions, collective-level 18 heritability is higher under most conditions, but can be lower when the function relating 19 particle to cell-level traits is sensitive to small fluctuations in the state of the particles 20 within the collective. Rather than being an impediment to major transitions, we show that 21 collective-level heritability superior to that of the lower-level units can often arise ‘for 22 free’, simply as a byproduct of collective formation. 23 24 . CC-BY 4.0 International license peer-reviewed) is the author/funder. It is made available under a The copyright holder for this preprint (which was not . http://dx.doi.org/10.1101/041830 doi: bioRxiv preprint first posted online Feb. 29, 2016;