title: Extended flowering intervals of bamboos evolved by discrete multiplication.
abstract: Numerous bamboo species collectively flower and seed at dramatically extended, regular intervals - some as long as 120 years. These collective seed releases, termed 'masts', are thought to be a strategy to overwhelm seed predators or to maximise pollination rates. But why are the intervals so long, and how did they evolve? We propose a simple mathematical model that supports their evolution as a two-step process: First, an initial phase in which a mostly annually flowering population synchronises onto a small multi-year interval. Second, a phase of successive small multiplications of the initial synchronisation interval, resulting in the extraordinary intervals seen today. A prediction of the hypothesis is that mast intervals observed today should factorise into small prime numbers. Using a historical data set of bamboo flowering observations, we find strong evidence in favour of this prediction. Our hypothesis provides the first theoretical explanation for the mechanism underlying this remarkable phenomenon.
authors.affiliation: Program for Evolutionary Dynamics, Harvard University, Cambridge, Massachusetts, 02138, USA.|Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts, 02138, USA.
authors.forename: Carl
authors.initials: C
authors.lastname: Veller
authors.affiliation: Program for Evolutionary Dynamics, Harvard University, Cambridge, Massachusetts, 02138, USA.|Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts, 02138, USA.|Department of Mathematics, Harvard University, Cambridge, Massachusetts, 02138, USA.
authors.forename: Martin A
authors.initials: MA
authors.lastname: Nowak
authors.affiliation: Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts, 02138, USA.
authors.forename: Charles C
authors.initials: CC
authors.lastname: Davis
mesh_terms: D031723:Bambusa / Q000502:physiology*; D005075:Biological Evolution; D035264:Flowers / Q000502:physiology*; D008962:Models, Theoretical; D010507:Periodicity; D006109:Poaceae / Q000502:physiology; D054817:Pollination
keywords: Bamboos; biological clocks; masting; phenology