Evolutionary jumping and breakthrough in tree masting evolution

Many long-lived plants such as trees show masting or intermittent and synchronized reproduction. In a coupled chaos system describing the dynamics of individual-plant resource budgets, masting occurs when the resource depletion coefficient k (ratio of the reproductive expenditure to the excess resource reserve) is large. Here, we mathematically studied the condition for masting evolution. In an infinitely large population, we obtained a deterministic dynamical system, to which we applied the pairwise invasibility plot and convergence stability of evolutionary singularity analyses. We prove that plants reproducing at the same rate every year are not evolutionarily stable. The resource depletion coefficient k increases, and the system oscillates with a period of 2 years (high and low reproduction) if k<1. Alternatively, k may evolve further and jump to a value >1, resulting in the sudden start of intermittent reproduction. We confirm that a high survivorship of young plants (seedlings) in the light-limited understory favors masting evolution, as previously suggested by computer simulations and field observations. The stochasticity caused by the finiteness of population size also promotes masting evolution.