Search

We investigate the effect of auto-correlated yield on the evolutionarily stable germination fraction of dormant seeds. By using both analytics and numerics, we first show that in a regime of small fluctuations a positive correlation reduces dormancy and a negative correlation enhances dormancy. By extending the numerical analysis we also show that in the regime of large fluctuations a more complex picture emerges where also negative correlations can reduce dormancy.

Dormant seeds in permanent soil seed banks change their germination probability with age, but little is known about the causes of this behavior. Since current adaptive models do not consider the age structure of the seed bank, the sole explanation is that changes in germination probability with age are due to passive accidental factors or to decay of seeds. Here we present a theory, which shows that such changes might be adaptive. In particular, in density-regulated populations, the evolutionarily stable fraction of germinating seeds in each age class increases with age whenever age-dependent mortality of dormant seeds remains constant or increases with age.

In this article, we consider a bet-hedging model with density dependence for germination behavior of dormant seeds. We show how to compute accurate values of the evolutionary stable germination fraction using a method based on expansion around the average seed bank size. The expansion is made up to the fourth order and is expressed in terms of the first four moments of the distribution of the year-to-year variation in the average yield per adult plant. This method leads to a simple algebraic equation, which can be solved without recurring to simulations of the seed bank dynamics. We first show the analytical derivation under general assumptions about the effect of density dependence. We then test our results with a numerical analysis where an explicit form of the density dependence has been taken.