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Abstract: 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. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: This is the second of two papers dedicated to the relationship between population models of competition and biodiversity. Here, we consider species assembly models where the population dynamics is kept far from fixed points through the continuous introduction of new species, and generalize to such models the coexistence condition derived for systems at the fixed point. The ecological overlap between species and shared preys, that we define here, provides a quantitative measure of the effective interspecies competition and of the trophic network topology. We obtain distributions of the overlap from simulations of a new model based both on immigration and speciation, and show that they are in good agreement with those measured for three large natural food webs. As discussed in the first paper, rapid environmental fluctuations, interacting with the condition for coexistence of competing species, limit the maximal biodiversity that a trophic level can host. This horizontal limitation to biodiversity is here combined with either dissipation of energy or growth of fluctuations, which in our model limit the length of food webs in the vertical direction. These ingredients yield an effective model of food webs that produce a biodiversity profile with a maximum at an intermediate trophic level, in agreement with field studies. [Copyright &y& Elsevier]

Abstract: This is the first of two papers where we discuss the limits imposed by competition to the biodiversity of species communities. In this first paper, we study the coexistence of competing species at the fixed point of population dynamic equations. For many simple models, this imposes a limit on the width of the productivity distribution, which is more severe the more diverse the ecosystem is (1994, Theor. Popul. Biol. 45, 227–276). Here we review and generalize this analysis, beyond the “mean-field”-like approximation of the competition matrix used in previous works, and extend it to structured food webs. In all cases analysed, we obtain qualitatively similar relations between biodiversity and competition: the narrower the productivity distribution is, the more species can stably coexist. We discuss how this result, considered together with environmental fluctuations, limits the maximal biodiversity that a trophic level can host. [Copyright &y& Elsevier]