``How do plant species coexist?" is the important biological problem.  So we focus on the mechanism of multiple plant species coexistence. Especially, we investigate the relationship between the limited nutrient utilization and plant species coexistence. 

In general, plant species uptake nutrient and utilize some part of it for reproduction. Ujiie (1991) reported that the nutrient content of seed determines its germination rate. Therefore we consider how the limited nutrient availability is related to the possibility of coexistence of species by using a lottery model. The original lottery model was proposed by Chesson and Warner (1981) and suggested that two species can coexist in a fluctuating environment but cannot in a constant one.  However original lottery model assumed that there is enough nutrient to reproduce seeds.  

In this presentation, we assume that the amount of germinated seeds (f(x)) depends on nutrient (x). It is shown that the possibility of plant species under a constant environment is promoted if f(x) is discontinuous such as  f(x)=m x/(a+x) (for f(x)>L) and f(x)=0 (for 0≤f(x)≤L) where m>0, a>0, L>0. So we need to pay attention to whether reproduction function has a jump (i.e. in f(x) at f(x)=L.) when we discuss about the multiple species coexistence.