抄録
In the well known Volterra models resources are unlimited. However, if one regards resources as one of the netrients (e.g. nitrogen, carbon, phosphorus, etc), resources are limited in a fixed region. Therefore studying the models with limited resources and its behavior are important.
This paper has studied two cases of material-cycling ecosystems whose species use renewable-limited resource in common; in one case the species utilize resource directly and in the other case indirectly. For example, being concerned with the nitrogen cycle, there is an ecosystem consisting of phytoplanktons and zooplanktons in a bay. In this case zooplanktons utilize phytoplanktons as resource directly. Moreover, in a one-crop area it can be considered that the system consists of resource (plant), the first consumer (an insect using plant) and the second consumers (insects being parasitic on the first consumer). In such case, parasitic insects utilize resource indirectly through the first consumer. These examples correspond to the above two cases respectively.
Some interesting results are as follows. In both cases, a selection occurs among n species and we can know which species survive by the comparison of macroscopic parameter, i.e., the species having smallest macro-parameter value can survive. There exists a difference between two cases with respect to the available utilization of resource. The species utilizing resource directly can use it more efficiently than the species utilizing indirectly.
