Solved: 2830 Consumer-resource models often have the following general form R9 fsRd 2

Chapter 7, Problem 28

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2830 Consumer-resource models often have the following general form R9 fsRd 2 tsR, Cd C9 tsR, Cd 2 hsCd where fsRd is a function describing the rate of replenishment of the resource, tsR, Cd describes the rate of consumption of the resource, and hsCd is the rate of loss of the consumer. The constant is the conversion efficiency of resources into consumers and lies between zero and one. Construct the phase plane, including all nullclines, equilibria, and arrows indicating the direction of movement in the plane. Describe how consumer and resource abundance are predicted to change over time. 28. A chemostat is an experimental consumer-resource system. If the resource is not self-reproducing, then it can be modeled by choosing fsRd , tsR, Cd bRC, and hsCd C, where all constants are positive. 29. A model for self-reproducing resources is obtained by choosing fsRd rR, tsR, Cd bRC, and hsCd C, where all constants are positive. 30. A model for self-reproducing resources with limited growth is obtained by choosing fsRd rRs1 2 RyKd, tsR, Cd bRC, and hsCd C. Assume all constants are positive and K . ysbd.