Donald Ludwig, Steve Carpenter, and W. Brock. 2003. Optimal phosphorus loading for a potentially eutrophic lake. Ecological Applications 13:1135–1152.

Appendices

Appendix A: A derivation of the difference equations.
Ecological Archives A013-019-A1.

Appendix B: An algorithm for calculation of the expected discounted present value (PV).
Ecological Archives A013-019-A2.

Appendix C: A depiction of phosphorus loadings as function of P (P in lake) and M (P in mud) for three different discount rates.
Ecological Archives A013-019-A3.

Appendix D: A figure comparing optimal P loadings and present values (PV) for policies taking account of and neglecting uncertainty in Pc, for discount rate = 0.01.
Ecological Archives A013-019-A4.

Appendix E: A figure showing optimal P loadings as a function of P (P in lake) and M (P in mud) for = 0.05.
Ecological Archives A013-019-A5.

Appendix F: A figure showing trajectories that correspond to Appendix E (and related to Fig. 10).
Ecological Archives A013-019-A6.

Appendix G: A figure analogous to Fig. 10 but with a lower discount rate ( =0.01).
Ecological Archives A013-019-A7.

Appendix H: A figure showing trajectories that correspond to Appendix F, but with the discount rate of Appendix G.
Ecological Archives A013-019-A8.

Appendix I: A depiction of the percentage sensitivity in Pc.
Ecological Archives A013-019-A9.

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