State-of-the-Art in Ecological Modelling

State-of-the-Art in Ecological Modelling covers the proceedings of the Conference on Ecological Modeling, held in Copenhagen, Denmark from August 28 to September 2, 1978. The book focuses on ecological modeling, particularly prey-predator models, lake and river models, toxic substances models, and holistic approaches to ecological modeling. The selection first discusses review presentations of ecological modeling, including river models, prey-predator models, application of graphical methods, and lake models. The application of microcosms in ecological modeling; water quality and irrigation in agriculture models; and distribution and effect of toxic substances models are also elaborated. The text then takes a look at the models of sea and coastal areas, atmospheric pollution, ecosystems in the lithosphere, and water management. The book surveys multi-species of planktons and nutrients model of lake eutrophication and modeling of vertical temperature distribution and its implication on biological processes in lakes. Topics include mathematical expression of multi-species of planktons and nutrients model in lake ecosystem; observation data on water quality and planktons; and models for vertical temperature distribution. The selection is a dependable reference for readers wanting to dig deeper into ecological modeling.

1;Front Cover;1 2;State-of-the-Art in Ecological Modelling;2 3;Copyright Page;5 4;Table of Contents;6 5;Preface;8 6;INTERNATIONAL SOCIETY FOR ECOLOGICAL MODELLING AN INTRODUCTION ;10 7;Part A: Invited State-of-the-Art or Review Papers;20 7.1;CHAPTER 1. MODELS OF RIVERS;22 7.1.1;1. INTRODUCTION;22 7.1.2;2. A BRIEF DESCRIPTION OF SOME MATHEMATICAL WATER QUALITY MODELS;23 7.1.3;3. APPLICATION OF WATER QUALITY MODELS;31 7.1.4;4. SUMMARY;42 7.1.5;5. LITERATURE;45 7.2;CHAPTER 2. MODELING OF ECOLOGICAL PROCESS AND ECOSYSTEMS WITH PARTIAL RESPONSE STRUCTURES: A REVIEW AND A NEW PARADIGM FOR DIAGNOSIS OF EMERGENT ECOSYSTEM DYNAMICS AND PATTERNS;68 7.2.1;ABSTRACT;68 7.2.2;INTRODUCTION;69 7.2.3;REVIEW;70 7.2.4;OTHER MODELS;79 7.2.5;NICHE (PRS) AND ENVIRONMENTAL STRUCTURE AND GEOGRAPHY;81 7.2.6;APPENDIX: DETAILED ANALYSIS OF INDIVIDUAL TRANSECTS;104 7.3;CHAPTER 3. MICROCOSMS AS ECOSYSTEMS FOR TESTING ECOLOGICAL MODELS;136 7.3.1;ABSTRACT;136 7.3.2;INTRODUCTION;136 7.3.3;KINDS OF MICROCOSMS;138 7.3.4;FUTURE DIRECTIONS IN MICROCOSM RESEARCH;152 7.3.5;CONCLUSIONS;165 7.3.6;ACKNOWLEDGMENTS;166 7.3.7;REFERENCES;166 7.4;CHAPTER 4. STATE-OF-THE-ART OF PREDATOR-PREY SYSTEMS MODELING;172 7.4.1;Abstract;172 7.4.2;Introducti on;173 7.4.3;A. Time - dependent predator - prey models;173 7.4.4;B. Space-time-dependent predator-prey models;201 7.4.5;REFERENCES;224 7.5;CHAPTER 5. FATE OF TOXIC ORGANIC SUBSTANCES IN THE AQUATIC ENVIRONMENT;228 7.5.1;ABSTRACT;228 7.5.2;EXPOSURE ASSESSMENT: THE NEED AND THE PROBLEM;230 7.5.3;BASIS FOR A COMPUTATIONAL MODEL;233 7.5.4;VALIDATION;242 7.5.5;GENERAL APPLICATIONS;246 7.5.6;REFERENCES;251 7.6;CHAPTER 6. STATE OF THE ART IN HYDRO-CHEMICAL MODELING OF IRRIGATED AGRICULTURE;256 7.6.1;ABSTRACT;256 7.6.2;INTRODUCTION;256 7.6.3;MODEL CLASSIFICATION;258 7.6.4;ASSESSMENT OF IRF MODELING;265 7.6.5;SUMMARY;272 7.6.6;ACKNOWLEDGMENTS;272 7.6.7;REFERENCES;273 7.7;CHAPTER 7. MODELING PROCESS FOR ASSESSING WATER QUALITY PROBLEMS AND DEVELOPING APPROPRIATE SOLUTIONS IN IR
RIGATED AGRICULTURE;278 7.7.1;ABSTRACT;278 7.7.2;INTRODUCTION;278 7.7.3;IRRIGATION WATER MANAGEMENT;279 7.7.4;RIVER BASIN SALINITY PLANNING;285 7.7.5;MODELING PROCESS;290 7.7.6;CONCLUSIONS;297 7.7.7;ACKNOWLEDGMENTS;299 7.7.8;REFERENCES;300 7.8;CHAPTER 8. STATE OF THE ART OF EUTROPHICATION MODELS;302 7.8.1;1. Introduction;302 7.8.2;2. The state of the art;302 7.8.3;3. Next generation of eutrophication models;305 8;Part B: Original Papers;308 8.1;CHAPTER 9. SOME ASPECTS OF AN ESTUARINE ECOSYSTEM MODEL - GEMBASE;310 8.1.1;Abstract;310 8.1.2;Introduction;311 8.1.3;Systems Analysis;312 8.1.4;Modelling Strategy;313 8.1.5;Computer Program;314 8.1.6;The hydrodynamic sub-routine HYDROB ;314 8.1.7;The primary production sub-routine PRIPRO;315 8.1.8;Data Base;316 8.1.9;Simulation Strategy;317 8.1.10;Conclusions;319 8.1.11;Acknowledgements;320 8.1.12;References;321 8.2;CHAPTER 10. A SIMULATION MODEL OF ESTUARINE SUBSYSTEM COUPLING AND CARBON EXCHANGE WITH THE SEA- 1. MODEL STRUCTURE;332 8.2.1;INTRODUCTION;332 8.2.2;THE NORTH INLET ESTUARY AND MODEL;333 8.2.3;MATHEMATICAL FORMULATION;335 8.2.4;COMPONENT EVALUATION;345 8.2.5;SIMULATION RESULTS AND DISCUSSION;346 8.2.6;SYSTEM CHARACTERISTICS;353 8.2.7;LITERATURE CITED;373 8.3;CHAPTER 11. MODELLING THE DISTRIBUTION OF CHROMIUM IN A DANISH FIRTH;376 8.3.1;1. Introduction;376 8.3.2;2. The model;376 8.3.3;3. Discussion and conclusion;382 8.3.4;REFERENCES;383 8.4;CHAPTER 12. MODELLING THE FATE OF ATMOSPHERIC FLUORIDE IN A COASTAL SEMIARID REGION: I. SYSTEMS ANALYSIS AND IDENTIFICATION;384 8.4.1;Model objectives and boundaries ;387 8.4.2;Idcrelification of state varielles ;388 8.4.3;ElrKP... >?.. ÁÃÑÑ^.-:. >~"l. Jj;e~ r, controls;389 8.4.4;Structure of the model proposed ;399 8.4.5;Aknowledgements ;400 8.4.6;Refereces ;411 8.5;CHAPTER 13. FLOOD PLAIN MANAGEMENT MODELS FOR ECONOMIC, ENVIRONMENTAL & ECOLOGICAL IMPACT ANALYSIS;414 8.5.1;SUMMARY;414 8.5.2;1. SYMBOLS;415 8.5.3;2. INTRODUCTION;415 8.5.4;3. METHODOLOGY;418 8.5.5;4. ANALYSIS;41
9 8.5.6;5. RESULTS;421 8.5.7;6. DISCUSSION;423 8.5.8;7. CONCLUSIONS;424 8.5.9;8. ACKNOWLEDGEMENT;424 8.5.10;9. REFERENCES;425 8.6;CHAPTER 14. PROBABILISTIC AND STOCHASTIC ASPECTS OF UNCERTAINTIES IN GROUNDWATER MODELLING;428 8.6.1;1. INTRODUCTION;428 8.6.2;2. DISCRETISATION OF THE PARTIAL DIFFERENTIAL EQUATION;430 8.6.3;3. INTEGRATION OF THE FIRST ORDER SYSTEM OF DIFFERENTIAL EQUATIONS;433 8.6.4;4. THE PROBABILISTIC APPROACH IN ERROR DETERMINATION;436 8.6.5;5. The stochastic approach in error dtermination ;443 8.6.6;6. Conclusions;450 8.6.7;Bibliography;451 8.7;CHAPTER 15. REGIONAL WATER QUALITY MANAGEMENT;452 8.7.1;ABSTRACT;452 8.7.2;INTRODUCTION;452 8.7.3;THE OPTIMIZATION MODEL;452 8.7.4;THE OPTIMIZATION MODEL - AN EXAMPLE;455 8.7.5;CONCLUSION;458 8.7.6;REFERENCES;458 8.8;CHAPTER 16. THE WATER QUALITY PLANNING MODEL;460 8.8.1;ABSTRACT;460 8.8.2;INTRODUCTION;461 8.8.3;REVIEW OF THE EXISTING WATER QUALITY MODELS;463 8.8.4;QUAL I;464 8.8.5;QUAL II;465 8.8.6;STORM Model;465 8.8.7;STATISTICAL MODELS;467 8.8.8;AGRICULTURAL RUNOFF QUALITY-QUANTITY MODELS (ARM);468 8.8.9;EPA STORMWATER MANAGEMENT MODEL;469 8.8.10;THE WATER QUALITY PLANNING MODEL;470 8.8.11;FACTORS IN THE SELECTION OF THE MODEL;472 8.8.12;DESCRIPTION OF THE MODEL;474 8.8.13;FORMULATIONS;476 8.8.14;COMPUTATIONAL PROCEDURE;480 8.8.15;ASSUMPTIONS;481 8.8.16;INPUT DATA REQUIREMENTS;483 8.8.17;RESULTS;484 8.8.18;CALIBRATION RESULTS;484 8.8.19;BACKPUMPING RESULTS;487 8.8.20;DISCUSSION;487 8.8.21;ANALYSIS OF THE OUTPUT IN EVALUATING BACKPUMPING SCHEMES;491 8.8.22;CONCLUSIONS;492 8.8.23;ACKNOWLEDGEMENTS;493 8.8.24;NOTATIONS;495 8.8.25;BIBLIOGRAPHY;497 8.9;CHAPTER 17. A PRODUCTION MODEL FOR LAND APPLICATION OF WASTEWATER ;500 8.9.1;Introduction;500 8.9.2;Mathematical Models;500 8.9.3;General Methodology;500 8.9.4;Wastewater Collection - Sanitary Sewer Systems;501 8.9.5;Wastewater Treatment Flow and Mass Balance;503 8.9.6;Economic Pipeline Design;503 8.9.7;Surge;503 8.9.8;Wastewater Export Management System;504 8.9.
9;Regional Water Supply Model;506 8.9.10;Areawide Study of Land Application of Wastewater;508 8.9.11;Summary and Conclusions;509 8.10;CHAPTER 18. MULTI-SPECIES OF PLANKTONS AND NUTRIENTS MODEL OF LAKE EUTROPHICATION - A SIMULATION STUDY IN LAKE BIWA;510 8.10.1;ABSTRACT.;510 8.10.2;1. INTRODUCTION;511 8.10.3;2. BASIC STRUCTURE OF EUTROPHICATION MODEL OF LAKE BIWA;513 8.10.4;3. MATHEMATICAL EXPRESSION OF MULTI-SPECIES OF PLANKTONS AND NUTRIENTS MODEL IN LAKE ECOSYSTEM ;516 8.10.5;4. PARAMETERS IN THE MODEL;520 8.10.6;5. INPUT DATA TO THE MODEL ;523 8.10.7;6. OBSERVATION DATA ON WATER QUALITY AND PLANKTONS;523 8.10.8;7. IDENTIFICATION OF THE MODEL;525 8.10.9;8. DISCUSSION AND CONCLUDING REMARKS;533 8.10.10;ACKNOWLEDGEMENT;534 8.10.11;REFERENCES;535 8.11;CHAPTER 19. A DISCRETE LAKE MODEL AND ITS SENSITIVITY STUDY ;536 8.11.1;I - INTRODUCTION;536 8.11.2;II - THE MODEL ;537 8.11.3;Ill - MODEL SIMULATIONS AND SENSITIVITY STUDY;539 8.11.4;IV - CALIBRATION;543 8.11.5;V - CONCLUSION ;545 8.11.6;REFERENCES;545 8.12;CHAPTER 20. MODELLING OF VERTICAL TEMPERATURE DISTRIBUTION AND ITS IMPLICATION ON BIOLOGICAL PROCESSES IN LAKES;554 8.12.1;INTRODUCTION;554 8.12.2;HYDRODYNAMICS OF LAKES;556 8.12.3;MODELS FOR VERTICAL TEMPERATURE DISTRIBUTION;558 8.12.4;AN EXAMPLE OF PHYSICAL PERTURBATION; PUMPED STORAGE POWER OPERATION;564 8.12.5;Acknowledgements;568 8.12.6;References;569 8.13;CHAPTER 21. THE USE OF MANAGEMENT MODELS FOR LAKES AT THE WATER QUALITY INSTITUTE, DENMARK;570 8.13.1;ABSTRACT;570 8.13.2;INTRODUCTION;570 8.13.3;EUTROPHICATION MODEL OF SHALLOW LAKES, "LAVSOE";572 8.13.4;MODEL OF HORIZONTALLY SEGMENTED SHALLOW LAKES. "BOXSOE" ;579 8.13.5;MODEL OF DEEP, STRATIFIED LAKES;581 8.13.6;CONCLUSION;583 8.13.7;REFERENCES;585 8.14;CHAPTER 22. THE AQUATIC ECOSYSTEM MODEL MS. CLEANER;588 8.14.1;INTRODUCTION;589 8.14.2;STATE-VARIABLES;589 8.14.3;PROCESS REPRESENTATIONS;593 8.14.4;SEGMENT LINKING;603 8.14.5;INTERACTIVE CAPABILITY;603 8.14.6;VERIFICATION;605 8.14.7;PERTURBATIONS AND SENSIT
IVITY ANALYSIS;605 8.14.8;SUMMARY;607 8.14.9;ACKNOWLEDGEMENTS;607 8.14.10;REFERENCES;608 8.15;CHAPTER 23. "COMPARATIVE STUDIES ON EUTROPHICATION IN LARGE SCALE -MODEL RESERVOIRS";612 8.15.1;Introduction;612 8.15.2;Observations;612 8.15.3;Analysis;613 8.15.4;Primary production;613 8.15.5;Loss-terms;617 8.15.6;Results and discussion;619 8.15.7;Conclusions ;622 8.15.8;Acknowledgement;622 8.15.9;Literature;623 8.16;CHAPTER 24. THE USE OF EXPERIMENTAL ECOLOGY IN SIMULATING ALGAL BLOOMS;626 8.16.1;SUMMARY;626 8.16.2;1. INTRODUCTION;628 8.16.3;2. DESCRIPTION OF MODELS;631 8.16.4;3. DISCUSSION;640 8.16.5;4. ACKNOWLEDGMENTS;642 8.16.6;5.1 APPENDIX I DYNAMO flow diagram and equations;642 8.16.7;APPENDIX II : DYNAMO-LISTING OF THE MODIFIED NAM-MODEL. ;647 8.16.8;6. REFERENCES;649 8.17;CHAPTER 25. COMPARISON OF THE POSSIBLE EFFECTS OF INTERNAL SEICHES ON THE PLANKTON POPULATION OF SELECTED LAKES;656 8.17.1;ABSTRACT;656 8.17.2;INTRODUCTION;657 8.17.3;METHODS;657 8.17.4;RESULTS AND DISCUSSION;659 8.17.5;CONCLUSIONS;661 8.17.6;REFERENCES;662 8.18;CHAPTER 26. A MODEL OF THE PLANKTON DYNAMICS IN AN EUTROPHIC SHALLOW LAKE BASED ON FIELD DATA;670 8.18.1;Introduction;670 8.18.2;The modeling approach;671 8.18.3;The application of time integrated equations;672 8.18.4;The model equations;674 8.18.5;The solution of these equations;676 8.18.6;Summary and conclusions;679 8.18.7;References:;680 8.19;CHAPTER 27. OPTIMUM HARVESTING OF PREDATORS IN A RANDOM ENVIRONMENT;684 8.19.1;Introduction;684 8.19.2;A prey-predator system with harvesting;685 8.19.3;Optimum harvesting rate;689 8.19.4;Harvesting in a Random Environment;690 8.19.5;Examples;691 8.19.6;Conclusions;699 8.19.7;REFERENCES;701 8.20;CHAPTER 28. SUSTAINABLE YIELD STRATEGIES FROM AN AGE STRUCTURED TWO-SEASON BEVERTON-HOLT TYPE MODEL;702 8.20.1;ABSTRACT ;702 8.20.2;1. INTRODUCTION;703 8.20.3;2. FORMULATION OF MODEL;704 8.20.4;3. SUSTAINABLE YIELD STRATEGIES;707 8.20.5;4. MAXIMUM SUSTAINABLE YIELD;711 8.20.6;5. NUMERICAL EXAMPLE;713 8.20.
7;6. CONCLUSION;718 8.20.8;REFERENCES;720 8.21;CHAPTER 29. MODELING OF BIOCHEMICAL CYCLES AND THE STUDY OF TRANSFORMATION PROCESSES OF CHEMICAL COMPOUNDS;722 8.21.1;Modeling of Phosphorus Transformation and Biochemical Oxygen Consumption;723 8.21.2;Modeling of Nitrogen Transformations and Biochemical Oxygen Consumption;735 8.21.3;Conclusion;744 8.21.4;APPENDIX;746 8.21.5;REFERENCES ;747 8.22;CHAPTER 30. TOWARDS THE DEVELOPMENT OF EFFICIENT SOFTWARE FOR ENVIROMENTAL MODELS;750 8.22.1;Abstract;750 8.22.2;1. Introduction;750 8.22.3;2. The Hermite cubic elements;751 8.22.4;3. Method description and flexibility : Prey-preditor models with spatial diffusion;753 8.22.5;4. Efficiency;757 8.22.6;REFERENCES;758 8.23;CHAPTER 31. CATASTROPHE THEORY APPLIED TO WATER QUALITY REGULATION OF RIVERS;760 8.23.1;Abstract;760 8.23.2;Introduction ;760 8.23.3;An oxygen model;761 8.23.4;The simplified oxygen model;762 8.23.5;A generalized oxygen model;767 8.23.6;Aknowledgements;767 8.23.7;References;767 8.24;CHAPTER 32. BEST COMBINATION OF INPUTS, CHOICE FROM PRODUCTION FORMULAS ;768 8.24.1;INTRODUCTION:;768 8.24.2;DESCRIPTION OF PROBLEMS;768 8.24.3;FORMULATION OF OBJECTIVES;771 8.24.4;RESULT;775 8.24.5;DISCUSSION;776 8.24.6;CONCLUSIONS;777 8.24.7;References;778 8.25;CHAPTER 33. TOWARDS AN ECOLOGICALLY-ORIENTATED SIMULATION LANGUAGE;780 8.25.1;INTRODUCTION;780 8.25.2;SIMULATION LANGUAGES IN CUPRENT USE;781 8.25.3;DESIRABLE FEATURES IN AN ECOLOGICALLY-ORIENTATED SIMULATION LANGUAGE;785 8.25.4;CONCLUSION - THE ADVANTAGES OF AN ECOLOGICALLY-ORIENTATED SIMULATION LANGUAGE;792 8.25.5;BIBLIOGRAPHY;795 8.26;CHAPTER 34. RECENT DEVELOPMENTS OF SIMULATING DISTURBED CELL RENEWAL SYSTEMS ON MINICOMPUTERS;798 8.26.1;SUMMARY;798 8.26.2;INTRODUCTION;799 8.26.3;SPECIFICATIONS OF THE CELL RENEWAL MODEL;799 8.26.4;MODEL OF THE CELL RENEWAL SYSTEM;801 8.26.5;DISCUSSION OF SELECTED SIMULATION RESULTS;803 8.26.6;CONCLUDING REMARKS;809 8.26.7;REFERENCES;809 8.27;CHAPTER 35. THE UTILITY OF THE SIMSCRIPT II LANGU
AGE FOR THE SIMULATION OF COMPLEX PREDATOR - PREY RELATIONSHIPS;810 8.27.1;THE SIMSCRIPT II LANGUAGE;811 8.27.2;TEMPORARY ENTITIES;811 8.27.3;REMOVE ROVER FROM KENNEL;815 8.27.4;REMOVE THE FIRST DOG FROM KENNEL;815 8.27.5;EXAMPLE OF APPLICATION;821 8.27.6;DISCUSSION AND CONCLUSIONS;824 8.27.7;REFERENCES;824 8.28;CHAPTER 36. EXERGY AND ECOLOGICAL BUFFER CAPACITY;838 8.28.1;Abstract;838 8.28.2;Introduction;838 8.28.3;Chemical constraints ;839 8.28.4;Physical constraints;840 8.28.5;Thermodynamical constraints;841 8.28.6;Ecological buffer capacity;848 8.28.7;Partial buffer capacities;849 8.28.8;Biological constraints;851 8.28.9;Topological constraints;852 8.28.10;Conclusion ;853 8.28.11;Appendix: Mathematical notation ;854 8.28.12;List of References;855 8.29;CHAPTER 37. MODELLING LICHEN REINVASION FOR MONITORING AMELIORATING ENVIRONMENTS;856 8.29.1;Introduction;856 8.29.2;Single species monitoring;856 8.29.3;Modelling the reinvasion;857 8.29.4;Conclusions;859 8.29.5;REFERENCES;863 9;Part C: Working Session;864 9.1;CHAPTER 38. STATE-OF-THE-ART, working session;866 9.1.1;1, Introduction;866 9.1.2;2. MODELLING AGRICULTURAL WATER POLLUTANTS;867 9.1.3;3. PLANKTON MODELS;869 9.1.4;4. HOLISTIC APPROACH IN ECOLOGY;871 9.1.5;5. PREDATOR-PREY MODELS;873 9.1.6;6. SEDIMENT-WATER INTERACTION;879 9.1.7;7. APPLICATION OF MICROCOSMS;882 9.1.8;8. MODELLING THE FATE AND EFFECT OF TOXIC SUBSTANCES;885 9.1.9;9. LAKE AND RIVER MODELS;887 9.1.10;REFERENCES;892 10;LIST OF PARTICIPANTS;898