Modeling of ecological systemsSyllabus

Subject code

İF-3087y

Credits

5

Student workload

150

Semester

Spring semester

Academic year

2025-2026

Subject type

Mandatory

Form of education

Full-time

Language of instruction

Azerbaijani

In-class hours

a) 45 saat mühazirə b) 15 saat seminar

Out-of-class hours

a) 36 saat MRTSİ b) 54 saat TSİ

This subject teaches the theoretical and practical foundations of mathematical modeling used in the study and management of ecological systems. within the scope of the subject, the issues of building mathematical and statistical models, identification of parameters, optimization methods, computer modeling of environmental processes and forecasting and optimal design of processes related to environmental protection are analyzed.

• lecture
• interactive discussion
• presentations
• teamwork
• problem-based learning
• seminar

1. 1

   CLO 1: It explains the basic concepts, principles and types of mathematical models of ecological systems modeling.

2. 2

   CLO 2: Selects an appropriate mathematical model for ecological processes.

3. 3

   CLO 3: Defines the parameters and constraints required to build mathematical models of ecological systems.

4. 4

   CLO 4: It applies mathematical models for the analysis and prediction of ecological processes.

5. 5

   CLO 5: Evaluates the results of mathematical modeling and justifies the adequacy of the model.

6. 6

   CLO 6: Uses computer-based modeling techniques to optimize ecological systems.

1. 1.
   Topic: 2 classification of mathematical models applied in ecological systemsLecture

   Forms of modeling, physical modeling, analog modeling, intuitive modeling, signal modeling, physical and mathematical modeling

   • Explains the nature of mathematical modeling in ecological systems and its role in solving environmental problems. distinguishes the main classification of mathematical models (deterministic, stochastic, static, dynamic, discrete, continuous, empirical and mechanistic models). compares the advantages and limitations of different model types.
2. 2.
   Topic: 3 application of ecological systems and modelsLecture

   Composition and functions of ecosystems, ecosystem dynamics, basics of ecological models, application of ecosystem models

   • Explains the structure, components and principles of operation of ecological systems. defines the areas of application of mathematical models used in the study of ecological systems. chooses a suitable model for solving various environmental problems and justifies its choice.
3. 3.
   Topic: 4 economic-mathematical modeling process and classificationLecture

   General information about the economic-mathematical modeling process, functions of the modeled system, capabilities of the modeled system

   • Explains the nature, purpose and application areas of economic-mathematical modeling. it describes the main stages of the economic-mathematical modeling process (problem definition, model construction, parameter selection, solution, verification and analysis of results). distinguishes the main classification of economic-mathematical models (deterministic, stochastic, static, dynamic, linear, non-linear, discrete and continuous models).
4. 4.
   Topic: 5 general information about the system concept. systematic approachLecture

   Concept of system and its important features, division of models into classes according to application areas, systematic analysis and its stages

   • Explains the concept of the system, its main features and elements. differentiates types of systems (open, closed, static, dynamic, simple and complex systems). it explains the essence, principles and importance of a systematic approach.
5. 5.
   Topic: 6 identification of technological processes and technological systemLecture

   General information on the identification of technological processes, the main directions for studying chemical-technological processes, a chemical technological object is usually under the influence of various factors

   • Explains the essence, purpose and importance of identification of technological processes. describes the concept of a technological system, its structure and main components. it explains the stages of identification of technological processes (data collection, model selection, parameter estimation and model verification).
6. 6.
   Topic: 7 the main directions of building mathematical modelsLecture

   Collection of primary data, construction of mathematical models of chemical technological processes, passive and active experimental methods of setting up the experiment depending on the order of collection of basic statistical materials

   • It explains the purpose, essence and basic principles of building mathematical models. distinguishes the main directions of building mathematical models (analytical, statistical, experimental, simulation and optimization approaches). describes the stages of model building (problem formulation, hypothesis determination, selection of variables and parameters, model formulation, verification and improvement).
7. 7.
   Topic: 8 the role of the computer in the modeling processLecture

   The use of the computer in the modeling process and its important role, stages of computer (simulation) modeling, universal instrumental means of creating models

   • Explains the role and importance of computer technologies in the modeling process. defines the software tools used in the construction, calculation and analysis of mathematical models. describes the stages of computer-based modeling (data entry, model building, simulation, processing and visualization of results).
8. 8.
   Topic: 9 static and dynamic mathematical modelsLecture

   Economic-mathematical modeling process and its essence, classification of economic-mathematical methods, division of economic-mathematical models into static and dynamic models according to the time factor

   • Explains the nature, properties and application fields of static and dynamic mathematical models. identifies and compares the main differences between static and dynamic models. he chooses the appropriate type of model for solving various problems and justifies his choice.
9. 9.
   Subject: 10 areas of application of economic-mathematical methodsLecture

   Application of economic-mathematical methods, purpose in models of real economic systems, development of a mathematical model, mathematical analysis of the model, data structure and algorithm development

   • Explains the essence, purpose and importance of economic-mathematical methods. defines the main areas of application of economic-mathematical methods (economics, management, finance, logistics, production, marketing and risk management). chooses a suitable mathematical method for solving various economic problems and justifies its choice.
10. 10.
    Topic: 11mathematical model of industrial waste water purification processes from metal ionsLecture

    Absorption treatment of waste water, sorption dynamics model, complete mathematical model of sorption dynamics in non-equilibrium mode

    • Explains the impact of metal ions contained in industrial waste water on the environment. it distinguishes the main methods of metal ion removal processes (chemical precipitation, adsorption, ion exchange, membrane technologies, etc.). explains the principles of building mathematical models of metal ion purification processes.
11. 11.
    Topic: 12 environmental problems of the oil industryLecture

    Sources of oil pollution of the sea and the effect of oil on living organisms, modeling of the process of spreading oil and oil products in the sea, methods of combating oil pollution, mathematical models of the process of spreading oil in the sea

    • It explains the impact of the oil industry on the environment and the main environmental problems. it identifies the sources of pollution arising during oil production, processing and transportation. analyzes the effects of oil industry on soil, water, atmosphere and living world.
12. 12.
    Topic: 13 methods of combating oil pollution and modeling the process of spreading oil in the seaLecture

    Causes of sea water pollution with oil and oil products, methods of combating oil pollution, mathematical models of the process of spreading oil into the sea

    • Explains the causes of oil pollution and its effects on marine ecosystems. differentiates oil pollution control methods (mechanical, physical, chemical and biological methods) and explains their application features. it determines the main factors affecting the spread of oil in the sea (wind, wave, current, temperature and physico-chemical properties of oil).
13. 13.
    Topic: 14 modeling the process of soil pollution with oilLecture

    Reasons for soil pollution with oil, mathematical model of the process of oil seepage into the soil, mathematical model of the process of spreading oil on the earth's surface

    • It explains the causes of soil oil pollution and its impact on the environment. identifies the main factors (soil type, porosity, humidity, temperature and physico-chemical properties of oil) that affect the spread and migration of oil in the soil. explains the principles of mathematical modeling of the process of soil pollution with oil
14. 14.
    Topic: 15 landscape ecology and land use modelingLecture

    Landscape ecology, land use impact on ecosystems, land use modeling

    • Explains the nature of landscape ecology, its main concepts and research objects. defines the role of mathematical models in land use planning and management. analyzes landscape structure, functions and ecological processes.
15. 15.
    Topic: 16 modeling of agriculture and water resourcesLecture

    Fields of application of agricultural models, main directions of modeling of water resources, application of integrated models

    • Explains the nature and importance of mathematical modeling in agriculture and water resources management. identifies the main factors affecting agricultural production and use of water resources. distinguishes the main mathematical models used in the modeling of water balance, irrigation systems and agricultural processes.
16. 16.
    Topic: 17 biogeography and species distribution modelsLecture

    The role of various factors in the spread of species, the dynamics and model of the spread of species, the effect of climate change on ecosystems

    • Explains the nature, purpose and basic concepts of biogeography. determines the natural and anthropogenic factors affecting the geographical distribution of living species. distinguishes the main mathematical models and methods used in species distribution modeling.
17. 17.
    Topic: 18 population modelsLecture

    Concept of population, verhulst model in population, malthus model and population, ecological, elemental and human population

    • Explains the nature, purpose and role of population models in ecological systems. it identifies the main factors affecting population dynamics (birth, death, migration, resources and environmental factors). distinguishes the main mathematical models describing population growth (exponential, logistic and other population models).
18. 18.
    Topic: 19 population growth modelsLecture

    Exponential growth model, logistic growth model, natural resource management, stochastic growth model

    • Explains the nature, purpose and application areas of population growth models. identifies the main factors affecting population growth (birth, death, migration, resource limitations, and environmental factors). distinguishes the main mathematical models describing population growth (exponential, logistic and other growth models).
19. 19.
    Topic: 20 models of interspecies interactionLecture

    Types of interactions between species, parasitism and mutualism, commensialism and predation

    • Explains the nature, types and ecological importance of interspecies interactions. it distinguishes interspecific relationships such as competition, predator-prey, parasite-host and mutualism. explains the basic mathematical models (lotka–volterra and other ecological models) that describe interspecies interactions.
20. 20.
    Topic: 21 ecosystem dynamics and stabilityLecture

    In this topic, concepts of the structure, dynamics and stability of ecosystems, biotic and abiotic factors affecting the functioning of ecosystems, assessment of ecosystem stability, mathematical modeling of ecological processes, prediction of ecosystem changes and the role of modeling in ensuring sustainable development are studied.

    • Explains the essence, basic concepts and ecological importance of ecosystem dynamics and stability. identifies biotic and abiotic factors that affect the structure and dynamics of ecosystems. distinguishes the main mathematical models and methods used in the study of ecosystem dynamics.
21. 21.
    Topic: 23 modeling of local and global ecosystemsLecture

    Modeling at the local level, modeling of global ecosystems

    • Explains the nature, characteristics and differences of local and global ecosystems. distinguishes the main mathematical models and methods used in modeling local and global ecosystems. identifies biotic, abiotic, and anthropogenic factors that influence ecosystem modeling.
22. 22.
    Topic: 1 concept of models in ecological systems, their classification and applicationSeminar

    This subject studies simplified mathematical or graphical representation — models — of ecological processes (population dynamics, energy flow, pollution spread). within the scope of the topic, the functions of models, their classification according to their complexity (conceptual, simulation, predictive models) and the practical application areas of these models for making decisions in environmental management are investigated.

    • Explains the concept of the model, its essence and role in the study of ecological systems. distinguishes the main classification of models used in ecological systems (conceptual, physical, mathematical, deterministic, stochastic, static and dynamic models). chooses the appropriate type of model for solving environmental problems and justifies its choice.
23. 23.
    Topic: 2 economic-mathematical modeling process, application areas and identification of technological processesSeminar

    This subject covers the application of mathematical methods in the management of production, economy and technological processes. within the scope of the topic, the stages of economic-mathematical model construction (problem setting, variable selection, equation system formulation, analysis), their application areas in strategic planning and identification of technological processes — i.e., the methods of building a mathematical model of a real system based on input and output parameters are considered.

    • Explains the essence, purpose and main stages of economic-mathematical modeling. defines the areas of application of economic-mathematical models (economy, management, production, logistics, ecology, etc.). explains the essence and basic principles of identification of technological processes.
24. 24.
    Topic: 3 the main directions of building mathematical-static and mathematical-dynamic models and the role of the computer in modelingSeminar

    This subject covers the application of mathematical methods in the management of production, economy and technological processes. within the scope of the topic, the stages of economic-mathematical model construction (problem setting, variable selection, equation system formulation, analysis), their application areas in strategic planning and identification of technological processes — i.e., the methods of building a mathematical model of a real system based on input and output parameters are considered.

    • Explains the nature, properties and application fields of static and dynamic mathematical models. defines the main stages and directions of building mathematical models. compares the differences between static and dynamic models and selects the appropriate model type for different problems.
25. 25.
    Topic: 4 environmental problems of the oil industry and mathematical models of industrial waste water purification process from metal ionsSeminar

    This topic covers the anthropogenic effects of the oil and gas industry on the environment (soil, water, atmosphere) and the process of neutralization of water containing heavy metals, which is a special waste of this industry. in the topic, sources of pollution arising during oil extraction and processing, kinetic and dynamic mathematical models of cleaning metal ions (for example, pb 2+ , cu 2+ , cr 6+ ) from the water environment by sorption, ion exchange or precipitation methods are analyzed.

    • Explains the main environmental problems of the oil industry and their impact on the environment. it determines the environmental risks of metal ions contained in industrial wastewater. it explains the methods of purification of metal ions from waste water and the principles of mathematical modeling of these processes.
26. 26.
    Topic: 6 biogeography and species distribution models population growth modelsSeminar

    This topic describes the patterns of geographical distribution of living organisms and their number dynamics. the biogeography section examines species distribution ranges, environmental factors (climate, topography, competition) that influence their location, and distribution models (eg, the theory of "island biogeography"). in the part of population growth models, how the number of living things changes over time — exponential (unlimited) and logistic (limited by the capacity of the environment) growth models is explained through mathematical equations.

    • Explains the essence of biogeography, its basic concepts and the factors affecting the geographical distribution of species. distinguish between the main mathematical models that describe the distribution of species and population growth. identifies biotic, abiotic and anthropogenic factors affecting population growth.
27. 27.
    Topic: 7 interspecies interaction models, ecosystem dynamics and stabilitySeminar

    This topic explains the interaction of organisms within the ecosystem (predator-prey, competition, symbiosis) with mathematical models. here, through classical models such as "lotka-volterra" equations, the number dynamics of species, how the ecosystem changes over time (succession) and self-regulation against external influences (stability) are analyzed.

    • Explains the nature, basic concepts and ecological importance of interspecies interactions and ecosystem dynamics. distinguish between interspecific relationships such as competition, predator-prey, parasite-host, and mutualism and evaluate their impact on the ecosystem. explains the basic mathematical models used in modeling interspecies interactions and ecosystem dynamics.
28. 28.
    Topic: 8 simulation of ecosystem processes, modeling of local and global ecosystemsSeminar

    This topic involves the creation of digital copies of complex processes occurring in ecosystems (carbon cycle, food chain, climate change). the simulation acts as a "digital laboratory" in situations where it is difficult or dangerous to conduct real environmental experiments. it compares the scale, data requirements, and predictive capabilities of local models (eg, the pollution dynamics of a lake or forest massif) and global models (eg, changes in earth's average temperature and biome migration).

    • It explains the essence, purpose and application areas of the simulation of ecosystem processes and local-global ecosystem modeling. distinguishes the main mathematical and computer models used in the simulation of ecosystem processes. identifies biotic, abiotic, and anthropogenic factors that influence the modeling of local and global ecosystems.
29. 29.
    Topic: 1 definition, types, classification and application of models in ecological systemsIndependent work

    This topic covers the representation of ecological processes (population dynamics, energy flow, material circulation, etc.) in mathematical, graphical or physical forms, the nature, types and application of these models in the management of real ecosystems. ecological modeling is a key tool for simplifying complex natural phenomena and transforming them into manageable parameters.

    • Explains the concept of the model, its essence and role in the study of ecological systems. distinguishes the main types and classification of models used in ecological systems (conceptual, physical, mathematical, deterministic, stochastic, static and dynamic models). selects the appropriate type of model for the study of ecological systems and justifies its choice.
30. 30.
    Topic: 2 economic-mathematical static and dynamic modeling process and systematic approachIndependent work

    This topic covers the expression of complex economic and ecological processes with quantitative indicators, the influence of the time factor on the models, and the investigation of the interrelationships between the elements of the system as a single mechanism. economic-mathematical modeling plays the role of scientific reasoning in decision-making.

    • Explains the nature, purpose and characteristics of static and dynamic models of economic-mathematical modeling. identifies and compares the main differences between static and dynamic mathematical models. it explains the main stages of the economic-mathematical modeling process (setting the problem, building the model, selecting parameters, solving, checking and analyzing the results).
31. 31.
    Topic: 3 environmental problems of the oil industry and a mathematical model of industrial waste water purification processes from metal ionsIndependent work

    This topic covers the anthropogenic impacts of the oil and gas sector on the environment (soil, water, air), especially the danger of heavy metals present in industrial wastewater to the ecosystem and the optimization of these water treatment technologies through mathematical models.

    • Explains the main environmental problems of the oil industry and their impact on the environment. it identifies the environmental and human health risks posed by metal ions in industrial wastewater. it explains the main methods of metal ion removal processes and the principles of mathematical modeling of these processes.
32. 32.
    Topic: 4 methods of combating oil pollution of land and sea water, modeling of oil pollution of sea water and landIndependent work

    This topic covers the physical, chemical and biological treatment technologies applied during oil spills, as well as mathematical modeling approaches that predict the dynamics of the spread of this pollution.

    • It explains the causes of oil pollution of land and sea water, the mechanisms of its spread and its impact on the environment. distinguishes the main methods of combating oil pollution (mechanical, physical, chemical and biological methods) and explains their application characteristics. identifies the main factors affecting the spread of oil in seawater and land and analyzes their influence on the process.
33. 33.
    Topic: 5 agricultural and water resource modeling of biogeography and species distributionIndependent work

    This topic includes the analysis of the patterns of geographic distribution of living organisms (biogeography), as well as the optimization through mathematical models of agricultural productivity and the management of water resources, which are critical to human activity. these systems are important for ensuring ecological resilience in the face of climate change and anthropogenic impacts.

    • Explains basic concepts of biogeography, patterns of geographic distribution of species, and the role of modeling in agriculture and water resource management. identifies biotic, abiotic, and anthropogenic factors affecting species distribution, agricultural production, and water resource status. distinguishes the main mathematical models and methods used in the modeling of species distribution, agriculture and water resources.
34. 34.
    Topic: 22 simulation of ecosystem processesLecture

    This topic covers the study of natural processes occurring in ecosystems through computer models and simulation methods. during the simulation, interactions between living things (predator-prey relationships, competition, symbiosis), population dynamics, energy flow, substance circulation and the effect of environmental factors on the ecosystem are modeled. within the framework of the topic, various scenarios are established and changes that may occur in ecosystems are predicted, the role of simulation in making scientifically based decisions for the management of natural resources and the protection of biodiversity is studied. also, the skills of analyzing environmental processes using mathematical modeling, system dynamics and computer programs are formed.

    • Explains the concept of simulation of ecosystem processes. it defines the main components of the ecosystem and their interrelationships. it models ecological processes such as population dynamics, energy flow, and material cycling.
35. 35.
    Topic: 1 concept of model in ecological systems and its typesLecture

    Ekoloji sistemlərdə modelləşdirmə və onun əhəmiyyəti, model anlayışı və onun növləri, modelləşdirmə haqqında ümumi məlumat və onun mahiyyəti

    • Explains the concept of a model and explains the role of a model in scientific research. it explains the nature of the ecological model and its importance in the study of the environment. defines the main characteristics of ecological systems (complexity, interaction, dynamics, etc.).
36. 36.
    Topic: 5 methods of combating oil pollution of sea waters and land, modeling of land use, agriculture and water resources.Seminar

    This topic combines two major directions: 1) environmental cleaning technologies and 2) digital modeling of resource management. physical (barriers, mechanical collection), chemical (dispersants) and biological (bioremediation) methods of combating oil pollution of the marine and land environment are considered. at the same time, the methods of building and optimizing mathematical models for the productivity of agricultural fields, soil erosion, irrigation systems and the dynamics of underground/surface water resources are analyzed.

    • Explains the causes and environmental consequences of oil pollution of sea waters and land. differentiates the methods of combating oil pollution (mechanical, physical, chemical and biological methods) and evaluates their advantages and disadvantages. explains the principles of modeling the spread of oil spills and understands the importance of forecasting.

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