Mathematical Modeling in Ecology: A Workbook for Students

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The book should also serve as a stepping-stone both to advanced mathematical works like Stability of Biological Communities by Yu. Svirezhev and D. Straskraba and A. Gnauch Elsevier, Amsterdam, JavaScript is currently disabled, this site works much better if you enable JavaScript in your browser. Mathematical Modeling Free Preview.

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Software used to produce Chapter 6 simulations. It provides a graphic user interface, and tabular as well as graphical output.

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Adequate for most ecological applications is the Runge Kutta 4th order integration routine as an alternative to Euler integration, which is not recommendable for equations even or the complexity of the Lotka Volterra system, which is an elementary starting point for population dynamic studies. An advantage of the software is its accessibility. A drawback is the lacking option to display trajectories in a 3d-coordinate system. Additional material.

Further Reading from the book and additional recommendations. Many textbooks exist on ordinary differential equations, often with a very specific focus. From our perspective we would select the following books and webpages that expand on the contents provided in this chapter:. Edelstein-Keshet L Mathematical models in biology, 2nd edn.

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We will use the computational language R to learn about matrix models, and how to conduct sensitivity and elasticity analyses. Course description : Space is an important factor in structuring many ecological populations and communities. For example, some organisms, such as plants, have no mobility throughout most of their life history stages and rely on the dispersal of their propagules to move to new locations.

For plants, where that seed is deposited will determine the availability of resources, interactions with neighboring plants, and future interactions with pollinators, disperses, herbervores, etc.

We will examine a variety of approaches to incorporate space into models to explore spatial patterns, population spread, and coexistence, including individual-based models, integrodifference equations, and metapopulation models. Course Description: Optimal control theory is an optimization method for deriving control policies. It is the science of maximizing the returns from and minimizing the costs of the operation of physical, social, and economic processes.

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In particular, it deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved. Thus, the optimal control problem includes a cost functional, that is a function of state and control variables. Planning des cours. Petersburg, Florida, USA.

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At the end of this course, participants will: Understand the concept of population dynamics and different modeling approaches, Learn how to collect demographic data, build a life cycle diagram and parameterize matrix and integral projection models, Gain theoretical and practical experience developing deterministic and stochastic models and interpreting results to test hypotheses in epidemiology, ecology, evolution and conservation biology, Learn how to use different packages in R to conduct simulations and graph results.

Learn how to analyze biological data with mixed effects models in R.

Mathematical Modeling in Ecology: A Workbook for Students - C. Jeffries - Google Books

Pedagogical Framework This summer school is fortunate to have highly experienced resource fellows who have developed a plethora of excellent research and teaching practices during their careers. Homework program — Exercises and homework will be assigned at the end of each lecture. Targeted and scaffolded instruction Available Technology — The University of Cheikh Anta Diop is well resourced with the latest digital technology resources laptops, projectors, wireless network and internet. Student Performance Recognition — Students will be presented with certificates of attendance at the end of the school as recognition of their attendance and participation in the school activities.

Mathematical Modeling in Ecology

Capability of computing equilibrium states and isoclines in 2-dimensional systems. Be able to determine the existence of periodic solutions in 2-dimensional systems. Understanding of the concept of local stability equilibrium and periodic solutions. Compute stability of equilibrium and periodic solutions. Introduction of bifurcation problem in 1 and 2 dimensional systems.

Understanding of the concept of chaos. Validate infectious disease models via data assimilation.