This chapter introduces for and while loops. To demonstrate their use, we create a basic difference-equation model of exponential growth and discuss the different advantages and drawbacks of numerical and analytical models.

This is a conceptual chapter (i.e., no coding) that introduces the components of stock-and-flow models and then investigates different types of expected system growth (linear, exponential, logistic, as well as overshoot) and common causes of each. The role of feedbacks in complex systems is introduced.

Using examples of disease and fire spread, this chapter addresses spatial modeling using neighbor interactions.

In this chapter we describe several data visualization strategies available with the ggplot2 module, which will be our main visualization method going forward. We download a very large air quality dataset from the EPA’s web page and show how we can use R to highlight important pieces, using graphing tools to explore the question of how temperature affects tropospheric ozone levels. We introduce readers to subsetting and combining datasets, as well as transforming them between long and wide formats.

In this chapter readers go through the creation of a reusable function. In Chapter 5 we created a data frame with some basic information on individual trees in a stand; here we create a function to calculate the biomass of those trees using allometric equations and introduce the idea of optional arguments and default values. Next, we learn to use one of R’s most powerful functions for linear modeling, allowing us to do things like statistical testing and linear regression with very little effort.

This chapter provides resources for a deeper investigation of some of the concepts in the book.

In this chapter we incorporate environmental resistance into an analytical model. We explain how the functional form of the equation falls out of assumptions about potential interactions, and how “the balance of nature” results from terms of different order in the change equation. We then show how steady-state analysis can be used to estimate certain parameters from data, as well as how to find growth rates. All of this is combined into an analysis of what level of management would be required to control an invasive plant to below a threshold population, discussing the idea of the stability of states.

This chapter introduces reading and writing to external files. It first explains the directory structure in Windows and Apple/Linux systems, and then explains how to use this within R to store and access datasets. We focus on .csv files, but also discuss R binaries and text files.

In this chapter we discuss the differences between continuous and discrete-time models, the advantages of each, and so on. We work through the Lotka–Volterra model using the Euler approximation and investigate step sizes in order to discuss artifacts (errors due to poor approximation) and what models can and can’t tell you.

This chapter walks readers through the process of downloading and installing the R language and RStudio, and introduces them to the integrated development environment.

This chapter introduces “conveyors” to better simulate important delays, like time for hatching, juvenile period, age-dependent death rates, and so on, using two population models from the literature where growth delays cannot be ignored in the modeling: elephant populations and mosquito control using the release of infertile males. Readers work with “stacks” to see how to move data through these devices efficiently in difference equations (elephant population), as well as delay-differential equations (mosquito control) for continuous time.

This chapter introduces the idea of phase space and builds upon the stability landscape idea presented earlier in the context of stable and unstable steady states. Energy minimization in phase space translates into a conceptual model for optimization, where we can use the R module NLOPTR for global optimization and parameter fitting.

This chapter covers some of the benefits of R in the environmental sciences outside of modeling, what modeling can be used for, and the role it can play in both research and understanding data. It also explains the layout of the book and how to use the text.

While every law student must study torts, not every torts student has the same experience. More than 30 universities in Australia offer this subject, in courses of different lengths, focusing on different torts delivered by different methods, and assessed in different ways. The most common assessment is the open-book exam, which requires students to answer hypothetical problem-solving questions and discuss essay-type questions. No matter how these courses are designed and delivered, every student’s journey has common aspects, and this chapter aims to help you to navigate through your course by focusing on the issues that concern all students. This book is written primarily for students who may not yet have developed the full range of study techniques that lead to success in their legal studies. Torts is a fascinating subject of study but, because it is frequently taught in the first year of law, students sometimes struggle – not because they cannot understand the law or because they are not interested in the law, but because they do not know how to study the law effectively. This chapter explains how to organise your study so that you can achieve the results that you deserve.