There are two major parts to this book. The first part (Chapters 1–4) introduces the mathematics of populations. This section begins with models based on iteration of reproduction curves; these can be done geometrically, with a hand calculator or with a computer. Starting with Malthus’s model of geometric population growth and proceeding to models whose solutions are chaotic, we introduce various mathematical methods for studying and simulating model systems. Other topics include age structure and infinitesimal sampling intervals. The second, third, and fourth chapters are shorter than the first, and they are separated only because they study quite separate population phenomena. These chapters introduce ideas of probability theory to model random events in populations. Random models and their non-random analogues are developed, and through the chapters we discover how the random and non-random models are related. Two problems from genetics are studied in Chapter 2, Chapter 3 is about two problems from epidemics, and Chapter 4 is about dispersal processes. The models in Chapter 1 do not account for random sampling effects in populations, but the examples in the next three chapters do. The intention is to expose students early to ideas of probability in modeling, to build random and non-random models of similar phenomena, and to understand how the two are related.
KeywordsMarkov Chain Model Random Model Exhaustible Resource Fundamental Biological Process Hand Calculator
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