An Introduction to Mathematical Models in Ecology and by Mike Gillman

By Mike Gillman

Scholars usually locate it tricky to understand basic ecological and evolutionary options as a result of their inherently mathematical nature. Likewise, the applying of ecological and evolutionary idea frequently calls for a excessive measure of mathematical competence.

This publication is a primary step to addressing those problems, delivering a huge advent to the main equipment and underlying thoughts of mathematical versions in ecology and evolution. The ebook is meant to serve the wishes of undergraduate and postgraduate ecology and evolution scholars who have to entry the mathematical and statistical modelling literature necessary to their matters.

The ebook assumes minimum arithmetic and statistics wisdom while masking a wide selection of equipment, lots of that are on the fore-front of ecological and evolutionary examine. The ebook additionally highlights the purposes of modelling to functional difficulties akin to sustainable harvesting and organic keep an eye on.

Key beneficial properties:

  • Written basically and succinctly, requiring minimum in-depth wisdom of arithmetic
  • Introduces scholars to using laptop types in either fields of ecology and evolutionary biology
  • Market - senior undergraduate scholars and starting postgraduates in ecology and evolutionary biology

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Extra resources for An Introduction to Mathematical Models in Ecology and Evolution: Time and Space

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The sum of probabilities in a pdf is 1. 73% 2σ 3σ Fig. 1 Areas under the normal probability density function, showing the percentage of events occurring between one, two or three standard deviations (σ) either side of the mean (µ). or the uniform distribution of rolls of a die, or continuous, such as the normal distribution (Fig. 1). For a continuous distribution we cannot say that a variable will have a certain value but instead we say that it can lie between different values with a certain probability.

5 Population dynamics and diversification in continuous time What of organisms whose life cycles do not fit the simple assumptions of annual plants or insects? From the point of view of population dynamics there are three important differences between long-lived organisms and annual organisms. First, the former may begin reproducing after more than 1 year. Second, they may survive after reproduction and possibly reproduce again. The dynamics of such populations needs to be described with respect to particular ages or stages of the population and will be the subject of Chapter 4.

3 Density-independent population dynamics A species with population dynamics that are relatively easy to model is one that reproduces and then dies in the same year. Certain insect species and annual plants fall into this category. Consider populations of a hypothetical annual plant. The seed germinates in spring, the seedlings grow in the summer and reach a size for flowering and seed set in late summer. The seed are produced and over-winter in the soil. The life cycle is then repeated (Fig. 5).

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