Download An Introduction to Mathematical Models in Ecology and by Mike Gillman PDF

By Mike Gillman

Scholars frequently locate it tough to understand primary ecological and evolutionary options due to their inherently mathematical nature. Likewise, the appliance of ecological and evolutionary idea usually calls for a excessive measure of mathematical competence.

This publication is a primary step to addressing those problems, supplying a extensive creation to the foremost tools and underlying options of mathematical types in ecology and evolution. The booklet 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 topics.

The ebook assumes minimum arithmetic and data wisdom when masking a wide selection of equipment, lots of that are on the fore-front of ecological and evolutionary examine. The e-book additionally highlights the purposes of modelling to useful difficulties resembling sustainable harvesting and organic keep watch over.

Key gains:

  • Written sincerely and succinctly, requiring minimum in-depth wisdom of arithmetic
  • Introduces scholars to using machine versions 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

Example text

The Poisson distribution is an example of a discrete pdf as it is concerned with counts of events. A Poisson process is recognized by its properties of homogeneity and independence. By homogeneity, we mean that the probability of an event occurring per unit time or space remains constant. The assumptions of independence and homogeneity mean that the Poisson distribution is a useful null model in ecology and evolution. For example, we might hypothesize that the distribution of plants in a field are clumped or aggregated because the plant reproduces asexually from its roots.

Why do some populations fluctuate enormously while others persist at or around a particular size over time? What governs the dynamics of populations? Why do some species persist while others go extinct? Clearly, modelling cannot answer all of these questions, but it can help in identifying some of the major processes and help quantify the different levels of fluctuation and the likelihood of certain dynamics including the end point of extinction. This chapter starts off the investigation into stability in temporal models that concludes in Chapter 5.

2 may accurately predict dynamics over a short period of time, when the assumptions of constant rates of survival and fecundity will hold. This is likely to occur at relatively low population densities, such as when an annual plant species is colonizing a recently ploughed field. In Chapter 5 we will see how to model systems to achieve a more realistic process of stability; that is, the model of the ball in the cup (Fig. 2). 4 Density-independent growth in numbers of lineages Just as populations increase or decrease in the numbers of individuals with time, so clades will change in the numbers of species or other taxon with time.

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