New PDF release: An Introduction to Mathematical Models in Ecology and

By Mike Gillman

ISBN-10:

ISBN-13: 0246810121416

ISBN-10: 140517515X

ISBN-13: 9781405175159

ISBN-10: 1405194898

ISBN-13: 9781405194891

Scholars frequently locate it tricky to understand primary ecological and evolutionary suggestions due to their inherently mathematical nature. Likewise, the applying of ecological and evolutionary thought frequently calls for a excessive measure of mathematical competence.

This ebook is a primary step to addressing those problems, delivering a wide creation to the main tools and underlying techniques of mathematical versions in ecology and evolution. The e-book 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 booklet assumes minimum arithmetic and facts wisdom when overlaying a large choice of tools, a lot of that are on the fore-front of ecological and evolutionary examine. The ebook additionally highlights the functions of modelling to functional difficulties equivalent to sustainable harvesting and organic keep an eye on.

Key beneficial properties:

  • Written in actual fact and succinctly, requiring minimum in-depth wisdom of arithmetic
  • Introduces scholars to using desktop 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 info for An Introduction to Mathematical Models in Ecology and Evolution: Time and Space

Sample text

5N t where Nt is the number of species at the end of a given time period. You will see that we also have a parameter equivalent to λ, the finite rate of population increase. This can be defined as a diversification rate, for which we will use the symbol R. In Chapter 3 we will discuss ways in which these processes can be modelled as probabilities (or as values sampled from a probability distribution) rather than fixed values. 2, in which terms are multiplied, can be log-transformed to produce an additive model.

In the discrete-time model it was found that population change was geometric in form (Fig. 11a). Now consider a continuously reproducing population. For a description of continuous geometric population change the separate points in Fig. 11d). If a population is changing geometrically (exponentially) then the curve (Fig. 8) where Nt is the population size at time t and N0 is the initial population size. 8 is describing continuous change, t can take any value. At each point on the smooth exponential curve it is possible to determine the rate of population change by differentiation.

This study made use of Sepkoski’s compendium of fossil marine genera and showed that changes in diversity over the last 540 Myr are consistent with a random walk. This does not necessarily mean that the underlying processes are stochastic, but that the net result of the processes causing change appears to be random. Indeed, the same data set has also been used to address periodicity in the fossil record. Most famously, it was the basis of Raup and Sepkoski’s analysis that led to the idea of mass extinction events, such as the endPermian and end-Cretaceous (Raup & Sepkoski 1982), which, in turn, were linked with periodicity of approximately 26 Myr and a galactic cause of extinction (Raup & Sepkoski 1984).

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An Introduction to Mathematical Models in Ecology and Evolution: Time and Space by Mike Gillman


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