# Likelihood, entropy and species diversity; some comparisons in a Sumatran forest

Rennolls, Keith
(2001)
*Likelihood, entropy and species diversity; some comparisons in a Sumatran forest.*
In: Proceedings: Forest Biometry, Modelling and Information Systems.
Proceedings: Forest Biometry, Modelling and Information Systems, Greenwich, London, UK.

## Abstract

In attempts to conserve the species diversity of trees in tropical forests, monitoring of diversity in inventories is essential. For effective monitoring it is crucial to be able to make meaningful comparisons between different regions, or comparisons of the diversity of a region at different times. Many species diversity measures have been defined, including the well-known abundance and entropy measures. All such measures share a number of problems in their effective practical use. However, probably the most problematic is that they cannot be used to meaningfully assess changes, since thay are only concerned with the number of species or the proportions of the population/sample which they constitute.

A natural (though simplistic) model of a species frequency distribution is the multinomial distribution. It is shown that the likelihood analysis of samples from such a distribution are closely related to a number of entropy-type measures of diversity. Hence a comparison of the species distribution on two plots, using the multinomial model and likelihood methods, leads to generalised cross-entropy as the LRT test statistic of the null that the species distributions are the same.

Data from 30 contiguous plots in a forest in Sumatra are analysed using these methods. Significance tests between all pairs of plots yield extremely low p-values, indicating strongly that it ought to been "Obvious" that the observed species distributions are different on different plots.

In terms of how different the plots are, and how these differences vary over the whole study site, a display of the degrees of freedom of the test, (equivalent to the number of shared species) seems to be the most revealing indicator, as well as the simplest.

Item Type: | Conference Proceedings |
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Title of Proceedings: | Proceedings: Forest Biometry, Modelling and Information Systems |

Additional Information: | [1] This paper was first presented at Forest Biometry, Modelling and Information Science, a IUFRO 4.11 (International Union of Forest Research Organisations: Statistical Methods, Mathematics, and Computing) conference, held at the University of Greenwich, London, UK in June 2001. It was given within the Biodiversity theme. |

Uncontrolled Keywords: | diversity, trees, tropical forests |

Subjects: | Q Science > QA Mathematics > QA76 Computer software S Agriculture > SD Forestry |

Pre-2014 Departments: | School of Computing & Mathematical Sciences School of Computing & Mathematical Sciences > Department of Computer Science School of Computing & Mathematical Sciences > Statistics & Operational Research Group |

Related URLs: | |

Last Modified: | 14 Oct 2016 09:01 |

URI: | http://gala.gre.ac.uk/id/eprint/573 |

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