### Abstract

ABSTRACT: Brillouin's equation (H) for species diversity from information theory is to be preferred for the purposes of applied ecology over the equation of Shannon (H′) or the more commonly used approximate equation (H″). By its use, the difficult problem of delimiting the extent of the community being sampled in a stream survey can be avoided. Moreover, Brillouin's equation gives the exact diversity of the fully censused collection, whreas Shannon's diversity can only be approximated with a biased estimator. If we regard a sample as a message from the environment to the ecologist, Brillouin's equation is the proper one for computing its diversity. The product moment correlation coefficient between Brillouin's H for the total number of individuals from a group of samples and for randomly chosen subsets of 100 individuals from each sample was nearly as high as the correlation between H and H″ based on the total samples. This indicates that small sample sizes may give a useful diversity index. Replicated subsamples show that much smaller samples than are normally used can discriminate between communities from polluted and unpolluted environments. The use of smaller samples should reduce the cost of stream surveys.

Original language | English (US) |
---|---|

Pages (from-to) | 125-135 |

Number of pages | 11 |

Journal | JAWRA Journal of the American Water Resources Association |

Volume | 13 |

Issue number | 1 |

DOIs | |

State | Published - Feb 1977 |

### Fingerprint

### Keywords

- analytical techniques
- aquatic life
- community analysis
- diversity
- macrobenthic organisms
- stream surveys

### ASJC Scopus subject areas

- Ecology
- Water Science and Technology
- Earth-Surface Processes

### Cite this

**ANALYSIS OF DATA FROM BIOLOGICAL SURVEYS OF STREAMS : DIVERSITY AND SAMPLE SIZE.** / Kaesler, Roger L.; Herricks, Edwin E.

Research output: Contribution to journal › Article

*JAWRA Journal of the American Water Resources Association*, vol. 13, no. 1, pp. 125-135. https://doi.org/10.1111/j.1752-1688.1977.tb01996.x

}

TY - JOUR

T1 - ANALYSIS OF DATA FROM BIOLOGICAL SURVEYS OF STREAMS

T2 - DIVERSITY AND SAMPLE SIZE

AU - Kaesler, Roger L.

AU - Herricks, Edwin E

PY - 1977/2

Y1 - 1977/2

N2 - ABSTRACT: Brillouin's equation (H) for species diversity from information theory is to be preferred for the purposes of applied ecology over the equation of Shannon (H′) or the more commonly used approximate equation (H″). By its use, the difficult problem of delimiting the extent of the community being sampled in a stream survey can be avoided. Moreover, Brillouin's equation gives the exact diversity of the fully censused collection, whreas Shannon's diversity can only be approximated with a biased estimator. If we regard a sample as a message from the environment to the ecologist, Brillouin's equation is the proper one for computing its diversity. The product moment correlation coefficient between Brillouin's H for the total number of individuals from a group of samples and for randomly chosen subsets of 100 individuals from each sample was nearly as high as the correlation between H and H″ based on the total samples. This indicates that small sample sizes may give a useful diversity index. Replicated subsamples show that much smaller samples than are normally used can discriminate between communities from polluted and unpolluted environments. The use of smaller samples should reduce the cost of stream surveys.

AB - ABSTRACT: Brillouin's equation (H) for species diversity from information theory is to be preferred for the purposes of applied ecology over the equation of Shannon (H′) or the more commonly used approximate equation (H″). By its use, the difficult problem of delimiting the extent of the community being sampled in a stream survey can be avoided. Moreover, Brillouin's equation gives the exact diversity of the fully censused collection, whreas Shannon's diversity can only be approximated with a biased estimator. If we regard a sample as a message from the environment to the ecologist, Brillouin's equation is the proper one for computing its diversity. The product moment correlation coefficient between Brillouin's H for the total number of individuals from a group of samples and for randomly chosen subsets of 100 individuals from each sample was nearly as high as the correlation between H and H″ based on the total samples. This indicates that small sample sizes may give a useful diversity index. Replicated subsamples show that much smaller samples than are normally used can discriminate between communities from polluted and unpolluted environments. The use of smaller samples should reduce the cost of stream surveys.

KW - analytical techniques

KW - aquatic life

KW - community analysis

KW - diversity

KW - macrobenthic organisms

KW - stream surveys

UR - http://www.scopus.com/inward/record.url?scp=84980314503&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84980314503&partnerID=8YFLogxK

U2 - 10.1111/j.1752-1688.1977.tb01996.x

DO - 10.1111/j.1752-1688.1977.tb01996.x

M3 - Article

AN - SCOPUS:84980314503

VL - 13

SP - 125

EP - 135

JO - Journal of the American Water Resources Association

JF - Journal of the American Water Resources Association

SN - 1093-474X

IS - 1

ER -