Rural System's


For complex questions, simple examples can often help develop answers.

Imagine 3 forests as shown in the table below. In Forest A there are 5 species and within each species there are 10 animals. Even if unusual, the distribution of such numbers is possible and used only to illustrate the difficulty of the question. The numbers in the other forests are shown. Which forest A, B, or C has the most diversity? They all have the same number of animals (50 in each). The question becomes more complicated if each forest had a very different number of species in each. That number of species is called by some people "diversity" and by others, it is called "species richness."
Forest Species 1 Species 2 Species 3 Species 4 Species 5
A 10 10 10 10 10
B 40 5 2 2 1
C 21 4 9 6 10

Let us stick to the question about the species in the table, i.e., which forest has the greatest diversity of abundance? From one perspective, those in Forest A are dispersed as evenly as possible, and some would argue as diversely as possible. In Forest B the statistical variance is high but there is a recognized pattern, hardly random or chaotic. In Forest C the species seem to be randomly distributed. The criterion for diversity has not been agreed upon by the scientific community or others. As with many other words, "diversity" can have many meanings.

The ecologists often use the Shannon-Weiner index of diversity. It is a mathemetical index that is largest when species are most evenly distributed (as in Forest A). Species often seem to be distributed in nature as in Forest B … and using a logarithm to analyze the distribution seems useful. Some people think that using statistical "variance" expressive of how abundance is distributed around an average can be useful.

While diversity is used widely in ecology and in environmental circles, it is used in many different ways and with many different definitions. There are now over 2000 technical papers on the topic and few people will invest time in studying more than a few. There are more that 20 federal laws relating to bio-diversity. There remains within circles of thoughtful people the need for parsimonious work to clarify it meaning as nominal, descriptive or objective. We have studied ecological diversity, found over 15 major mathematical expressions, and have found that many, using the same data, produce counterintuitive results. We have found 3 distinct words (or counterpoles) with the same meaning in situations: diversity, similarity, and variety; they are confounded by "richness," "equitability," and "evenness."

Spatial diversity is often studied using the poisson distribution. The less regularly or evenly distributed (an orchard is regularly distributed), the lower the index. When the distribution appears clumped, the distribution index is very large. When randomly distributed, the index is 1.0.

We present some of our analyses of these mathematical expressions and the consequences of their use within conditions of litigation, usually about whether bio-diversity has been achieved or not. We have done computer analyses and now know that when the abundance of any species (including deleting a species as if it was exterminated) is changed within our computer simulator, half of the indices increase and half decrease. We know that there are over 20 federal and state laws and regulations about "biodiversity" and we sense the intent of such laws but they are not clear and agencies have been sued for not achieving some level of biodiversity. Conditions are intolerable for the environment, management directives, and the agents attempting to interpret the effects of land treatment under the premises of experimental and continually adjusting "adaptive management," also within agency guidelines.

We know that even distribution of species (numbers evenly distributed or equal in each category) is not desired (black vultures equal in abundance in the same area with gold finches?). We know that there are endangered species, by definition in low abundance.(e.g., in Forest B above). We know that species Designation change with taxonomic study and revisions. We know that inappropriate groupings of species occur (e.g., based on size or temporary coloration) when taxonomists are not available (funded or expertise supported over time) for adequate classification precision. We know from dozens of studies over long periods that numbers fluctuate widely between years and sampling periods within a year, and that the statement is predictable: "the counts were so variable that we could draw no sound statistical conclusions about change or differences." We know that species are still being discovered. We now believe that an index can be useful, expressive of

  1. species in each category (e.g., mammals, fish, birds, large plants-not-trees or shrubs, mollusks (terrestrial and aquatic))…not collective or total for the Forest.
  2. the rate of decline in the negative logarithm, base e, of the first four species(like the reverse-J of uneven-age forest management). The estimated rank-order total abundance within the Forest is an adequate descriptor, readily gotten, and lends itself well to managerial influence. The numerical index (a proportional change) of the abundance of the four most abundant species compared to the 2005 "baseline" tends to communicate likely desired stability or change for the future.

We believe that a descriptive text can be useful such as at ../ModernWildFauna/variety.htm. The biodiversity record of research areas e.g., Ramseys Draft in Augusta County, should be especially well developed.

We think that potential faunal resources of each District can be listed and thus new recreational gains made as people explore the area to see the species on the lists of each faunal category. Similar plant species lists can and should be made available, e.g., down loaded or when purchased from Rural System cooperators.

The ecological services are as important as the diverse elements. These need to be developed further. See ../ModernWildFauna/services.htm

Based on forest type and age, we believe that a short-term index of probable avian species richness and should be used. Since probable median densities can be estimated, then these should be assumed and used, if desired, to develop a species and abundance index of diversity, preferably that above or the Simpson index (analogous to the Shannon-Weiner index). Similar estimates can be made for the other large faunal groups and major plant species groups. These are first estimates and to be improved with studies and inventories.

For the other species groups, we recommend using simple richness estimates and projections (as shown here) for maximum richness within Ranger Districts and the total Forest.

We think that a simulator can aid the public and students of biodiversity in comprehending the often difficulty mathematics and assumptions of laws and concepts of biodiversity. Such a simulator can enable assumptions about changes in animals or plants and the effects of such changes on several important indices, including the one proposed.

The National Commission on Science for Sustainable Forestry (NCSSF) released Science, Biodiversity and Sustainable Forestry, a report presenting the findings of its first two years of work, at the USDA Forest Service Centennial Congress. The Commission is a program of the National Council for Science and the Environment (NCSE). Salwasser continued, "One result of this is continued confusion over the complimentary roles of reserves and working forests in biodiversity conservation. We now know it is possible to conduct cost-effective conservation strategies and also allow for the sustainable production of natural resources which enhance the quality of human life."


May 13, 2012