In a particular (natural) environment biological diversity can quantified, For example, a 4 X 4 meter square area in a carrot patch has 300 carrot plants, all the same species. It has a very low biodiversity index of 1/300, or 0.003.
A 4 X 4 meter square area in the forest has 1 pine tree, 1 fern, 1 conifer tree, 1 moss, and 1 lichen, for a total of 5 different species and 5 individuals. The biodiversity index here is high, 5/5 = 1.
Is the shanon wineer index relevant for enviromental recondition like garden and city park ?
If the garden or park is planted as a monoculture, then biodiversity (by your definition) will be low. But if weeds are allowed to grow, then biodiversity will naturally increase. Some indigenous ecosystems can have low plant biodiversity, for example some wetlands or alpine environments, while others, such as rain forests, can have very high plant biodiversity :)
I'm not exactly sure I understand the question you are asking. Diversity can be either higher or lower in a natural area versus a non natural area. Just depends on the specific areas being compared, and the number of species and their abundances in each of those areas. If you're asking will the diversity index for a community that consists of only one species always be lower than the diversity index for a community that consists of mulitple species, regardless of how many total individuals there are in each community, the answer is yes.
Sure. Use of a biodiversity index is relevant anytime you want to quantify overall diversity in a particular area. Doesn't matter whether the area is pristine/natural, or not. However, Simpson's Index is considered a more robust diversity index than the Shannon-Weiner Index. Measuring Biological Diversity by Anne E. Magurran has a good section on the values/downsides of various biodiversity indices.
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