Biodiversity consists of the variety of life on earth.
It contains several components:
Species richness is the number of species in a given area.
Equitability (=evenness): (in glossary) Uniformity of abundance in an assemblage of species. Equitability is greatest when species are equally abundant.
Diversity index: some overall measure of diversity. Usually combines aspects of richness and evenness. The most commonly used index is the Shannon index (H')
H'= - S {pilog(pi)}
Where the summation is over all species and pi is the relative abundance of species i. H' is high if there are many species, or if evenness is high.
See an example calculation

species-individual curve: a plot of the cumulative number of species encountered vs. the cumulative number of individuals captured.

species-area curve: a plot of the (cumulative) number of species encountered as a function of area.

Species-area curves can be used to compare different regions:

PATTERNS OF SPECIES RICHNESS
Species richness is not constant through space. SR (for plants and animals) is negatively related to:
positively related to:
and have a complex relationship with:
Islands tend to have low SR
Gause's principle, Gause's law, competitive exclusion principle, or CEP (modified from glossary): "No two species can coexist indefinitely on the same limiting resource"
The CEP has been experimentally verified in simple systems, as well as in mathematical models.
However, we often observe not just two, but hundreds of species coexisting in a community. One of the major goals of community ecology is to determine the nature of coexistence in the face the CEP. This is the paradox of the plankton.
competitive exclusion: the situation in which at least one species is driven to local extinction (that is, excluded from a community) by interspecific competition.
The Principle: Given a suite of species, interspecific competition will result in the exclusion of all but one species.
Conditions:
Corollary:
The greater the degree to which these conditions are broken, the greater the number of species which can coexist.
Examples of Species Richness Hypotheses
Environmental variability hypothesis: higher SR is expected where there is more environmental variability (violates condition #3)
Niche specialization hypothesis: higher SR is expected if species are specialists (violates #4)
Mass effect: Higher SR is expected if a region is surrounded by different habitats, because of constant dispersal from these other habitats (violates #7)

High species richness is expected in regions with intermediate levels of disturbance (violates #1, #2, #3, and sometimes #5)

RICHNESS AND SUCCESSION
Must be treated on a case-by-case basis. However, many forests show the following patterns:
Future: climate change (specialists will be at most risk).
Some "Background Extinction" is natural (probably less than 1 per century). However, documented extinctions are hundreds of times this rate, and undocumented extinctions (i.e. an extinction before a species is described) is doubtless much higher.