The delineation of natural areas in New Zealand: A numerical study of the distribution of grasses in New Zealand

[First paragraph(s)...]
I have here limited my treatment of the role of grasses in delimiting natural areas to their numerical distribution in relation to those areas where they occur. The basis ofthis treatment is the relation
S = K log A
i.e., the number of species in an area is proportional to the logarithm of the area. The number of the species common to any two areas A1 and A2 can be expressed
S1 + S2 - S
and the estimated number
K (log A1 + log A2 - log AT)
The ratio of the actual to estimated number is the ratio of homogeneity. When the flora of the two areas is truly homogeneous the ratio is equal to one. The success of the treatment depends in the first place on the adequacy of our know ledge of the distribution of the grasses. I am relying on the labels of some 10,000 specimens of our grasses in the New Zealand herbaria. In the second place, it depends on the basis upon which we draw the boundaries for the areas to be measured. We can readily recognise the well defined boundaries of the vertical zones: the subpolar (alpine), the cool temperate (montane), warm temperate (lowland). Throughout most of New Zealand the zones coincide closely with the contours of 6000-4000 ft., 4000-2000 ft., and 2000-sea level. It is a different matter to divide these zones into areas. We have one rather unsatisfactory boundary which is generally accepted, dividing the islands along the main mountain axis into east and west. Any other boundaries for major areas must always be purely arbitrary. New Zealand topography, climate and soils help to explain our problem.