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A common approach to estimating the total number of extant species in a taxonomic group is to extrapolate from the temporal pattern of known species descriptions. A formal statistical approach to this problem is provided. The approach is applied to a number of global datasets for birds, ants, mosses, lycophytes, monilophytes (ferns and horsetails), gymnosperms and also to New World grasses and UK flowering plants. Overall, our results suggest that unless the inventory of a group is nearly complete, estimating the total number of species is associated with very large margins of error. The strong influence of unpredictable variations in the discovery process on species accumulation curves makes these data unreliable in estimating total species numbers.

Summary The Monte Carlo test proposed by Barnard, often used in investigating spatial distributions, gives a “blurred” critical region, in which values of the test statistic have a certain probability of being judged significant. The effect of increasing the number of simulations on this blurring is investigated.

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Nutrients and other soluble substances move to roots by diffusion and by mass flow induced by the transpiration stream. Our alm is to relate the concentration of solute to its distanee from the root surface and the absorption time, in terms of the diffusion eharacteristics of the solute in the soil, the movement of the solvent, and the absorbing power of the root.Roots move through the soll at rates of the order of 1 cm per day; and an element of root absorbs for many days after it is prodnced. Diffusion throngh the soll occurs over distances of a few mm per day at most, and high transpiration rates may induce watet to move around 1 mm per day near the root surface. Hence we shall regard the direction of movement as normal to the root surface.N y e and S pier s 9 expressed the variation of concentration around unit length of root with time and radial distance in terms of a second order partial differential equation, which they did not solve; though they did discuss the variation of concentration with radial distance in the speeial case when a steady state was attained after long times. Nye 7 has also given an analytical solution for the corresponding problem of absorption at a planar surface, which gives an insight into the complexities of the cy]indrical case. We give here computer solutions of the Nye and Spiers equation, and include a more comprehensive boundary condition.--459