The theoretical foundation for frequency estimates as used in plant ecology is investigated and developed further. An equation is derived linking the quadrat size, plant unit size, density and aggregation of units with the absence value. From this it is shown that, (1) a much greater amount of information on the species pattern can be obtained, if the frequency estimate is combined with an estimate of the average else of the plant unit,
(2) frequency estimates made with a single quadrat size oan be used to detect differences in patterns but not details of the patterns,
(3) on the assumption of random distribution, frequency estimates with two sizes of quadrats will provide information on the density, and the size of the plant units,
(4) a theoretical minimum of three quadrat sizes, or two sizes of quadrat and an estimate of plant unit size, is required to detect any departure from a random distribution. In practice this would involve considerable replication to ensure reliable results.
The relationships for sampling, (1) with volumes, and (2)along a thread, or rod, of known radius, are also developed.
These relationships, and those of the species-area curve as used for the distribution of higher plants are then shown to be applicable to investigations on the distribution of soil and rhizosphere fungi.
Using one quadrat size, significant differences are shown to be present between the rhizosphere fungal populations from (1) the same root system at different depths, (2) the same root system at different plant ages, (3) different species of plants both in the field and in the bushhouse, (4) plants grown in limed and unlimed soil, (3) plants subject to the treatments of shading and strangling. No significant differences are shown to be present between the rhizospheres of (1) roots of raring age in the same root system in a uniform environment, (2) Fasarium wilt resistant and Fusarium wilt susceptible varities of tomato, and (3) nematode infested and normal roots on the same plant.
Significant interactions between: fungal species within the zhizospbere are also demonstrated.