A. Steven Corbet

Bio: A. Steven Corbet is an academic researcher. The author has contributed to research in topics: Population & Rank abundance curve. The author has an hindex of 1, co-authored 1 publications receiving 2915 citations.

The Relation Between the Number of Species and the Number of Individuals in a Random Sample of an Animal Population

Abstract: Part 1. It is shown that in a large collection of Lepidoptera captured in Malaya the frequency of the number of species represented by different numbers of individuals fitted somewhat closely to a hyperbola type of curve, so long as only the rarer species were considered. The data for the commoner species was not so strictly `randomized', but the whole series could be closely fitted by a series of the logarithmic type as described by Fisher in Part 3. Other data for random collections of insects in the field were also shown to fit fairly well to this series. Part 2. Extensive data on the capture of about 1500 Macrolepidoptera of about 240 species in a light-trap at Harpenden is analysed in relation to Fisher's mathematical theory and is shown to fit extremely closely to the calculations. The calculations are applied first to the frequency of occurrence of species represented by different numbers of individuals--and secondly to the number of species in samples of different sizes from the same population. The parameter ` alpha ', which it is suggested should be called the `index of diversity', is shown to have a regular seasonal change in the case of the Macrolepidoptera in the trap. In addition, samples from two traps which overlooked somewhat different vegetation are shown to have ` alpha ' values which are significantly different. It is shown that, provided the samples are not small, ` alpha ' is the increase in the number of species obtained by increasing the size of a sample by e (2.718). A diagram is given (Fig. 8) from which any one of the values, total number of species, total number of individuals and index of diversity (alpha), can be obtained approximately if the other two are known. The standard error of alpha is also indicated on the same diagram. Part 3. A theoretical distribution is developed which appears to be suitable for the frequencies with which different species occur in a random collection, in the common case in which many species are so rare that their chance of inclusion is small. The relationships of the new distribution with the negative binomial and the Poisson series are established. Numerical processes are exhibited for fitting the series to observations containing given numbers of species and individuals, and for estimating the parameter alpha representing the richness in species of the material sampled; secondly, for calculating the standard error of alpha, and thirdly, for testing whether the series exhibits a significant deviation from the limiting form used. Special tables are presented for facilitating these calculations.

Ecological Diversity and its Measurement

Abstract: Definitions of diversity. Measuring species diversity. Choosing an index and interpreting diversity measures. Sampling problems. Structural diversity. Applications of diversity measures. Summary.

Measurement of diversity

Abstract: THE 'characteristic' defined by Yule1 and the 'index of diversity' defined by Fisher2 are two measures of the degree of concentration or diversity achieved when the individuals of a population are classified into groups. Both are defined as statistics to be calculated from sample data and not in terms of population constants. The index of diversity has so far been used chiefly with the logarithmic distribution. It cannot be used everywhere, as it does not always give values which are independent of sample size ; it cannot do so, for example, when applied to an infinite population of individuals classified into a finite number of groups. Williams3 has pointed out a relationship between the characteristic and the index of diversity when both are applied to a logarithmic distribution. The present purpose is to define and examine a measure of concentration in terms of population constants.

The Nonconcept of Species Diversity: A Critique and Alternative Parameters.

Abstract: The recent literature on species diversity contains many semantic, conceptual, and technical problems. It is suggested that, as a result of these problems, species diversity has become a meaningless concept, that the term be abandoned, and that ecologists take a more critical approach to species—number relations and rely less on information theoretic and other analogies. As multispecific collections of organisms possess numerous statistical properties which conform to the conventional criteria for diversity indices, such collections are not intrinsically arrangeable in linear order along some diversity scale. Several such properties or "species composition parameters" having straightforward biological interpretations are presented as alternatives to the diversity approach. The two most basic of these are simply ▵1=[n/n—1][1—Σi(N_i/_N)2] =the proportion of potential interindividual encounters which is interspecific (as opposed to intraspecific), assuming every individual in the collection can encounter all other individuals, E(Sn) = Σi [1—(N—Nin)/(Nn)] =the expected number of species in a sample of n individuals selected at random from a collection containing N individuals, S species, and Ni individuals in the ith species.

Nonparametric estimation of the number of classes in a population

Abstract: On applique la methode d'Efron (1981, 1982) a la construction d'intervalles de confiance bases sur des distributions du bootstrap