János Izsák

Quadratic diversity: Its maximization can reduce the richness of species

In recent decades numerous diversity indices have been introduced. Among them the quadratic entropy index Q expresses the mean difference between two individuals chosen from the community at random. Differing from diversity indices habitually employed, Q does not satisfy a property postulated earlier for those measures. Namely, the uniform distribution of species does not necessarily yield the maximal index value. Q is based on the difference matrix of species. For a given matrix one can seek for the vector yielding the maximum quadratic entropy. This task leads to a quadratic programming problem. Using the appropriate program of a program package, we determined the maximum vector for a genetic difference matrix of crane species, as published in the literature. We discovered that some components (frequencies) in the maximum vector are equal to zero. That is, by maximizing the quadratic diversity some species can be eliminated. We discuss briefly the possible implications of this observation. Moreover, even if all elements in the maximum vector are positive, the elements can differ.

Some practical aspects of fitting and testing the Zipf-Mandelbrot model

SummaryThe standardization of distribution fitting procedures is recommended also in informetrics. We examined the possibility of that standardization when fitting the Zipf-Mandelbrot (ZM) distribution. After propositions of possible steps of standardization, we stress the unique role of maximum likelihood estimates concerning the chi-square goodness-of-fit tests. We touch upon the possible correlation between the parameters of the ZM distribution. A numerical example demonstrates the method and the results.

Diversity studies of salmonella incidents in some domestic livestock and their potential relevance as indicators of niche width.

This study attempts to determine whether or not livestock are becoming more susceptible to epidemics of salmonella infections by the analysis of published data on the annual number of reported infections in various animals. The number of incidents reported each year may be subject to a variety of biases due to temporal and geographical differences in reporting practices. This study analysed these reports by the calculation of diversity indices which are not subject to some of these potential biases. The relationship between the ecological concept of niche width and the diversity of species or types occupying that niche is discussed. The diversity of salmonella types reported in fowl has shown a highly significant decline over the 13-year period 1976-88. It is suggested that this declining diversity may be related to the declining niche width of the biotope available to this pathogen. Although speculative, this reduction in niche width could be related to a declining genetic diversity in the host animals or to an increasing intensification of animal husbandry.

Effect of 2-mercaptoethanol on some metabolic indices of ageing of CBA/Ca inbred mice

It has been shown in several studies that 2-mercaptoethanol (2-ME) improves the life span and aspects of life performance of laboratory animals. To obtain further details on the beneficial effects of 2-ME, a long-term study has been performed on male CBA/Ca inbred mice treated with this antioxidant. Four month-old mice were each given 4 micrograms of 2-ME in physiological saline via intraperitoneal (i.p.) injection 3 x per week. Measurements were made of the following: cold tolerance (heat performance), apparent total body protein turnover (T1/2), changes in the major lipid and fatty acid compositions of the liver, superoxide dismutase activity and formation of malondialdehyde and observations on a range of pathological changes. It was found that the basal rectal temperatures of the treated mice were higher and in the oldest group, heat performance capacity was better than those of the controls. After about 1 year of age the apparent biological half-life time of total body protein (T1/2) was observed to be shorter in the treated mice. Significant increases were observed to occur in the proportions of the polyunsaturated fatty acids in the lipids of the liver in the mice injected with 2-ME. Although no differences were observed in the superoxide dismutase activities, malondialdehyde concentrations in the livers of the experimental mice were significantly increased. Autopsy data showed that Dunn-sarcomas associated with amyloidoses occurred more frequently in the untreated mice.

A typical interdisciplinary topic: questions of the mortality dynamics

Dynamic characteristics of mortality experience are intensely studied in demography and in experimental gerontology. The classic Gompertz-Makeham function is also a significant starting point of numerous investigations in this topic. By comparative analysis of human vital statistics, one can observe characteristic secular and topological variations of the Gompertz parameters. Some of these findings are reviewed briefly in the article. Some other related questions are also touched upon. For example, the concept of the maximum life span is criticised. A thorough overview of literature data makes it clear that the general male mortality excess is by far not so unambiguous as is widely supposed. Surprisingly simple stochastic models, published by one of us in the recent past, can serve as theoretical background for the Gompertz law. Further studies would be necessary to check the biological relevance of these models.

Changes of neoplasm concentration with geographical co-ordinates

We investigated the regional differences in diversity--from another respect concentration--of causes of cancer mortality in England and Wales. Statistical analyses of published mortality data were done, using the jackknifed estimate of the Shannon index, for each region, sex and age group and year of death. In males diversity of cancer death causes is secularly increasing whilst it is decreasing in females. Latitude was negatively associated with diversity in male 45+ year age groups and longitude negatively associated with diversity in male 65+ age groups. Although, there were some significant associations in the female groups, there was no general trend across age groups as found in males. These trends remained after accounting for regional variation in past smoking behaviour. We suggest that the observed patterns may be related to prior occupational exposures and non-identified environmental and socioeconomical factors. It is concluded that techniques drawn from population ecology have a potential value in epidemiological studies of human disease. Ecological methods by themselves are likely to be of value in hypothesis generation rather than hypothesis testing.

Population dynamic models leading to logarithmic and Yule distribution

A significant field of species abundance distribution (SAD) has a population dynamical character, in which it is supposed that the stochastic speciation process and the evolution of different species are determined by the same linear birth and death process. The distributions of the number of individuals after the speciation tend to a discrete limit distribution depending on some condition if the observation time increases. In the earlier publications, in general, the speciation process was supposed to be a homogeneous Poisson process. In a more realistic case, if the speciation process is inhomogeneous Poisson, the investigation of the model is obviously more difficult. In this paper we deal with the models, in which the birth and death intensities are identical, the speciation rate is bounded, locally integrable and has asymptotically power type behaviour. Limit parameters for these models, depending on the speciation rate, are proportional to a logarithmic or (exactly or asymptotically) Yule distribution. In connection with the sample statistics some results are derived in general and also in special cases (logarithmic and Yule distribution), which are related to the random choice of a species or an individual from the whole population of the system.