Estimating inbreeding in large, semi-isolated populations: effects of varying generation lengths and of migration.

The purpose of the study reported here was to investigate two important assumptions used in a recently reported new method of estimating inbreeding in large, relatively isolated populations over historic times. The method, based on modeling the genealogical "paradox," produces values of Pearl's coefficients, Z, a measure of inbreeding or genealogical coalescence, as a function of time. In this study, the effects on inbreeding of two important assumptions made in earlier studies, namely those of using a constant generation length and of ignoring migration, have been investigated for the population of Britain. First, by relating the median age of women at childbirth to the development level of various societies, the variation of the generation lengths for different periods in historic Britain were estimated. Values of Z for two types of varying generation lengths were then calculated and compared with the case of constant generation length. Second, the population curve for Britain used in earlier studies was modified to obtain the subpopulation at any time during the past two millennia that was descended from the pre-Roman British Celts. Values of Z for the case with migration were then calculated and compared with the case for no migration. It is shown that these two assumptions may be taken into account if and when required. Both the effect of a varying generation length and the effect of migration on Z were found to be 20-40%, when no known value of inbreeding was used, and 2-5%, when a known value of inbreeding was used.

A standard approach to measurement uncertainties for scientists and engineers in medicine.

The critical nature of health care demands high performance levels from medical equipment. To ensure these performance levels are maintained, medical physicists and biomedical engineers conduct a range of measurements on equipment during acceptance testing and on-going quality assurance programs. Wherever there are measurements, there are measurement uncertainties with potential conflicts between the measurements made by installers, owners and occasionally regulators. Prior to 1993, various methods were used to calculate and report measurement uncertainties. In 1993, the International Organization for Standardization published the Guide to the Expression of Uncertainty in Measurement (GUM). The document was jointly published with six international organizations principally involved in measurements and standards. The GUM is regarded as an international benchmark on how measurement uncertainty should be calculated and reported. Despite the critical nature of these measurements, there has not been widespread use of the GUM by medical physicists and biomedical engineers. This may be due to the complexity of the GUM. Some organisations have published guidance on the GUM tailored to specific measurement disciplines. This paper presents the philosophy behind the GUM, and demonstrates, with a medical physics measurement example, how the GUM recommends uncertainties be calculated and reported.

A comparison of inbreeding rates in India, Japan, Europe and China.

This is a report on an application of a new method for estimating inbreeding rates in large, semi-isolated populations over time. This study is intended to further show the versatility of the method. In a previous study, the method was shown to be useful in analysing the effect of details in a single population curve on inbreeding. In this study, the method is applied to the population curves of India, Japan, Europe and China over the past two millennia, to allow inter-comparisons of the inbreeding within those populations. Anthropologists traditionally concentrate on small isolates within a country for the estimation of inbreeding. Those isolates, however, might not be representative of the country as a whole. The method used in this study attempts to estimate inbreeding over large regions over an extended period of time. The method models the genealogical 'paradox' and yields estimates of the average inbreeding in terms of Pearl's coefficient Z, as a function of time. It is first assumed that the whole population of each country is the adult (breeding) population, corresponding to minimum inbreeding. It is found that the more complex the population curve examined, the greater the precision of the Z curves obtained. The effect of incorporating a single known value of inbreeding into the analyses is also investigated. This procedure produces a more realistic situation where the adult (breeding) population is considerably less than the entire population. It is shown, that if it is assumed that the whole population of the country is the adult (breeding) population, then a present day person from one of the four regions/countries studied is descended from between 72% and 97% of the early medieval population of the particular country. On the other hand, if a known value of inbreeding for Britain is incorporated into the analysis, these values become of the order of 1% for the older-settled regions/countries, and about 16% for Japan. However, that value for Japan is reduced to about 1% when a known value of inbreeding for this country is used. Although some uncertainty in these results remains, the versatility of the method demonstrated here will provide more accurate results, as better input-data become available.

Experimental simulation of A-bomb gamma ray spectra for radiobiology studies.

Improved radiation protection of humans requires a better understanding of the mechanisms of radiation action and accurate estimates of radiation risk for both internal and external radiations. The Japanese atomic bomb survivors represent one of the most important sources of human data on the late carcinogenic effects of ionising radiations. The present study was undertaken to investigate whether it would be possible to use hospital radiotherapy/radiobiology equipment to mimic the spectra encountered in Hiroshima and Nagasaki. The estimated total gamma ray fluence spectra (including both prompt and delayed photons) at both Hiroshima and Nagasaki, for distances of 500, 1000, 1500 and 2000 m have been evaluated using DS86 data and previously unpublished information for delayed gamma radiations which constitute the major contribution to survivor doses. Monte Carlo (EGS4) simulations were performed to transport these photons through the body in order to investigate the variation in electron spectra for various body organs. The electron spectra obtained for these fluences at, for example, the colon, have been matched with combinations of electron spectra produced by linear accelerators to within 5% SD. These will, for the first time, enable a direct link to be made between radiobiological studies (for example, on mammography spectra) and the epidemiological data from Japan, which currently underpin radiation risk estimates.

New method of estimating inbreeding in large semi-isolated populations with application to historic Britain.

The purpose of this paper is to introduce a new method of estimating inbreeding in large, relatively isolated, populations over historic times, to demonstrate its application, and indicate some of its limitations and future developments. The method is based on the "paradox" of genealogy, and requires only that the variation of the population size be known, at least reasonably well, over an extended historic period. In this study a method has been developed to model this "paradox" which allows an estimation of the minimum level of inbreeding necessary for a given population curve in terms of values of Pearl's coefficients for each generation. As an example, the method is applied to the population of Britain. It is found that the frequency of siblings occurring in the same generation of a pedigree varies with the population size according to the Fermi-Dirac equation of statistical physics. The effect of introducing a single known estimate of inbreeding into the model is to make the otherwise diverse results for both the actual numbers of ancestors in a generation and the corresponding coefficients of inbreeding to converge.

Finger doses received during 153Sm injections.

This study was undertaken to determine the dose received by the skin of the fingers of clinical and laboratory staff during injections of 153Sm. The use of 153Sm, chelated with ethylenediaminetetramethylene phosphonic acid (153Sm-EDTMP), is coming into more frequent use in radionuclide therapy since its approval by the U.S. Food and Drug Administration in March 1997. 153Sm emits a range of medium-energy therapeutically useful beta particles that have been found beneficial in the palliation of metastatic bone cancer pain. It also emits a range of gamma rays. Calculations have been undertaken to provide the beta-particle and gamma-ray dose rates, at a depth within the skin corresponding roughly to the basal cell layer, when the finger is placed in direct contact with the external surface of a syringe containing 153Sm. The beta-particle dose rates were modeled using an empirically based Monte Carlo approach previously described by Beddoe and Kelly. The gamma-ray dose rates were modeled using a distributed point source approach previously reported by Pattison et al. In the calculations it is assumed that a typical administered activity is 2.6 GBq, with a finger-syringe contact time of 30 s. The skin dose, due to both beta particles and gamma rays when the finger is centrally placed over an active volume of 0.3 mL in a 1-mL syringe, is calculated to be 77 mGy per injection. Similarly, for an active volume of 1.0 mL in a 2.5-mL syringe, the dose is calculated to be 10 mGy per injection. In view of the ICRP recommended weekly skin dose limit of 10 mGy, both of the above two doses are excessive. If, however, the fingers are placed at the rear end of the syringe barrel, where they are only exposed to the gamma rays, the above two doses are reduced to 0.069 and 0.139 mGy per injection, respectively. Both of these two doses are well within the recommended weekly dose limits for the skin. It is found that the weekly dose limit for the skin is readily exceeded if the fingers are in direct contact with the external surface of the syringe and located over the active volume. However, if handled at the rear end of the syringe barrel, a typical weekly workload can be managed without exceeding the recommended dose limits.