Selfishness and altruism can coexist when help is subject to diminishing returns.

Altruism and selfishness are 30-50% heritable in man in both Western and non-Western populations. This genetically based variation in altruism and selfishness requires explanation. In non-human animals, altruism is generally directed towards relatives, and satisfies the condition known as Hamilton's rule. This nepotistic altruism evolves under natural selection only if the ratio of the benefit of receiving help to the cost of giving it exceeds a value that depends on the relatedness of the individuals involved. Standard analyses assume that the benefit provided by each individual is the same but it is plausible in some cases that as more individuals contribute, help is subject to diminishing returns. We analyse this situation using a single-locus two-allele model of selection in a diploid population with the altruistic allele dominant to the selfish allele. The analysis requires calculation of the relationship between the fitnesses of the genotypes and the frequencies of the genes. The fitnesses vary not only with the genotype of the individual but also with the distribution of phenotypes amongst the sibs of the individual and this depends on the genotypes of his parents. These calculations are not possible by direct fitness or ESS methods but are possible using population genetics. Our analysis shows that diminishing returns change the operation of natural selection and the outcome can now be a stable equilibrium between altruistic and selfish alleles rather than the elimination of one allele or the other. We thus provide a plausible genetic model of kin selection that leads to the stable coexistence in the same population of both altruistic and selfish individuals. This may explain reported genetic variation in altruism in man.

Population genetic models can be used to study the evolution of the interacting behaviours of parents and their progeny.

An example of the evolution of the interacting behaviours of parents and progeny is studied using iterative equations linking the frequencies of the gametes produced by the progeny to the frequencies of the gametes in the parental generation. This population genetics approach shows that a model in which both behaviours are determined by a single locus can lead to a stable equilibrium in which the two behaviours continue to segregate. A model in which the behaviours are determined by genes at two separate loci leads eventually to fixation of the alleles at both loci but this can take many generations of selection. Models of the type described in this paper will be needed to understand the evolution of complex behaviour when genomic or experimental information is available about the genetic determinants of behaviour and the selective values of different genomes.

Consanguinity and the transmission/disequilibrium test for allelic association.

Consanguineous marriages, usually between first cousins or between uncle and niece, are common in certain societies. The transmission/disequilibrium test (TDT) compares the transmission from parents to an affected child of alleles at a marker locus, and differential transmission indicates linkage and allelic association between the marker locus and a disease locus. We investigate the consequences for the TDT, as a test for allelic association, of consanguineous marriages. For each parental marker mating type, we calculate the frequency of each disease mating type, and the associated probability that an offspring is affected. We use Bayes' Theorem to estimate the probability that an affected child inherits the given allele from a heterozygous parent, then combine our results across marker mating types. The effect of consanguineous marriage is usually small. For candidate genes, the effects were greater for uncle-niece marriages, for rare disease alleles, and for high genotype relative risk. For markers, the effects were generally negligible. The Type I error probability of the TDT is essentially unchanged by intermarriage, except for a purely recessive disease allele. The power of the TDT is increased for a recessive allele and decreased for a dominant allele. However, consideration of levels of consanguinity that arise in practice indicates that standard power calculations for the TDT will usually need only minor modification.

Using information from both parents when testing for association between marker and disease loci.

Several extensions of the transmission/disequilibrium test (TDT) to multi-allelic markers now exist. In some of these, however, separate tests must be performed on male and female parents because of the non-independence of parental transmission patterns, reducing power, and complicating interpretation of the test results. Here we show that this non-independence is asymptotically irrelevant when using the allelic TDT of Bickeböller and Clerget-Darpoux [(1995) Genet Epidemiol 12:577-582], allowing the analysis of data from both parents simultaneously.

A likelihood ratio test for detecting patterns of disease-marker association.

A likelihood ratio test of disease-marker association is proposed, based on the observation of marker alleles transmitted from parents to affected children. The proposed association test has the advantage of identifying the population pattern of disease-marker association, differentiating between marker alleles that are positively and negatively associated with the disease. The power of the test for detecting association is evaluated and compared with three existing multi-allelic tests for some specific disease-marker association patterns. The power of the parametric tests depends crucially on the pattern of disease-marker association. An over-parameterised association model is less detrimental in terms of power than an under parameterised model.

Randomization tests of disease-marker associations.

A powerful test for population association of a disease with alleles at a bi-allelic marker locus is the transmission/disequilibrium test (TDT). A generalization of the test to multi-allelic marker loci is proposed which utilizes the maximal association of individual alleles with the disease, given by the maximum TDT statistic, TDT(max). To overcome the multiple testing problem encountered when using the maximal association to test the null hypothesis of no disease-marker association, a randomization procedure is developed. An investigation of the power of the test suggests that the randomization procedure performs almost as well as a recently proposed likelihood based test of linkage disequilibrium. The advantage of the new test is that it can be applied sequentially, based on a one-sided version of the TDT statistic, for investigating patterns of association of several individual alleles with the disease.

Testing candidate genes that may affect susceptibility to leprosy.

Several statistical methods have been used to search familial data sets for marker alleles associated with the occurrence of a disease. In the present paper, a recently developed method is used to re-analyze published data on leprosy and candidate genes at the HLA loci. This new method of analysis, the randomization transmission disequilibrium test (TDT), confirmed previous conclusions that there was no significant evidence against random transmission at the HLA-A locus but significant positive association with the HLA-DR2 allele. The randomization TDT detected significant protective associations, that had not previously been found, with alleles HLA-B8 in Egyptian families and HLA-B21 (current nomenclature B x 4901, 5001-5002) in South Indian families, highlighting a major advantage of permutation tests in analyzing candidate gene loci with rare alleles. These findings provide evidence that HLA class I restricted T lymphocytes may be of protective importance in leprosy.

Separating the environmental and genetic factors that may be causes of bovine spongiform encephalopathy.

The initial cause of the bovine spongiform encephalopathy (BSE) epidemic is generally accepted to have been the feeding of infected animal protein to cattle. The proportion of animals affected in any year in a particular herd has generally been low. This suggests either considerable variation in the extent of challenge of the individual animals or variation in their susceptibility to challenge or both. There is known to be genetic variation in susceptibility in other spongiform encephalopathies, such as scrapie in sheep. However, earlier indications that there may be associations between the incidence of BSE in cattle and polymorphisms and mutations in the PrP gene have not been confirmed (Hunter et al. 1994). Here, we attempt to model the likely extent of challenge of the individual animals in five Holstein Friesian pedigree herds and also the distribution of incubation times to the date of clinical onset. By studying the incidence of the disease in related animals we first found that single locus genetic models fitted the data much better than a non-genetic model. This was the first statistical evidence found of genetic variation in susceptibility to BSE. A check on the model in which individual animals were randomly allocated to 'parents' showed that the result was due to the lack of allowance in the non-genetic model for those animals insufficiently challenged or, for non-genetic reasons, resistant to their level of challenge. Thus there is still no evidence, molecular or statistical, for genetic variation in susceptibility. The importance of checking the attribution of genetic effects in complex models by the random allocation of progeny to parents is clear.

Optimal diets for egg production.

1. The Reading model for the egg production of a flock as determined by the intake of a single amino acid is based on the assumption that other amino acid intakes are not limiting egg production. This can result in an overestimation of the optimum intakes of each amino acid considered. 2. In this paper a model is introduced and an optimisation procedure presented that will allow the calculation of the optimal amounts of each of a number of amino acid intakes. 3. The method is illustrated by an example and the sensitivity of the results to different methods of calculation and different values of the parameters investigated. 4. A computer program, available from the authors, calculates optimal amino acid intakes for a flock defined in terms of the distribution of body weight and potential maximum egg production of the birds; the cost of the amino acids and the value of a unit of extra egg production. The program also allows the flock to be divided into 2 sub-flocks according to body weight and optimal diets calculated for each sub-flock.

The incidence of bovine spongiform encephalopathy in the progeny of affected sires and dams.

Case control study techniques were used to compare the incidence of bovine spongiform encephalopathy (BSE) in the progeny of two affected sires and 110 affected dams with the incidence of BSE in the progeny of animals known to be unaffected at the last record. All the progeny were born before the ban on ruminant-derived protein in feedstuffs issued in July 1988. The results provide little, if any, evidence of differences between the incidence in the progeny of the affected animals and the incidence in the progeny of the presumed unaffected animals. Data from five herds were used in a logistic regression analysis to study the effects of the disease status of the dam and the age of the dam at the birth of the calf on the incidence of BSE. The disease status of the dam did not significantly affect the disease status of its progeny, after allowance had been made for the effects of herd, year and the age at last record of the progeny. The difficulty of establishing maternal transmission if a high proportion of the dams are incubating the disease and transmission can occur early in the incubation period is discussed.

Using marker-maps in marker-assisted selection.

A method of using information on the location of markers to improve the efficiency of marker-assisted selection (MAS) in a population produced by a cross between two inbred lines is developed. The method is closer to mapping QTL than the selection index approaches to MAS described by previous authors. We use computer simulations to compare our method with phenotypic selection and two selection index approaches, simulations being performed on three genetic maps. The simulations show that whilst MAS can be considerably more efficient than phenotypic selection differences between the three MAS methods are slight. Which of the MAS methods is best depends on a number of factors: in particular the genetic map, the time scale under consideration ant the population size are of importance.

The need for inpatient palliative care facilities for noncancer patients in the Thames Valley.

Inpatient facilities in palliative care units are generally considered to be mainly for cancer patients. We present and discuss the results of a survey that attempted to estimate the number of noncancer patients requiring inpatient palliative care. Questionnaires sent to all general practices in the Thames Valley area asked about the diagnosis and the number of bed-days that would have been required for each noncancer patient in the practice dying in the last year or still in their care. The replies suggest that about 11 noncancer patients per practice per year were in need of respite or continuing care. For the Thames Valley area this would amount to at least 66,000 bed-days per year for noncancer patients, compared with the current provision, mainly for cancer patients, of about 40,000 bed-days per year. The diagnoses involved and the reasons why our figures may overestimate need, are discussed. There can be no doubt that, if the need is to be met, current facilities will be inadequate and additional beds and services will be required.

Carrier risk calculations for recessive diseases when not all the mutant alleles are detectable.

The number of recessive diseases, such as cystic fibrosis, in which some but not all of the mutations causing the disease can be detected using genetic probes, is certain to increase. For counselling purposes, the probability that a consultand known not to have a detectable mutation is nevertheless a carrier, needs to be calculated with as much accuracy as possible. This paper describes a program, available from the author, written specifically to make these calculations. As an example, results are presented for cystic fibrosis, assuming an incidence of 1 in 2,400 and that 80% of the mutations, being delta F508 mutations, are detectable. Numerical results are given when information may be available on the parents, one or two sibs and one or two children of the consultand. When test results are available on the children, the test status of the spouse of the consultand is relevant and may also be available. Risk calculations are also presented when an aunt (uncle) of the consultand has cystic fibrosis. Finally, disease and carrier risks are given for the child of first cousins, neither of whom has a detectable mutation.

An allelocentric view of life-history evolution.

For the case of weak selection, random assortment of gametes, and density-independent population regulation, we here establish the conditions under which an allele will spread in a population, with particular reference to the life-history effects of the allele, its level of dominance, and sex differences in its effects. Our treatment is simpler than that of Charlesworth (1980), but the results are essentially the same. We show that two quantities govern the selective dynamics of a two-allele single-locus system; these are level of dominance, and the difference between the per copy rates of increase of the alleles in homozygous populations. Our main conclusion is that the eventual outcome of evolution is unaffected by an allele's level of dominance, or sex differences in its effects, provided there is no overdominance. However, speed of progress to fixation is, of course, affected by these factors, and equations are derived to show how level of dominance affects speed of progress to fixation. When a dominant allele only affects the life history of one sex, its rate of spread is half that if both sexes are affected. The relationship between actual and intrinsic rates of increase is discussed and formulae are given showing the relationship for the case of weak selection.

Statistical evaluation of the fixed-dose procedure.

The fixed-dose procedure (FDP) was proposed by the British Toxicology Society in 1984 as an alternative to the LD50 study in the assessment of the acute oral toxicity of a substance. This paper presents a statistical evaluation of this procedure. A mathematical description of the FDP shows that the starting dose can affect the toxic classification of a substance. The toxic classification based on the FDP is compared with that based on an LD50 test. This shows that, in general, the FDP is likely to result in the same classification or a less toxic one than the LD50 procedure. However, for substances with very shallow dose-response slopes, the FDP is likely to result in the same classification or a more toxic one. The expected number of animals that will be tested and will die using the FDP will be reduced compared with the LD50 study. The results from the international validation study carried out in 1989 showed agreement with the results predicted from the mathematical model.

Estimating the locations and the sizes of the effects of quantitative trait loci using flanking markers.

The use of information from flanking markers to estimate the position and size of the effect of a quantitative trait locus (QTL) lying between two markers is shown to be affected by QTLs lying in neighbouring regions of the chromosome. In some situations the effects of two QTLs lying outside the flanked region are reinforced in such a way that a 'ghost' QTL may be mistakenly identified as a real QTL. These problems are discussed in the framework of a backcross using a regression model as the analytical tool to present the theoretical results. Regression models that use information obtained from three or more nearby markers are shown to be useful in separating the effects of QTLs in neighbouring regions. A simulated data set exemplifies the problem and is analysed by the interval mapping method as well as by the regression model.

Tests for the statistical significance of protein sequence similarities in data-bank searches.

A suite of tests to evaluate the statistical significance of protein sequence similarities is developed for use in data bank searches. The tests are based on the Wilbur-Lipman word-search algorithm, and take into account the sequence lengths and compositions, and optionally the weighting of amino acid matches. The method is extended to allow for the existence of a sequence insertion/deletion within the region of similarity. The accuracy of statistical distributions underlying the tests is validated using randomly generated sequences and real sequences selected at random from the data banks. A computer program to perform the tests is briefly described.