Robert N. Curnow

Missing markers when estimating quantitative trait loci using regression mapping

When using molecular markers to estimate the locations and sizes of effects of QTLs in plant populations a common problem is the loss of marker genotypes for many individuals. Here we present a method that uses the information from individuals with missing marker genotypes when fitting regression mapping models using two or three neighbouring markers. The approach uses other nearby markers to recover information from the individuals with missing markers. The method is presented in detail for the two markers regression mapping technique applied to backcross or double haploid populations. The method is exemplified with a simulated data set and with data on a quantitative character in double haploid lines of barley. Generalizations of the method to three markers regression mapping models and to F2 populations are outlined.

Repeated challenge with prion disease: the risk of infection and impact on incubation period.

Natural exposure to prion disease is likely to occur throughout successive challenges, yet most experiments focus on single large doses of infectious material. We analyze the results from an experiment in which rodents were exposed to multiple doses of feed contaminated with the scrapie agent. We formally define hypotheses for how the doses combine in terms of statistical models. The competing hypotheses are that only the total dose of infectivity is important (cumulative model), doses act independently, or a general alternative that interaction between successive doses occurs (to raise or lower the risk of infection). We provide sample size calculations to distinguish these hypotheses. In the experiment, a fixed total dose has a significantly reduced probability of causing infection if the material is presented as multiple challenges, and as the time between challenges lengthens. Incubation periods are shorter and less variable if all material is consumed on one occasion. We show that the probability of infection is inconsistent with the hypothesis that each dose acts as a cumulative or independent challenge. The incubation periods are inconsistent with the independence hypothesis. Thus, although a trend exists for the risk of infection with prion disease to increase with repeated doses, it does so to a lesser degree than is expected if challenges combine independently or in a cumulative manner.

Analysis of the Bovine Spongiform Encephalopathy Maternal Cohort Study: the Discordant Case–Control Pairs

SUMMARY The progeny of the affected and non-affected dams in the bovine spongiform encephalopathy (BSE) cohort study were paired in terms of their farm of origin and approximate date of birth. This paper presents an exact logistic regression analysis that avoids modelling the differences between the pairs and so analyses only the discordant pairs. There is some evidence that the pairs in which the affected animal was born to the affected dam tend to be those in which the onset of BSE in the affected dam preceded or occurred soon after the calving. This suggests some occurrence of maternal transmission.

Locating genes involved in human diseases

The increasing amount of information that is becoming available about the structure and composition of the DNA constituting the human chromosomes has provided new opportunities to locate genes that affect susceptibilities to a range of diseases. The accurate location of these genes is important in genetic counselling and in understanding the effects of genes that may result in disease. Various methods of analysing the data when DNA information is available at a single marker locus for an affected child and his or her parents are reviewed and applied to data on insulin-dependent diabetes mellitus. The importance of distinguishing between the association of alleles at a marker locus and at a disease locus resulting from chromosomal linkage from that resulting from other causes is emphasized.

The use of markov chain models in studying the evolution of the proteins

In a recent paper Giulio & Caldararo (1987) used a Markov chain model to study the evolution of proteins. Unfortunately, their use of a first-order Markov chain model at the amino acid level is incorrect. The model has to be applied at the codon level [Jorre & Curnow (1975a)] followed by amalgamation of the codon states corresponding to each amino acid and of the three codons specifying termination. The model is correctly applied in this paper. The results obtained do not differ substantially from those obtained by Giulio & Caldararo (1987). The interpretation of the results as supporting the neutralist view of protein evolution is criticized.

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 Hamiltons 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.

Genetic polymorphisms between altruism and selfishness close to the Hamilton threshold rb = c

Genes that in certain conditions make their carriers altruistic are being identified, and altruism and selfishness have shown to be heritable in man. This raises the possibility that genetic polymorphisms for altruism/selfishness exist in man and other animals. Here we characterize some of the conditions in which genetic polymorphisms may occur. We show for dominant or recessive alleles how the positions of stable equilibria depend on the benefit to the recipient, b, and the cost to the altruist, c, for diploid altruists helping half or full sibs, and haplodiploid altruists helping sisters. Stable polymorphisms always occur close to the Hamilton threshold rb = c. The position of the stable equilibrium moves away 0 or 1 with both increases in c, the cost paid by the altruist, and increasing divergence from the Hamilton threshold, and alleles for selfishness can reach frequencies around 50%. We evaluate quantitative estimates of b, c and r from field studies in the light of these predictions, but the values do not fall in the regions where genetic polymorphisms are expected. Nevertheless, it will be interesting to see as genes for altruism are discovered whether they are accompanied by alternate alleles for selfishness.

Evolution of discrimination in populations at equilibrium between selfishness and altruism

Where there is genetically based variation in selfishness and altruism, as in man, altruists with an innate ability to recognise and thereby only help their altruistic relatives may evolve. Here we use diploid population genetic models to chart the evolution of genetically-based discrimination in populations initially in stable equilibrium between altruism and selfishness. The initial stable equilibria occur because help is assumed subject to diminishing returns. Similar results were obtained whether we used a model with two independently inherited loci, one controlling altruism the other discrimination, or a one locus model with three alleles. The latter is the opposite extreme to the first model, and can be thought of as involving complete linkage between two loci on the same chromosome. The introduction of discrimination reduced the benefits obtained by selfish individuals, more so as the number of discriminators increased, and selfishness was eventually eliminated in some cases. In others selfishness persisted and the evolutionary outcome was a stable equilibrium involving selfish individuals and both discriminating and non-discriminating altruists. Heritable variation in selfishness, altruism and discrimination is predicted to be particularly evident among full sibs. The suggested coexistence of these three genetic dispositions could explain widespread interest within human social groups as to who will and who will not help others. These predictions merit experimental and observational investigation by primatologists, anthropologists and psychologists.

Pooling DNA in the identification of parents

The preliminary pooling of DNA samples to reduce the number of tests required to identify which of a set of potential parents could be the parent of an individual progeny plant is discussed. The progeny plant may be homozygous or heterozygous at the marker locus involved and the marker alleles of the other parent plant may or may not be known. The expected number of tests is derived for varying pool sizes when the DNA of each parent plant is in one and only one DNA pool. Optimal pool sizes are calculated for a range of number of potential parents and of marker allele frequencies. Designs with each parent in more than one pool and the sequential use of up to three independent marker loci are also discussed.

OPTIMAL PLANNING OF COCOA CLONAL SELECTION PROGRAMMES

Data from three cocoa ( Theobroma cacao ) clonal selection trials are used to investigate the genetic and environmental components of variation in yield and the percentage of total pods affected by black pod disease ( Phytophtora pod rot). Simulations based on these estimated components of variation are then used to discuss the best choice in future of numbers of clones, replicates and years of harvest to maximise selection advances in the traits measured. The three main conclusions are the need to increase the number of clones at the expense of the number of replicates of each clone, the diminishing returns from additional years of harvesting and the importance of widening the genetic base of the clones chosen to be tested.