An agglomerative hierarchical approach to visualization in Bayesian clustering problems.

Clustering problems (including the clustering of individuals into outcrossing populations, hybrid generations, full-sib families and selfing lines) have recently received much attention in population genetics. In these clustering problems, the parameter of interest is a partition of the set of sampled individuals--the sample partition. In a fully Bayesian approach to clustering problems of this type, our knowledge about the sample partition is represented by a probability distribution on the space of possible sample partitions. As the number of possible partitions grows very rapidly with the sample size, we cannot visualize this probability distribution in its entirety, unless the sample is very small. As a solution to this visualization problem, we recommend using an agglomerative hierarchical clustering algorithm, which we call the exact linkage algorithm. This algorithm is a special case of the maximin clustering algorithm that we introduced previously. The exact linkage algorithm is now implemented in our software package PartitionView. The exact linkage algorithm takes the posterior co-assignment probabilities as input and yields as output a rooted binary tree, or more generally, a forest of such trees. Each node of this forest defines a set of individuals, and the node height is the posterior co-assignment probability of this set. This provides a useful visual representation of the uncertainty associated with the assignment of individuals to categories. It is also a useful starting point for a more detailed exploration of the posterior distribution in terms of the co-assignment probabilities.

The value of suction wound drain after carotid and femoral artery surgery: a randomised trial using duplex assessment of the volume of post-operative haematoma.

BACKGROUND: The use of vacuum suction drains after carotid endarterectomy (CEA) and groin dissection for arterial reconstruction surgery remains controversial. A large multicentre prospective randomised trial would be needed to show any difference if clinical end points (infection and haematoma) are used. Therefore, we conducted a study to evaluate the value of wound drainage using accurate duplex measurement of haematoma expecting a 25% difference in volume between drained and non-drained wounds. PATIENTS AND METHODS: Seventy consecutive patients undergoing CEA and 73 patients who underwent 106 groins dissection were separately and blindly randomised into two groups: group (a) with wound drain and group (b) without wound drain. A duplex scan was carried out post-operatively to document the presence and volume of any wound haematoma. RESULTS: The majority of wounds did not show any evidence of collections. 1. In the CEA patients duplex scan revealed wound haematoma in 8 patients with a median volume of 25 ml (5-65) in group (a) in comparison to 7 wound haematomas 31 ml (3-72) in group (b). Median suction drain drainage was 42 ml (10-120) when used. There was no significant difference between the two groups. Three patients 4.3% (two from the drain group) underwent evacuation of haematoma post-operatively.2. In the groin dissection patients most of the documented collections were trivial. Ultrasound scans showed 21 collections (20%), of these 7 (34%) were in group (a) and 14 (66%) were in group (b). There was no significant difference in wound collections between the two groups (p = 0.28). Only 5 collections (75%) exceeded 10 ml, three of them were in the drain group. One patient (1%), who did not have a drain, developed a wound collection, which needed re-exploration. When a drain was used the median drainage was 64.5 ml (range 10-220). CONCLUSION: These results based on accurate measurement of wound collection suggest that there is no benefit in terms of reduction of the volume of haematoma on wound drainage after CEA or arterial reconstruction surgery involving the groin. A selective policy of use of drainage is therefore recommended.

Population structure of the beetle pests Phyllodecta vulgatissima and P. vitellinae on UK willow plantations.

Phyllodecta (= Phratora) vulgatissima and P. vitellinae (Coleoptera: Chrysomelidae) are important pests of willows and poplars. Their differences in host species preference may provide a non-chemical control strategy for pest control. However, little is known about population structure with respect to hosts, regions or seasons. Using five microsatellites, 850 P. vulgatissima and 1100 P. vitellinae individuals, comprising 17 and 22 UK samples, respectively, were genotyped. High diversity was observed at all loci. Migrant numbers exchanged per generation (Nm) were high (2.1-12.6 for P. vulgatissima and 0.9-12.2 for P. vitellinae), suggesting high genetic exchange between samples. Estimates of population differentiation (FST) and analyses of the data using Bayesian methods (Partition and Structure) showed little evidence of subdivision in relation to geography, sampling time or host.

A Bayesian approach to the identification of panmictic populations and the assignment of individuals.

We present likelihood-based methods for assigning the individuals in a sample to source populations, on the basis of their genotypes at co-dominant marker loci. The source populations are assumed to be at Hardy-Weinberg and linkage equilibrium, but the allelic composition of these source populations and even the number of source populations represented in the sample are treated as uncertain. The parameter of interest is the partition of the set of sampled individuals, induced by the assignment of individuals to source populations. We present a maximum likelihood method, and then a more powerful Bayesian approach for estimating this sample partition. In general, it will not be feasible to evaluate the evidence supporting each possible partition of the sample. Furthermore, when the number of individuals in the sample is large, it may not even be feasible to evaluate the evidence supporting, individually, each of the most plausible partitions because there may be many individuals which are difficult to assign. To overcome these problems, we use low-dimensional marginals (the 'co-assignment probabilities') of the posterior distribution of the sample partition as measures of 'similarity', and then apply a hierarchical clustering algorithm to identify clusters of individuals whose assignment together is well supported by the posterior distribution. A binary tree provides a visual representation of how well the posterior distribution supports each cluster in the hierarchy. These methods are applicable to other problems where the parameter of interest is a partition of a set. Because the co-assignment probabilities are independent of the arbitrary labelling of source populations, we avoid the label-switching problem of previous Bayesian methods.

The decay of linkage disequilibrium under random union of gametes: how to calculate Bennett's principal components.

How rapidly does an arbitrary pattern of statistical association among a set of loci decay under meiosis and random union of gametes? This problem is non-trivial, even in the case of an infinitely large population where selection and other forces are absent. J. H. Bennett (1954, Ann. Hum. Genet. 18, 311-317) found that, for an arbitrary number of loci with an arbitrary linkage map, it is possible to define measures of linkage disequilibrium that decay geometrically with time. He found a recursive method for deriving expressions for these variables in terms of "allelic moments" (the factorial moments about the origin of the "allelic indicators"), and expressions for the allelic moments in terms of his new variables. However, Bennett no where stated his recursive algorithm explicitly, nor did he give a general formula for his measures of linkage disequilibrium, for an arbitrary number of loci. Recursive definitions of Bennett's variables were obtained by Lyubich. However, the expressions generated by these recursions are not the same as those found by Bennett. (They do not express Bennett's variables as functions of the allelic moments.) Lyubich's derivations employ genetic algebras. Here, I present a method for obtaining explicit expressions for Bennett's variables in terms of the allelic moments. I show that the transformation from the allelic moments to Bennett's variables and the inverse transformation always have the form that Bennett claimed. (This transformation and its inverse have essentially the same form.) I present general recursions for calculating the coefficients in the forward transformation and the coefficients in the inverse transformation. My derivations involve combinatorial arguments and ordinary algebra only. The special case of unlinked loci is briefly discussed.

The dynamics of infinitesimally rare alleles, applied to the evolution of mutation rates and the expression of deleterious mutations.

A new method is presented for analysing the dynamics of a classical model where infinitesimally rare alleles segregate at an infinite number of unlinked loci, and where the alleles at different loci have equivalent effects. The dynamics of the distribution of the number of rare alleles per individual (the "phenotypic distribution") can be followed without knowing the frequencies of individual genotypes. Meiosis and random union of gametes have a very simple effect on the factorial cumulants of the phenotypic distribution which are consequently the natural set of variables to follow. An exact solution is presented for the dynamics of rare alleles under mutation and multiplicative selection. This solution has a simple representation in terms of the factorial cumulants. Unlike the QLE (quasi-linkage equilibrium) solution, this solution applies even when the population is far from linkage equilibrium. This approach is extended to analyse the joint dynamics of infinitesimally rare alleles at an infinite number of unlinked loci, together with a locus (with arbitrary allele frequencies) with which they interact. This more general method is used to investigate (1) the joint dynamics of a modifier of the mutation rate, together with deleterious alleles under mutation and multiplicative selection, and (2) the fate of an allele that ameliorates or exacerbates the fitness effects of deleterious alleles. When a new modifier allele causes a large change in the mutation rate, strong linkage disequilibrium is generated during its progress. However, using this new approach based on factorial cumulants, it is found that a remarkably simple invasion condition applies to alleles at the modifier locus, even when strong linkage disequilibrium is generated.

Evolutionarily stable mutation rates.

I investigate the hypothesis that mutation rates in natural populations are determined by a balance between: (1) selection against deleterious mutations favouring lower mutation rates, and (2) selection opposing further reduction of the mutation rate, resulting from the costs incurred by more stringent proof-reading and repair (for example, a reduction in the rate of DNA replication). The influence of advantageous mutations is assumed to be negligible. In a previous paper, I analysed the dynamics of a modifier of the mutation rate in a large sexual population, where (infinitesimally rare) deleterious alleles segregate at an infinite number of unlinked loci with symmetric multiplicative fitness effects. A simple condition was obtained for a modifier allele to increase in frequency. Remarkably, this condition does not depend on the allele frequencies at the modifier locus. Here, I show that (as a consequence), given any set of possible values of the mutation rate (any set of possible modifier alleles), there always exists a single globally stable value of the mutation rate. This is an unusually strong form of "evolutionary stability" for a sexual population. Less surprisingly the optimum mutation rate in an asexual population has similar stability properties. Furthermore, in the case of an asexual population, it is not necessary to make any special assumptions about the selection acting against deleterious mutations, except that a deterministic mutation-selection equilibrium exists. I present a simple method for identifying the evolutionarily stable value of the mutation rate, given the function alpha(U) relating the value of the mutation rate to the fitness cost of maintaining this rate. I also argue that if there is a highly conserved relationship between the rate of replication per base, and the rate of mutation per base, and if this relationship has the form of a power law, then the remarkable uniformity of the per genome mutation rate in DNA based microbes can be explained.

Linkage disequilibrium and the infinitesimal limit.

Under the classical Fisher-Bulmer infinitesimal model of quantitative genetics, the within-family distribution for an additive trait with no environmental component is Gaussian with mean at the mid-parent value and a variance which is the same for all families. When an additive trait is determined by unlinked loci, the Fisher-Bulmer model can arise in the limit as the number of loci contributing to variation in the trait increases. However, a counterexample is presented where the Fisher-Bulmer model fails to arise in the infinite locus limit because there is too much linkage disequilibrium. An example is also presented where a degenerate form of the Fisher-Bulmer model arises. Under what conditions does the Fisher-Bulmer model arise in the infinite locus limit? It follows from the central limit theorem that the within-family distribution is Gaussian. But, under what conditions is the within-family distribution the same for almost all families in the population? An alternative population genetic derivation of the Fisher-Bulmer model is presented for a population at linkage equilibrium. This approach is then extended to allow many patterns of linkage disequilibrium. Diallelic models are used to illustrate the type of linkage disequilibrium allowed. The results on the limiting behaviour of population genetic models with many unlinked loci can be regarded as special cases of a more general limiting property of sequences of random variables. A possible application of this more general result to models of cultural inheritance is suggested.

Evolutionary consequences of a trade-off between parental effort and mating effort.

I investigate the joint evolution of male and female strategies in a dioecious population where individuals can increase their access to mates by attacking or threatening rivals. In some species where individuals can increase their mating success in this way, both sexes allocate resources to parental effort. There may be a trade-off between parental effort and mating effort (for conflict over access to mates). If so, what factors must be included in the model for parental effort by both sexes to be evolutionarily stable? I analyse a simple game theoretic model that allows conflict over access to mates. Three versions of this model are analysed. In the simplest version, variation among individuals of each sex is allowed only in their total parental effort. The more elaborate versions of the model also allow variation in the parental investment per offspring. When this type of variation is allowed, a pair of male and female strategies can only be evolutionary stable if one sex alone contributes all parental effort. However, when non-heritable variation in the resources available to individuals is introduced (the third version of the model), parental effort by both sexes can be maintained.

The regulation of assisted reproductive technology in Australia: issues and solutions.

The legislative response to assisted reproduction technology had been inappropriate and inflexible for such a rapidly developing area of medicine. A national system of regulation, consisting of a merger of components of already established committees and based on the United Kingdom system introduced in 1990, would overcome the legislative differences between States, and provide a more responsible and responsive regulatory system.

Delaying transfer to the third day post-insemination, to select non-arrested embryos, increases development to the fetal heart stage.

The purpose of this study was to determine whether delaying embryo transfer by 24 h, until day 3 post-insemination, allowed improved selection of non-arrested embryos for transfer. We have retrospectively analysed pregnancy rates in a large series of patients who had embryo transfer either on day 2 or on day 3 post-insemination over a 27 month period. From January 1990 to March 1992, 567 patients received embryo transfer on day 2, and 661 patients had transfer on day 3 post-insemination, but these transfers were not contemporary. Pregnancy rates were slightly higher in patients who had embryo transfer on day 3 (37%) than in those patients who had their embryos transferred on day 2 (35%), but this difference was not significant. The implantation rate, as measured by the proportion of embryos developing to the fetal heart stage, was significantly higher following transfer on day 3 (23%) than after transfer on day 2 (19%) (P < 0.05), suggesting that selection of viable embryos is improved on day 3. Furthermore, of the embryos which gave rise to a fetal sac, significantly fewer miscarried before the fetal heart stage (P < 0.05) following transfer on day 3 (6%) than after transfer on day 2 (12%). Delaying transfer until day 3 provides a further 24 h to observe embryo development. During this period 16% of embryos arrested or became developmentally retarded; thus waiting until day 3 allowed these embryos to be identified and avoided for consideration for transfer. Embryo transfer may be safely delayed until day 3, and this may help in selecting embryos most likely to implant and develop after transfer.

Acute limb deterioration during intra-arterial thrombolysis.

Approximately 12 per cent of limbs undergoing intra-arterial thrombolysis (IAT) develop distal embolism or extension of thrombus during the procedure. These are usually of little clinical consequence and can be treated by increasing the rate of administration of the lytic agent. However, in some patients the clinical condition of the limb deteriorates rapidly. In an attempt to define the incidence of acute limb deterioration during IAT, information was collected from five centres in the UK with experience of the technique. A total of 866 treatments were recorded, with 20 limbs (2.3 per cent) undergoing acute deterioration. This complication was more common during the treatment of thrombosed popliteal aneurysm than during that of emboli or thrombosed atheromatous arteries or grafts (P < 0.001). The amputation rate associated with the complication was high, and operative intervention provided better results than continuation of lysis.

The electronic information revolution and how to exploit it.

Medical information is increasingly stored in electronic format, enabling faster and more flexible access to the literature. Online, compact disc and floppy disc databases are widely available. The origins and development of these different database media are described. The strengths and weaknesses of each, and the ways in which they complement each other, are examined. Ease of access to medical information can result in data management problems; the role of bibliographic software in ensuring full exploitation of the electronic information revolution is therefore emphasized.

Mycotic aneurysm of the cervical carotid artery due to Salmonella enteritidis.

A case of mycotic carotid aneurysm due to Salmonella enteritidis infection is reported. The features of the condition and the principles of treatment are described.

Primary breast carcinoma in patients with malignant melanoma.

Malignant melanoma and primary breast cancer are tumours which have an association based on genetic and hormonal factors. It is not generally appreciated that there is an increased incidence of melanoma in patients with breast cancer and vice versa. We present two cases of patients who developed breast carcinoma following previous treatment for melanoma. We review previous reports of this association and examine the theoretical reasons why this should be so. Medical practitioners should be aware of this association in order to alter their index of suspicion appropriately.