Family based studies and genetic epidemiology: theory and practice.

Family based studies have underpinned many successes in uncovering the causes of monogenic and oligogenic diseases. Now research is focussing on the identification and characterisation of genes underlying common diseases and it is widely accepted that these studies will require large population based samples. Population based family study designs have the potential to facilitate the analysis of the effects of both genes and environment. These types of studies integrate the population based approaches of classic epidemiology and the methods enabling the analysis of correlations between relatives sharing both genes and environment. The extent to which such studies are feasible will depend upon population- and disease-specific factors. To review this topic, a symposium was held to present and discuss the costs, requirements and advantages of population based family study designs. This article summarises the features of the meeting held at The University of Sheffield, August 2006.

On the structure of protein-protein interaction networks.

We present a simple model for the underlying structure of protein-protein pairwise interaction graphs that is based on the way in which proteins attach to each other in experiments such as yeast two-hybrid assays. We show that data on the interactions of human proteins lend support to this model. The frequency of the number of connections per protein under this model does not follow a power law, in contrast to the reported behaviour of data from large-scale yeast two-hybrid screens of yeast protein-protein interactions. Sampling sub-graphs from the underlying graphs generated with our model, in a way analogous to the sampling performed in large-scale yeast two-hybrid searches, gives degree distributions that differ subtly from the power law and that fit the observed data better than the power law itself. Our results show that the observation of approximate power law behaviour in a sampled sub-graph does not imply that the underlying graph follows a power law.

Modelling dominance hierarchy formation as a multi-player game.

Animals who live in groups need to divide available resources amongst themselves. This is often achieved by means of a dominance hierarchy, where dominant individuals obtain a larger share of the resources than subordinate individuals. This paper introduces a model of dominance hierarchy formation using a multi-player extension of the classical Hawk-Dove game. Animals play non-independent pairwise games in a Swiss tournament which pairs opponents against those which have performed equally well in the conflict so far, for a fixed number of rounds. Resources are divided according to the number of contests won. The model, and its emergent properties, are discussed in the context of experimental observations.

Association between two tumour necrosis factor intronic polymorphisms and HLA alleles.

The gene for tumour necrosis factor (TNF) lies at the telomeric end of the class III region of the major histocompatibility complex (MHC). Polymorphisms within this gene have been implicated in the genetic background of a large number of common human diseases. Recently two polymorphisms, TNF +489 and +691, have been described in the first intron of TNF (+489, G to A transition; +691, G deletion) and disease associations have been reported; however, the pattern of linkage disequilibrium with other MHC alleles has not been studied. We have therefore studied the association of TNF alleles with HLA-DR, -DQ and -B alleles in 216 healthy individuals from the north of England. The frequencies of the uncommon alleles were 0.08 (+489A) and 0.05 (+691Gdel). The +489A allele is associated with carriage of DRB1*1104, DQB1*0301, B18 and B35. The +691Gdel allele is associated with carriage of DRB1*13 *11, DQB1*0301 and B44. Knowledge of the pattern of association, indicating probable linkage disequilibrium, between these TNF alleles may be useful in studies aimed at determining the role of this locus in the genetic background of the large number of diseases which show genetic associations with MHC haplotypes.

TNF +489 polymorphism does not contribute to susceptibility to rheumatoid arthritis.

OBJECTIVES: To determine if a tumour necrosis factor (TNF +489) polymorphism is associated with susceptibility to rheumatoid arthritis (RA). METHODS: Two European populations were studied: 217 controls and 238 patients from the north of England and 145 controls and 179 patients from Spain. HLA-DRB1 and TNF +489 markers were typed using polymerase chain reaction based methods. RESULTS: Strong associations were demonstrated with shared epitope (SE) encoding HLA-DRB1 alleles in the English (OR = 2.9 [2.2-3.9]) and Spanish (OR = 2.3 [1.6-3.3]) populations, however no association was found with TNF +489 alleles. Furthermore carriage of TNF +489A was not associated with the presence of radiological erosions, rheumatoid nodules or rheumatoid factor. CONCLUSION: The role of the TNF locus in the genetic background of RA is unclear, however, our data does not support the previous reported association of the TNF +489A allele with RA susceptibility or severity.

A functional polymorphism of toll-like receptor 4 is not associated with likelihood or severity of meningococcal disease.

Human Toll-like receptor 4 (TLR4) transduces proinflammatory cytokine release by human cells in response to lipopolysaccharide (LPS). This study tested the hypothesis that, if TLR4 is rate limiting for a successful response to bacterial LPS in humans, a human gene polymorphism that results in the amino acid substitution Asp299Gly and causes reduced expression and function of TLR4 should influence susceptibility to or severity of natural gram-negative infection. The allele frequency of the Asp299Gly polymorphism was 5.9% among 879 blood donors, 6.5% among 1047 patients with microbiologically proven meningococcal disease, and 4.1% among 86 patients who died of meningococcal disease. No significant differences were observed, including those analyzed after stratification of the infected population by age and by meningococcal serogroup. Therefore, this functional TLR4 polymorphism does not influence susceptibility to or severity of meningococcal disease.

A sequential-arrivals model of territory acquisition II.

Birds arrive sequentially at their breeding ground where the nest sites vary in value (measured by reproductive success). Each bird may choose a vacant site or challenge an occupier for its site. In the latter case, the occupier is presumed to be the more-likely winner; the loser incurs a cost and must go to a vacant site. In a previous paper (Broom et al., 1997, J. theor. Biol.189, 257-272), we considered the optimal strategy. However, that optimal strategy was complex and perhaps could not be realized in real bird populations, making possibly costly demands both perceptually and at the coding level. With this in mind we introduce certain restricted classes of strategy, and consider how populations might evolve. Computer simulations of various populations have been performed to model the competition amongst several strategies in the presence of recurrent mutations. Certain combinations of strategies persisted and corresponded approximately to the ESSs found in Broom et al. (1997).

Evolution in knockout conflicts: the fixed strategy case.

A group of individuals resolve their disputes by a knockout tournament. In each round of the tournament, the remaining contestants form pairs which compete, the winners progressing to the next round and the losers being eliminated. The payoff received depends upon how far the player has progressed and a cost is incurred only when it is defeated. We only consider strategies in which individuals are constrained to adopt a fixed play throughout the successive rounds. The case where individuals can vary their choice of behaviour from round to round will be treated elsewhere. The complexity of the system is investigated and illustrated both by special cases and numerical examples.

Combined sib-TDT and TDT provide evidence for linkage of the interleukin-1 gene cluster to erosive rheumatoid arthritis.

Rheumatoid arthritis (RA) is a common disease of unknown aetiology which usually causes progressive destruction of the joints. Familial aggregation, twin studies and segregation analyses suggest that there is a genetic component to RA and the HLA-DRB1 locus in the major histocompatibility complex on chromosome 6 has been shown to be linked to, and associated with, RA susceptibility. It is likely that other genes with weaker effects are also involved, which may be difficult to detect using conventional parametric and non-parametric linkage methods. We have implemented the combined sib-TDT and TDT, in addition to parametric and non-parametric linkage methods, to investigate the candidate genes of the interleukin-1 (IL-1) gene cluster on chromosome region 2q13, since IL-1 is an important cytokine in the control of the inflammatory response that is central to RA pathology. Several tightly linked IL-1 cluster markers yielded suggestive evidence for linkage in the combined TDT in those families in which affected siblings did not share two HLA-DRB1 alleles identical by descent. The evidence was significant in those with severe disease, as assessed by the presence of bone erosions. In contrast, there was no evidence of linkage using non-parametric linkage analysis, but parametric analysis revealed weak evidence of linkage when marker-trait disequilibrium was incorporated into the analysis. The data provide preliminary evidence for linkage of genes of the IL-1 cluster to RA and suggest a possible role for this region in severe erosive disease.

Sperm competition. II-post-copulatory guarding

A two round sperm competition model is analysed to determine which male strategy is advantageous for fertilization of a given set of eggs; guarding a particular female or searching for another copulation. A guarding male is one who would guard if he mates in the first round (which may not occur) whilst a non-guarding male decides on how much sperm to allocate if given the opportunity to inseminate a female in round one. Guarding behaviour is defined in terms of a probability of preventing a further insemination if challenged by a rival male. Sperm success with a single female obeys the "raffle principle". An evolutionarily stable strategy (ESS) approach is used to ascertain the best non-guarding ejaculation strategy. We show that for each fixed proportion of guarders in the population the strategies are ordered and that only a single guarding strategy need be considered. The model predicts that there will be evolution to either the guarding strategy or a single non-guarding strategy or a polymorphic combination of guarding and some (or all) of the non-guarding strategies. The conditions for coexistence to occur were shown to be rare in comparison to those necessary for a monomorphism. Copyright 1999 Academic Press.

Sperm competition I: basic model, ESS and dynamics.

We examine models of sperm competition to determine which strategies are evolutionarily stable according to game theory. Games are considered in which the males of a species must divide a fixed amount of sperm between a fixed number of rounds in competition over fertilization of a given set of eggs. Sperm success with a single female is allocated using the raffle principle". A two round model is formulated and we show that the evolutionarily stable strategy (ESS) is a pure strategy in which a male should use at least half his sperm in the first round if given the opportunity to mate. The ESS is unique and globally stable, in contrast to most classical ESSs which are only locally stable. The model is extended to include the effects of sperm replenishment and egg oviposition between rounds. Both serve to increase the ESS amount of sperm inseminated in round one.

On the probabilities of identity states in permutable populations.

Génin and Clerget-Darpoux recently discussed the derivation of the probabilities of identity states for populations in which there was some degree of kinship, primarily to allow the extension of the classical affected-sib-pair method to such populations. It is argued here that their derivation makes certain assumptions that are valid only for some very restricted population models and that are not needed for an appropriate treatment. Here the probabilities of the identity states of two individuals with a given genealogical relationship are specified in terms of the kinship parameters of the underlying population, from which the founders of the individuals' genealogy have been randomly selected. It is argued that an appropriate representation for a permutable population, one in which gene identity does not depend on the pattern of genes across individuals, requires three parameters. This representation is related to that of Génin and Clerget-Darpoux and to that of Weir.

An evaluation of the application of the genetic algorithm to the problem of ordering genetic loci on human chromosomes using radiation hybrid data.

We consider the problem of ordering detectable genetic loci along a chromosome by minimizing the number of obligatory breaks that can be inferred from radiation hybrid data. The problem bears some resemblance to the travelling-salesman problem, for which genetic algorithms have been used with considerable success. We find that the results from other studies on closely related problems are not directly transferable, and although we did find a genetic algorithm that performed well in this application it would appear that this algorithm is highly sensitive to any changes in the problem. Moreover, a very simple stochastic algorithm performed almost as well as our much more complicated and computer-intensive genetic algorithm and it did so in a fraction of the time. While we do not dispute that genetic algorithms can work on large complicated problems, the various modifications and fine-tuning necessary for good performance tend to be highly problem specific and they are often only arrived at after an exhaustive exploration of possibilities. Thus, we would dispute any claim that genetic algorithms are robust in their form and range of applicability.

A sequential-arrivals model of territory acquisition

Birds arrive sequentially at their breeding ground where the nest sites vary in value (measured by reproductive success). Each bird must either choose a vacant site or challenge an occupier for its site. In the latter case we assume the occupier to be the more likely winner. The loser of the contest incurs a cost and must go to a vacant site. The rational strategy for such a contest is found. There is a threshold phenomenon; early arrivals occupy vacant sites, late arrivals fight. This result is intuitively reasonable, but the sequence of sites chosen is complex. A recursive method for specifying the solution is described and applied explicitly to some illustrative cases.Copyright 1997 Academic Press Limited Copyright 1997 Academic Press Limited

ESS patterns: adding pairs to an ESS.

The notion of a pattern of evolutionarily stable strategies was introduced by Cannings and Vickers in 1988 (J. Theor. Biol. 132:387-420). In this paper a specific class of patterns is considered. Suppose that there is an evolutionarily stable strategy (ESS) on some set of n strategies {1,2,...,n} and that new strategies {n + 1,n + 2,...,n + k} are added. Supposing that for this new enlarged conflict there is still an ESS on {1,2,...,n} and also that there are ESSs on {n + i,j} for 1 < or = i < or = k and j epsilon Si [symbol: see text] {1,2,...,n}, the authors investigate the restrictions on the Si. These restrictions are related to certain properties of strong tournaments introduced by Reid and Beineke. We also specify, given the Si, what ESSs of the form {n + i,n + j} can be added.

An investigation to determine whether clusters of cancer types exist in nine breast-ovary families.

Monte-Carlo simulations were carried out on nine BRCA1-linked families selected from the 1993 Breast Cancer Linkage Consortium. These families all displayed a prevalence of both breast and ovarian cancers, but little evidence was found to conclude that sufferers of either type formed clusters in particular branches of families. It was noted that the application of these methods to larger pedigrees with known probands would be useful in further clarifying the issue.

Multiple trial two strategy conflicts.

Much work has been done on iterated conflicts where the one-trial conflict is the Prisoner's Dilemma. The present paper is concerned with an iterated contest where the underlying contest has two pure strategies and the underlying payoff matrix is general; this therefore includes the Prisoner's Dilemma as a special case. By limiting the player's memory severely we can almost completely specify the Evolutionary Stable Strategies (ESS) of the two- and infinite-trial conflicts derived from this underlying payoff matrix.