A dynamic network population model with strategic link formation governed by individual preferences.

Historically most evolutionary models have considered infinite populations with no structure. Recently more realistic evolutionary models have been developed using evolutionary graph theory, which considered the evolution of structured populations. The structures involved in these populations are typically fixed, however, and real populations change their structure over both long and short time periods.

Estimating the ratios of the stationary distribution values for Markov chains modeling evolutionary algorithms.

The evolutionary algorithm stochastic process is well-known to be Markovian. These have been under investigation in much of the theoretical evolutionary computing research. When the mutation rate is positive, the Markov chain modeling of an evolutionary algorithm is irreducible and, therefore, has a unique stationary distribution.

Estimating the parameters of a model for protein-protein interaction graphs.

We find accurate approximations for the expected number of three-cycles and unchorded four-cycles under a stochastic distribution for graphs that has been proposed for modelling yeast two-hybrid protein-protein interaction networks. We show that unchorded four-cycles are characteristic motifs under this model and that the count of unchorded four-cycles in the graph is a reliable statistic on which to base parameter estimation. Finally, we test our model against a range of experimental data, obtain parameter estimates from these data and investigate possible improvements in the model.

The probability density of the total IBD length over a single autosome in unilineal relationships.

Several authors have studied identity by descent (IBD) by way of a continuous recombination process along a chromosome. Despite its potential uses in, for example, gene mapping or delineation of biological relationships there has been no exact algebraic result given for the probability density function of the IBD proportion in any familial relationship. Other authors have derived algebraic approximations in the case of half-sibs by way of the Poisson clumping heuristic and used computational methods to compute the distribution function of the IBD sharing for unilineal relationships.

Simulating realistic zero loop pedigrees using a bipartite Prufer code and graphical modelling.

Graph algorithms previously developed by the authors are adapted to simulate pedigrees similar to those used in genetic linkage studies which associate disease phenotypes with specific genomic locations. Pedigrees are chosen uniformly at random from the set of those with specified numbers of individuals and matings and which contain no loops. Summary statistics from pedigrees generated in this way can be used to check real pedigrees for anomalies due to biased sampling or phenotypic effects on the pedigree structure.

Sequential genotyping within TDT families.

We demonstrate that, given a limited amount of genotyping resources, the power of a TDT study can be increased substantially by genotyping within families sequentially. By sequential genotyping we mean that one parent in a family should be typed and then the decision on whether to continue genotyping the family is based on this parent's genotype. If it is decided to continue genotyping then a further decision is made about whether to genotype the offspring once the second parent has been genotyped.

Recombination can evolve in large finite populations given selection on sufficient loci.

It is well known that an allele causing increased recombination is expected to proliferate as a result of genetic drift in a finite population undergoing selection, without requiring other mechanisms. This is supported by recent simulations apparently demonstrating that, in small populations, drift is more important than epistasis in increasing recombination, with this effect disappearing in larger finite populations. However, recent experimental evidence finds a greater advantage for recombination in larger populations.

Enumeration and simulation of marriage node graphs on zero-loop pedigrees.

We present a method that for the marriage node graph of a zero-loop pedigree will enumerate all possible pedigrees that share the same underlying tree structure. The enumeration method leads naturally to a scheme for simulating from a uniform distribution on such pedigrees. This is extended to simulating pedigrees for which the underlying marriage node graph is a tree of any particular size.

The identity by descent process along the chromosome.

The probabilities of the various possible identity by descent (IBD) states at a locus captures all the genealogical information for that locus for the set of individuals under consideration. Here we study the stochastic process of the IBD state as one moves across the genome of a set of individuals. In general it is no longer sufficient to specify the IBD state, one needs to increase the state space if one is to maintain the Markov property, as has been discussed by for instance McPeak and Sun [Am J Hum Genet 2000;66:1076-1094] and Browning and Browning [Theor Popul Biol 2002;62:1-8].

Patch leaving strategies and superparasitism: an asymmetric generalized war of attrition.

When several competitors deplete a patch, it can be advantageous for each of them to stay provided that others leave, whereas, on the other hand, staying longer decreases the expected payoff for everyone. This situation can be considered as a generalized war of attrition. Previous studies have shown that optimal patch leaving strategies become stochastic and the expected leaving time is much larger than predicted by the marginal value theorem when competitors interfere.

RECSIM and INDSTATS: probabilities of identity in general genealogies.

RECSIM takes a general genealogy and simulates the transmission of chromosomes through that genealogy. INDSTATS extracts some basic statistics from the output of RECSIM.

Variation within genes encoding interleukin-1 and the interleukin-1 receptor antagonist influence the severity of meningococcal disease.

Background: Genetically determined variation in proinflammatory cytokine release influences severity of meningococcal disease and other serious infections.

Objective: To ascertain the relative frequencies of single nucleotide polymorphisms within the interleukin-1 gene locus among patients who survived and those who died of meningococcal disease and a control population of blood donors.

Design: Association study.