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A sharp minimum on the mean number of steps taken in adaptive walks.

It was recently conjectured by H.A. Orr that from a random initial point on a random fitness landscape of alphabetic sequences with one-mutation adjacency, chosen from a larger class of landscapes, no adaptive algorithm can arrive at a local optimum in fewer than on average e-1 steps. Here, using an example in which the mean number of steps to a local optimum equals (A-1)/A, where A is the number of distinct "letters" in the "alphabet" from which sequences are constructed, it is shown that as originally stated, the conjecture does not hold. It is also demonstrated that (A-1)/A is a sharp minimum on the mean number of steps taken in adaptive walks on fitness landscapes of alphabetic sequences with one-mutation adjacency. As the example that achieves the new lower bound has properties that are not often considered as potential attributes for fitness landscapes-non-identically distributed fitnesses and negative fitness correlations for adjacent points-a weaker set of conditions characteristic of more commonly studied fitness landscapes is proposed under which the lower bound on the mean length of adaptive walks is conjectured to equal e-1.

Adaptation, Physiological↗

Analytical methods for studying the evolution of paralogs using duplicate gene datasets.

Gene duplication is widely viewed as an important source of raw material for functional innovation in proteins because at least some duplicate copies will evolve new or slightly modified functions. The study of the molecular processes by which functional innovation occurs interests both evolutionary biologists and protein chemists, and the development of methods to investigate these processes has led to a productive meeting of disciplines and an availability of complementary approaches for exploring datasets. This has resulted in insights into past events, prediction of current function, and prediction of future change. The methods fall broadly into two categories: those that rely on detection of shifts in selective constraints and those that rely on detection of correlations between molecular changes and functional shifts. Strengths and limitations of the methods are evaluated here in the context of the question being addressed, the input required, and the specific metric that is evaluated in each test.

Databases, Genetic↗

Sample size calculations for classical association and TDT-type methods using family data.

Transmission Disequilibrium Test (TDT)-based methods have been advocated by several authors for testing that a marker-phenotype association is actually due to linkage and not to uncontrolled stratification. As a pre-requisite of TDT-type methods is the presence of an association between marker and phenotype, one may wish to first investigate the association using a classical association study, and then to check by a TDT approach whether this association is actually due to linkage. We propose an estimating equation (EE) procedure, to compute analytically the minimum sample size of sibship data required to detect the association between a marker and a quantitative phenotype, and that required to confirm it by two TDT methods. We show that, when the marker allele frequency is low or high, the number of informative sibs needed in TDT-type methods can be lower than the number required in an association analysis, and even more so when the familial clustering is strong. However, in all cases, the number of sibs that need to be sampled to get the appropriate number of informative sibs for analysis is always larger for TDT methods than for an association study. In a phenotype-first strategy, this number may be critical when investigating costly phenotypes.

Alleles↗

Fertility and mortality differentials among selected tribal population groups of north-western and eastern India.

Selection potential based on differential fertility and mortality has been computed for six tribal groups inhabiting different geo-climatic conditions, namely: Sahariya, Mina and Bhil of the State of Rajasthan, north-western India, and Munda, Santal and Lodha of the State of West Bengal, eastern India. Irrespective of the methodology, the total index of selection was found to be highest among Lodhas (0.668), followed by Sahariyas (0.524), Santals (0.462), Bhils (0.386), Mundas (0.353) and Minas (0.334). Incidentally, Lodha and Sahariya are two of the seventy-four notified primitive tribal groups of India, and these two study populations show the highest index of total selection, mainly because of a higher embryonic and postnatal mortality. The relative contribution of the fertility component to the index of total selection is higher than the corresponding mortality component in all tribal groups. The analysis of postnatal mortality components indicates that childhood mortality constitutes the bulk of postnatal mortality, suggesting that children under 5 years need better health care in these tribal groups.

Adult↗

Modeling with measured genotypes: effects of the vitamin D receptor gene, age, and latent genetic and environmental factors on bone mineral density.

We use empirical data to demonstrate a recently proposed framework for including measured genotypes in structural equation models (Van den Oord and Snieder, 2002). The sample consisted of 227 MZ pairs, 197 DZ pairs, and 41 DZ twins without co-twin. The mean age of the female twins was 57 years. The analysis aimed at studying the effect of the vitamin D receptor (VDR) gene polymorphism (VDRGP) on bone mineral density (BMD). Whereas age affected the BMD measures via independent pathways, the effects of the VDRGP plus latent genetic and environmental factors were consistent with a common pathway model. VDRGP explained 0.3% to 0.5% of the variance. These analyses demonstrated that (i) regardless of how much is known about the gene and its products at a molecular level, meaningful questions can be addressed concerning how genes co-act with other variables at a "higher" phenotypic level; (ii) measured genotypes can be treated like any other variable so that the whole structural equation models framework can in principle directly be applied; and (iii) measured genotypes do not need to have large effects to study mechanisms underlying complex traits, and it may even be argued that particularly genes with small effects are better studied within the context of models with multiple variables.

Age Factors↗

Susceptibility to testicular germ-cell tumours in a 129.MOLF-Chr 19 chromosome substitution strain.

The identification of genes that control susceptibility to testicular germ-cell tumours (TGCTs), the most common cancer affecting young men, has been difficult. In laboratory mice, TGCTs arise from primordial germ cells in only the 129 inbred strains, and susceptibility is under multigenic control. The spontaneously arising mutation Ter (ref. 5) on mouse chromosome 18 (Refs 6,7) increases TGCT frequency on a 129/Sv background. We originally used Ter in genetic crosses to identify loci that control tumorigenesis. A genome scan of tumour-bearing progeny from backcrosses between the 129/Sv-Ter/+ and MOLF/Ei strains provided modest evidence that MOLF-derived alleles on chromosome 19 enhance development of bilateral TGCTs (ref. 9). To obtain independent evidence for linkage to the MOLF chromosome, we made an autosomal chromosome substitution strain (CSS; or 'consomic strain') in which chromosome 19 of 129/Sv+/+ was replaced by its MOLF-derived homologue. The unusually high frequency of TGCTs in this CSS (even in the absence of the Ter mutation) provides evidence confirming the genome survey results, identifies linkage for a naturally occurring strain variant allele that confers susceptibility to TGCTs and illustrates the power of CSSs in complex trait analysis.

Alleles↗

Evolving responsively: adaptive mutation.

A basic principle of genetics is that the likelihood that a particular mutation occurs is independent of its phenotypic consequences. The concept of adaptive mutation seemed to challenge this principle with the discoveries of mutations stimulated by stress, some of which allow adaptation to the stress. The emerging mechanisms of adaptive genetic change cast evolution, development and heredity into a new perspective, indicating new models for the genetic changes that fuel these processes.

Adaptation, Physiological↗

Mechanisms of noise-resistance in genetic oscillators.

A wide range of organisms use circadian clocks to keep internal sense of daily time and regulate their behavior accordingly. Most of these clocks use intracellular genetic networks based on positive and negative regulatory elements. The integration of these "circuits" at the cellular level imposes strong constraints on their functioning and design. Here, we study a recently proposed model [Barkai, N. & Leibler, S. (2000) Nature (London), 403, 267-268] that incorporates just the essential elements found experimentally. We show that this type of oscillator is driven mainly by two elements: the concentration of a repressor protein and the dynamics of an activator protein forming an inactive complex with the repressor. Thus, the clock does not need to rely on mRNA dynamics to oscillate, which makes it especially resistant to fluctuations. Oscillations can be present even when the time average of the number of mRNA molecules goes below one. Under some conditions, this oscillator is not only resistant to but, paradoxically, also enhanced by the intrinsic biochemical noise.

Algorithms↗

Intron evolution as a population-genetic process.

Debate over the mechanisms responsible for the phylogenetic and genomic distribution of introns has proceeded largely without consideration of the population-genetic forces influencing the establishment and retention of novel genetic elements. However, a simple model incorporating random genetic drift and weak mutation pressure against intron-containing alleles yields predictions consistent with a diversity of observations: (i) the rarity of introns in unicellular organisms with large population sizes, and their expansion after the origin of multicellular organisms with reduced population sizes; (ii) the relationship between intron abundance and the stringency of splice-site requirements; (iii) the tendency for introns to be more numerous and longer in regions of low recombination; and (iv) the bias toward phase-0 introns. This study provides a second example of a mechanism whereby genomic complexity originates passively as a "pathological" response to small population size, and raises difficulties for the idea that ancient introns played a major role in the origin of genes by exon shuffling.

Alleles↗

Fundamental theorem of natural selection under gene-culture transmission.

A generalized fundamental theorem of natural selection is derived for populations incorporating both genetic and cultural transmission. The phenotype is determined by an arbitrary number of multiallelic loci with two-factor epistasis and an arbitrary linkage map, as well as by cultural transmission from the parents. Generations are discrete but partially overlapping, and mating may be nonrandom at either the genotypic or the phenotypic level (or both). I show that cultural transmission has several important implications for the evolution of population fitness, most notably that there is a time lag in the response to selection such that the future evolution depends on the past selection history of the population.

Animals↗

MZ twinning: chance or determinism? An essay in nonlinear dynamics (chaos).

Classically, researchers considered monozygotic twinning (MZT) a random phenomenon. This paper tests the hypothesis with the aid of nonlinear dynamics techniques. The latter can tell true randomness from chance-like variation. Chaos, the endpoint of the threshold state of a nonlinear deterministic system, can mimic constrained randomness. From a practical standpoint, recognizing chaos in a time series data set means that the paradigmatic multifactorial model of causation is essentially ruled out. Specifically, time series of MZ, DZ, and single maternities were analysed. First, spectral analysis was used to uncover periodicities embedded in the series. Second, a singular value decomposition was undertaken to reduce noise from the series. Third, phase space attractors were drawn up that describe the 'asymptotic' trajectory of the system at any time. Results suggested that DZ, MZ, and single maternities shared a similar 32-year periodicity. Owing to two interwoven similar periodicities, the single-maternity cycle kinetics proved to be faster than that of DZ's. The MZ series was the only one to display secondary interacting harmonics, thus eliciting a rather unusual trajectory in the bidimensional phase space. The MZ time points were not spread in a haphazard fashion; on the contrary, a fine structure was present that did not reduce to a limit cycle such as the one characterizing the DZ- or the single-maternity trajectory. It was concluded that a complex nonlinear dynamic underlies MZ twinning. Therefore, calling for extrinsic causes to account for what appears to be random variation overtime would be pointless. MZ twinning should rather be traced to a limited number of intrinsic and deterministic interacting system components. The most likely candidates are presented and discussed.

Bias↗

Coding polymorphism for phylogeny reconstruction.

The methodology of coding polymorphic taxa has received limited attention to date. A search of the taxonomic literature revealed seven types of coding methods. Apart from ignoring polymorphic characters (sometimes called the fixed-only method), two main categories can be distinguished: methods that identify the start of a new character state with the origin of an evolutionary novelty, and methods that identify the new state with the fixation of a novelty. The methods of the first category introduce soft reversals, yielding signals that support cladograms incompatible with true phylogenies. We conclude that coding the plesiomorphy is the method to be preferred, unless the ancestral state is unknown, in which case coding as ambiguous is recommended. This holds for coding polymorphism in species as well as in supraspecific taxa. In this light we remark on methods proposed by previous authors.

Animals↗

Disequilibrium likelihoods for fine-scale mapping of a rare allele.

Genetic linkage studies based on pedigree data have limited resolution, because of the relatively small number of segregations. Disequilibrium mapping, which uses population associations to infer the location of a disease mutation, provides one possible strategy for narrowing the candidate region. The coalescent process provides a model for the ancestry of a sample of disease alleles, and recombination events between disease locus and marker may be placed on this ancestral phylogeny. These events define the recombinant classes, the sets of sampled disease copies descending from the meiosis at which a given recombination occurred. We show how Monte Carlo generation of the recombinant classes leads to a linkage likelihood for fine-scale mapping from disease haplotypes. We compare single-marker disequilibrium mapping with interval-disequilibrium mapping and discuss how the approach may be extended to multipoint-disequilibrium mapping. The method and its properties are illustrated with an example of simulated data, constructed to be typical of fine-scale mapping of a rare disease in the Japanese population. The method can take into account known features of population history, such as changing patterns of population growth.

Algorithms↗

Sequence diversity in 36 candidate genes for cardiovascular disorders.

Two strategies involving whole-genome association studies have been proposed for the identification of genes involved in complex diseases. The first one seeks to characterize all common variants of human genes and to test their association with disease. The second one seeks to develop dense maps of single-nucleotide polymorphisms (SNPs) and to detect susceptibility genes through linkage disequilibrium. We performed a molecular screening of the coding and/or flanking regions of 36 candidate genes for cardiovascular diseases. All polymorphisms identified by this screening were further genotyped in 750 subjects of European descent. In the whole set of genes, the lengths explored spanned 53.8 kb in the 5' regions, 68.4 kb in exonic regions, and 13 kb in the 3' regions. The strength of linkage disequilibrium within candidate regions suggests that genomewide maps of SNPs might be efficient ways to identify new disease-susceptibility genes, provided that the maps are sufficiently dense. However, the relatively large number of polymorphisms within coding and regulatory regions of candidate genes raises the possibility that several of them might be functional and that the pattern of genotype-phenotype association might be more complex than initially envisaged, as actually has been observed in some well-characterized genes. These results argue in favor of both genomewide association studies and detailed studies of the overall sequence variation of candidate genes, as complementary approaches.

Apolipoproteins B↗

A general modeling strategy for gene regulatory networks with stochastic dynamics.

A stochastic genetic toggle switch model that consists of two identical, mutually repressive genes is built using the Gillespie algorithm with time delays as an example of a simple stochastic gene regulatory network. The stochastic kinetics of this model is investigated, and it is found that the delays for the protein productions can highly weaken the global fluctuations for the expressions of the two genes, making the two mutually repressive genes coexist for a long time. Starting from this model, we propose a practical modeling strategy for more complex gene regulatory networks. Unlike previous applications of the Gillespie algorithm to simulate specific genetic networks dynamics, this modeling strategy is proposed for an ensemble approach to study the dynamical properties of these networks. The model allows any combination of gene expression products, forming complex multimers, and each one of the multimers is assigned to a randomly chosen gene promoter site as an activator or inhibitor. In addition, each gene, although it has only one promoter site, can have multiple regulatory sites and distinct rates of translation and transcription. Also, different genes have different time delays for transcription and translation and all reaction constant rates are initially randomly chosen from a range of values. Therefore, the general strategy here proposed may be used to simulate real genetic networks.

Algorithms↗

Automatic extraction of motifs represented in the hidden Markov model from a number of DNA sequences.

MOTIVATION: Automatic extraction of motifs that occur frequently on a set of unaligned DNA sequences is useful for predicting the binding sites of unknown transcription factors. Several programs for this purpose have been released. However, in our opinion, they are not practical enough to be applied to a large number of upstream sequences. RESULTS: We propose a new program called YEBIS (Yet another Environment for the analysis of BIopolymer Sequences) which is capable of extracting a set of motifs, without any a priori knowledge, from a number of functionally related DNA sequences. Using the hidden Markov model, these motifs are represented in a more general form than other conventional methods, such as the weight matrix method. When applied to several sets of benchmark data, it was found that YEBIS had comparable capability to the existing methods, but was much faster. Moreover, it could extract all known motifs from the LTR sequences (long terminal repeat sequences) in a single run. Finally, it could be successfully applied to approximately 400 human promoter sequences and some of the extracted motifs turned out to be known cis-elements. Therefore, YEBIS could be a practical tool for exploring the upstream sequences of genomic ORFs, some of which are regulated in a similar fashion. AVAILABILITY: YEBIS will be distributed to academic users free of charge. All requests should be sent to the address below. CONTACT: E-MAIL: yada@tokyo.jst.go.jp

Algorithms↗

Analysis of high density expression microarrays with signed-rank call algorithms.

MOTIVATION: We consider the detection of expressed genes and the comparison of them in different experiments with the high-density oligonucleotide microarrays. The results are summarized as the detection calls and comparison calls, and they should be robust against data outliers over a wide target concentration range. It is also helpful to provide parameters that can be adjusted by the user to balance specificity and sensitivity under various experimental conditions. RESULTS: We present rank-based algorithms for making detection and comparison calls on expression microarrays. The detection call algorithm utilizes the discrimination scores. The comparison call algorithm utilizes intensity differences. Both algorithms are based on Wilcoxon's signed-rank test. Several parameters in the algorithms can be adjusted by the user to alter levels of specificity and sensitivity. The algorithms were developed and analyzed using spiked-in genes arrayed in a Latin square format. In the call process, p-values are calculated to give a confidence level for the pertinent hypotheses. For comparison calls made between two arrays, two primary normalization factors are defined. To overcome the difficulty that constant normalization factors do not fit all probe sets, we perturb these primary normalization factors and make increasing or decreasing calls only if all resulting p-values fall within a defined critical region. Our algorithms also automatically handle scanner saturation.

Algorithms↗

GenomeMixer: a complex genetic cross simulator.

UNLABELLED: GenomeMixer is a cross-platform application that simulates meiotic recombination events for large and complex multigenerational genetic crosses among sexually reproducing diploid species and outputs simulated progeny to several standard mapping programs. AVAILABILITY: Documentation, C++ source, and binaries for Mac OS X and x86 Linux are freely available at http://www.nervenet.org/genome_mixer/. GenomeMixer can be compiled on any system with support for the Trolltech Qt toolkit, including Windows.

Chromosome Mapping↗