Simple aspects of foodweb complexity

Foodweb data are examined to obtain a number of indices of the complexity of the webs, such as connectance and mean length of food chains. The index β = E/V (E = number of interactions, V = number of kinds of organism) takes values with mean 1·88 and fractional root mean square deviation 0·27, over a set of thirty foodwebs. These are about equally divided between sink and community webs. Mean chain length is smaller in sink webs than in community webs. It is suggested that the small spread of the β values results from a balance between this and the greater number of chains in the sink webs, when expressed on a scale suggested by a trophic partition of the kinds of organism. Comments are made on a model of foodwebs with an optimal connectance for stability, and on currently available general methods for studying complexity and stability.     

Ethical aspects of statistical practice

This paper embodies a personal view of the ethical considerations that the author believes should be continuously in the mind of any applied statistician or biometrician whose work involves extensive collaboration with other persons and organizations. It looks particularly at the contribution of the International Statistical Institute to the codification of principles, the duties of the statistician in relation to data and the interests of his employer or client, his responsibilities to his professional colleagues and towards society as a whole, and, by no means least; the responsibility of the client towards the statistician who works with him.     

Exploring the complexity of the HIV-1 fitness landscape

Although fitness landscapes are central to evolutionary theory, so far no biologically realistic examples for large-scale fitness landscapes have been described. Most currently available biological examples are restricted to very few loci or alleles and therefore do not capture the high dimensionality characteristic of real fitness landscapes. Here we analyze large-scale fitness landscapes that are based on predictive models for in vitro replicative fitness of HIV-1. We find that these landscapes are characterized by large correlation lengths, considerable neutrality, and high ruggedness and that these properties depend only weakly on whether fitness is measured in the absence or presence of different antiretrovirals. Accordingly, adaptive processes on these landscapes depend sensitively on the initial conditions. While the relative extent to which mutations affect fitness on their own (main effects) or in combination with other mutations (epistasis) is a strong determinant of these properties, the fitness landscape of HIV-1 is considerably less rugged, less neutral, and more correlated than expected from the distribution of main effects and epistatic interactions alone. Overall this study confirms theoretical conjectures about the complexity of biological fitness landscapes and the importance of the high dimensionality of the genetic space in which adaptation takes place.     

Surprising complexity of the ancestral apoptosis network

Background

Apoptosis, one of the main types of programmed cell death, is regulated and performed by a complex protein network. Studies in model organisms, mostly in the nematode Caenorhabditis elegans, identified a relatively simple apoptotic network consisting of only a few proteins. However, analysis of several recently sequenced invertebrate genomes, ranging from the cnidarian sea anemone Nematostella vectensis, representing one of the morphologically simplest metazoans, to the deuterostomes sea urchin and amphioxus, contradicts the current paradigm of a simple ancestral network that expanded in vertebrates.

Results

Here we show that the apoptosome-forming CED-4/Apaf-1 protein, present in single copy in vertebrate, nematode, and insect genomes, had multiple paralogs in the cnidarian-bilaterian ancestor. Different members of this ancestral Apaf-1 family led to the extant proteins in nematodes/insects and in deuterostomes, explaining significant functional differences between proteins that until now were believed to be orthologous. Similarly, the evolution of the Bcl-2 and caspase protein families appears surprisingly complex and apparently included significant gene loss in nematodes and insects and expansions in deuterostomes.

Conclusion

The emerging picture of the evolution of the apoptosis network is one of a succession of lineage-specific expansions and losses, which combined with the limited number of 'apoptotic' protein families, resulted in apparent similarities between networks in different organisms that mask an underlying complex evolutionary history. Similar results are beginning to surface for other regulatory networks, contradicting the intuitive notion that regulatory networks evolved in a linear way, from simple to complex.     

Quantifying and analyzing the network basis of genetic complexity

Genotype-to-phenotype maps exhibit complexity. This genetic complexity is mentioned frequently in the literature, but a consistent and quantitative definition is lacking. Here, we derive such a definition and investigate its consequences for model genetic systems. The definition equates genetic complexity with a surplus of genotypic diversity over phenotypic diversity. Applying this definition to ensembles of Boolean network models, we found that the in-degree distribution and the number of periodic attractors produced determine the relative complexity of different topology classes. We found evidence that networks that are difficult to control, or that exhibit a hierarchical structure, are genetically complex. We analyzed the complexity of the cell cycle network of Sacchoromyces cerevisiae and pinpointed genes and interactions that are most important for its high genetic complexity. The rigorous definition of genetic complexity is a tool for unraveling the structure and properties of genotype-to-phenotype maps by enabling the quantitative comparison of the relative complexities of different genetic systems. The definition also allows the identification of specific network elements and subnetworks that have the greatest effects on genetic complexity. Moreover, it suggests ways to engineer biological systems with desired genetic properties.     

Some statistical aspects of sampling in morphometry

Morphometry requires, in addition to the accurate counting of points, intersections and transections, meticulous attention to sampling. Methods are described and discussed for ensuring that adequate samples are obtained for a given standard error. For all situations in which stratification is used, the importance of increasing the number of the early strata for reducing the variance is emphasized.     

Dynamical and statistical models of vertebrate population dynamics

Population dynamics methodology now powerfully combines discrete time models (with constant parameters, density dependence, random environment, and/or demographic stochasticity) and capture-recapture models for estimating demographic parameters. Vertebrate population dynamics has strongly benefited from this progress: survival estimates have been revised upwards, trade-offs between life history traits have been demonstrated, analyses of population viability and management are more and more realistic. Promising developments concern random effects, multistate and integrated models. Some biological questions (density dependence, links between individual and population levels, and diversification of life histories) can now be efficiently attacked.     

Biochemical and statistical network models for systems biology

The normal and abnormal behavior of a living cell is governed by complex networks of interacting biomolecules. Models of these networks allow us to make predictions about cellular behavior under a variety of environmental cues. In this review, we focus on two broad classes of such models: biochemical network models and statistical inference models. In particular, we discuss a number of modeling approaches in the context of the assumptions that they entail, the types of data required for their inference, and the range of their applicability.     

Epidemiological and statistical aspects of the AIDS epidemic: introduction

In 1988, a government working party studied estimates of incidence and prevalence of numbers of acquired immunodeficiency syndrome (AIDS) cases. They investigated a series of epidemiological, statistical and mathematical problems associated with predicting trends in incidences of AIDS. This paper introduces a series of papers that give a fuller and more technical exposition of the appendixes of that working party report. The papers provide a brief background to the current state of knowledge on the epidemiology of the infection and the disease; a deterministic model for human immunodeficiency virus (HIV) transmission in the male homosexual community in England and Wales is introduced. Back-projection methods are studied in two papers, following the distribution of the incubation period of the disease. The concept of minimum size of the epidemic is introduced. Mathematical functions to describe the spread of HIV infection are refined by using past trends in the incidence of AIDS to estimate values for some parameters. Survival times for AIDS patients from the point of diagnosis are considered and evidence for changes in male homosexual sexual behaviour is studied; lag-time from the point of diagnosis to the report of the case is also examined. There is a comparative analysis of the AIDS epidemic in various European countries. The incubation period of HIV in patients with haemophilia A and B infections and the problems associated with making predictions for different at-risk groups or small subgroups based on geographical area are discussed. Reasons for fluctuation between the number of reported cases from month to month are provided.     

Logical, epistemological and statistical aspects of nature-nurture data interpretation

In this paper the nature of the reasoning processes applied to the nature-nurture question is discussed in general and with particular reference to mental and behavioral traits. The nature of data analysis and analysis of variance is discussed. Necessarily, the nature of causation is considered. The notion that mere data analysis can establish "real" causation is attacked. Logic of quantitative genetic theory is reviewed briefly. The idea that heritability is meaningful in the human mental and behavioral arena is attacked. The conclusion is that the heredity-IQ controversy has been a "tale full of sound and fury, signifying nothing". To suppose that one can establish effects of an intervention process when it does not occur in the data is plainly ludicrous. Mere observational studies can easily lead to stupidities, and it is suggested that this has happened in the heredity-IQ arena. The idea that there are racial-genetic differences in mental abilities and behavioral traits of humans is, at best, no more than idle speculation.     

Techniques and statistical data analysis in molecular population genetics

Following the development of PCR methods, molecular techniques have become widely used for detecting genetic variation in natural populations. Most nucleotide changes can be detected by these techniques. Many of these changes probably reflect silent substitutions that are likely to be selectively neutral, making them particularly suitable to population genetic studies. In this paper, we review the published literature on molecular population genetics, with respect to the genome assayed (nuclear, mitochondrial or chloroplast), the organisms studied, the molecular techniques used, and the biological problems addressed. Several molecular techniques are then compared using experimental results obtained from a population genetic study of the Mytilus complex in the North Atlantic and Mediterranean. Finally, the most appropriate theoretical tools to analyse molecular population genetic data are discussed.     

Some aspects of autotetraploid population dynamics

Summary Self-compatible autotetraploids are likely to set much of their seed by selfing. Formulae are presented for the frequencies in any generation of states of loci, from homozygous to quadri-allelic, considering the frequencies of selfing and of double reduction but not allowing for the effects of inbreeding depression on population structure. The changing structure of populations over generations is also explored by computer simulation, incorporating selection against inbreds but ignoring double reduction. The findings are discussed in relation to mass-selection programmes.     

A network model for the correlation between epistasis and genomic complexity

The study of genetic interactions (epistasis) is central to the understanding of genome organization and evolution. A general correlation between epistasis and genomic complexity has been recently shown, such that in simpler genomes epistasis is antagonistic on average (mutational effects tend to cancel each other out), whereas a transition towards synergistic epistasis occurs in more complex genomes (mutational effects strengthen each other). Here, we use a simple network model to identify basic features explaining this correlation. We show that, in small networks with multifunctional nodes, lack of redundancy, and absence of alternative pathways, epistasis is antagonistic on average. In contrast, lack of multi-functionality, high connectivity, and redundancy favor synergistic epistasis. Moreover, we confirm the previous finding that epistasis is a covariate of mutational robustness: in less robust networks it tends to be antagonistic whereas in more robust networks it tends to be synergistic. We argue that network features associated with antagonistic epistasis are typically found in simple genomes, such as those of viruses and bacteria, whereas the features associated with synergistic epistasis are more extensively exploited by higher eukaryotes.