Encoding power in communication networks.

In animal societies, conflicts can be resolved by combatants or through third-party intervention. In gregarious species, conflicts among pairs can spread to involve multiple individuals. In the case of large conflicts, containment and termination of aggression by third parties is important. Successful intervention relies on consensus among combatants about the intervener's capacity to use force. We refer to this consensus as power. We measure it and study how it arises, using as our model system a pigtailed macaque (Macaca nemestrina) society. In macaques, the degree to which one individual perceives another as capable of using force is communicated using a special dominance signal. Group consensus about an individual's capacity to use force arises from the network of signaling interactions. We derive a formalism to quantify consensus in the network. We find that the power distribution is fat tailed and power is a strong predictor of social variables including request for support, intervention cost, and intensity. We develop models to show how dominance-signaling strategies promote robust power distributions despite individual signaling errors. We suggest that when considering correlated interactions among many individuals it can be more useful to emphasize coarse-grained information stored at the group level--behavioral macrostates--over detailed information at the individual level.

Models of experimental evolution: the role of genetic chance and selective necessity.

We present a theoretical framework within which to analyze the results of experimental evolution. Rapidly evolving organisms such as viruses, bacteria, and protozoa can be induced to adapt to laboratory conditions on very short human time scales. Artificial adaptive radiation is characterized by a list of common observations; we offer a framework in which many of these repeated questions and patterns can be characterized analytically. We allow for stochasticity by including rare mutations and bottleneck effects, demonstrating how these increase variability in the evolutionary trajectory. When the product Np, the population size times the per locus error rate, is small, the rate of evolution is limited by the chance occurrence of beneficial mutations; when Np is large and selective pressure is strong, the rate-limiting step is the waiting time while existing beneficial mutations sweep through the population. We derive the rate of divergence (substitution rate) and rate of fitness increase for the case when Np is large and illustrate our approach with an application to an experimental data set. A minimal assumption of independent additive fitness contributions provides a good fit to the experimental evolution of the bacteriophage phiX174.

Stability and evolution of overlapping genes.

When the same sequence of nucleotides codes for regions of more than one functional polypeptide, this sequence contains overlapping genes. Overlap is most common in rapidly evolving genomes with high mutation rates such as viruses, bacteria, and mitochondria. Overlap is thought to be important as: (1) a means of compressing a maximum amount of information into short sequences of structural genes; and (2) as a mechanism for regulating gene expression through translational coupling of functionally related polypeptides. The stability of overlapping codes is examined in relation to the information cost of overlap and the mutation rate of the genome. The degree of overlap in a given population will tend to become monomorphic. Evolution toward partial overlap of genes is shown to depend on a convex cost function of overlap. Overlap does not evolve when expression of overlapping genes is mutually exclusive and produced by rare mutations to the wild-type genome. Assuming overlap increases coupling between functionally related genes, the conditions favoring overlap are explored in relation to the kinetics of gene activation and decay. Coupling is most effective for genes in which the gene overlapping at its 5' end (leading gene) decays rapidly, while the gene overlapping at the 3' end (induced gene) decays slowly. If gene expression can feedback on itself (autocatalysis), then high rates of activation favor overlap.

The evolution of virus-induced apoptosis.

Viruses from several different families are able to exploit their host's cell death programmes so as to maximize viral fitness. Consideration of the evolution of such strategies has lead to the suggestion that the virus should inhibit apoptosis, in order to prolong the life of the cell and thereby maximize the number of progeny virions. The host, on the other hand, should stimulate apoptosis thereby inhibiting viral growth and blocking viral spread. For example, the function of the latent membrane protein I (LMPI) of the Epstein-Barr virus and the bcl-2 homologue gene A179L of African swine fever virus is to inhibit apoptosis. However, in other cases it is the virus that stimulates cell death or the host that benefits from inhibiting apoptosis, such as in fatal alphavirus encephalitis. This has been explained by assuming that virus-induced apoptosis in non-regenerating cells would be detrimental to the host. We present a mathematical framework for understanding virus-induced apoptosis which accounts for these two opposite solutions to virus infection with respect to the mode of virus replication and the life cycle of the target cell.

The spatial dynamics of prion disease.

An important component of the latency period of the transmissible spongiform encephalopathies (prion diseases) can be attributed to delays during the propagation of the infectious prion isoform, PrPSc, through peripheral nervous tissues. A growing body of data report that the host prion protein, PrPC, is required in both peripheral and central nervous tissues for susceptibility to infection. We introduce a mathematical model, which treats the PrPSc as a mobile infectious pathogen, and show how peripheral delays can be understood in terms of the intercellular dispersal properties of the PrPSc strain, its decay rate, and its efficiency at transforming the PrPC. It has been observed that when two pathogenic strains co-infect a host, the presence of the first inoculated strain can slow down, or stop completely, the spread of the second strain. This is thought to result from a reduced concentration of host protein available for conversion by the second strain. Our model can explain the mechanisms of such interstrain competition and the time-course of the increased delay. The model provides a link between those data suggesting a role for a continuous chain of PrP-expressing tissue linking peripheral sites to the brain, and data on prion strain competition.

T-cell induced pathogenesis in HIV: bystander effects and latent infection.

The progress of HIV is accompanied by the infection and decline of the population of CD4+ cells. This reduction in cells results from both cytolytic influences of the virus and virus-specific cytotoxic T-cell (CTL) responses. We seek to characterize the extent of CD4+ reduction caused by HIV-specific CTLs at equilibrium. Here we show that intermediate levels of cytotoxic killing of infected cells can be inferior to both strong and weak or absent immune responses. We further show that the deleterious effects of the CTL response are made worse by a slow immune response. Bystander effects in which uninfected cells are thought to be eliminated by non-specific CTL activation lead to small or negligible reductions in uninfected CD4+ cells. Latently infected cells containing pro-viral DNA and which become activated at a constant rate ensure that the immune response is more effective for a larger range of CTL activities and reduces T-cell associated pathology.

An error limit for the evolution of language.

On the evolutionary trajectory that led to human language there must have been a transition from a fairly limited to an essentially unlimited communication system. The structure of modern human languages reveals at least two steps that are required for such a transition: in all languages (i) a small number of phonemes are used to generate a large number of words; and (ii) a large number of words are used to a produce an unlimited number of sentences. The first (and simpler) step is the topic of the current paper. We study the evolution of communication in the presence of errors and show that this limits the number of objects (or concepts) that can be described by a simple communication system. The evolutionary optimum is achieved by using only a small number of signals to describe a few valuable concepts. Adding more signals does not increase the fitness of a language. This represents an error limit for the evolution of communication. We show that this error limit can be overcome by combining signals (phonemes) into words. The transition from an analogue to a digital system was a necessary step toward the evolution of human language.

Genetic instability and the evolution of angiogenic tumor cell lines (review).

Advanced tumor growth requires the formation of new blood vessels (angiogenesis). Whether new blood vessels are formed or not depends on a balance between angiogenesis inhibitors and promoters. Host tissue, as well as tumor cells, express inhibitory factors preventing angiogenesis. During cancer progression, tumor cell lines evolve which produce factors promoting the angiogenic switch. We use mathematical models in order to examine the conditions required for angiogenic cell lines to emerge and hence for the disease to progress. We find that genetic instability, defined as a much elevated mutation rate of somatic cells, is required for the emergence of angiogenic tumor cells. This is because a high mutation rate ensures that within a short period of time, a sufficiently high number of angiogenic cells are generated. This founder population of mutant cells is large enough to overcome the inhibitory factors produced by the tissue thereby inducing the angiogenic switch through the production of promoters. In the absence of genetic instability, angiogenic cells cannot fix, even if the relevant mutations are generated at low levels in the tumor cell population. This is because angiogenic promoters will not be sufficiently abundant to counter the influence of inhibitory factors. In this context, the inhibition of angiogenesis can be viewed as a host defense ensuring that the tumor need be genetically unstable if it is to grow and progress beyond a certain size limit. We observe that genetic instability is of value early in tumorigenesis but becomes a liability later. This is because instability decreases the fitness of the angiogenic tumor once it has become established.

Selective imitation for a private sign system.

A distinctive feature of all human languages is the diverse and arbitrary nature of the sign (signifier). This can be interpreted as stating that the mapping between signals and referents is established by convention rather than by functional constraints. This property of the sign provides for a great deal of linguistic flexibility and is a key component of symbolic communication. Game theoretic models to describe signal imitation are investigated with a view to understanding how non-arbitrary (indexical) animal-style signals might 'evolve' culturally into diverse, arbitrary signs. I explore the evolutionary hypothesis that private, arbitrary signs emerge as a result of selective imitation within a socially structured population. Once arbitrary signs have emerged, they contribute towards greater assortative interactions among individuals using a shared sign system. In natural populations, the models for imitation will very often be close kin. Hence, kinship provides one mechanism for the creation of true symbols. An imitation-structured population can support many more sign systems than an equivalent non-structured population and is one in which symbols become the dominant force in assortative interactions.

Levels of selection in positive-strand virus dynamics.

Conflicting selection pressures occurring over the life cycle of an organism constitute serious challenges to the robustness of replication. Viruses present a credible model system for analysing problems that arise through evolutionary conflicts of interest. We present a multi-level selection model for the life cycle of positive-strand RNA viruses. The model combines within-cell replication kinetics and protein synthesis, and between-cell population dynamics of virion production and transmission. We show how these two levels of within-host selection interact to produce tradeoffs in the life history strategy of a virus without consideration of host mortality. We find that viruses evolve towards intermediate rather than maximum encapsidation rates. This can be interpreted as selection for intermediate virulence through cellular persistence. We characterize a theoretical persistence threshold arising from the trade-off between genome replication and genetic translation within the cell. We present counter-intuitive relationships whereby increasing genome decay rates and rates of encapsidation lead to increases in the abundance of virus-encoded proteins. Data from poliovirus suggest that viruses might be unable to resolve the vertical conflicts of interests among different levels of selection.

The paradoxical dynamics of prion disease latency.

A salient characteristic of the prion diseases--including Creutzfeldt-Jakob disease and bovine spongiform encephalopathy in cattle--is an extended asymptomatic incubation period followed by a rapid and often fatal clinical phase. We present a kinetic model of progression of infection based upon the existence of a bottleneck in the natural protein pathways within the cell. The model can reconcile the different time-scales of the pre-clinical and clinical phases, and is able to account for the dependency of the duration of the incubation period on several important governing factors, including the inoculum size, the phenotype of the host, and the phenotype of the pathogenic form of the prion protein. Our results suggest that saturation events--first of the rate of pathogenic transformation (an auto-catalysis ceiling), and subsequently of the bottleneck in the protein pathways--could be fundamental in determining the dynamics of infection.

The evolution of language.

The emergence of language was a defining moment in the evolution of modern humans. It was an innovation that changed radically the character of human society. Here, we provide an approach to language evolution based on evolutionary game theory. We explore the ways in which protolanguages can evolve in a nonlinguistic society and how specific signals can become associated with specific objects. We assume that early in the evolution of language, errors in signaling and perception would be common. We model the probability of misunderstanding a signal and show that this limits the number of objects that can be described by a protolanguage. This "error limit" is not overcome by employing more sounds but by combining a small set of more easily distinguishable sounds into words. The process of "word formation" enables a language to encode an essentially unlimited number of objects. Next, we analyze how words can be combined into sentences and specify the conditions for the evolution of very simple grammatical rules. We argue that grammar originated as a simplified rule system that evolved by natural selection to reduce mistakes in communication. Our theory provides a systematic approach for thinking about the origin and evolution of human language.

Selection by somatic signals: the advertisement of phenotypic state through costly intercellular signals.

We develop a model of intercellular signalling, to explore the possibility that the signals exchanged between cells within a body may be subject to many of the same evolutionary pressures as signals exchanged between individuals whose genetic interests conflict. Evolutionary signalling theory maintains that signals, to be reliable indicators of need, intention or quality must be more costly than would be required merely to transmit a message. Cost guarantees that poor quality individuals are less able to display the high magnitude signals produced by the higher quality individuals. Receivers have been favoured by natural selection to attend only to the costliest signals, and thereby acquire honest information from the signaller. Hence the extravagant, costly ornamentation found among males of many species, ensures that females can accurately choose among them on the basis of their qualities. However, because somatic cells are normally perfectly genetically related, and are often denied access to the germ line, there will be minimal genetic conflicts of interest. This appears to imply that reliable intercellular signals should be produced without the need for cost to ensure their reliability. Nevertheless, we show that whenever cells vary in their phenotypic qualities in ways relevant to the fitness of the body, and given that there exists a class of cell that remains "ignorant' of its phenotypic state, costly intercellular signalling will evolve as a form of quality control. Specifically, we show that given variation in the cell population, signal cost will aid the identification and removal of cells that over-represent their true phenotypic state, and which therefore could lower fitness. Cells that under-represent their state are simply outcompeted by other cells. The cells of a body employ signals in a variety of intercellular interactions, including the development of the nervous system, the formation of neuromuscular junctions, and during the establishment of the immune repetoire. In each of these cases, cells may employ costly signals to advertise their phenotypic quality to other cells, and we review the evidence in support of this hypothesis: in effect, the cells may possess a molecular counterpart to the peacock's tail.

Defining CTL-induced pathology: implications for HIV.

The relationship between virus and host cells is multifactorial and nonlinear. This indicates that the effect of an immune response on infection can lead to several different outcomes. These include severe immunopathology. We seek to define properties of CTL-induced pathology in viral infections and examine the implications for HIV disease progression. We find that CTL-induced pathology is observed if the rate of viral replication is fast relative to the CTL responsiveness of the host. Theoretical predictions are consistent with empirical data on LCMV infection. These conditions are also sufficient to induce pathology in HIV infection. However, the absence of HIV-specific CTL can result in an equivalent depletion of the CD4 T cell pool as a consequence of the short life span of activated T cells. A mathematical model describing the evolution of HIV coreceptor usage in the context of lytic and nonlytic CD8 cell responses might account for the relatively long time span required to result in disease. Viral evolution toward parameter ranges allowing CTL-induced pathology is difficult to achieve. It requires the emergence of fast viral replication together with escape from nonlytic CTL responses. However, according to the model, fast viral replication can result in the evolution of virus strains that are susceptible to chemokine-mediated inhibition of viral replication.

Mapping the parameters of prion-induced neuropathology.

We present a theoretical framework that enables us to dissect out the parametric dependencies of the pathogenesis of prion diseases. We are able to determine the influence of both host-dependent factors (connectivity, cell density, protein synthesis rate, and cell death) and strain-dependent factors (cell tropism, virulence, and replication rate). We use a model based on a linked system of differential equations on a lattice to explore how the regional distribution of central nervous system pathology in Creutzfeldt-Jakob disease, Gerstmann-Sträussler-Scheinker syndrome, and fatal familial insomnia relates to each of these factors. The model then is used to make qualitative predictions about the pathology for two possible hypothetical triggers of neuronal loss in prion diseases. Pathological progression in overexpressing mouse models has been shown to depend on the site of initial infection. The model allows us to compare the pathologies resulting from different inoculation routes.

The evolution of exploitation and honesty in animal communication: a model using artificial neural networks.

Conflicts of interest arise between signaller and receiver in most kinds of biological communication. Some authors have argued that this conflict is likely to give rise to deceit and exploitation, as receivers lag behind in the coevolutionary 'arms race' with signallers. Others have argued that such manipulation is likely to be short-lived and that receivers can avoid being deceived by paying attention to signals that are costly and hence 'unfakeable.' These two views have been hard to reconcile. Here, we present results from simulations of signal evolution using artificial neural networks, which demonstrate that honesty can coexist with a degree of exploitation. Signal cost ensures that receivers are able to obtain some honest information, but is unable to prevent exploitative signalling strategies from gaining short-term benefits. Although any one receiver bias that is open to exploitation will subsist for only a short period of time once signallers begin to take advantage of it, new preferences of this kind are constantly regenerated through selection and random drift. Hidden preferences and sensory exploitation are thus likely to have an enduring influence on the evolution of honest, costly signals. At the same time, honesty and cost are prerequisites for the evolution of exploitation. When signalling is cost-free, selection cannot act to maintain honesty, and receivers rapidly evolve to ignore signals. This leads to a reduction in the extent of hidden preference, and a consequent loss of potential for exploitation.

Evolutionary preservation of redundant duplicated genes.

Gene duplication events produce both perfect and imperfect copies of genes. Perfect copies are said to be functionally redundant when knockout of one gene produces no 'scoreable', phenotypic effects. Preserving identical, duplicate copies of genes is problematic as all copies are prone to accumulate neutral mutations as pseudogenes, or more rarely, evolve into new genes with novel functions. We summarise theoretical treatments for the invasion and subsequent evolutionary modification of functionally redundant genes. We then consider the preservation of functionally identical copies of a gene over evolutionary time. We present several models for conserving redundancy: asymmetric mutation, asymmetric efficacy, pleiotropy, developmental buffering, allelic competition and regulatory asymmetries. In all cases, some form of symmetry breaking is required to maintain functional redundancy indefinitely.

Prion's progress: patterns and rates of molecular evolution in relation to spongiform disease.

Modification of the cellular prion protein has been correlated with the acquisition of several neurodegenerative diseases, including kuru, scrapie, bovine spongiform encephalopathy (BSE), and Creutzfeldt-Jakob disease (CJD). Sequence conservation and amino acid identity are known to influence the efficacy of interspecific transmission. We analyzed patterns of interspecific genetic variation with a view toward identifying features related to disease transmission. The reconstructed gene trees and amino acid tree were compared with the species tree, and all discordances observed were related to the species barrier of disease transmission. The rates of synonymous substitution, nonsynonymous substitution, and nucleotide content were determined for the protein-coding gene. Substitutions implicated in each of the prion diseases were found to occur in regions of the protein that are least variable across all species-opposite to the pattern of variability expected from interaction with an infectious pathogen. Amino acid residues related to the species barrier form a single cluster associated with the first alpha-helical domain of the protein. Residues related to sporadic and hereditary human prion disease form two separate clusters, associated with the second and third alpha-helical domains. Taken together, these results are consistent with the view that prion diseases arise from accidents in protein folding, rather than infection with an undiscovered virus-like particle. We speculate that the differences in disease phenotype between transmissable and hereditary forms could result from interactions between different parts of the protein during propagation.