On analytical approaches to epidemics on networks

One way to describe the spread of an infection on a network is by approximating the network by a random graph. However, the usual way of constructing a random graph does not give any control over the number of triangles in the graph, while these triangles will naturally arise in many networks (e.g. in social networks). In this paper, random graphs with a given degree distribution and a given expected number of triangles are constructed. By using these random graphs we analyze the spread of two types of infection on a network: infections with a fixed infectious period and infections for which an infective individual will infect all of its susceptible neighbors or none. These two types of infection can be used to give upper and lower bounds for R(0), the probability of extinction and other measures of dynamics of infections with more general infectious periods.     

Population dynamics of botanical epidemics involving primary and secondary infection

In this paper we study the dynamical properties of models for botanical epidemics, especially for soil-borne fungal infection. The models develop several new concepts, involving dual sources of infection, host and inoculum dynamics. Epidemics are modelled with respect to the infection status of whole plants and plant organs (the G model) or to lesion density and size (the SW model). The infection can originate in two sources, either from the initial inoculum (primary infection) or by a direct transmission between plant tissue (secondary infection). The first term corresponds to the transmission through the free-living stages of macroparasites or an external source of infection in certain medical models, whereas the second term is equivalent to direct transmission between the hosts in microparasitic infections. The models allow for dynamics of host growth and inoculum decay. We show that the two models for root and lesion dynamics can be derived as special cases of a single generic model. Analytical and numerical methods are used to analyse the behaviour of the models for static, unlimited (exponential) and asymptotically limited host growth with and without secondary infection, and with and without decay of initial inoculum. The models are shown to exhibit a range of epidemic behaviour within single seasons that extends from simple monotonic increase with saturation of the host population, through temporary plateaux as the system switches from primary to secondary infection, to effective elimination of the pathogen by the host outgrowing the fungal infection. For certain conditions, the equilibrium values are shown to depend on initial conditions. These results have important consequences for the control of plant disease. They can be applied beyond soil-borne plant pathogens to mycorrhizal fungi and aerial pathogens while the principles of primary and secondary infection with host and inoculum dynamics may be used to link classical models for both microparasitic and macroparasitic infections.     

The cholera: The epidemics and their social-demographic features in Southern Italy

Cholera, as it was regarding each infective disease of which nobody knew its aetiologic agent or, in any way, if its agent was present really, was for the Calabrian people an unknown enemy that nobody knew anything about either its behaviour or the modality of its penetration into the human body. During many years characterized by a medical methodological obscurantism, Calabrian people lived, during the different choleric epidemics, on a daily life based upon the ignorance, and the pseudo-treatments, and pseudo-physicians. During the cholera epidemics, not only the people groped in the dark, but also the governmental authorities were confused because were subdivided into those who supported the theory of the epidemics spread and those who supported the theory of the contagion spread. It must be emphasized that from the XX century, when the pathologies due to natural agents were reduced and were substituted with those due to humans, cholera influenced very much the demography and the social-cultural features of the Southern Italy.     

From heroin epidemics to methamphetamine epidemics: Modelling substance abuse in a South African province

The global rise in the use of methamphetamine has been documented to have reached epidemic proportions. Researchers have focussed on the social implications of the epidemic. A typical drug use cycle consists of concealed drugs use after initiation, addiction, treatment-recovery-relapse cycle, whose dynamics are not well understood. The model by White and Comiskey [41], on heroin epidemics, treatment and ODE modelling, is modified to model the dynamics of methamphetamine use in a South African province. The analysis of the model is presented in terms of the methamphetamine epidemic threshold R₀. It is shown that the model has multiple equilibria and using the center manifold theory, the model exhibits the phenomenon of backward bifurcation where a stable drug free equilibrium co-exists with a stable drug persistent equilibrium for a certain defined range of R₀. The stabilities of the model equilibria are ascertained and persistence conditions established. Furthermore, numerical simulations are performed; these include fitting the model to the available data on the number of patients with methamphetamine problems. The implications of the results to drug policy, treatment and prevention are discussed.     

The causes of repeated genetic evolution

A general understanding of the evolutionary process is limited by the contingency of each evolutionary event, making it difficult, even retrospectively, to explain why things have unfolded the way they have. The repeated evolution of similar traits in organisms facing similar environmental conditions is a pervasive phenomenon, including for animal morphology, and is considered a strong evidence for adaptive evolution. Examples of repeated evolution of particular traits offer a unique opportunity to ask whether evolution has followed similar or different genetic paths. Case studies reveal that although multiple genetic paths were often possible to evolve a morphological trait, similar evolutionary trajectories have been followed repeatedly in independent lineages, suggesting that biases influence the course of genetic evolution. In the light of these examples we examine several factors influencing the genetic paths of adaptive evolution and in particular how the interplay between natural selection and genetic variations carves out predictable genetic trajectories of morphological evolution.     

The genetic basis of evolution, adaptation and speciation

A primary question in biology concerns the genetic basis of the evolution of novel traits, often in response to environmental changes, and how this can subsequently cause species isolation. This topic was the focus of the symposium on the Genetics of Speciation and Evolution at the annual meeting of the Canadian Society for Ecology and Evolution, held in Banff in May 2011. The presentations revealed some of the rapid advances being made in understanding the genetic basis of adaptation and speciation, as well as the elegant interplay between an organism's genetic complement and the environment that organism experiences.     

The effect of population structure on the rate of evolution

Ecological factors exert a range of effects on the dynamics of the evolutionary process. A particularly marked effect comes from population structure, which can affect the probability that new mutations reach fixation. Our interest is in population structures, such as those depicted by ‘star graphs’, that amplify the effects of selection by further increasing the fixation probability of advantageous mutants and decreasing the fixation probability of disadvantageous mutants. The fact that star graphs increase the fixation probability of beneficial mutations has lead to the conclusion that evolution proceeds more rapidly in star-structured populations, compared with mixed (unstructured) populations. Here, we show that the effects of population structure on the rate of evolution are more complex and subtle than previously recognized and draw attention to the importance of fixation time. By comparing population structures that amplify selection with other population structures, both analytically and numerically, we show that evolution can slow down substantially even in populations where selection is amplified.     

The effect of recombination on the neutral evolution of genetic robustness

Conventional population genetics considers the evolution of a limited number of genotypes corresponding to phenotypes with different fitness. As model phenotypes, in particular RNA secondary structure, have become computationally tractable, however, it has become apparent that the context dependent effect of mutations and the many-to-one nature inherent in these genotype-phenotype maps can have fundamental evolutionary consequences. It has previously been demonstrated that populations of genotypes evolving on the neutral networks corresponding to all genotypes with the same secondary structure only through neutral mutations can evolve mutational robustness [E. van Nimwegen, J.P. Crutchfield, M. Huynen, Neutral evolution of mutational robustness, Proc. Natl. Acad. Sci. USA 96(17), 9716-9720 (1999)], by concentrating the population on regions of high neutrality. Introducing recombination we demonstrate, through numerically calculating the stationary distribution of an infinite population on ensembles of random neutral networks that mutational robustness is significantly enhanced and further that the magnitude of this enhancement is sensitive to details of the neutral network topology. Through the simulation of finite populations of genotypes evolving on random neutral networks and a scaled down microRNA neutral network, we show that even in finite populations recombination will still act to focus the population on regions of locally high neutrality.     

The standard genetic code enhances adaptive evolution of proteins

The standard genetic code, by which most organisms translate genetic material into protein metabolism, is non-randomly organized. The Error Minimization hypothesis interprets this non-randomness as an adaptation, proposing that natural selection produced a pattern of codon assignments that buffers genomes against the impact of mutations. Indeed, on the average any given point mutation has a lesser effect on the chemical properties of the utilized amino acid than expected by chance. Might it also, however, be the case that the non-random nature of the code effects the rate of adaptive evolution? To investigate this, here we develop population genetic simulations to test the rate of adaptive gene evolution under different genetic codes. We identify two independent properties of a genetic code that profoundly influence the speed of adaptive evolution. Noting that the standard genetic code exhibits both, we offer a new insight into the effects of the "error minimizing" code: such a code enhances the efficacy of adaptive sequence evolution.     

Interactions of genetic and cultural evolution: Models and examples

This paper proposes models and examples of five principal modes of interaction between genes and culture in human evolution. Because genes and culture ultimately interact in the minds of individuals, the models are focused on individual level processes of constrained microevolution. The central hypotheses are (1) that cultural evolution as well as genetic evolution commonly proceeds by the differential transmission of alternative instructions among individuals, (2) that genetic and cultural processes directly interact through mutual influence on each other's differentials of transmission in a population, (3) that the cultural process is often self-selecting by its own criteria, and (4) that these criteria generally operate to enhance rather than oppose human adaptation. Evolutionary change at higher levels, which is particularly important in sociocultural evolution, is interpreted as restructuring the nature and extent of the variability available at the individual level. To clarify the conceptual differences of the models and hopefully to stimulate related analyses in other areas, I discuss selected examples of each of these interactions. I conclude with some remarks on the relative importance of the models to human ecology and evolution.     

The effect of multifunctionality on the rate of evolution in yeast

Multifunctional genes are expected to evolve at lower rates because mutations in such genes that improve one function might often have deleterious effects on other functions. Here we tested for an association between multifunctionality and evolutionary rates in genes of Saccharomyces cerevisiae, and we find a highly significant negative correlation between the number of biological processes in which a gene is involved in and its rate of evolution. However, the magnitude of this effect is small, and the results do not support the notion that multifunctionality limits a gene's rate of evolution.     

The relations between metabolic variations and genetic evolution of different species

Metabonomics has been applied in many bio-related scientific fields. Nevertheless, some animal research works are shown to fail when they are extended to humans. Therefore, it is essential to figure out suitable animal modeling to mimic human metabolism so that animal findings can serve humans. In this study, two kinds of commonly selected body fluids, serum and urine, from humans and various experimental animals were characterized by integration of nuclear magnetic resonance (NMR) spectroscopy with multivariate statistical analysis to identify the interspecies metabolic differences and similarities at a baseline physiological status. Our results highlight that the dairy cow and pig may be an optimal choice for transportation and biodistribution studies of drugs and that the Kunming (KM) mouse model may be the most effective for excretion studies of drugs, whereas the Sprague–Dawley (SD) rat could be the most suitable candidate for animal modeling under overall considerations. The biochemical pathways analyses further provide an interconnection between genetic evolution and metabolic variations, where species evolution most strongly affects microbial biodiversity and, consequently, has effects on the species-specific biological substances of biosynthesis and corresponding biological activities. Knowledge of the metabolic effects from species difference will enable the construction of better models for disease diagnosis, drug metabolism, and toxicology research.     

The evolutionary effect of endemic infectious disease: Continuous models for an invariant pathogen

Continuous deterministic models are used to investigate the relationship between the epidemiology of endemic infectious disease and the genetics of natural selection in the host population when a specific genetic locus controls susceptibility to disease under a variety of circumstances. One locus, two allele genes are considered in the contexts of haploid and diploid host populations while the agent of infection is assumed to be invariant. It is found that polymorphic equilibria exist and are stable for certain parameter combinations in each of the cases studied. The equilibrium levels of gene frequencies and disease prevalence depend on both genetic and epidemic factors.     

Morphological evolution and genetic differentiation in Daphnia species complexes

Despite many ecological and evolutionary studies, the history of several species complexes within the freshwater crustacean genus Daphnia (Branchiopoda, Anomopoda) is poorly understood. In particular, the Daphnia longispina group, comprising several large-lake species, is characterized by pronounced phenotypic plasticity, many hybridizing species and backcrossing. We studied clonal assemblages from lakes and ponds comprising daphnids from several species complexes. In order to reveal patterns of reticulate evolution and introgression among species, we analysed three data sets and compared nuclear, mtDNA and morphological divergence using animals from 158 newly established clonal cultures. By examining 15 nuclear and 11 mitochondrial (12S/16S rDNA) genetic characters (allozymes/restriction enzymes), and 48 morphological traits, we found high clonal diversity and discontinuities in genotypic and morphological space which allowed us to group clones by cytonuclear differentiation into seven units (outgroup D. pulex). In contrast to six groups emerging from nuclear divergence (related to three traditional species, D. cucullata, D. galeata, D. hyalina and three pairwise intermediate hybrids), a seventh group of clones was clearly resolved by morphological divergence: distinct mtDNA haplotypes within one nuclear defined cluster, ‘D. hyalina’, resembled traditional D. hyalina and D. rosea phenotypes, respectively. In other nuclear defined clusters, association between mtDNA haplotype and morphology was low, despite hybridization being bidirectional (reciprocal crosses). Morphological divergence was greatest between young sister species which are separated on the lake/pond level, suggesting a significant role for divergent selection during speciation along with habitat shifts. Phylogenetic analyses were restricted to four cytonuclear groups of clones related to species. mtDNA and nuclear phylogenies were consistent in low genetic divergence and monophyly of D. hyalina and D. rosea. Incongruent patterns of phylogenies and different levels of genetic differentiation between traditional species suggest reticulate evolutionary processes.     

A hardware interpretation of the evolution of the genetic code

A quantitative rationale for the evolution of the genetic code is developed considering the principle of minimal hardware. This principle defines an optimal code as one that minimizes for a given amount of information encoded, the product of the number of physical devices used by the average complexity of each device. By identifying the number of different amino acids, number of nucleotide positions per codon and number of base types that can occupy each such position with, respectively, the amount of information, number of devices and the complexity, we show that optimal codes occur for 3, 7 and 20 amino acids with codons having a single, two and three base positions per codon, respectively. The advantage of a code of exactly 4 symbols is deduced, as well as a plausible evolutionary pathway from a code of doublets to triplets. The present day code of 20 amino acids encoded by 64 codons is shown to be the most optimal in an absolute sense. Using a tetraplet code further evolution to a code in which there would be 55 amino acids is in principle possible, but such a code would deviate slightly more than the present day code from the minimal hardware configuration. The change from a triplet code to a tetraplet code would occur at about 32 amino acids. Our conclusions are independent of, but consistent with, the observed physico-chemical properties of the amino acids and codon structures. These correlations could have evolved within the constrains imposed by the minimal hardware principle.     

The role of intragenomic recombination rate in the evolution of population's genetic pool

In a simple computer model of population evolution, we have shown that frequency of recombination between haplotypes during the gamete production influences the effectiveness of the reproduction strategy. High recombination rates keeps the fraction of defective alleles low while low recombination rate or uneven distributed recombination spots change the strategy of genomes' evolution and result in the accumulation of heterozygous loci in the genomes. Even short fragment of chromosome with restricted recombination influences the genetic structure of neighboring regions.     

The effect of phenotypic plasticity on evolution in multipeaked fitness landscapes

When facing the challenge of developing an individual that best fits its environment, nature demonstrates an interesting combination of two fundamentally different adaptive mechanisms: genetic evolution and phenotypic plasticity. Following numerous computational models, it has become the accepted wisdom that lifetime acclimation (e.g. via learning) smooths the fitness landscape and consequently accelerates evolution. However, analytical studies, focusing on the effect of phenotypic plasticity on evolution in simple unimodal landscapes, have often found that learning hinders the evolutionary process rather than accelerating it. Here, we provide a general framework for studying the effect of plasticity on evolution in multipeaked landscapes and introduce a rigorous mathematical analysis of these dynamics. We show that the convergence rate of the evolutionary process in a given arbitrary one-dimensional fitness landscape is dominated by the largest descent (drawdown) in the landscape and provide numerical evidence to support an analogous dominance also in multidimensional landscapes. We consider several schemes of phenotypic plasticity and examine their effect on the landscape drawdown, identifying the conditions under which phenotypic plasticity is advantageous. The lack of such a drawdown in unimodal landscapes vs. its dominance in multipeaked landscapes accounts for the seemingly contradictory findings of previous studies.     

The genetic implications of biological and cultural structuring processes during hominid evolution

Human populations are genetically structured through biological reproduction but reproduction is socially structured through culturally expressed systems of marriage, hence the need to take into account the cultural dimension of human societies when considering the genetic structure of modern human populations. The interplay between these two structuring processes is examined through the implications of a biologically based primate form of social organization versus a culturally based foraging form of social organization for an anomaly between the genetic differentiation implied by micro-evolutionary genetic models versus the species-wide pattern of morphological change implied by hominid fossil evidence. Simulation is used to derive the pattern for genetic differentiation at the level of the living group for both forms of social organization and a competition model is added to the genetic model as a way to resolve the anomaly. The importance of the competition model for the transition from a biologically based to a culturally based form of social organization is discussed.