Simple stochastic birth and death models of genome evolution: was there enough time for us to evolve?

MOTIVATION: The distributions of many genome-associated quantities, including the membership of paralogous gene families can be approximated with power laws. We are interested in developing mathematical models of genome evolution that adequately account for the shape of these distributions and describe the evolutionary dynamics of their formation. RESULTS: We show that simple stochastic models of genome evolution lead to power-law asymptotics of protein domain family size distribution. These models, called Birth, Death and Innovation Models (BDIM), represent a special class of balanced birth-and-death processes, in which domain duplication and deletion rates are asymptotically equal up to the second order. The simplest, linear BDIM shows an excellent fit to the observed distributions of domain family size in diverse prokaryotic and eukaryotic genomes. However, the stochastic version of the linear BDIM explored here predicts that the actual size of large paralogous families is reached on an unrealistically long timescale. We show that introduction of non-linearity, which might be interpreted as interaction of a particular order between individual family members, allows the model to achieve genome evolution rates that are much better compatible with the current estimates of the rates of individual duplication/loss events.     

Divergent evolution of a structural proteome: phenomenological models

We develop models of the divergent evolution of genomes; the elementary object of sequence dynamics is the protein structural domain. To identify patterns of organization that reflect mechanisms of evolution, we consider the individual genomes of many procaryote species, studying the arrangement of protein structural domains in the space of all polypeptide structures. We view the network of structural similarities as a graph, called the organismal Protein Domain Universe Graph (oPDUG); vertices represent types of structural domains and edges represent strong structural similarity. As observed before, each oPDUG is a highly nonrandom graph, as evidenced in the vertex degree distribution, which resembles a Pareto law (which has a power-law asymptotic). To explain this and other peculiar properties of the oPDUGs, we construct an evolving-graph model for the long-timescale evolutionary dynamics of oPDUGs, containing only divergent mechanisms of domain discovery. The model generates degree distributions (resembling Pareto laws) and clustering-coefficient distributions that are characteristic of the oPDUGs. In the infinite-graph limit, we analytically compute the exponent for specific biological parameters, as well as the complete phase diagram of the model, finding two distinct regimes of domain innovation dynamics. Thus, divergent evolutionary dynamics quantitatively explains the nonrandom organization of oPDUGs.     

Temporal variation can facilitate niche evolution in harsh sink environments

We examine the impact of temporal variation on adaptive evolution in "sink" environments, where a species encounters conditions outside its niche. Sink populations persist because of recurrent immigration from sources. Prior studies have highlighted the importance of demographic constraints on adaptive evolution in sinks and revealed that adaptation is less likely in harsher sinks. We examine two complementary models of population and evolutionary dynamics in sinks: a continuous-state quantitative-genetics model and an individual-based model. In the former, genetic variance is fixed; in the latter, genetic variance varies because of mutation, drift, and sampling. In both models, a population in a constant harsh sink environment can exist in alternative states: local maladaptation (phenotype comparable to immigrants from the source) or adaptation (phenotype near the local optimum). Temporal variation permits transitions between these states. We show that moderate amounts of temporal variation can facilitate adaptive evolution in sinks, permitting niche evolution, particularly for slow or autocorrelated variation. Such patterns of temporal variation may particularly pertain to sinks caused by biotic interactions (e.g., predation). Our results are relevant to the evolutionary dynamics of species' ranges, the fate of exotic invasive species, and the evolutionary emergence of infectious diseases into novel hosts.     

Hydration dynamics near a model protein surface

The evolution of water dynamics from dilute to very high concentration solutions of a prototypical hydrophobic amino acid with its polar backbone, N-acetyl-leucine-methylamide (NALMA), is studied by quasi-elastic neutron scattering (QENS) and molecular dynamics (MD) simulation for both the completely deuterated and completely hydrogenated leucine monomer. The NALMA-water system and the QENS data together provide a unique study for characterizing the dynamics of different hydration layers near a prototypical hydrophobic side chain and the backbone of which it is attached. We observe several unexpected features in the dynamics of these biological solutions under ambient conditions. The NALMA dynamics shows evidence of de Gennes narrowing, an indication of coherent long timescale structural relaxation dynamics. The translational and rotational water dynamics at the highest solute concentrations are found to be highly suppressed as characterized by long residential time and slow diffusion coefficients. The analysis of the more dilute concentration solutions models the first hydration shell with the 2.0 M spectra. We find that for outer layer hydration dynamics that the translational diffusion dynamics is still suppressed, although the rotational relaxation time and residential time are converged to bulk-water values. Molecular dynamics analysis of the first hydration shell water dynamics shows spatially heterogeneous water dynamics, with fast water motions near the hydrophobic side chain, and much slower water motions near the hydrophilic backbone. We discuss the hydration dynamics results of this model protein system in the context of protein function and protein-protein recognition.     

Spatial processes and evolutionary models: a critical review

Evolution is a fundamentally population level process in which variation, drift and selection produce both temporal and spatial patterns of change. Statistical model fitting is now commonly used to estimate which kind of evolutionary process best explains patterns of change through time using models like Brownian motion, stabilizing selection (Ornstein–Uhlenbeck) and directional selection on traits measured from stratigraphic sequences or on phylogenetic trees. But these models assume that the traits possessed by a species are homogeneous. Spatial processes such as dispersal, gene flow and geographical range changes can produce patterns of trait evolution that do not fit the expectations of standard models, even when evolution at the local‐population level is governed by drift or a typical OU model of selection. The basic properties of population level processes (variation, drift, selection and population size) are reviewed and the relationship between their spatial and temporal dynamics is discussed. Typical evolutionary models used in palaeontology incorporate the temporal component of these dynamics, but not the spatial. Range expansions and contractions introduce rate variability into drift processes, range expansion under a drift model can drive directional change in trait evolution, and spatial selection gradients can create spatial variation in traits that can produce long‐term directional trends and punctuation events depending on the balance between selection strength, gene flow, extirpation probability and model of speciation. Using computational modelling that spatial processes can create evolutionary outcomes that depart from basic population‐level notions from these standard macroevolutionary models.     

Nonuniform processes of chromosome evolution in sedges (Carex: Cyperaceae)

Holocentric chromosomes-chromosomes that lack localized centromeres-occur in numerous unrelated clades of insects, flatworms, and angiosperms. Chromosome number changes in such organisms often result from fission and fusion events rather than polyploidy. In this study, I test the hypothesis that chromosome number evolves according to a uniform process in Carex section Ovales (Cyperaceae), the largest New World section of an angiosperm genus renowned for its chromosomal variability and species richness. I evaluate alternative models of chromosome evolution that allow for shifts in both stochastic and deterministic evolutionary processes and that quantify the rate of evolution and heritability/phylogenetic dependence of chromosome number. Estimates of Ornstein-Uhlenbeck model parameters and tree-scaling parameters in a generalized least squares framework demonstrate that (1) chromosome numbers evolve rapidly toward clade-specific stationary distributions that cannot be explained by constant variance (Brownian motion) evolutionary models, (2) chromosome evolution in the section is rapid and exhibits little phylogenetic inertia, and (3) explaining the phylogenetic pattern of chromosome numbers in the section entails inferring a shift in evolutionary dynamics at the root of a derived clade. The finding that chromosome evolution is not a uniform process in sedges provides a novel example of karyotypic orthoselection in an organism with holocentric chromosomes.     

What paths do advantageous alleles take during short‐term evolutionary change?

Combining experimental evolution with whole‐genome resequencing is a promising new strategy for investigating the dynamics of evolutionary change. Published studies that have resequenced laboratory‐selected populations of sexual organisms have typically focused on populations sampled at the end of an evolution experiment. These studies have attempted to associate particular alleles with phenotypic change and attempted to distinguish between different theoretical models of adaptation. However, neither the population used to initiate the experiment nor multiple time points sampled during the evolutionary trajectory are generally available for examination. In this issue of Molecular Ecology, Orozco‐terWengel et al. (2012) take a significant step forward by estimating genome‐wide allele frequencies at the start, 15 generations into and at the end of a 37‐generation Drosophila experimental evolution study. The authors identify regions of the genome that have responded to laboratory selection and describe the temporal dynamics of allele frequency change. They identify two common trajectories for putatively adaptive alleles: alleles either gradually increase in frequency throughout the entire 37 generations or alleles plateau at a new frequency by generation 15. The identification of complex trajectories of alleles under selection contributes to a growing body of literature suggesting that simple models of adaptation, whereby beneficial alleles arise and increase in frequency unimpeded until they become fixed, may not adequately describe short‐term response to selection.     

Nuclear–mitochondrial epistasis: a gene's eye view of genomic conflict

We use population genetic models to investigate the cooperative and conflicting synergistic fitness effects between genes from the nucleus and the mitochondrion. By varying fitness parameters, we examine the scope for conflict relative to cooperation among genomes and the utility of the “gene's eye view” analytical approach, which is based on the marginal average fitness of specific alleles. Because sexual conflict can maintain polymorphism of mitochondrial haplotypes, we can explore two types of evolutionary conflict (genomic and sexual) with one epistatic model. We find that the nuclear genetic architecture (autosomal, X‐linked, or Z‐linked) and the mating system change the regions of parameter space corresponding to the evolution by sexual and genomic conflict. For all models, regardless of conflict or cooperation, we find that population mean fitness increases monotonically as evolution proceeds. Moreover, we find that the process of gene frequency change with positive, synergistic fitnesses is self‐accelerating, as the success of an allele in one genome or in one sex increases the frequency of the interacting allele upon which its success depends. This results in runaway evolutionary dynamics caused by the positive intergenomic associations generated by selection. An inbreeding mating system tends to further accelerate these runaway dynamics because it maintains favorable host–symbiont or male–female gene combinations. In contrast, where conflict predominates, the success of an allele in one genome or in one sex diminishes the frequency of the corresponding allele in the other, resulting in considerably slower evolutionary dynamics. The rate of change of mean fitness is also much faster with positive, synergistic fitnesses and much slower where conflict is predominant. Consequently, selection rapidly fixes cooperative gene combinations, while leaving behind a slowing evolving residue of conflicting gene combinations at mutation–selection balance. We discuss how an emphasis on marginal fitness averages may obscure the interdependence of allelic fitness across genomes, making the evolutionary trajectories appear independent of one another when they are not.     

Stick-and-diffuse and caged diffusion: a comparison of two models of synaptic vesicle dynamics

Two models were recently proposed to enable us to understand the dynamics of synaptic vesicles in hippocampal neurons. In the caged diffusion model, the vesicles diffuse in small circular cages located randomly in the bouton, while in the stick-and-diffuse model the vesicles bind and release from a cellular cytomatrix. In this article, we obtain analytic expressions for the fluorescence correlation spectroscopy (FCS) autocorrelation function for the two models and test their predictions against our earlier FCS measurements of the vesicle dynamics. We find that the stick-and-diffuse model agrees much better with the experiment. We find also that, due to the slow dynamics of the vesicles, the finite experimental integration time has an important effect on the FCS autocorrelation function and demonstrate its effect for the different models. The two models of the dynamics are also relevant to other cellular environments where mobile species undergo slow diffusionlike motion in restricted spaces or bind and release from a stationary substrate.     

The Genome of the Obligate Intracellular Parasite Trachipleistophora hominis: New Insights into Microsporidian Genome Dynamics and Reductive Evolution

The dynamics of reductive genome evolution for eukaryotes living inside other eukaryotic cells are poorly understood compared to well-studied model systems involving obligate intracellular bacteria. Here we present 8.5 Mb of sequence from the genome of the microsporidian Trachipleistophora hominis, isolated from an HIV/AIDS patient, which is an outgroup to the smaller compacted-genome species that primarily inform ideas of evolutionary mode for these enormously successful obligate intracellular parasites. Our data provide detailed information on the gene content, genome architecture and intergenic regions of a larger microsporidian genome, while comparative analyses allowed us to infer genomic features and metabolism of the common ancestor of the species investigated. Gene length reduction and massive loss of metabolic capacity in the common ancestor was accompanied by the evolution of novel microsporidian-specific protein families, whose conservation among microsporidians, against a background of reductive evolution, suggests they may have important functions in their parasitic lifestyle. The ancestor had already lost many metabolic pathways but retained glycolysis and the pentose phosphate pathway to provide cytosolic ATP and reduced coenzymes, and it had a minimal mitochondrion (mitosome) making Fe-S clusters but not ATP. It possessed bacterial-like nucleotide transport proteins as a key innovation for stealing host-generated ATP, the machinery for RNAi, key elements of the early secretory pathway, canonical eukaryotic as well as microsporidian-specific regulatory elements, a diversity of repetitive and transposable elements, and relatively low average gene density. Microsporidian genome evolution thus appears to have proceeded in at least two major steps: an ancestral remodelling of the proteome upon transition to intracellular parasitism that involved reduction but also selective expansion, followed by a secondary compaction of genome architecture in some, but not all, lineages.     

Delineating the longitudinal tumor evolution using organoid models

Cancer is an evolutionary process fueled by genetic or epigenetic alterations in the genome. Understanding the evolutionary dynamics that are operative at different stages of tumor progression might inform effective strategies in early detection, diagnosis, and treatment of cancer. However, our understanding on the dynamics of tumor evolution through time is very limited since it is usually impossible to sample patient tumors repeatedly. The recent advances in in vitro 3D organoid culture technologies have opened new avenues for the development of more realistic human cancer models that mimic many in vivo biological characteristics in human tumors. Here, we review recent progresses and challenges in cancer genomic evolution studies and advantages of using tumor organoids to study cancer evolution. We propose to establish an experimental evolution model based on continuous passages of patient-derived organoids and longitudinal sampling to study clonal dynamics and evolutionary patterns over time. Development and integration of population genetic theories and computational models into time-course genomic data in tumor organoids will help to pinpoint the key cellular mechanisms underlying cancer evolutionary dynamics, thus providing novel insights on therapeutic strategies for highly dynamic and heterogeneous tumors.     

Dynamics of a physiologically structured population in a time-varying environment

Physiologically structured population models have become a valuable tool to model the dynamics of populations. In a stationary environment such models can exhibit equilibrium solutions as well as periodic solutions. However, for many organisms the environment is not stationary, but varies more or less regularly. In order to understand the interaction between an external environmental forcing and the internal dynamics in a population, we examine the response of a physiologically structured population model to a periodic variation in the food resource. We explore the addition of forcing in two cases: (A) where the population dynamics is in equilibrium in a stationary environment, and (B) where the population dynamics exhibits a periodic solution in a stationary environment. When forcing is applied in case A, the solutions are mainly periodic. In case B the forcing signal interacts with the oscillations of the unforced system, and both periodic and irregular (quasi-periodic or chaotic) solutions occur. In both cases the periodic solutions include one and multiple period cycles, and each cycle can have several reproduction pulses.     

Symmetric competition as a general model for single-species adaptive dynamics

Adaptive dynamics is a widely used framework for modeling long-term evolution of continuous phenotypes. It is based on invasion fitness functions, which determine selection gradients and the canonical equation of adaptive dynamics. Even though the derivation of the adaptive dynamics from a given invasion fitness function is general and model-independent, the derivation of the invasion fitness function itself requires specification of an underlying ecological model. Therefore, evolutionary insights gained from adaptive dynamics models are generally model-dependent. Logistic models for symmetric, frequency-dependent competition are widely used in this context. Such models have the property that the selection gradients derived from them are gradients of scalar functions, which reflects a certain gradient property of the corresponding invasion fitness function. We show that any adaptive dynamics model that is based on an invasion fitness functions with this gradient property can be transformed into a generalized symmetric competition model. This provides a precise delineation of the generality of results derived from competition models. Roughly speaking, to understand the adaptive dynamics of the class of models satisfying a certain gradient condition, one only needs a complete understanding of the adaptive dynamics of symmetric, frequency-dependent competition. We show how this result can be applied to number of basic issues in evolutionary theory.     

Molecular Clock of Neutral Mutations in a Fitness-Increasing Evolutionary Process

The molecular clock of neutral mutations, which represents linear mutation fixation over generations, is theoretically explained by genetic drift in fitness-steady evolution or hitchhiking in adaptive evolution. The present study is the first experimental demonstration for the molecular clock of neutral mutations in a fitness-increasing evolutionary process. The dynamics of genome mutation fixation in the thermal adaptive evolution of Escherichia coli were evaluated in a prolonged evolution experiment in duplicated lineages. The cells from the continuously fitness-increasing evolutionary process were subjected to genome sequencing and analyzed at both the population and single-colony levels. Although the dynamics of genome mutation fixation were complicated by the combination of the stochastic appearance of adaptive mutations and clonal interference, the mutation fixation in the population was simply linear over generations. Each genome in the population accumulated 1.6 synonymous and 3.1 non-synonymous neutral mutations, on average, by the spontaneous mutation accumulation rate, while only a single genome in the population occasionally acquired an adaptive mutation. The neutral mutations that preexisted on the single genome hitchhiked on the domination of the adaptive mutation. The successive fixation processes of the 128 mutations demonstrated that hitchhiking and not genetic drift were responsible for the coincidence of the spontaneous mutation accumulation rate in the genome with the fixation rate of neutral mutations in the population. The molecular clock of neutral mutations to the fitness-increasing evolution suggests that the numerous neutral mutations observed in molecular phylogenetic trees may not always have been fixed in fitness-steady evolution but in adaptive evolution.     

Biological applications of the theory of birth-and-death processes

In this review, we discuss applications of the theory of birth-and-death processes to problems in biology, primarily, those of evolutionary genomics. The mathematical principles of the theory of these processes are briefly described. Birth-and-death processes, with some straightforward additions such as innovation, are a simple, natural and formal framework for modeling a vast variety of biological processes such as population dynamics, speciation, genome evolution, including growth of paralogous gene families and horizontal gene transfer and somatic evolution of cancers. We further describe how empirical data, e.g. distributions of paralogous gene family size, can be used to choose the model that best reflects the actual course of evolution among different versions of birth-death-and-innovation models. We conclude that birth-and-death processes, thanks to their mathematical transparency, flexibility and relevance to fundamental biological processes, are going to be an indispensable mathematical tool for the burgeoning field of systems biology.     

Convergence to a novel environment: comparative method versus experimental evolution

Abstract Laboratory adaptation allows researchers to contrast temporal studies of experimental evolution with comparative studies. The comparative method is here taken to mean the inference of microevolutionary processes from comparisons among contemporaneous populations of diverse origins, from one or multiple species. The data contrasted here come from Drosophila subobscura populations that were introduced to the laboratory at several different times and from two different locations. Two questions were addressed. First, can we correctly infer evolutionary dynamics from comparative data collected simultaneously from disparate populations? In most cases, we could, except for the character of starvation resistance. Second, are the evolutionary dynamics inferred from the comparative approach similar to those revealed by temporal studies of experimental evolution? For fecundity characters, they were. Overall the results show that both comparative and temporal studies are useful, though the former can be uninformative for characters with complex evolutionary trajectories.     

The "protocell": a mathematical model of self-maintenance

The concepts of self-generation, autonomous boundary and self-maintenance are explained briefly. The "protocell" is presented as a model of self-maintenance which is based on simple physical mechanisms of diffusion and reaction. The time evolution of the surface of the protocell is taken into account explicitly in the form of a Stefan condition giving rise to a non-linear feedback of the surface motion to the reaction and diffusion processes inside the protocell. The spatio-temporal dynamics are investigated, particularly in the neighbourhood of the stationary states, showing a self-maintaining behaviour under a certain range of nutritional conditions. Under another set of conditions we find an instability leading to a division process so that the population of protocells becomes self-maintaining instead of the single individual. The presented formulation of the protocell model is crucially improved compared with a previous version which required boundary conditions at infinity. The previous version was not strictly self-maintaining since dynamics outside the cell were essential for its behaviour.     

Parasite transmission among relatives halts Red Queen dynamics

The theory that coevolving hosts and parasites create a fluctuating selective environment for one another (i.e., produce Red Queen dynamics) has deep roots in evolutionary biology; yet empirical evidence for Red Queen dynamics remains scarce. Fluctuating coevolutionary dynamics underpin the Red Queen hypothesis for the evolution of sex, as well as hypotheses explaining the persistence of genetic variation under sexual selection, local parasite adaptation, the evolution of mutation rate, and the evolution of nonrandom mating. Coevolutionary models that exhibit Red Queen dynamics typically assume that hosts and parasites encounter one another randomly. However, if related individuals aggregate into family groups or are clustered spatially, related hosts will be more likely to encounter parasites transmitted by genetically similar individuals. Using a model that incorporates familial parasite transmission, we show that a slight degree of familial parasite transmission is sufficient to halt coevolutionary fluctuations. Our results predict that evidence for Red Queen dynamics, and its evolutionary consequences, are most likely to be found in biological systems in which hosts and parasites mix mainly at random, and are less likely to be found in systems with familial aggregation. This presents a challenge to the Red Queen hypothesis and other hypotheses that depend on coevolutionary cycling.     

The complete genome sequence of a dog: a perspective

A complete, high-quality reference sequence of a dog genome was recently produced by a team of researchers led by the Broad Institute, achieving another major milestone in deciphering the genomic landscape of mammalian organisms. The genome sequence provides an indispensable resource for comparative analysis and novel insights into dog and human evolution and history. Together with the survey sequence of a poodle previously published in 2003, the two dog genome sequences allowed identification of more than 2.5 million single nucleotide polymorphisms within and between dog breeds, which can be used in evolutionary analysis, behavioral studies and disease gene mapping.(1)