A birth–death model of ageing: from individual-based dynamics to evolutive differential inclusions

Journal of Mathematical Biology - Ageing’s sensitivity to natural selection has long been discussed because of its apparent negative effect on an individual’s fitness. Thanks to the...     

Transition probabilities for general birth–death processes with applications in ecology, genetics, and evolution

A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with n current particles, a new particle is born with instantaneous rate λ(n) and a particle dies with instantaneous rate μ(n). Currently no robust and efficient method exists to evaluate the finite-time transition probabilities in a general birth-death process with arbitrary birth and death rates. In this paper, we first revisit the theory of continued fractions to obtain expressions for the Laplace transforms of these transition probabilities and make explicit an important derivation connecting transition probabilities and continued fractions. We then develop an efficient algorithm for computing these probabilities that analyzes the error associated with approximations in the method. We demonstrate that this error-controlled method agrees with known solutions and outperforms previous approaches to computing these probabilities. Finally, we apply our novel method to several important problems in ecology, evolution, and genetics.     

Random selection—A simple model based on linear birth and death processes

Linear birth and death processes are used to derive simple expressions for sequential extinction times and gene fixation probabilities in asexual populations.     

How well can the exponential-growth coalescent approximate constant-rate birth–death population dynamics?

One of the central objectives in the field of phylodynamics is the quantification of population dynamic processes using genetic sequence data or in some cases phenotypic data. Phylodynamics has been successfully applied to many different processes, such as the spread of infectious diseases, within-host evolution of a pathogen, macroevolution and even language evolution. Phylodynamic analysis requires a probability distribution on phylogenetic trees spanned by the genetic data. Because such a probability distribution is not available for many common stochastic population dynamic processes, coalescent-based approximations assuming deterministic population size changes are widely employed. Key to many population dynamic models, in particular epidemiological models, is a period of exponential population growth during the initial phase. Here, we show that the coalescent does not well approximate stochastic exponential population growth, which is typically modelled by a birth–death process. We demonstrate that introducing demographic stochasticity into the population size function of the coalescent improves the approximation for values of R₀ close to 1, but substantial differences remain for large R₀. In addition, the computational advantage of using an approximation over exact models vanishes when introducing such demographic stochasticity. These results highlight that we need to increase efforts to develop phylodynamic tools that correctly account for the stochasticity of population dynamic models for inference.     

Biomanipulation and food-web dynamics — the importance of seasonal stability

Responses of phytoplankton biomass were monitored in pelagic enclosures subjected to manipulations with nutrients (+N/P), planktivore roach (Rutilus rutilus) and large grazers (Daphnia) in 18 bags during spring, summer and autumn in mesotrophic Lake Gjersjøen. In general, the seasonal effects on phytoplankton biomass were more marked than the effects of biomanipulation. Primary top-down effects of fish on zooplankton were conspicuous in all bags, whereas control of phytoplankton growth by grazing was observed only in the nutrient-limited summer situation. The effect of nutrient additions was pronounced in summer, less in spring and autumn; additions of fish gave the most pronounced effect in spring. The phytoplankton/zooplankton biomass ratio remained high (10–100) in bags with fish, with the highest ratios in combination with fertilization. The ratio decreased in bags without fish to<2 in most bags, but a real grazing control was only observed in bags with addition ofDaphnia. No direct grazing effects could be observed on the absolute or relative biomass of cyanobacteria (mainlyOscillatoria agardhii). The share of cyanobacteria in total phytoplankton biomass was lowest in summer (7–26%), higher in spring (39–63%) and more than 90% in the autumn experiment. The development of the cyanobacterial biomass was rather synchronous in all bags in all the three experiments. A high biomass ofDaphnia gave no increase in the pool of dissolved nutrients in spring, a slight increase in summer and a pronounced increase in autumn. While a strong decrease in the P/C-cell quota of the phytoplankton was observed from spring to autumn, no effect of grazing or nutrient release could be related to this P/C-status. The experiments indicate that such systems, with high and stable densities of inedible cyanobacteria, are rather insensitive to short-term (3–4 weeks) biomanipulation efforts. This is supported by observations on the long-term development of the lake.

     

Molecular dynamics simulation of the melting processes of core–shell and pure nanoparticles

Core–shell nanoparticles are nanosized particles that consist of a core and a shell, constructed from different metallic elements. Core–shell nanoparticles have received extensive attention, owing to their various potential applications such as paints, optical films and catalysts. Herein, we investigate the melting behaviours of different core–shell nanoparticles under continuous heating using molecular dynamics simulation. Different metallic elements were examined as core–shell and pure nanoparticles. Five different processes were observed during the melting of core–shell nanoparticles. In contrast, only one process was identified during the melting of pure nanoparticles. These processes were influenced by the nanoparticle size, shell thickness and differences between the lattice constants and melting point temperatures of the metallic elements. Our simulation provides microscopic insights into the melting behaviours of existing and proposed core–shell nanoparticles that would be highly beneficial towards the fabrication of materials with different chemical coatings.     

American geneticists and the eugenics movement: 1905–1935

Conclusion I have attempted to show that between 1905 and 1935, both internal and external factors were important in producing and influencing geneticists' attitudes toward the eugenics movement. Internal factors operated in several ways during this period. In the first decade of the century, discoveries within genetics supplied geneticists a mode of expression to evoke their already existing social concern by providing a new vocabulary with which to present eugenic proposals. In addition, because these findings were relatively easy to explain to the layman, it became an easy matter for geneticists to popularize eugenics. After 1915, by suggesting the complexity of inheritance, other developments within genetics helped dim their initial enthusiasm for the movement. During this period, factors external to the science of genetics also were important. By producing a general interest in social affairs among many geneticists, the intellectual and social milieu of the late 1800's lay the foundations for their early participation in the eugenics movement. In the 1920's and 1930's the subjection of genetic theory to support preconceived social and political doctrines prompted them to renounce the movement publicly.While both internal and external factors operated on geneticists, the lesson of this study is that external factors were more important in influencing their attitudes toward the movement than internal factors. At the turn of the century, geneticists inherited from Social Darwinism a general interest in applying biological principles to the analysis of social problems; discoveries within genetics mainly provided a convenient and persuasive terminology with which to express their interest. Later, both internal and external factors caused their enthusiasm for the movement to wane, but their public renunciation of it was caused primarily by external factors alone.The importance of external factors is seen to be even greater by considering the model I suggested to explain the development of social responsibility in modern form among scientists. According to this model, social responsibility results after a crisis in the social uses of a given science—as a response to external factors. This model appears to account satisfactorily for the emergence of geneticists' sense of social responsibility: alarmed by eugenicists' frequent endorsement of Nazi eugenic programs, many geneticists claimed it was their duty to explain the facts of their science to the public so that the layman could see for himself the scientific errors of racism. Geneticists were now presenting the layman the facts, though not necessarily interpreting the facts for him. This same pattern—the emergence of modern social responsibility after an externally induced crisis-appears to be present in the other examples that I gave.The ironies revealed by this study are many. First, it is ironic that principles of genetics created feelings of both pessimism and optimism among many geneticists. Early developments in genetics-Mendel's laws, the concept of unit inheritance, and Weismann's theory-supplemented Social Darwinism in creating an atmosphere of pessimism among many geneticists by posing the grim assumption that human defects are hereditarily determined and incapable of medical cure. In recognizing the importance of heredity in development, many geneticists for a while were overly pessimistic in their forecasts of the evolutionary future of the human race. These same three genetic developments, however, by suggesting the feasibility of a eugenics program, of controlling reproduction to eliminate defective genes from the population, provided a remedy to the problem they had helped create.It is also ironic that even though the classical eugenics movement has been discredited in America for over thirty years, many individuals today are speaking of certain dangers to society in terms remarkably similar to those used by the classical eugenicists. The explosion of the atomic bomb created a sudden awareness among the public of the dangers of gene mutation from radiation and other sources⁴¹. Today, as topics such as the genetic load are increasingly discussed, many individuals are experiencing a growing alarm over the future genetic condition of the American people, a marked concern over the rising genetic and financial costs to society of modern medicine for preserving defectives and allowing them to reproduce.Although geneticists in the 1930's generally abandoned the ideal of using science to prescribe policy, to construct ends for social action, it was this ideal which initially attracted many of them to the eugenics movement in the first place. In the early years of the century, geneticists viewed science in a new light: as a restraint upon conduct. Hitherto, science had been valued for its products, for releasing man from old burdens, for supplying him new opportunities to enjoy and to explore life. In supporting the eugenics movement, geneticists departed from this mode. They now appealed to science, not for a particular product, but to determine who should and who should not reproduce. They let science act as a constraint upon their actions; they let science tell them that individual desires are less important than the biological and moral imperative of improving the human race⁴². Thus, it becomes understandable why many geneticists for a time regarded eugenics as a religion, for they had permitted biology to assume religion's traditional function of defining permissible conduct. The history of geneticists' involvement with the eugenics movement reminds us that science can play many roles and be put to many purposes.     

Water deficit and growth. Co-ordinating processes without an orchestrator?

Water deficit affects plant growth via reduced carbon accumulation, cell number and tissue expansion. We review the ways in which these processes are co-ordinated. Tissue expansion and its sensitivity to water deficit may be the most crucial process, involving tight co-ordination between the mechanisms which govern cell wall mechanical properties and plant hydraulics. The analyses of sensitivities, time constants and genetic correlations suggest that tissue expansion is loosely co-ordinated with cell division and carbon accumulation which may have limited direct effects on growth under water deficit. We therefore argue for essentially uncoupled mechanisms with feedbacks between them, rather than for a co-ordinated re-programming of all processes. Consequences on plant modelling and plant breeding in dry environment are discussed.     

Sitting movement in elderly subjects with and without Parkinson’s disease: A biomechanical study

The aim of the present study was to compare kinetic, kinematic, and electromyographic variables during the sitting movement between healthy elderly and in those with Parkinson’s disease (PD) with moderate involvement. We hypothesized that subjects with PD would show difficulty in selecting the muscles for the task and that this could be related to the co-activation pattern and would be reflected in the behavior of some biomechanical variables. Fifteen subjects participated in this study, seven healthy subjects (NN group) and eight with Parkinson’s disease. Electromyography (EMG) activity of the tibialis anterior (TA), soleus (SO), vastus medialis oblique (VMO), biceps femoris (BF), and erector spinae (ES) were recorded, and biomechanical variables were calculated, during four phases of the sitting movement. Compared to healthy subjects, the subjects with PD showed more flexion at the ankle, knee, and hip joints in the initial position and lower joint velocity. However, the EMG activity and hip, knee, and ankle joint torques were not different during all phases of movement. The sitting movement in PD subjects with moderate involvement generates EMG activity and joint torques similar to healthy elderly subjects. Only a reduced movement velocity was found in PD patients during the sitting task.     

Complex eco-evolutionary dynamics induced by the coevolution of predator–prey movement strategies

Evolutionary Ecology - The coevolution of predators and prey has been the subject of much empirical and theoretical research that produced intriguing insights into the interplay of ecology and...     

Are the fusion processes involved in birth, life and death of the cell depending on tilted insertion of peptides into membranes?

Various peptide segments have been modeled as asymmetric amphipathic alpha-helices. Theoretical calculations have shown that they insert obliquely into model membranes. They have been named "tilted peptides". Molecular modeling results reported here also evidence the presence of tilted peptides in ADM-1 protein of Caenorhabditis elegans that may be involved in fusion events, in meltrin alpha, a protein implicated in myoblast fusion, in hemagglutinin of influenza virus, in the E2 glycoprotein of rubella virus, in the S protein of hepatitis B virus, in a subdomain of Ebola virus and in the malaria CS protein. Experimental results have indicated that tilted peptide fragments may be involved in cellular life events like sperm-egg fecondation, muscle development, protein translocation through signal sequences and cellular death caused by viral infection or parasite infestation. We speculate that membrane destabilization by these tilted peptides may be an important common step in life processes involving fusion phenomena.     

Part–whole relations between food webs and the validity of local food-web descriptions

This work analyzes the relationship between large food webs describing potential feeding relations between species and smaller sub-webs thereof describing relations actually realized in local communities of various sizes. Special attention is given to the relationships between patterns of phylogenetic correlations encountered in large webs and sub-webs. Based on the current theory of food-web topology as implemented in the matching model, it is shown that food webs are scale invariant in the following sense: given a large web described by the model, a smaller, randomly sampled sub-web thereof is described by the model as well. A stochastic analysis of model steady states reveals that such a change in scale goes along with a re-normalization of model parameters. Explicit formulae for the re-normalized parameters are derived. Thus, the topology of food webs at all scales follows the same patterns, and these can be revealed by data and models referring to the local scale alone. As a by-product of the theory, a fast algorithm is derived which yields sample food webs from the exact steady state of the matching model for a high-dimensional trophic niche space in finite time.     

Nanotube–polymer composites: insights from Flory–Huggins theory and mesoscale simulations

Carbon nanotube (CNT)-polymer composites, with potential applications in structural materials, optoelectronics, sensors, biocatalysis, and thermal and electromagnetic shielding are an important emerging area of nanotechnology. However, progress has been slow due to difficulties in dispersing CNTs into the polymer matrix. We attack the problem from a Flory-Huggins theory point of view, and present novel simulations of the dispersion process at the mesoscale. The solubility parameter of the CNTs is mapped out as a function of tube diameter, and compared with that of well-known polymers. Parallel alignment of CNTs with the application of shear, and dispersion by attaching organic functional groups are also investigated.     

Acetylation and phosphorylation processes modulate Tau’s binding to microtubules: A molecular dynamics study

The microtubule-associated protein Tau has its normal function impaired when undergoing post-translational modifications. In this work, molecular modelling techniques were used to infer the effects of acetylation and phosphorylation in Tau's overall conformation, electrostatics, and interactions, but mostly in Tau's ability to bind microtubules. Reported harmful Lys sites were mutated by its acetylated form, generating eight different acetylated Tau (aTau) analogues. Similarly, phosphorylation sites found in normal brains and in Alzheimer’s lesioned brains were considered to design phosphorylated Tau (pTau) analogues. All these designed variants were evaluated in intracellular fluid and near a microtubule (MT) model. Our in silico findings demonstrated that the electrostatic changes, due to the absence of positive Lys’ charges in acetylation cases, or the increasingly negative charge in the phosphorylated forms, hamper the association to the MT tubulins in most cases. Post-translational modifications also pose very distinct conformations to the ones described for native Tau, which hinders the microtubule-binding region (MTBR) and turns difficult the expected binding. Our study elucidates important molecular processes behind Tau abnormal function which can inspire novel therapeutics to address Alzheimer’s disease.     

Effects of fasting on collective movement and fission–fusion dynamics in both homogeneous and heterogeneous shoals of a group-living cyprinid fish species

The present study aimed to reveal the effect of fasting (21 days) on collective movement and interaction dynamics in both homogeneous (eight members fed a commercial diet or deprived of food) and heterogeneous (four fed + four starved members) shoals of juvenile qingbo (Spinibarbus sinensis). The authors of this study measured the shoaling behaviour in both a commonly used rectangular open arena with no spatial complexity and a radial arm maze. When measured in the open arena, the starved shoals had a faster swimming speed and acceleration rate and a longer interindividual distance than the fed shoals, possibly because of the elevated foraging motivation. Nonetheless, the values of the heterogeneous groups were similar to those of the fed groups. Furthermore, in contrast to the fish in homogeneous shoals, the starved fish in heterogeneous shoals showed a slower acceleration rate and speed than fed members in heterogeneous shoals. These results, combined with the relationships of variables at the among- and within-shoal levels, suggested that starved fish limited their motion in heterogeneous shoals to maintain group cohesion but that the fed fish contributed more to maintaining shoal structure, possibly because of the higher energy expenditure required for movement changes. When monitored in a radial arm maze, starved shoals showed more fission–fusion episodes without sacrificing group cohesion, as they adaptively adjusted the frequency and duration of each majority choice. The among-shoal variation revealed that the heterogeneous groups showed less variation in the open arena but more variation in the radius maze than did the homogeneous groups. This difference might arise because dominant members have opposite effects on shoal behaviour and consensus decisions. In conclusion, the present study showed opposite effects of feeding states on collective behaviour between homogeneous and heterogeneous shoals, possibly because of the complicated interactions among members with different energy storage levels and foraging motivations. Furthermore, the heterogeneous groups showed a difference between shoal behaviour in the open area and exploration in the radial arm maze. Future studies manipulating the personality composition of starved and fed members of heterogeneous groups might yield interesting results.     

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.