Non-equilibrium allele frequency spectra via spectral methods

A major challenge in the analysis of population genomics data consists of isolating signatures of natural selection from background noise caused by random drift and gene flow. Analyses of massive amounts of data from many related populations require high-performance algorithms to determine the likelihood of different demographic scenarios that could have shaped the observed neutral single nucleotide polymorphism (SNP) allele frequency spectrum. In many areas of applied mathematics, Fourier Transforms and Spectral Methods are firmly established tools to analyze spectra of signals and model their dynamics as solutions of certain Partial Differential Equations (PDEs). When spectral methods are applicable, they have excellent error properties and are the fastest possible in high dimension; see Press et al. (2007). In this paper we present an explicit numerical solution, using spectral methods, to the forward Kolmogorov equations for a Wright–Fisher process with migration of K populations, influx of mutations, and multiple population splitting events.     

When it is too hot for photosynthesis: heat-induced instability of photosynthesis in relation to respiratory burst, cell permeability changes and H₂O₂ formation

Photosynthesis rate (A_n) becomes unstable above a threshold temperature, and the recovery upon return to low temperature varies because of reasons not fully understood. We investigated responses of A_n, dark respiration and chlorophyll fluorescence to supraoptimal temperatures of varying duration and kinetics in Phaseolus vulgaris asking whether the instability of photosynthesis under severe heat stress is associated with cellular damage. Cellular damage was assessed by Evans blue penetration (enhanced membrane permeability) and by H₂O₂ generation [3,3′‐diaminobenzidine 4HCl (DAB)‐staining]. Critical temperature for dark fluorescence (F₀) rise (T_F) was at 46–48 °C, and a burst of respiration was observed near T_F. However, A_n was strongly inhibited already before T_F was reached. Membrane permeability increased with temperature according to a switch‐type response, with enhanced permeability observed above 48 °C. Experiments with varying heat pulse lengths and intensities underscored the threshold‐type loss of photosynthetic function, and indicated that the degree of photosynthetic deterioration and cellular damage depended on accumulated heat‐dose. Beyond the ‘point of no return’, propagation of cellular damage and reduction of photosynthesis continued upon transfer to lower temperatures and photosynthetic recovery was slow or absent. We conclude that instability of photosynthesis under severe heat stress is associated with time‐dependent propagation of cellular lesions.     

Variation in aggressive behaviour in the poeciliid fish Brachyrhaphis episcopi: Population and sex differences

Aggression is often positively correlated with other behavioural traits such as boldness and activity levels. Comparisons across populations can help to determine factors that promote the evolution of such traits. We quantified these behaviours by testing the responses of wild-caught poeciliid fish, Brachyrhaphis episcopi, to mirror image stimuli. This species occurs in populations that experience either high or low levels of predation pressure. Previous studies have shown that B. episcopi from low predation environments are less bold than those that occur with many predators. We therefore predicted that fish from high predation populations would be more aggressive and more active than fish from low predation populations. However, we found the opposite - low predation fish approached a mirror and a novel object more frequently than high predation fish suggesting that ‘boldness’ and aggression were higher in low predation populations, and that population-level boldness measures may vary depending on context. When tested individually, low predation fish inspected their mirror image more frequently. Females, but not males, from low predation sites were also more aggressive towards their mirror image. Variation in female aggression may be driven by a trade-off between food availability and predation risk. This suggests that the relationship between aggression and boldness has been shaped by adaptation to environmental conditions, and not genetic constraints.     

Follow up estimation of Aedes aegypti entomological parameters and mathematical modellings

The dengue virus is a vector-borne disease transmitted by mosquito Aedes aegypti and the incidence is strongly influenced by temperature and humidity which vary seasonally. To assess the effects of temperature on dengue transmission, mathematical models are developed based on the population dynamics theory. However, depending on the hypotheses of the modelling, different outcomes regarding to the risk of epidemics are obtained. We address this question comparing two simple models supplied with model's parameters estimated from temperature-controlled experiments, especially the entomological parameters regarded to the mosquito's life cycle in different temperatures. Once obtained the mortality and transition rates of different stages comprising the life cycle of mosquito and the oviposition rate, we compare the capacity of vector reproduction (the basic offspring number) and the risk of infection (basic reproduction number) provided by two models. The extended model, which is more realistic, showed that both mosquito population and dengue risk are situated at higher values than the simplified model, even that the basic offspring number is lower.     

Homology modeling, docking, molecular dynamics simulation, and structural analyses of coxsakievirus B3 2A protease: an enzyme involved in the pathogenesis of inflammatory myocarditis

2A protease of the pathogenic coxsackievirus B3 is key to the pathogenesis of inflammatory myocarditis and, therefore, an attractive drug target. However lack of a crystal structure impedes design of inhibitors. Here we predict 3D structure of CVB3 2A^pro based on sequence comparison and homology modeling with human rhinovirus 2A^pro. The two enzymes are remarkably similar in their core regions. However they have different conformations at the N-terminal. A large number of N-terminal hydrophobic residues reduce the thermal stability of CVB3 2A^pro, as we confirmed by fluorescence, western blot and turbidity measurement. Molecular dynamic simulation revealed that elevated temperature induces protein motion that results in frequent movement of the N-terminal coil. This may therefore induce successive active site changes and thus play an important role in destabilization of CVB3 2A^pro structure.     

内蒙古赛罕乌拉自然保护区狼的数量分布和食物组成

2006年1月至2008年12月,在内蒙古赛罕乌拉国家级自然保护区运用样线法和粪便分析法,对狼(Canis lupus)的生态分布和食物组成开展了研究。研究结果:保护区狼的数量至少7只,密度为(4.18±2.88)只/100km2,主要分布于保护区的圣山和庆云山核心区。在圣山主要活动于山脊、道路和沟谷;在庆云山主要活动于山脊。草兔(Lepus capensis)和植物在狼的食物组成中出现率最高,其食物组成在年度间存在显著差异(P<0.01),冬春与夏秋季节间差异不显著(P>0.05)。     

Transitions of interaction outcomes in a uni-directional consumer-resource system

A uni-directional consumer-resource system of two species is analyzed. Our aim is to understand the mechanisms that determine how the interaction outcomes depend on the context of the interaction; that is, on the model parameters. The dynamic behavior of the model is described and, in particular, it is demonstrated that no periodic orbits exist. Then the parameter (factor) space is shown to be divided into four regions, which correspond to the four forms of interaction outcomes; i.e. mutualism, commensalism, parasitism and amensalism. It is shown that the interaction outcomes of the system transition smoothly among these four forms when the parameters of the system are varied continuously. Varying each parameter individually or varying pairs of parameters can also lead to smooth transitions between the interaction outcomes. The analysis leads to both conditions for which each species achieves its maximal density, and situations in which periodic oscillations of the interaction outcomes emerge.     

Minimal models of growth and decline of microbial populations

Dynamics of growth and decline of microbial populations were analysed and respective models were developed in this investigation. Analysis of the dynamics was based on general considerations concerning the main properties of microorganisms and their interactions with the environment which was supposed to be affected by the activity of the population. Those considerations were expressed mathematically by differential equations or systems of the equations containing minimal sets of parameters characterizing those properties. It has been found that: (1) the factors leading to the decline of the population have to be considered separately, namely, accumulation of metabolites (toxins) in the medium and the exhaustion of resources; the latter have to be separated again into renewable (‘building materials’) and non-renewable (sources of energy); (2) decline of the population is caused by the exhaustion of sources of energy but no decline is predicted by the model because of the exhaustion of renewable resources; (3) the model determined by the accumulation of metabolites (toxins) in the medium does not suggest the existence of a separate ‘stationary phase’; (4) in the model determined by the exhaustion of energy resources the ‘stationary’ and ‘decline’ phases are quite discernible; and (5) there is no symmetry in microbial population dynamics, the decline being slower than the rise. Mathematical models are expected to be useful in getting insight into the process of control of the dynamics of microbial populations. The models are in agreement with the experimental data.     

A three-species model explaining cyclic dominance of Pacific salmon

The four-year oscillations of the number of spawning sockeye salmon (Oncorhynchus nerka) that return to their native stream within the Fraser River basin in Canada are a striking example of population oscillations. The period of the oscillation corresponds to the dominant generation time of these fish. Various—not fully convincing—explanations for these oscillations have been proposed, including stochastic influences, depensatory fishing, or genetic effects. Here, we show that the oscillations can be explained as an attractor of the population dynamics, resulting from a strong resonance near a Neimark Sacker bifurcation. This explains not only the long-term persistence of these oscillations, but also reproduces correctly the empirical sequence of salmon abundance within one period of the oscillations. Furthermore, it explains the observation that these oscillations occur only in sockeye stocks originating from large oligotrophic lakes, and that they are usually not observed in salmon species that have a longer generation time.     

Perturbation analysis of 6DoF flight dynamics and passive dynamic stability of hovering fruit fly Drosophila melanogaster

Insects exhibit exquisite control of their flapping flight, capable of performing precise stability and steering maneuverability. Here we develop an integrated computational model to investigate flight dynamics of insect hovering based on coupling the equations of 6 degree of freedom (6DoF) motion with the Navier-Stokes (NS) equations. Unsteady aerodynamics is resolved by using a biology-inspired dynamic flight simulator that integrates models of realistic wing-body morphology and kinematics, and a NS solver. We further develop a dynamic model to solve the rigid body equations of 6DoF motion by using a 4th-order Runge-Kutta method. In this model, instantaneous forces and moments based on the NS-solutions are represented in terms of Fourier series. With this model, we perform a systematic simulation-based analysis on the passive dynamic stability of a hovering fruit fly, Drosophila melanogaster, with a specific focus on responses of state variables to six one-directional perturbation conditions during latency period. Our results reveal that the flight dynamics of fruit fly hovering does not have a straightforward dynamic stability in a conventional sense that perturbations damp out in a manner of monotonous convergence. However, it is found to exist a transient interval containing an initial converging response observed for all the six perturbation variables and a terminal instability that at least one state variable subsequently tends to diverge after several wing beat cycles. Furthermore, our results illustrate that a fruit fly does have sufficient time to apply some active mediation to sustain a steady hovering before losing body attitudes.