Nonlinear Analysis of the Dynamics of DNA Breathing

The base pairs that encode the genetic information in DNA show large amplitude localized excitations called DNA breathing. We discuss the experimental observations of this phenomenon and its theoretical analysis. Starting from a model introduced to study the thermal denaturation of DNA, we show that it can qualitatively describe DNA breathing but is quantitatively not satisfactory. We show how the model can be modified to be quantitatively correct. This defines a nonlinear lattice model, which is interesting in itself because it has nonlinear localized excitations, forming a new class of discrete breather.     

Biomechanics of a muscular hydrostat: a model of lapping by a reptilian tongue

We have developed a quantitative model of an example of a muscular hydrostat, a reptilian tongue, and have used this model to study a functional movement, protrusion and retrusion, a form of lapping. The model tongue consists of a longitudinal muscle that shortens the tongue when it contracts, and a circumferential muscle wrapped around the longitudinal muscle that lengthens the tongue when it contracts. The anatomy of the model tongue and the pattern of activation of its muscles are based on studies of the tongue of the lizard Tupinambis nigropunctatus (Smith 1984). The mechanics of pressure vessels were used to derive a relationship between the forces in the two muscles. Muscle force production was modelled as the product of length/tension properties, force/velocity properties, and activation due to neural inputs (incorporating both recruitment and firing period). Passive forces were modeled as a force in parallel with the longitudinal muscle. Muscle activation dynamics were modeled as a first order low pass filter. When the model tongue is short, the two muscles can lengthen or shorten it with comparable forces, but as it lengthens, the force that the circumferential muscle can exert drops precipitously. When the tongue is long, it can neither be very stiff, nor can it generate much force. The model also reproduces the kinematics of lapping movements actually observed in Tupinambis.     

A Jarman/Bell model of primate feeding niches

Some of the behavioral-ecological variation in the primate order can be explained by reference to a general model known as the Jarman/Bell principle. This principle involves a scaling relationship between metabolism and body size which suggests that body size is a fundamental tactic in an animal's feeding strategy. Relatively accurate predictions regarding the diets of primates of known body weight follow from this model. In addition, it can be expanded to predict the kinds of adaptations that would appear in animals that deviate from the expected size/diet pattern. The model is general enough such that, when joined with feeding strategy theory, it can be applied to extinct organisms. In this context it is suggested that Pleistocene hominid ecology was characterized more by omnivory than carnivory.     

Dynamical analysis of a multi-strain model of HIV in the presence of anti-retroviral drugs

One major drawback associated with the use of anti-retroviral drugs in curtailing HIV spread in a population is the emergence and transmission of HIV strains that are resistant to these drugs. This paper presents a deterministic HIV treatment model, which incorporates a wild (drug sensitive) and a drug-resistant strain, for gaining insights into the dynamical features of the two strains, and determining effective ways to control HIV spread under this situation. Rigorous qualitative analysis of the model reveals that it has a globally asymptotically stable disease-free equilibrium whenever a certain epidemiological threshold (R t 0) is less than unity and that the disease will persist in the population when this threshold exceeds unity. Further, for the case where R t 0 > 1, it is shown that the model can have two co-existing endemic equilibria, and competitive exclusion phenomenon occurs whenever the associated reproduction number of the resistant strain (R t r) is greater than that of the wild strain (R t w). Unlike in the treatment model, it is shown that the model without treatment can have a family of infinitely many endemic equilibria when its associated epidemiological threshold (R(0)) exceeds unity. For the case when [Formula in text], it is shown that the widespread use of treatment against the wild strain can lead to its elimination from the community if the associated reduction in infectiousness of infected individuals (treated for the wild strain) does not exceed a certain threshold value (in this case, the use of treatment is expected to make R t w < R t r.     

遗传算法在转录因子结合位点识别中的应用

遗传算法是模拟生物进化过程的计算模型,是一种全局优化搜索算法。将遗传算法与转录因子结合位点识别问题相结合的新方法,以一致性序列模型作为保守motif的描述模型,通过对motif序列与待测序列的比对问题进行编码,将其转化成搜索空间中的优化问题,利用遗传算法来搜索最优解,预测转录因子的结合位点。实验结果表明,这种新的方法是有效的,它在占用少量内存的情况下能够准确地识别出待测转录因子结合位点。     

Rarefaction and extrapolation of species richness using an area‐based Fisher's logseries

Fisher's logseries is widely used to characterize species abundance pattern, and some previous studies used it to predict species richness. However, this model, derived from the negative binomial model, degenerates at the zero‐abundance point (i.e., its probability mass fully concentrates at zero abundance, leading to an odd situation that no species can occur in the studied sample). Moreover, it is not directly related to the sampling area size. In this sense, the original Fisher's alpha (correspondingly, species richness) is incomparable among ecological communities with varying area sizes. To overcome these limitations, we developed a novel area‐based logseries model that can account for the compounding effect of the sampling area. The new model can be used to conduct area‐based rarefaction and extrapolation of species richness, with the advantage of accurately predicting species richness in a large region that has an area size being hundreds or thousands of times larger than that of a locally observed sample, provided that data follow the proposed model. The power of our proposed model has been validated by extensive numerical simulations and empirically tested through tree species richness extrapolation and interpolation in Brazilian Atlantic forests. Our parametric model is data parsimonious as it is still applicable when only the information on species number, community size, or the numbers of singleton and doubleton species in the local sample is available. Notably, in comparison with the original Fisher's method, our area‐based model can provide asymptotically unbiased variance estimation (therefore correct 95% confidence interval) for species richness. In conclusion, the proposed area‐based Fisher's logseries model can be of broad applications with clear and proper statistical background. Particularly, it is very suitable for being applied to hyperdiverse ecological assemblages in which nonparametric richness estimators were found to greatly underestimate species richness.     

Model for the regulation of size in the wing imaginal disc of Drosophila

For animal development it is necessary that organs stop growing after they reach a certain size. However, it is still largely unknown how this termination of growth is regulated. The wing imaginal disc of Drosophila serves as a commonly used model system to study the regulation of growth. Paradoxically, it has been observed that growth occurs uniformly throughout the disc, even though Decapentaplegic (Dpp), a key inducer of growth, forms a gradient. Here, we present a model for the control of growth in the wing imaginal disc, which can account for the uniform occurrence and termination of growth. A central feature of the model is that net growth is not only regulated by growth factors, but by mechanical forces as well. According to the model, growth factors like Dpp induce growth in the center of the disc, which subsequently causes a tangential stretching of surrounding peripheral regions. Above a certain threshold, this stretching stimulates growth in these peripheral regions. Since the stretching is not completely compensated for by the induced growth, the peripheral regions will compress the center of the disc, leading to an inhibition of growth in the center. The larger the disc, the stronger this compression becomes and hence the stronger the inhibiting effect. Growth ceases when the growth factors can no longer overcome this inhibition. With numerical simulations we show that the model indeed yields uniform growth. Furthermore, the model can also account for other experimental data on growth in the wing disc.     

Mapping the complexity of ecological models

We propose to define the complexity of an ecological model as the statistical complexity of the output it produces. This allows for a direct comparison between data and model complexity. Working with univariate time series, we show that this measure ‘blindly’ discriminates among the different dynamical behaviours a model can exhibit. We then search a model parameter space in order to segment it into areas of different dynamical behaviour and calculate the maximum complexity a model can generate. Given a time series, and the problem of choosing among a number of ecological models to study it, we suggest that models whose maximum complexity is lower than the time series complexity should be disregarded because they are unable to reconstruct some of the structures contained in the data. Similar reasoning could be used to disregard models’ subdomains as well as areas of unnecessary high complexity. We suggest that model complexity so defined better captures the difficulty faced by a user in managing and understanding the behaviour of an ecological model than measures based on a model ‘size’.     

The effect of variability on host feeding and reproductive success in parasitoids

We model the behaviour of a solitary parasitoid that can either eat a host or lay an egg on it. When the parasitoid does not die as a result of starvation, it should always lay an egg on a host. We compute the parasitoid's lifetime reproductive success in this case, and illustrate the effects of the mean time to find hosts and the variance in this time. We then develop a state-dependent model in which the decision to eat the host or lay an egg on it depend on the parasitoid's state. This model is used to explore the effects of variability in the time to find hosts on the parasitoid's lifetime reproductive success. It is shown that there can be a non-monotonic relationship between reproductive success and variability.     

A goodness-of-fit test for multinomial logistic regression

This article presents a score test to check the fit of a logistic regression model with two or more outcome categories. The null hypothesis that the model fits well is tested against the alternative that residuals of samples close to each other in covariate space tend to deviate from the model in the same direction. We propose a test statistic that is a sum of squared smoothed residuals, and show that it can be interpreted as a score test in a random effects model. By specifying the distance metric in covariate space, users can choose the alternative against which the test is directed, making it either an omnibus goodness-of-fit test or a test for lack of fit of specific model variables or outcome categories.     

Mechanistic models of population-level phenomena

This paper is about mechanisms and models, and how they interact. In part, it is a response to recent discussion in philosophy of biology regarding whether natural selection is a mechanism. We suggest that this debate is indicative of a more general problem that occurs when scientists produce mechanistic models of populations and their behaviour. We can make sense of claims that there are mechanisms that drive population-level phenomena such as macroeconomics, natural selection, ecology, and epidemiology. But talk of mechanisms and mechanistic explanation evokes objects with well-defined and localisable parts which interact in discrete ways, while models of populations include parts and interactions that are neither local nor discrete in any actual populations. This apparent tension can be resolved by carefully distinguishing between the properties of a model and those of the system it represents. To this end, we provide an analysis that recognises the flexible relationship between a mechanistic model and its target system. In turn, this reveals a surprising feature of mechanistic representation and explanation: it can occur even when there is a mismatch between the mechanism of the model and that of its target. Our analysis reframes the debate, providing an alternative way to interpret scientists’ “mechanism-talk”, which initially motivated the issue. We suggest that the relevant question is not whether any population-level phenomenon such as natural selection is a mechanism, but whether it can be usefully modelled as though it were a particular type of mechanism.     

一个描述多种产量-密度关系的经验模型

本文提出一个新的关于产量-密度关系的经验模型,该模型具有以下主要特点。(1) 能描述低密度下不存在种内干扰的产量-密度的直线关系;(2) 能描述从直线型、渐近无极限型、渐近极限型到变型抛物型等多种产量密度类型;(3)参数具有显著的生态学意义。 对温室和田间试验中种内干扰与产量密度关系的实例研究结果表明,该模型能很好地描述在不同程度的种内干扰下所产生的多种类型的产量-密度关系。     

Application of the mathematics of coupled oscillator systems to the analysis of the neural control of locomotion.

In many animals, the activities of limb motor neurons are rhythmic during locomotion. In some animals it is known that each limb is innervated by a local control center that resides in a discrete portion of the central nervous system. Each local control center is a biological oscillator. Since each limb moves with the same frequency as each other limb and with regulated phase delay with respect to each other limb, then it follows that the local control centers are coupled to one another. The locomotory pattern generator within the central nervous system is therefore a coupled oscillator system. The mathematics of coupled oscillator systems can assist in the construction of a model of the neural pattern generator. This model can be utilized to formulate testable predictions concerning the neural control of locomotion. Experimental data gathered from organisms in several phylums are consistent with the predictions of the model.     

陕西不同地区栓皮栎种群年龄结构动态模型的研究

栓皮栎种群动态模型能阐明其自然种群动态的规律,揭示种群的内在机制和对种群行为进行预测。矩阵模型是一种i状态分布方法,依靠矩阵形式来处理种群的特征分布,可以模拟和预测种群中各个年龄组的数量动态和年龄结构的变化,它能够从目前已知的年龄结构及种群的生存率和生育率,来推测种群的未来年龄结构。在研究栓皮栎种群动态时,也借用该模型对栓皮栎种群各年龄组的结构和数量动态作出预测。Leslie矩阵模型就是该模型中的一种,利用该模型的理论和方法,对栓皮栎种群的自然变化过程进行了模拟和预测。结果发现,从分布中心到分布边缘,随着生境的差异,栓皮栎种群产生幼苗的年龄级、内禀增长率、生育力和幼苗的数量都发生变化,预测结果与实际反映的情况基本一致,表明Leslie矩阵模型是一种较为理想的反映种群动态的模型。模型表达形式简单,参数生态学意义确切,应用精度高,从而达到准确预测栓皮栎种群动态的目的。     

Identification of tissue differentiation rates in a mechanobiological model of fracture healing

As a basis for model-based analysis of the processes in secondary fracture healing, a dynamical model is presented that characterises the physiological status in the fracture area by the location-dependent composition of tissues. Five types of tissue are distinguished: connective tissue, cartilage, bone, haematoma and avascular bone. A rule base is given that describes dynamical tissue differentiation processes. The rules consider not only a mechanical stimulus but also osteogenic and a vasculative factors as biological stimuli. Within this model structure, it is possible, e.g., to distinguish intramembranous from endochondral ossification processes. An objective function is introduced to assess accordance between the model-based simulation results and reference healing stages. By minimising this objective function, relevant tissue differentiation rates can be determined. For a reference process of secondary fracture healing it could be shown that the intramembranous ossification rate of 0.313%/day (from connective tissue to bone) is much smaller than the endochondral ossification rate of 1.136%/day (from cartilage to bone). In order to verify the model approach, it is transferred to simulate long bone distraction. Results show that healing patterns of bone distraction can be predicted. Using this method, it is possible to identify model parameters for individual subjects. This will allow a patient-specific analysis of tissue healing processes in future.     

Closing the larval loop: linking larval ecology to the population dynamics of marine benthic invertebrates

The majority of marine benthic invertebrates exhibit a complex life cycle that includes separate planktonic larval, and bottom-dwelling juvenile and adult phases. To understand and predict changes in the spatial and temporal distributions, abundances, population growth rate, and population structure of a species with such a complex life cycle, it is necessary to understand the relative importance of the physical, chemical and biological properties and processes that affect individuals within both the planktonic and benthic phases. To accomplish this goal, it is necessary to study both phases within a common, quantitative framework defined in terms of some common currency. This can be done efficiently through construction and evaluation of a population dynamics model that describes the complete life cycle.

Two forms that such a model might assume are reviewed: a stage-based, population matrix model, and a model that specifies discrete stages of the population, on the bottom and in the water column, in terms of simultaneous differential equations that may be solved in both space and time. Terms to be incorporated in each type of model can be formulated to describe the critical properties and processes that can affect populations within each stage of the life cycle. For both types of model it is shown how this might be accomplished using an idealized balanomorph barnacle as an example species. The critical properties and processes that affect the planktonic and benthic phases are reviewed. For larvae, these include benthic adult fecundity and fertilization success, growth and larval stage duration, mortality, larval behavior, dispersal by currents and turbulence, and larval settlement. It is possible to predict or estimate empirically all of the key terms that should be built into the larval and benthic components of the model. Thus, the challenge of formulating and evaluating a full life cycle model is achievable. Development and evaluation of such a model will be challenging because of the diverse processes which must be considered, and because of the disparities in the spatial and temporal scales appropriate to the benthic and planktonic larval phases. In evaluating model predictions it is critical that sampling schemes be matched to the spatial and temporal scales of model resolution.     

Presence-only data and the em algorithm

Summary .  In ecological modeling of the habitat of a species, it can be prohibitively expensive to determine species absence. Presence-only data consist of a sample of locations with observed presences and a separate group of locations sampled from the full landscape, with unknown presences. We propose an expectation–maximization algorithm to estimate the underlying presence–absence logistic model for presence-only data. This algorithm can be used with any off-the-shelf logistic model. For models with stepwise fitting procedures, such as boosted trees, the fitting process can be accelerated by interleaving expectation steps within the procedure. Preliminary analyses based on sampling from presence–absence records of fish in New Zealand rivers illustrate that this new procedure can reduce both deviance and the shrinkage of marginal effect estimates that occur in the naive model often used in practice. Finally, it is shown that the population prevalence of a species is only identifiable when there is some unrealistic constraint on the structure of the logistic model. In practice, it is strongly recommended that an estimate of population prevalence be provided.     

Permanence and Existence of Positive Periodic Solution for Diffusive Lotka-Volterra Model

OneOfthemostintereStingquestionSintnathematiedbiologyconcernsthes~ofSpecsinecologicalmodels.Forautonomoussystemwhichhavenodiffusion,therearemanyliteraturesabout~istenceanddondnance[1,2,3j.R~ly,manyauthorsfindthatthediffusionpzocessineCOIOgitalsystemPlaysanimPOrtantrole.Infact,diffusionoftenoccursinnatural~icalenvironxnent,thatistosay,whenonepatchisnotvaluabletolivein-spotescan~tOanother.SoLevin[4)firsteStablishedthemedelabbotautonomousLDthe-VolterraSystemwithdiffusionprocess.AfterLevin…     

Partitioning of root and shoot competition and the stability of savannas

A classic problem in coexistence theory is how grasses and trees coexist in savannas. A popular deterministic model of savannas, the rooting niche separation model, is based on an assumption that is not empirically supported in many savannas. Alternative models that do not rely on the rooting niche assumption invoke intricate stochastic mechanisms that limit their attractiveness as general models of savannas. In this article we develop an alternative deterministic model of grass-tree interactions and use it to analyze the conditions under which grass-tree coexistence is possible. The novel feature of this model is that it partitions aboveground and belowground competition and simulates the fact that fire and herbivory remove only aboveground biomass. The model predicts that stable coexistence of grasses and trees is possible, even when grasses and trees do not have separate rooting niches. We show that when aboveground competition is intense, grasses can be excluded by trees; under such conditions, fire can prevent grasses from exclusion and induce a stable savanna state. The model provides a general framework for exploring the interactive effects of competition, herbivory, and fire on savanna systems.     

Modeling the influence of nutrients, turbulence and grazing on Pfiesteria population dynamics

A semi-idealized marine ecosystem model, designed as a heuristic tool for exploring the population dynamics of non-inducible versus toxic forms of Pfiesteria is described. The model is based on empirical evidence suggesting that these differing functional types of Pfiesteria also differ substantially in terms of what they eat and how they utilize it to optimize their growth. Non-inducible strains are similar to other mixotrophic dinoflagellates, whereas toxic strains may consume organic matter and detritus, produce toxins and attack fish. In our model formulation we represent these differences in a simplified way: the non-inducible strain is kleptochloroplastidic and it can take up DIN, but it cannot utilize DON, whereas the toxic strain is heterotrophic, it cannot utilize DIN, but it can utilize DON directly. These differences give rise to very different impacts on prey and nutrient concentrations in our model. Under high DIN/DON ratio conditions, the non-inducible cells grew much faster and were therefore more likely to bloom, but this advantage is substantially mitigated when the DIN/DON ratio is low. A turbulence parameterization was also incorporated into our model. The effect of this was to reduce the grazing rate of Pfiesteria when turbulence levels are high. According to our model, increased turbulence is more detrimental to the toxic functional type because it grows more slowly. The further imposition of microzooplankton grazing in the model showed that top-down control effects can be very significant, which is consistent with both laboratory and field studies and the general idea that plankton blooms can only happen in the absence of substantial grazing control. In general, our model results suggest that non-toxic blooms are more likely to occur in more turbulent inorganic-nutrient rich conditions, which are often found in more open coastal and estuarine waters that are subject to high inorganic loading. In contrast, toxic blooms are more likely to occur in calm, organic-nutrient rich conditions, which are often found in shallow, protected tributaries that are subject to high organic nutrient loading. Our model results also support the idea that the absence of strong grazing pressure is a prerequisite to bloom formation for both non-inducible and toxic strains of Pfiesteria. These results are generally consistent with observed patterns of toxic Pfiesteria blooms in Chesapeake Bay, the Neuse River of North Carolina and many other coastal and estuarine environments.