Theorems on the invasion process in stage-structured populations with density-dependent dynamics

 Several theoretical results on evolution in stage-structured models with density-dependent dynamics are obtained. The first one concerns the invadable condition of mutant types when ‘density’ is considered as the weighted sum of the population densities at each stage. In the second and third results, it is shown that the invadability is equivalent to the increase of the weighted sum at equilibrium when certain conditions are satisfied. It is also shown that the sensitivity for the dominant eigenvalue is proportional to that for the weighted sum at equilibrium. Finally, a theorem on the coexistence of a wild and the mutant types is obtained and the condition for coexistence is discussed. A part of these results are the extended theorems of what Charlesworth (1971, 1980, 1994) has already obtained. Received: 26 October 1996     

The Robust Weighted Multi-Objective Game

This paper studies a class of multi-objective n-person non-zero sum games through a robust weighted approach where each player has more than one competing objective. This robust weighted multi-objective game model assumes that each player attaches a set of weights to its objectives instead of accessing accurate weights. Each player wishes to minimize its maximum weighted sum objective where the maximization is pointing to the set of weights. To address this new model, a new equilibrium concept-robust weighted Nash equilibrium is obtained. The existence of this new concept is proven on suitable assumptions about the multi-objective payoffs.     

The Worst-Case Weighted Multi-Objective Game with an Application to Supply Chain Competitions

In this paper, we propose a worst-case weighted approach to the multi-objective n-person non-zero sum game model where each player has more than one competing objective. Our “worst-case weighted multi-objective game” model supposes that each player has a set of weights to its objectives and wishes to minimize its maximum weighted sum objectives where the maximization is with respect to the set of weights. This new model gives rise to a new Pareto Nash equilibrium concept, which we call “robust-weighted Nash equilibrium”. We prove that the robust-weighted Nash equilibria are guaranteed to exist even when the weight sets are unbounded. For the worst-case weighted multi-objective game with the weight sets of players all given as polytope, we show that a robust-weighted Nash equilibrium can be obtained by solving a mathematical program with equilibrium constraints (MPEC). For an application, we illustrate the usefulness of the worst-case weighted multi-objective game to a supply chain risk management problem under demand uncertainty. By the comparison with the existed weighted approach, we show that our method is more robust and can be more efficiently used for the real-world applications.     

Algebraic stability indicators for ranked lists in molecular profiling

MOTIVATION: We propose a method for studying the stability of biomarker lists obtained from functional genomics studies. It is common to adopt resampling methods to tune and evaluate marker-based diagnostic and prognostic systems in order to prevent selection bias. Such caution promotes honest estimation of class prediction, but leads to alternative sets of solutions. In microarray studies, the difference in lists may be bewildering, also due to the presence of modules of functionally related genes. Methods for assessing stability understand the dependency of the markers on the data or on the predictor's type and help selecting solutions. RESULTS: A computational framework for comparing sets of ranked biomarker lists is presented. Notions and algorithms are based on concepts from permutation group theory. We introduce several algebraic indicators and metric methods for symmetric groups, including the Canberra distance, a weighted version of Spearman's footrule. We also consider distances between partial lists and an aggregation of sets of lists into an optimal list based on voting theory (Borda count). The stability indicators are applied in practical situations to several synthetic, cancer microarray and proteomics datasets. The addressed issues are predictive classification, presence of modules, comparison of alternative biomarker lists, outlier removal, control of selection bias by randomization techniques and enrichment analysis. AVAILABILITY: Supplementary Material and software are available at the address http://biodcv.fbk.eu/listspy.html     

Evolving cell models for systems and synthetic biology

This paper proposes a new methodology for the automated design of cell models for systems and synthetic biology. Our modelling framework is based on P systems, a discrete, stochastic and modular formal modelling language. The automated design of biological models comprising the optimization of the model structure and its stochastic kinetic constants is performed using an evolutionary algorithm. The evolutionary algorithm evolves model structures by combining different modules taken from a predefined module library and then it fine-tunes the associated stochastic kinetic constants. We investigate four alternative objective functions for the fitness calculation within the evolutionary algorithm: (1) equally weighted sum method, (2) normalization method, (3) randomly weighted sum method, and (4) equally weighted product method. The effectiveness of the methodology is tested on four case studies of increasing complexity including negative and positive autoregulation as well as two gene networks implementing a pulse generator and a bandwidth detector. We provide a systematic analysis of the evolutionary algorithm’s results as well as of the resulting evolved cell models.     

Effects of genotyping errors,missing values and segregation distortion in molecular marker data on the construction of linkage maps

A simulation study was performed to investigate the effects of missing values, typing errors and distorted segregation ratios in molecular marker data on the construction of genetic linkage maps, and to compare the performance of three locus-ordering criteria (weighted least squares, maximum likelihood and minimum sum of adjacent recombination fractions criteria) in the presence of such effects. The study was based upon three linkage groups of 10 loci at 2, 6, and 10 cM spacings simulated from a doubled-haploid population of size 150. Criteria performance were assessed using the number of replicates with correctly estimated orders, the mean rank correlation between the estimated and the true order and the mean total map length. Bootstrap samples from replicates in the maximum likelihood analysis produced a measure of confidence in the estimated locus order. The effects of missing values and/or typing errors in the data are to reduce the proportion of correctly ordered maps, and this problem worsens as the distances between loci decreases. The maximum likelihood criterion is most successful at ordering loci correctly, but gives estimated map lengths, which are substantially inflated when typing errors are present. The presence of missing values in the data produces shorter map lengths for more widely spaced markers, especially under the weighted least-squares criterion. Overall, the presence of segregation distortion has little effect on this population.     

An Adaptive Location‐Scale Test

Increasing locations are often accompanied by an increase in variability. In this case apparent heteroscedasticity can indicate that there are treatment effects and it is appropriate to consider an alternative involving differences in location as well as in scale. As a location‐scale test the sum of a location and a scale test statistic can be used. However, the power can be raised through weighting the sum. In order to select values for this weighting an adaptive design with an interim analysis is proposed: The data of the first stage are used to calculate the weights and with the second stage's data a weighted location‐scale test is carried out. The p‐values of the two stages are combined through Fisher's combination test. With a Lepage‐type location‐scale test it is illustrated that the resultant adaptive test can be more powerful than the ‘optimum’ test with no interim analysis. The principle to calculate weights, which cannot be reasonably chosen a priori, with the data of the first stage may be useful for other tests which utilize weighted statistics, too. Furthermore, the proposed test is illustrated with an example from experimental ecology.     

Rapid incorporation of functional rhodopsin into nanoscale apolipoprotein bound bilayer (NABB) particles

Human apolipoprotein A-I (apo A-I) and its engineered constructs form discoidal lipid bilayers upon interaction with lipids in vitro. We now report the cloning, expression, and purification of apo A-I derived from zebrafish (Danio rerio), which combines with phospholipids to form similar discoidal bilayers and may prove to be superior to human apo A-I constructs for rapid reconstitution of seven-transmembrane helix receptors into nanoscale apolipoprotein bound bilayers (NABBs). We characterized NABBs by gel-filtration chromatography, native polyacrylamide gradient gel electrophoresis, UV-visible photobleaching difference spectroscopy, and fluorescence spectroscopy. We used electron microscopy to determine the stoichiometry and orientation of rhodopsin (rho)-containing NABBs prepared under various conditions and correlated stability and signaling efficiency of rho in NABBs with either one or two receptors. We discovered that the specific activity of G protein coupling for single rhos sequestered in individual NABBs was nearly identical with that of two rhos per NABB under conditions where stoichiometry and orientation could be inferred by electron microscopy imaging. Thermal stability of rho in NABBs was superior to that of rho in various commonly used detergents. We conclude that the NABB system using engineered zebrafish apo A-I is a native-like membrane mimetic system for G-protein-coupled receptors and discuss strategies for rapid incorporation of expressed membrane proteins into NABBs.     

苏南主要森林类型的生物多样性调查与比较研究

维护生物多样性是森林的重要功能之一,也是森林可持续发展的重要内容。森林生态系统具有高生物多样性的特点,是生物多样性保护的重要领域。保护生物多样性的目的在于生物资源的持续增长和人类对生物资源的持续利用,以满足实施持续发展战略的需要。过去生物多样性的保护...     

Determining the number of clusters using the weighted gap statistic

Estimating the number of clusters in a data set is a crucial step in cluster analysis. In this article, motivated by the gap method (Tibshirani, Walther, and Hastie, 2001, Journal of the Royal Statistical Society B63, 411-423), we propose the weighted gap and the difference of difference-weighted (DD-weighted) gap methods for estimating the number of clusters in data using the weighted within-clusters sum of errors: a measure of the within-clusters homogeneity. In addition, we propose a "multilayer" clustering approach, which is shown to be more accurate than the original gap method, particularly in detecting the nested cluster structure of the data. The methods are applicable when the input data contain continuous measurements and can be used with any clustering method. Simulation studies and real data are investigated and compared among these proposed methods as well as with the original gap method.     

A model for neural control of gradation of muscle force

A mathematical muscle model is presented that relates neural control signals linearly to muscle force without violating important known physiological constraints, such as the size-principle (Henneman and Mendell 1981) and non-linear twitch summation (Burke et al. 1976). This linearity implies that the neural control signals (defined as a weighted sum of activities in a nerve bundle) can be interpreted as the internal representation of total muscle force. The model allows for different relative contributions from the two force-grading mechanisms, i.e. the recruitment of motor units and the modulation of their firing frequency. It can therefore be applied to a variety of (distal and proximal) muscles. Furthermore, it permits simple mechanisms for controlling muscle force, e.g. in superposed motor tasks. The model confirms our intuitive notion that a weighted sum of activities in a nerve bundle can directly represent an external controlled variable, which in this case is exerted muscle force.     

An alternating least squares approach to inferring phylogenies from pairwise distances

A computational method is presented for minimizing the weighted sum of squares of the differences between observed and expected pairwise distances between species, where the expectations are generated by an additive tree model. The criteria of Fitch and Margoliash (1967, Science 155:279-284) and Cavalli-Sforza and Edwards (1967, Evolution 21:550-570) are both weighted least squares, with different weights. The method presented iterates lengths of adjacent branches in the tree three at a time. The weighted sum of squares never increases during the process of iteration, and the iterates approach a stationary point on the surface of the sum of squares. This iterative approach makes it particularly easy to maintain the constraint that branch lengths never become negative, although negative branch lengths can also be allowed. The method is implemented in a computer program, FITCH, which has been distributed since 1982 as part of the PHYLIP package of programs for inferring phylogenies, and is also implemented in PAUP*. The present method is compared, using some simulated data sets, with an implementation of the method of De Soete (1983, Psychometrika 48:621-626); it is slower than De Soete's method but more effective at finding the least squares tree. The relationship of this method to the neighbor-joining method is also discussed.     

Optimal sibship selection for genotyping in quantitative trait locus linkage analysis

In this paper we present a novel method for selecting optimally informative sibships of any size for quantitative trait locus (QTL) linkage analysis. The method allocates a quantitative index of potential informativeness to each sibship on the basis of observed trait scores and an assumed true QTL model. Any sample of phenotypically screened sibships can therefore be easily rank-ordered for selective genotyping. The quantitative index is the sibship's expected contribution to the non-centrality parameter. This expectation represents the weighted sum of chi(2) test statistics that would be obtained given the observed trait values over all possible sibship genotypic configurations; each configuration is weighted by the likelihood of it occurring given the assumed true genetic model. The properties of this procedure are explored in relation to the accuracy of the assumed true genetic model and sibship size. In comparison to previous methods of selecting phenotypically extreme sibships for genotyping, the proposed method is considerably more efficient and is robust with regard to the specification of the genetic model.     

One Dimensional Turing-Like Handshake Test for Motor Intelligence

In the Turing test, a computer model is deemed to "think intelligently" if it can generate answers that are not distinguishable from those of a human. However, this test is limited to the linguistic aspects of machine intelligence. A salient function of the brain is the control of movement, and the movement of the human hand is a sophisticated demonstration of this function. Therefore, we propose a Turing-like handshake test, for machine motor intelligence. We administer the test through a telerobotic system in which the interrogator is engaged in a task of holding a robotic stylus and interacting with another party (human or artificial). Instead of asking the interrogator whether the other party is a person or a computer program, we employ a two-alternative forced choice method and ask which of two systems is more human-like. We extract a quantitative grade for each model according to its resemblance to the human handshake motion and name it "Model Human-Likeness Grade" (MHLG). We present three methods to estimate the MHLG. (i) By calculating the proportion of subjects'' answers that the model is more human-like than the human; (ii) By comparing two weighted sums of human and model handshakes we fit a psychometric curve and extract the point of subjective equality (PSE); (iii) By comparing a given model with a weighted sum of human and random signal, we fit a psychometric curve to the answers of the interrogator and extract the PSE for the weight of the human in the weighted sum. Altogether, we provide a protocol to test computational models of the human handshake. We believe that building a model is a necessary step in understanding any phenomenon and, in this case, in understanding the neural mechanisms responsible for the generation of the human handshake.     

Cross-linking reconsidered: binding and cross-linking fields and the cellular response.

We analyze a model for the reversible cross-linking of cell surface receptors by a collection of bivalent ligands with different affinities for the receptor as would be found in a polyclonal anti-receptor serum. We assume that the amount of cross-linking determines, via a monotonic function, the rate at which cells become activated and divide. In addition to the density of receptors on the cell surface, two quantities, the binding field and the cross-linking field, are needed to characterize the cross-linking curve, i.e., the equilibrium concentration of cross-linked receptors plotted as a function of the total ligand site concentration. The binding field is the sum of all ligand site concentrations weighted by their respective binding affinities, and the cross-linking field is the sum of all ligand site concentrations weighted by the product of their respective binding and cross-linking affinity and the total receptor density. Assuming that the cross-linking affinity decreases if the binding affinity decreases, we find that the height of the cross-linking curve decreases, its width narrows, and its center shifts to higher ligand site concentrations as the affinities decrease. Moreover, when we consider cross-linking-induced proliferation, we find that there is a minimum cross-linking affinity that must be surpassed before a clone can expand. We also show that under many circumstances a polyclonal antiserum would be more likely than a monoclonal antibody to lead to cross-linking-induced proliferation.     

Testosterone measured in infancy predicts subsequent sex-typed behavior in boys and in girls

The testes are active during gestation, as well as during early infancy. Testosterone elevation during fetal development has been shown to play a role in human neurobehavioral sexual differentiation. The role of early postnatal gonadal activation in human psychosexual development is largely unknown, however. We measured testosterone in 48 full term infants (22 boys, 26 girls) by monthly urinary sampling from day 7 postnatal to age 6 months, and related the area under the curve (AUC) for testosterone during the first 6 months postnatal to subsequent sex-typed behavior, at the age of 14 months, using the Pre-School Activities Inventory (PSAI), and playroom observation of toy choices. In boys, testosterone AUC correlated significantly with PSAI scores (Spearman's rho = 0.54, p = 0.04). In addition, play with a train and with a baby doll showed the anticipated sex differences, and play with the train correlated significantly and positively with testosterone AUC in girls (Spearman's rho = 0.43, p = 0.05), while play with the doll correlated significantly and negatively with testosterone AUC in boys (Spearman's rho = -0.48, p < 0.03). These results may support a role for testosterone during early infancy in human neurobehavioral sexual differentiation.     

Minimally colored trees

Each edge in a weighted colored tree has a nonnegative weight corresponding to the colors of its incident vertices. The sum of these weights is the weight of the tree. Algorithms of O(n) are known to find minimal colorings, that is, to assign colors from a given finite set to the vertices of a tree so as to minimize the weight of the tree. In this paper generating functions are used to find the number of minimal colorings and the average weight of each edge over such colorings, also using O(n) operations. Applications to evolutionary trees are given.     

Design of optimal cancer chemotherapy using a continuous-time state model of cell kinetics

A continuous bilinear model in state space is used to describe the cell kinetics of a tumor-cell population under the effects of chemotherapy. Firstly, the time-course behavior of a Chinese-hamster-ovary (CHO) cell population is simulated to demonstrate the utility of the model. Then, an optimal strategy for cancer treatment is derived, based on the need to balance the effects on both cancerous and normal tissues. The performance index minimized is the sum of the weighted tumor population and the weighted total drug dosage. The optimization problem has resulted in a two-point boundary-value problem (TPBVP) with a bang-bang control policy, which is solved by the switching-time variation method (STVM). Computer simulation of CHO cells is also carried out as a numerical example of determining optimal cancer chemotherapy.