The Analysis of Association Between Traits When Differences Between Trait States Matter

Because of their elementary significance in almost all fields of science, measures of association between two variables or traits are abundant and multiform. One aspect of association that is of considerable interest, especially in population genetics and ecology, seems to be widely ignored. This aspect concerns association between complex traits that show variable and arbitrarily defined state differences. Among such traits are genetic characters controlled by many and potentially polyploid loci, species characteristics, and environmental variables, all of which may be mutually and asymmetrically associated. A concept of directed association of one trait with another is developed here that relies solely on difference measures between the states of a trait. Associations are considered at three levels: between individual states of two variables, between an individual state of one variable and the totality of the other variable, and between two variables. Relations to known concepts of association are identified. In particular, measures at the latter two levels turn out to be interpretable as measures of differentiation. Examples are given for areas of application (search for functional relationships, distribution of variation over populations, genomic associations, spatiogenetic structure).     

Cost-Effectiveness Analysis of Optimal Control Measures for Tuberculosis

We propose and analyze an optimal control problem where the control system is a mathematical model for tuberculosis that considers reinfection. The control functions represent the fraction of early latent and persistent latent individuals that are treated. Our aim was to study how these control measures should be implemented, for a certain time period, in order to reduce the number of active infected individuals, while minimizing the interventions implementation costs. The optimal intervention is compared along different epidemiological scenarios, by varying the transmission coefficient. The impact of variation of the risk of reinfection, as a result of acquired immunity to a previous infection for treated individuals on the optimal controls and associated solutions, is analyzed. A cost-effectiveness analysis is done, to compare the application of each one of the control measures, separately or in combination.     

水分为限制因子的草地优化收获理论的研究

本文针对我国北方干旱、半干旱地区草地植物生长的主要限制因子,即水分问题,提出草地植物生物量和土壤水分的常微分方程模型。模拟的目标是一个生长期中植被生物量和土壤水分的变化。在此基础上,推导出了以维持系统平衡为前提,使总收获量达到可能的最大值的最优收获理论方程。最后求取模型在特定的情形下的解并讨论其表征和特点。具体模型求解的结果表明： (1)给定退化草地,围栏保护完全不加利用不一定是最佳恢复途径; (2)存在着最优的收获力投入,使草地植物的收获量达到极大值。     

Metacommunity Composition of Web-Spiders in a Fragmented Neotropical Forest: Relative Importance of Environmental and Spatial Effects

The distribution of beta diversity is shaped by factors linked to environmental and spatial control. The relative importance of both processes in structuring spider metacommunities has not yet been investigated in the Atlantic Forest. The variance explained by purely environmental, spatially structured environmental, and purely spatial components was compared for a metacommunity of web spiders. The study was carried out in 16 patches of Atlantic Forest in southern Brazil. Field work was done in one landscape mosaic representing a slight gradient of urbanization. Environmental variables encompassed plot- and patch-level measurements and a climatic matrix, while principal coordinates of neighbor matrices (PCNMs) acted as spatial variables. A forward selection procedure was carried out to select environmental and spatial variables influencing web-spider beta diversity. Variation partitioning was used to estimate the contribution of pure environmental and pure spatial effects and their shared influence on beta-diversity patterns, and to estimate the relative importance of selected environmental variables. Three environmental variables (bush density, land use in the surroundings of patches, and shape of patches) and two spatial variables were selected by forward selection procedures. Variation partitioning revealed that 15% of the variation of beta diversity was explained by a combination of environmental and PCNM variables. Most of this variation (12%) corresponded to pure environmental and spatially environmental structure. The data indicated that (1) spatial legacy was not important in explaining the web-spider beta diversity; (2) environmental predictors explained a significant portion of the variation in web-spider composition; (3) one-third of environmental variation was due to a spatial structure that jointly explains variation in species distributions. We were able to detect important factors related to matrix management influencing the web-spider beta-diversity patterns, which are probably linked to historical deforestation events.     

Simple nonsingular control approach to fed-batch fermentation optimization

Determination of the optimal feed rate for fed-batch fermentation is normally a problem in singular control with a state inequality constraint and as such is, in general, difficult to solve, especially for those described by a large number of dynamic mass balance equations. In this article we use a new set of state variables and the culture volume as the control variable. In this way the problem is converted to one of nonsingular control with the magnitude and rate constraints on the manipulated variable and can be numerically solved by a gradient-based technique, thus avoiding the difficulty associated with singular control problems. Examples are given to illustrate the method.     

Using parthenogenesis‐inducing Wolbachia for the selection of optimal lines of the egg parasitoid Trichogramma pretiosum for use in biocontrol

Trichogramma wasps (Hymenoptera: Trichogrammatidae) are egg parasitoids commonly employed in augmentative biological control releases against a variety of mainly lepidopteran pests. By exploiting the mechanism by which the endosymbiotic bacterium Wolbachia induces parthenogenesis in this genus, we created a set of completely homozygous Wolbachia‐infected recombinant isofemale lines (RILs), each consisting of a different combination of the genome of two well‐characterized lines of Trichogramma pretiosum Riley. We subsequently use 16 of these RILs to investigate the effect of genetic variation on various measures associated with offspring production under laboratory conditions. Unsurprisingly, substantial differences were found between the RILs in their propensity to parasitize hosts, the number of hosts they parasitize, and the levels of mortality in their offspring. Such measures can be used to choose an optimal line for biological control purposes. A method was also developed to characterize the 16 RILs using their allelic state at five loci. Essentially, this binary system uses high‐resolution melt analysis to resolve identity at each locus, with alleles originating from either the grandmaternal or grandpaternal line, and is such that each RIL can be distinguished from each other RIL by their allelic state at one or more loci. The method facilitates the easy diagnosis of line origin when two or more lines are competing with each other in competition assays, allowing for the design of more complicated tests of parasitoid quality. Future field experiments will determine which genetic line performs best under more realistic biological control conditions. The fact that these lines are infected with parthenogenesis‐inducing Wolbachia will allow for prolonged rearing without appreciable change in their genetic makeup, which should lead to a predictable biological control performance.     

Decision making by rats in an unpredictable laboratory environment: final decision rules

A simple laboratory situation was developed in order to test statistical decision making in the white rat. The subject's problem is to obtain rewards (water) which can be achieved by performing one of two possible alternative activities. The profitability of each of these two activities depends on the state of the test apparatus. The subject does not have perfect information about this state but information becomes available as a consequence of doing activity 1 and/or 2. The problem is expressed mathematically and the optimal behaviour calculated. The predictions from the theoretical model are compared with the actual performance of the rat. The conclusion is that the optimal solution predicts the average behaviour of a rat during a test session well. The variation in the responses however cannot be understood from the model. The set up is suitable for pharmacological and physiological behavioural research.     

Stochastic optimal therapy for enhanced immune response

Therapeutic enhancement of humoral immune response to microbial attack is addressed as the stochastic optimal control of a dynamic system. Without therapy, the modeled immune response depends upon the initial concentration of pathogens in a simulated attack. Immune response can be augmented by agents that kill the pathogen directly, that stimulate the production of plasma cells or antibodies, or that enhance organ health. Using a generic mathematical model of immune response to the infection (i.e., of the dynamic state of the system), previous papers demonstrated optimal (open-loop) and neighboring-optimal (closed-loop) control solutions that defeat the pathogen and preserve organ health, given initial conditions that otherwise would be lethal [Optimal Contr. Appl. Methods 23 (2002) 91, Bioinformatics 18 (2002) 1227]. Therapies based on separate and combined application of the agents were derived by minimizing a quadratic cost function that weighted both system response and drug usage, providing implicit control over harmful side effects. Here, we focus on the effects that corrupted or incomplete measurements of the dynamic state may have on neighboring-optimal feedback control. Imperfect measurements degrade the precision of feedback adjustments to therapy; however, optimal state estimation allows the feedback strategy to be implemented with incomplete measurements and minimizes the expected effects of measurement error. Complete observability of the perturbed state for this four state example is provided by measurement of four of the six possible pairs of two variables, either set of three variables, or all four variables. The inclusion of state estimation extends the applicability of optimal control theory for developing new therapeutic protocols to enhance immune response.     

A Bioeconomic Model of a Multi-site Fishery with Nonlinear Demand Function: Number of Sites Optimizing the Total Catch

We present a mathematical model of a fishery on several sites with a variable price. The model takes into account the evolution during the time of the resource, fish and boat movement between the different sites, fishing effort and price that varies with respect to supply and demand. We suppose that the movements of the boats and resource as well as the variation of the price go on at a fast time scale. We use methods of aggregation of variables in order to reduce the number of variables and we derive a reduced model governing two global variables, respectively the biomass of the resource and the fishing effort of the whole fishery. We look for the existence of equilibria of the aggregated model and perform local stability analysis. Two main cases can occur. The first one corresponds to over-exploitation leading to fish extinction. At extinction, the fishing effort tends to a positive value. The second case corresponds to a durable fishery equilibrium which is globally asymptotically stable. In the later case, we show that there exists a number of fishing sites that optimizes the total catch of the fishery.     

Optimal nonsingular control of fed-batch fermentation

Presented is a new simple method for multidimensional optimization of fed-batch fermentations based on the use of the orthogonal collocation technique. Considered is the problem of determination of optimal programs for fermentor temperature, substrate concentration in feed, feeding profile, and process duration. By reformulation of the state and control variables is obtained a nonsingular form of the optimization problem which has considerable advantage over the singular case since a complicated procedure for determination of switching times for feeding is avoided. The approximation of the state variables by Lagrange polynomials enables simple incorporation of split boundary conditions in the approximation, and the use of orthogonal collocations provides stability for integration of state and costate variables. The interpolation points are selected to obtain highest accuracy for approximation of the objective functional by the Radau-Lobatto formula. The control variables are determined by optimization of the Hamiltonian at the collocation points with the DFP method. Constraints are imposed on state and control variables.The method is applied for a homogeneous model of fermentation with volume, substrate, biomass, and product concentrations as the state variables. Computer study shows considerable simplicity of the method, its high accuracy for low order of approximation, and efficient convergence.     

The Curvilinear Relationship between State Neuroticism and Momentary Task Performance

A daily diary and two experience sampling studies were carried out to investigate curvilinearity of the within-person relationship between state neuroticism and task performance, as well as the moderating effects of within-person variation in momentary job demands (i.e., work pressure and task complexity). In one, results showed that under high work pressure, the state neuroticism–task performance relationship was best described by an exponentially decreasing curve, whereas an inverted U-shaped curve was found for tasks low in work pressure, while in another study, a similar trend was visible for task complexity. In the final study, the state neuroticism–momentary task performance relationship was a linear one, and this relationship was moderated by momentary task complexity. Together, results from all three studies showed that it is important to take into account the moderating effects of momentary job demands because within-person variation in job demands affects the way in which state neuroticism relates to momentary levels of task performance. Specifically, we found that experiencing low levels of state neuroticism may be most beneficial in high demanding tasks, whereas more moderate levels of state neuroticism are optimal under low momentary job demands.     

Sexually antagonistic coevolution in a mating system: combining experimental and comparative approaches to address evolutionary processes

We combined experimental and comparative techniques to study the evolution of mating behaviors within in a clade of 15 water striders (Gerris spp.). Superfluous multiple mating is costly to females in this group, and consequently there is overt conflict between the sexes over mating. Two alternative hypotheses that could generate interspecific variation in mating behaviors are tested: interspecific variation in optimal female mating rate versus sexually antagonistic coevolution of persistence and resistance traits. These potentially coevolving traits include male grasping and female antigrasping structures that further the interests of one sex over the other during premating struggles. Both processes are known to play a role in observed behavioral variation within species. We used two large sets of experiments to quantify behavioral differences among species, as well as their response to an environmentally (sex-ratio) induced change in optimal female mating rate. Our analysis revealed a large degree of continuous interspecific variation in all 20 quantified behavioral variables. Nevertheless, species shared the same set of behaviors, and each responded in a qualitatively similar fashion to sex-ratio alterations. A remarkably large proportion (> 50%) of all interspecific variation in the magnitude of behaviors, including their response to sex ratio, could be captured by a single multivariate axis. These data suggest tight coevolution of behaviors within a shared mating system. The pattern of correlated evolution was best accounted for by antagonistic coevolution in the relative abilities of each sex to control the outcome of premating struggles. In species where males have a relative advantage, mating activity is high, and the opposite is found in species where females have gained a relative advantage. Our analyses also suggested that evolution has been unconstrained by history, with no consistent evolutionary tendency toward or away from male or female relative advantage.     

Machine learning based control rights analysis of critical resources and the optimal ownership for management integration

The paper first divides control rights of critical resources into government macroeconomic regulation power and insider control power for the management. After the discussion of the current status of Chinese coal industry integration, the paper mathematically and empirically analyzes influences of the government and state owned enterprises’ management to ownership’s boundary, and suggests the optimal ownership in different cases. The contributions of the paper are as follows: (1) Based on incomplete contract theory, the paper builds two mathematical models -the model of management’s investment level of relationship-specific human capital and ownership boundary model demonstrating the government utility under different ownership cases; (2) With the application of numerical simulation and empirical test, the paper analyzes impacts on coal resource integration from the aspects of government regulation and insider control, and discusses the optimal option of ownerships. By the analysis of the control power and ownership boundary based on the models, the paper eventually raises the optimal option of ownership allocation.     

Optimal control of the Lotka–Volterra system: turnpike property and numerical simulations

The Lotka–Volterra model is a differential system of two coupled equations representing the interaction of two species: a prey one and a predator one. We formulate an optimal control problem adding the effect of hunting both species as the control variable. We analyse the optimal hunting problem paying special attention to the nature of the optimal state and control trajectories in long time intervals. To do that, we apply recent theoretical results on the frame to show that, when the time horizon is large enough, optimal strategies are nearly steady-state. Such path is known as turnpike property. Some experiments are performed to observe such turnpike phenomenon in the hunting problem. Based on the turnpike property, we implement a variant of the single shooting method to solve the previous optimisation problem, taking the middle of the time interval as starting point.     

Setting Single-Period Optimal Capacity Levels and Prices for Substitutable Products

In this paper, we consider how a company that has the flexibility to produce two substitutable products would determine optimal capacity levels and prices for these products in a single-period problem. We first consider the case where the firm is a price taker but can determine optimal capacity levels for both products. We then consider the case where the firm can set the price for one product and the optimal capacity level for the other. Finally, we consider the case where capacity is fixed for both products, but the firm can set prices. For each case, we examine the sensitivity of optimal prices and capacities to the problem parameters. Finally, we consider the case where each product is managed by a product manager trying to maximize individual product profits rather than overall firm profits and analyze how optimal price and capacity decisions are affected.     

Weather variables as predictors of Sphagnum growth on a bog

When surrounded by growing Sphagnum the rhizomes of Scirpus cespitosus grow vertically upwards in pace with the Sphagnum . It was found that there is a considerable variation in rhizome growth between years and it is assumed that this variation is determined by variation in Sphagnum growth. The latter variation is assumed to be dependent on the weather. Simple and multiple regression analysis of rhizome growth on various weather variables gave the following results: (1) Moisture conditions are decisive for the growth. (2) The distribution in time of the moisture is more important than mean values from a certain period. (3) Although moisture in June and August of the current year was important, the moisture conditions of August of the previous year explained ca 60% of the variation. (4) A combination of the two variables Birot's wetness index in August of the previous year and the same index in current June gave r²= 0.80.     

The numerical method for the optimal supporting position and related optimal control for the catalytic reaction system

This paper considers the numerical approximation for the optimal supporting position and related optimal control of a catalytic reaction system with some control and state constraints, which is governed by a nonlinear partial differential equations with given initial and boundary conditions. By the Galerkin finite element method, the original problem is projected into a semi-discrete optimal control problem governed by a system of ordinary differential equations. Then the control parameterization method is applied to approximate the control and reduce the original system to an optimal parameter selection problem, in which both the position and related control are taken as decision variables to be optimized. This problem can be solved as a nonlinear optimization problem by a particle swarm optimization algorithm. The numerical simulations are given to illustrate the effectiveness of the proposed numerical approximation method.     

Freshwater biodiversity at regional extent: determinants of macroinvertebrate taxonomic richness in headwater streams

We studied spatial variation of macroinvertebrate species richness in headwater streams at two spatial extents, within and across drainage systems, and assessed the relative importance of three groups of variables (local, landscape and regional) at each extent. We specifically asked whether the same variables proposed to control broad‐scale richness patterns of terrestrial organisms (temperature, topographic variability) are important determinants of species richness also in streams, or whether environmental factors effective at mainly local scales (in‐stream heterogeneity, potential productivity) constrain species richness in local communities. We used forward selection with two stopping criteria to identify the key environmental and spatial variables at each study extent. Eigenvector‐based spatial filtering was applied to evaluate spatial patterns in species richness, and variation partitioning was used to assess the amount of variation in richness attributable to purely environmental and spatial components. A prime regulator of richness variation at the bioregion extent was elevation range (increasing richness with higher topographic variability), whereas hydrological stability and temperature were unimportant. Water chemistry variables, particularly water color, exhibited strong spatially‐structured variation across drainage systems. Local environmental variables explained most of the variation in species richness at the drainage‐system extent, reflecting gradients in total phosphorus and water color (negative effect on richness). The importance of the pure spatial component was strongly region‐dependent, with a peak (60%) in one drainage system, suggesting the presence of unmeasured environmental factors. Our results emphasize the need for spatially‐explicit, regional studies to better understand geographical variation of freshwater biodiversity. Future studies need to relate species richness not only to local factors but also to broad‐scale climatic variables, recognizing the presence of spatially‐structured environmental variation.