Direct fitness for dynamic kin selection

The direct-fitness approach to modelling the evolution of social traits is an alternative to the classical inclusive-fitness-based approach. Despite both its utility and popularity, the direct-fitness approach has not yet been extended to include the analysis of dynamic traits, i.e. traits whose level of expression may vary over time. In this article, I apply the direct-fitness approach to cope with the evolution of a dynamic resource-allocation behaviour when this behaviour influences the fitness of relatives. I am able to implement the direct-fitness approach using components (reproductive value, fitness changes and measures of relatedness) found in standard, social-evolutionary models. I illustrate the modified direct-fitness model with an example studied by previous authors, and I show how the direct-fitness perspective can aid the validation of analytical results by means of a genetic algorithm.     

Simulation of an iterative learning control system for fed-batch cell culture processes

This paper describes an iterative learning control scheme for fed-batch operation where repetitive trajectory tracking tasks are required. The proposed learning strategy is model-independent, and it takes advantage of the repetitive feature of system operations with a certain degree of intelligence and requires only small size of dynamic database for the learning process. The convergence of the learning process is proven. An example of simultaneously tracking two predefined trajectories by iterative learning control with two control inputs is given to illustrate the methodology. Satisfactory performance of the learning system can be observed from the simulation results.     

Protein secondary structure prediction using dynamic programming

In the present paper, we describe how a directed graph was constructed and then searched for the optimum path using a dynamic programming approach, based on the secondary structure propensity of the protein short sequence derived from a training data set. The protein secondary structure was thus predicted in this way. The average three-state accuracy of the algorithm used was 76.70%.     

Optimization of fed-batch culture of hybridoma cells using dynamic programming: single and multi feed cases

The optimization of fed-batch culture of hybridoma cells is accomplished on a mathematical model using dynamic programming. Optimal feed trajectories are found using a seventh order model for a single feed stream containing both glucose and glutamine and for two separate feed streams of glucose and glutamine. Compared to a constant feed rate, optimal trajectories can improve the final MAb concentration by 11 % for the single feed case and by 20% for the multifeed case. Higher MAb concentrations can be expected for fed-batch optimization with feed enriched in nutrients.     

Optimization of CSTRs in series by dynamic programming

This article concerns the development of a simple yet effective procedure for optimizing the design of a reactor system employing CSTRs in series. The basic approach used in this work was to translate the problem of reactor design to a mathematical programming model. The resulting model was then solved by dynamic programming. The procedure was tested on an IBM 3033 computer and an IBM PC-compatible machine, the CORONA PC-II microcomputer. The results of this study indicate that the optimization procedure developed is very effective.     

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.     

Citric acid production by Candida lipolytica Y 1095 in cell recycle and fed-batch fermentors

The effect of dissolved oxygen on citric acid production and oxygen uptake by Candida lipolytica Y 1095 was evaluated in cell recycle and fed-batch fermentation systems. The maximum observed volumetric productivity, which occurred at a dilution rate of 0.06 h(-1), a dissolved oxygen concentration of 80%, and a biomass concentration of 5% w/v, in the cell recycle system, was 1.32 g citric acid/L . h. At these same conditions, the citric acid yield was 0.65 g/g and the specific citric acid productivity was 24.9 mg citric acid/g cell . h. In the cell recycle system, citric acid yields ranged from 0.45 to 0.72 g/g. Both the volumetric and specific citric acid productivities were dependent on the dilution rate and the concentration of dissolved oxygen in the fermentor. Similar productivities (1.29 g citric acid/L . h) were obtained in the fed-batch system operated at a cycle time of 36 h, a dissolved oxygen concentration of 80%, and 60 g total biomass. Citric acid yields in the fed-batch fermentor were consistently lower than those obtained in the cell recycle system and ranged from 0.40 to 0.59 g/g. Although citric acid yields in the fed-batch fermentor were lower than those obtained in the cell recycle system, higher citric:isocitric acid ratios were obtained in the fed-batch fermentor. As in the cell recycle system, both the volumetric and specific citric acid productivities in the fed-batch fermentor were dependent on the cycle time and dissolved oxygen concentration. (c) 1995 John Wiley & Sons, Inc.     

Optimization of biochemical systems by linear programming and general mass action model representations

A new method is proposed for the optimization of biochemical systems. The method, based on the separation of the stoichiometric and kinetic aspects of the system, follows the general approach used in the previously presented indirect optimization method (IOM) developed within biochemical systems theory. It is called GMA-IOM because it makes use of the generalized mass action (GMA) as the model system representation form. The GMA representation avoids flux aggregation and thus prevents possible stoichiometric errors. The optimization of a system is used to illustrate and compare the features, advantages and shortcomings of both versions of the IOM method as a general strategy for designing improved microbial strains of biotechnological interest. Special attention has been paid to practical problems for the actual implementation of the new proposed strategy, such as the total protein content of the engineered strain or the deviation from the original steady state and its influence on cell viability.     

A dynamic model of hypothermia as an adaptive response by small birds to winter conditions

We present a dynamic programming model which is used to investigate hypothermia as an adaptive response by small passerine birds in winter. The model predicts that there is a threshold function of reserves during the night, below which it is optimal to enter hypothermia, and above which it is optimal to rest. This threshold function decreases during the night, with a particularly sharp drop at the end of the night, representing the time and energy costs associated with returning to normal body temperature. The results of the model emphasise the trade-off between energy and predation, not just between foraging options, but also between foraging during the day and entering hypothermia at night. The value of being able to use hypothermia represents not just energy savings, but also reduced predation risk due to changes in the optimal foraging strategy. Conditions which give a high value of hypothermia are short photoperiod, variable food supply, low temperatures, poor and scarce food supplies.     

Optimization of fed-batch fermentation for xylitol production by Candida tropicalis

Xylitol, a functional sweetener, was produced from xylose by biological conversion using Candida tropicalis ATCC 13803. Based on a two-substrate fermentation using glucose for cell growth and xylose for xylitol production, fed-batch fermentations were undertaken to increase the final xylitol concentration. The effects of xylose and xylitol on xylitol production rate were studied to determine the optimum concentrations for fed-batch fermentation. Xylose concentration in the medium (100 g l⁻¹) and less than 200 g l⁻¹ total xylose plus xylitol concentration were determined as optimum for maximum xylitol production rate and xylitol yield. Increasing the concentrations of xylose and xylitol decreased the rate and yield of xylitol production and the specific cell growth rate, probably because of an increase in osmotic stress that would interfere with xylose transport, xylitol flux to secretion to cell metabolism. The feeding rate of xylose solution during the fed-batch mode of operation was determined by using the mass balance equations and kinetic parameters involved in the equations in order to increase final xylitol concentration without affecting xylitol and productivity. The optimized fed-batch fermentation resulted in 187 g l⁻¹ xylitol concentration, 0.75 g xylitol g xylose⁻¹ xylitol yield and 3.9 g xylitol l⁻¹ h⁻¹ volumetric productivity. Journal of Industrial Microbiology & Biotechnology (2002) 29, 16–19 doi:10.1038/sj.jim.7000257 Received 15 October 2001/ Accepted in revised form 30 March 2002     

Optimization of erythritol production by Candida magnoliae in fed-batch culture

A two-stage fed-batch process was designed to enhance erythritol productivity by the mutant strain of Candida magnoliae. The first stage (or growth stage) was performed in the fed-batch mode where the growth medium was fed when the pH of the culture broth dropped below 4.5. The second stage (or production stage) was started with addition of glucose powder into the culture broth when the cell mass reached about 75 g dry cell weight l⁻¹. When the initial glucose concentration was adjusted to 400 g l⁻¹ in the production stage, 2.8 g l⁻¹ h⁻¹ of overall erythritol productivity and 41% of erythritol conversion yield were achieved, which represented a fivefold increase in erythritol productivity compared with the simple batch fermentation process. A high glucose concentration in the production phase resulted in formation of organic acids including citrate and butyrate. An increase in dissolved oxygen level caused formation of gluconic acid instead of citric acid. Journal of Industrial Microbiology & Biotechnology (2000) 25, 100–103. Received 25 February 2000/ Accepted in revised form 08 June 2000     

Factors influencing route choice by avian migrants: a dynamic programming model of Pacific brant migration

We used stochastic dynamic programming to investigate a spectacular migration strategy in the black brant Branta bernicla nigricans, a species of goose. Black brant migration is well suited for theoretical analysis since there are a number of existing strategies that easily can be compared. In early autumn, almost the entire population of the black brant gathers at Izembek Lagoon on the Alaska Peninsula to stage and refuel before the southward migration. There are at least three distinct strategies, with most geese making a spectacular direct migration more than 5000km across the Gulf of Alaska to their wintering grounds in southern Baja California or mainland Mexico. This is a potentially dangerous strategy since foraging is not possible during the overseas passage. Some individuals instead use shorter flights to make a detour along the coast, a longer route that all individuals use for northwards migration in spring. Since flight costs accelerate with increasing body mass, migration by short flights is energetically cheaper than long-distance flights. A small but increasing part of the population has recently begun to winter at Izembek. We investigated this migration under two different suppositions using a dynamic state variable model. First, if the geese are free to make a strategic choice, under what assumptions should they prefer direct migration and under what assumptions should they prefer detour migration/winter residency? Second, provided that the dominating direct migration strategy is optimal, what conditions will force the geese to go for detour migration/winter residency? In the second case the geese may try to follow an optimal direct migration strategy, but stochastic events may force them to choose a suboptimal policy. We also simulated possible effects of global warming. The model suggests that the fuel level at arrival in Izembek and fuel gain rates are key factors and that tail winds must have been reliable in the past, otherwise direct migration could not have evolved. It also suggests that a change to milder winters may promote an unexpectedly abrupt change from long-distance to short-distance migration or winter residency. Finally, it produced a number of predictions that might be testable in the field.     

酵母菌半连续转化人参皂苷Rb1的条件优化

以单因素实验为基础,通过多因素方差分析实验对人参皂苷半连续转化的条件进行优化,选出最佳条件组合,得到最佳的补料方式,补料浓度为6%,补料体积为24mL,补料周期为12h,在此条件下人参皂苷Rb1生物转化达33.5%左右。在最佳补料条件下进行人参皂苷酵母菌转化,其稳定性好,转化率高,对工业生产有积极的推动作用。     

Adding physiological realism to dynamic state variable models of parasitoid host feeding

Summary The behavioural decisions of insect parasitoids have been the subject of dynamic state variable models, which explicitly incorporate the physiological state of the parasitoid, e.g. her age and egg load (number of mature eggs). Such models have been most recently applied to parasitoid host feeding, the consumption of host body fluids or tissues by the adult female wasp. The models developed to date, and recent empirical work withAphytis melinus, have highlighted the importance of the physiology associated with host feeding to the behavioural decision whether to host feed or oviposit. Below, I develop a new dynamic state variable model which incorporates the physiological features associated with host feeding inAphytis. My intention is to make qualitative predictions about the effects of various physiological featues on host-feeding behaviour and to make quantitative predictions about the relationship between egg load and host feeding inAphytis.     

Asset protection in juvenile salmon: how adding biological realism changes a dynamic foraging model

The "asset-protection principle" created by Clark is based ona dynamic programming model and states that individuals should(1) become more averse to predation risk as they accumulatefitness assets but (2) generally be more willing to acceptpredation risk later in the foraging season. To test whetherthese predictions hold under biologically meaningful foraging parameters, I constructed a dynamic model of the optimal trade-offbetween foraging and predator avoidance in juvenile salmon.The model incorporates temperature and body-size dependentbio-energetic constraints typical for juvenile fish, whichgrow by orders of magnitude over a season. In its simplestform using seasonally constant growth potential and a linear over-winter survival function, my results equal those of Clark'smodel. Adding a fitness function and environmental data fromfield studies accentuates the asset-protection effect and fundamentallychanges the seasonal pattern of optimal effort. Simulationof typical poor feeding conditions in mid-summer yields theprediction of increased foraging in the spring in anticipationof worsening conditions. Increasing overall predation riskresults in smaller fish at the end of the season with a trade-offbetween summer and winter survival. The model generates testablepredictions for juvenile salmon and provides insights for otherorganisms (particularly poikilotherms) that are subject tosize-dependent or seasonally changing foraging dynamics.     

A dynamic model of group-size choice in the coral reef fish Dascyllus albisella

We developed a dynamic programming model of group size choicefor settlingcoral reef fish to help understand variabilityin observed group sizes. Ratherthan calculating optimal groupsize, we modeled optimal choice and calculatedthe acceptablegroup sizes that arose from this choice. In the model, settlingindividualsweigh the fitness value of settling in a group against theexpectedfitness of searching another day and encountering other groups,choosingthe option with the higher value. Model results showed thatindividualssettling on any given day in the settling season have severalacceptablegroup sizes in which they can settle. The range of acceptablegroupsizes also changes across the season. Early in the season,when there is stilladequate time to grow, large groups (withhigher survival) have the highestfitness. Late in the season,when the ability to grow fast becomes moreimportant, smallgroups, which convey fast growth rates (although riskier),havehigher fitness. Thus, according to our model, even when fishall make thesame, simple decisions, a variety of outcomes arepossible, depending on thespecific options encountered andtemporally changing ecological pressures.Even when all fishbehave optimally, initial variability in group sizes willpersist.