INSTAR,a discrete event model for simulating zooplankton population dynamics

In this paper we discuss the basic principles of discrete event, individual oriented, data based modelling in ecology, and we present an application of this modelling strategy. The strategy is contrasted with some more conventional modelling strategies with respect to its purpose, its basic units and its heuristic properties.INSTAR applies this modelling strategy to the simulation of the fluctuations of the population structure and density of microcrustaceans through the year. The model encompasses one microcrustacean species at a time, and its interface with the rest of the ecosystem; it has been applied to several Cladocera and Copepoda species in a shallow eutrophic lake in the Netherlands (Vijverberg & Richter 1982a, b). Possibilities for extending the model are discussed.     

A density-dependent model of Cirsium vulgare population dynamics using field-estimated parameter values

Two versions of a stage-structured model of Cirsium vulgare population dynamics were developed. Both incorporated density dependence at one stage in the life cycle of the plant. In version 1 density dependence was assumed to operate during germination whilst in version 2 it was included at the seedling stage. Density-dependent parameter values for the model were estimated from annual census data in a factorial grazing experiment. Version 1 of the model produced significant estimates of density dependence under field conditions. The estimated values, when included in a simulation of the dynamics, produced two-point limit cycles under conditions of hard grazing. The limit cycles were most pronounced at the early rosette stage. Comparison of the effects of density dependence at the two different stages in the life cycle revealed a strong difference in predicted dynamics. This emphasizes the importance of determining where density dependence operates under field conditions and the potential problems of arbitrarily assigning it to particular life-history stages. Version 1 of the model produced a good prediction of observed mean plant density across the different grazing treatments (r ²=0.81, P<0.001).     

A mathematical model of population dynamics for Batesian mimicry system

We analyse a mathematical model of the population dynamics among a mimic, a corresponding model, and their common predator populations. Predator changes its search-and-attack probability by forming and losing its search image. It cannot distinguish the mimic from the model. Once a predator eats a model individual, it comes to omit both the model and the mimic species from its diet menu. If a predator eats a mimic individual, it comes to increase the search-and-attack probability for both model and mimic. The predator may lose the repulsive/attractive search image with a probability per day. By analysing our model, we can derive the mathematical condition for the persistence of model and mimic populations, and then get the result that the condition for the persistence of model population does not depend on the mimic population size, while the condition for the persistence of mimic population does depend the predator's memory of search image.     

数学判别模型在预测害虫种群动态上的应用

根据两个总体的Fisher判别准则,建立了预测害虫种群动态的数学判别模型,对山东省惠民县1967～1977年共11年二代棉铃虫发生程度的两类资料进行了数量分析,建立了数学模型：y＝0．0127x1－0．023X2,对历史资料的回代验证与独立样本的预测,符合率在90％以上。     

Ameboid cell motility: a model and inverse problem, with an application to live cell imaging data

In this article a mathematical model for ameboid cell movement is developed using a spring-dashpot system with Newtonian dynamics. The model is based on the facts that the cytoskeleton plays a primary role for cell motility and that the cytoplasm is viscoelastic. Based on the model, the inverse problem can be posed: if a structure like a spring-dashpot system is embedded into the living cell, what kind of characteristic properties must the structure have in order to reproduce a given movement of the cell? This inverse problem is the primary topic of this paper. On one side the model mimics some features of the movement, and on the other side, the solution to the inverse problem provides model parameters that give some insight, principally into the mechanical aspect, but also, through qualitative reasoning, into chemical and biophysical aspects of the cell. Moreover, this analysis can be done locally or globally and in different media by using the simplest possible information: positions of the cell and nuclear membranes. It is shown that the model and solution to the inverse problem for simulated data sets are highly accurate. An application to a set of live cell imaging data obtained from random movements of a human brain tumor cell (U87-MG human glioblastoma cell line) then provides an example of the efficiency of the model, through the solution of its inverse problem, as a way of understanding experimental data.     

一种模拟昆虫种群动态的改进的变维矩阵模型

提出了一种模拟昆虫种群动态的改进的变维矩阵模型,该模型以发有历期为维数,采用分解与合成的方法变维,并考虑了个体间的发育差异。经模拟检验,模型模拟结果略优于徐汝梅等（1981）变维矩阵模型的结果。     

Evaluation of the population dynamics of the forage legume (Lotus corniculatus), using matrix population models

The population dynamics of perennial crop plants are influenced by numerous factors, including management practices. Conditions in the field vary from year to year, and matrix population models are useful for evaluating population behaviour in relation to environmental variability. In Missouri, the stand persistence of birdsfoot trefoil ( Lotus corniculatus ), a perennial legume, is often limited by disease and poor seed production. A stage-based, matrix population model was developed to evaluate the population dynamics of birdsfoot trefoil in relation to clipping treatment. The plant growth stages represented in the model were seeds, seedlings, mature vegetative and reproductive plants. Two phases of population growth were evaluated in clipped and unclipped stands. Establishment-phase populations were characterized by relatively high mortality and low reproduction. Elasticity analysis indicated that growth of these populations was most sensitive to the survival of vegetative plants. Mature vegetative plants and seeds comprised the majority of surviving individuals in clipped and unclipped populations, respectively; however, establishment-phase populations under both management treatments tended toward extinction. Populations in the post-establishment phase of growth were characterized by relatively low mortality and high reproduction. Population growth in this phase of growth was most sensitive to seed production, and most individuals in these populations were at the seed stage.     

Asymptotic behaviour of a model of hierarchically structured population dynamics

 A hierarchically structured population model with a dependence of the vital rates on a function of the population density (environment) is considered. The existence, uniqueness and the asymptotic behaviour of the solutions is obtained transforming the original non-local PDE of the model into a local one. Under natural conditions, the global asymptotical stability of a nontrivial equilibrium is proved. Finally, if the environment is a function of the biomass distribution, the existence of a positive total biomass equilibrium without a nontrivial population equilibrium is shown. Received 16 February 1996; received in revised form 16 September 1996     

A three-dimensional vertex dynamics cell model of space-filling polyhedra simulating cell behavior in a cell aggregate

We developed a three-dimensional (3D) cell model of a multicellular aggregate consisting of several polyhedral cells to investigate the deformation and rearrangement of cells under the influence of external forces. The polyhedral cells fill the space in the aggregate without gaps or overlaps, consist of contracting interfaces and maintain their volumes. The interfaces and volumes were expressed by 3D vertex coordinates. Vertex movements obey equations of motion that rearrange the cells to minimize total free energy, and undergo an elementary process that exchanges vertex pair connections when vertices approach each other. The total free energy includes the interface energy of cells and the compression or expansion energy of cells. Computer simulations provided the following results: An aggregate of cells becomes spherical to minimize individual cell surface areas; Polygonal interfaces of cells remain flat; Cells within the 3D cell aggregate can move and rearrange despite the absence of free space. We examined cell rearrangement to elucidate the viscoelastic properties of the aggregate, e.g. when an external force flattens a cell aggregate (e.g. under centrifugation) its component cells quickly flatten. Under a continuous external force, the cells slowly rearrange to recover their original shape although the cell aggregate remains flat. The deformation and rearrangement of individual cells is a two-step process with a time lag. Our results showed that morphological and viscoelastic properties of the cell aggregate with long relaxation time are based on component cells where minimization of interfacial energy of cells provides a motive force for cell movement.     

An approach to the nonlinear dynamics of Russian wheat aphid population growth with the cusp catastrophe model

Many insect field populations, especially aphids, often exhibit irregular and even catastrophic fluctuations. The objective of the present study is to explore whether or not the population intrinsic rates of growth ( r _m) obtained under laboratory conditions can shed some light on the irregular changes of insect field populations. We propose to use the catastrophe theory, one of the earliest nonlinear dynamics theories, to answer the question. To collect the necessary data, we conducted a laboratory experiment to investigate population growth of the Russian wheat aphid (RWA), Diuraphis noxia (Mordvilko), in growth chambers. The experiment was designed as the factorial combinations of five temperatures and five host plant-growth stages (25 treatments in total): 1800 newly born RWA nymphs arranged in the 25 treatments (each treatment with 72 repetitions) were observed for their development, reproduction and survival through their entire lifetimes. After obtaining the population intrinsic rates of growth ( r _m) from the experimental data under various environmental conditions, we built a cusp catastrophe model for RWA population growth by utilizing r _m as the system state variable, and temperature and host plant-growth stage as control variables. The cusp catastrophe model suggests that RWA population growth is intrinsically catastrophic , and dramatic jumps from one state to another might occur even if the temperature and plant-growth stage change smoothly . Other basic behaviors of the cusp catastrophe model, such as catastrophic jumps , hystersis and divergence , are also expected in RWA populations. These results suggest that the answer to the previously proposed question should be yes.     

20-Hydroxyecdysone-induced changes in the cell volume of lepidopteran cells associated with population dynamics

Summary The insect cell line MRRL-CH derived from embryos of the lepidopteranManduca sexta responded rapidly, within 15 min, to 20-hydroxyecdysone (20-OH-Ec) (1×10⁻⁸ M) by increasing in cell volume. The induction time for this response contrasts with that for the cell elongation response that appears only after 24 to 48 h. The increase in cell volume represents the most rapid 20-OH-Ec-induced change in cell morphology reported to date. It also has some steroid specificity because no volume change was induced by ecdysone (4×10⁻⁶ M) under the experimental conditions. The magnitude of the cell volume response to 20-OH-Ec varied with the population dynamics of the cell line and was associatated with cell size at the time of treatment. This is a portion of a thesis submitted by L. H. E. in partial fulfillment of the requirements for the Ph.D. degree and published with the approval of the Director of the North Dakota Experiment Station as Journal Article 1130. Mention of a proprietary product or company name in this paper does not imply endorsement by the U.S. Department of Agriculture.     

A stochastic model of a cell population with quiescence

A cell population in which cells are allowed to enter a quiescent (nonproliferating) phase is analyzed using a stochastic approach. A general branching process is used to model the population which, under very mild conditions, exhibits balanced exponential growth. A formula is given for the asymptotic fraction of quiescent cells, and a numerical example illustrates how convergence toward the asymptotic fraction exhibits a typical oscillatory pattern. The model is compared with deterministic models based on semigroup analysis of systems of differential equations.     

Detecting autocatalytic dynamics in data modeled by a compartmental model

Modeling growth or reaction dynamics within a compartment in a compartmental model is often based on theoretical or first principle considerations. This approach is frequently applied due to the inability to observe or collect data directly from the compartment. When the internal dynamics are difficult to surmise, it is often the case that several competing models are constructed and compared in some way. In this paper, the dynamics which characterize the data of an autocatalytic process are used to describe a quantitative data analysis strategy to both recognize the presence of the autocatalytic process and to obtain some estimates of important parameters in the process. The compartmental model structure serves to communicate this dynamical information to the downstream compartments. This method has been applied to examine the dynamics of the engraftment of blood cells following hematopoietic stem cell transplantation in a clinical setting [Modeling the time to engraftment of white blood cells and platelets following autologous peripheral blood stem cell transplantation (2001)].     

Individual variation and population dynamics: lessons from a simple system

The mapping of environment, through variation in individuals' life histories, to dynamics can be complex and often poorly known. Consequently, it is not clear how important it is dynamically. To explore this, I incorporated lessons from an empirical system, a soil mite, into an individual-based model. Individuals compete for resource and allocate this according to eight 'genetic' rules that specify investment in growth or reserves (which influences survival or fecundity), size at maturation and reproductive allocation. Density dependence, therefore, emerges from competition for food, limiting individual's growth and fecundity. We use this model to examine the role that genetic and phenotypically plastic variation plays in dynamics, by fixing phenotypes, by allowing phenotypes to vary plastically and by creating genetic variation between individuals. Variation, and how it arises, influences short- and long-run dynamics in a way comparable in magnitude with halving food supply. In particular, by switching variation on and off, it is possible to identify a range of processes necessary to capture the dynamics of the 'full model'. Exercises like this can help identify key processes and parameters, but a concerted effort is needed across many different systems to search for shared understanding of both process and modelling.     

Integral projection models perform better for small demographic data sets than matrix population models: a case study of two perennial herbs

1. Matrix population models are widely used to describe population dynamics, conduct population viability analyses and derive management recommendations for plant populations. For endangered or invasive species, management decisions are often based on small demographic data sets. Hence, there is a need for population models which accurately assess population performance from such small data sets.
2. We used demographic data on two perennial herbs with different life histories to compare the accuracy and precision of the traditional matrix population model and the recently developed integral projection model (IPM) in relation to the amount of data.
3. For large data sets both matrix models and IPMs produced identical estimates of population growth rate (λ). However, for small data sets containing fewer than 300 individuals, IPMs often produced smaller bias and variance for λ than matrix models despite different matrix structures and sampling techniques used to construct the matrix population models.
4. Synthesis and applications . Our results suggest that the smaller bias and variance of λ estimates make IPMs preferable to matrix population models for small demographic data sets with a few hundred individuals. These results are likely to be applicable to a wide range of herbaceous, perennial plant species where demographic fate can be modelled as a function of a continuous state variable such as size. We recommend the use of IPMs to assess population performance and management strategies particularly for endangered or invasive perennial herbs where little demographic data are available.     

CFD of mixing of multi‐phase flow in a bioreactor using population balance model

Mixing in bioreactors is known to be crucial for achieving efficient mass and heat transfer, both of which thereby impact not only growth of cells but also product quality. In a typical bioreactor, the rate of transport of oxygen from air is the limiting factor. While higher impeller speeds can enhance mixing, they can also cause severe cell damage. Hence, it is crucial to understand the hydrodynamics in a bioreactor to achieve optimal performance. This article presents a novel approach involving use of computational fluid dynamics (CFD) to model the hydrodynamics of an aerated stirred bioreactor for production of a monoclonal antibody therapeutic via mammalian cell culture. This is achieved by estimating the volume averaged mass transfer coefficient (k_La) under varying conditions of the process parameters. The process parameters that have been examined include the impeller rotational speed and the flow rate of the incoming gas through the sparger inlet. To undermine the two‐phase flow and turbulence, an Eulerian‐Eulerian multiphase model and k‐ε turbulence model have been used, respectively. These have further been coupled with population balance model to incorporate the various interphase interactions that lead to coalescence and breakage of bubbles. We have successfully demonstrated the utility of CFD as a tool to predict size distribution of bubbles as a function of process parameters and an efficient approach for obtaining optimized mixing conditions in the reactor. The proposed approach is significantly time and resource efficient when compared to the hit and trial, all experimental approach that is presently used. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 32:613–628, 2016     

Invasion of an intermediate predator: Fish population dynamics in a mathematical model of a trophic chain (As applied to Syamozero lake)

A mathematical model is presented for the dynamics of a spatially heterogeneous predator-prey population system; a prototype is the Syamozero lake fish community. We show that the invasion of an intermediate predator can evoke chaotic oscillations in the population densities. We also show that different dynamic regimes (stationary, nonchaotic oscillatory, and chaotic) can coexist. The “choice” of a particular regime depends on the initial invader density. Analysis of the model solutions shows that invasion of an alien species is successful only in the absence of competition between the juvenile invaders and the native species.     

Equilibria and dynamics of selection at a diallelic autosomal locus in the Nagylaki-Crow continuous model of a monoecious population

Let birth rates and death rates be constant, birth rates positive, fertilities additive, and each birth rate not larger than twice any other birth rate. Global convergence to equilibria is proved for the model in the title. There is at most one polymorphic equilibrium or there are a continuum of equilibria. The phase portraits are given. If there is a polymorphic equilibrium, then the largest negatively invariant set in the state space is a continuous curve connecting the two fixation equilibria. This curve coincides with the Hardy-Weinberg manifold exactly when the death rate is additive. Disregarding extinction, the polymorphic equilibria are the same for the continuous model as for the corresponding discrete model exactly when the death rate is additive.     

A degree-day simulation model for the population dynamics of the rice bug, Leptocorisa acuta (Thunb.)

The rice bug, Leptocorisa acuta (Thunb.) is a major pest of the rice crop in India. A computer simulation model of the bug's population dynamics was formulated using the information generated on the thermal requirements of development stages. It is a mechanistic model which follows the state variable–rate variable approach. The model works based on the accumulation of heat units over stage-specific thresholds of development. Validation using light trap catches has shown that the model has satisfactory predictive value. Simulated population dynamics over the years were compared and the influence of global warming on bug population dynamics was predicted. The model can forecast the pest population in the field and help in timely adoption of management practices.