Growth and reproduction in higher plants I. Theoretical analysis by mathematical models

To analyse the whole life of higher plants, an attempt was made to describe their growth and reproduction by mathematical models based on the elements determining matter production and economy of the matter. A plant body was regarded as a compound system of two parts; “productive part” and “reproductive part”. A parameter (reproductive index) was introduced to connect these two parts, and a set of the mathematical models describing the quantitative growth of these two parts were established. Two basic patterns of reproduction in higher plants were distinguished into “D-reproduction” and “I-reproduction”. The state of matter production of the mother plant determined an initial size of the daughter plant in theD-reproduction, while, in theI-reproduction, it did not determine the initial size of the daughter, but determined the number of propagules. The model of each reproduction pattern was also constructed. A formula determining the initial size of a plant in a given generation was constructed as the model of theD-reproduction. The model for theI-reproduction described the number of propagules produced in a given generation. Some aspects of the plant life, e.g. the optimum reproductive index, the switch-over time from the vegetative to the reproductive growth phase, the seed number, types of expansive reproduction, were theoretically analysed and discussed under these mathematical models.     

A single theory explains two empirical laws applicable to plant populations

Two empirical laws, formulated independently, are known to be well satisfied in even-aged plant monocultures. One relates yield to plant density in different plant populations, and the other relates cumulative plant mass to cumulative plant number from the largest individual within a population. In this paper, we construct a mathematical model of plant growth under asymmetric competition between individuals in a population, where large individuals grow larger than small individuals because they pre-empt resources, especially light. The model categorizes influences on the growth of a plant into those from individuals larger than itself, and those from all individuals in the population. We derive the two laws from our model. Thus, individual growth, determined by asymmetric interaction between individuals in a population, can explain the two different laws relating to plant populations.     

Modeling the Individual Growth of Tetrahymena Sp. and its Population Consequences

ABSTRACT. Three types of mathematical growth models are presented to describe the individual growth of the ciliate Tetrahymena sp. feeding on the bacterium Pseudomonas fluorescens . Both organisms were isolated from a domestic waste-water treatment plant. Growth of individual ciliates and the consequences for the whole population are considered. Experimental data, obtained by following the individual ciliate during its lifespan from cell division to cell division, are used for parameter estimations. Differences between growth models for individuals turn out to have little effect on the specific population growth rate and the mean cell volume. In case of exponential growth of individuals the unstructured and structured population models are equivalent, even in time-variant environments. This knowledge can be applied in the stability analysis of food chains or forced systems. The results obtained facilitates quantification of protozoa biomass as a function of bacterial biomass in chemostats. More specifically, it highlights the dynamic behaviour of bacteria and protozoa in waste-water treatment plants.     

Modelling crop growth and biomass partitioning to shoots and roots in relation to nitrogen and water availability,using a maximization principle

Many crop models relate the allocation of dry matter between shoots and roots exclusively to the crop development stage. Such models may not take into account the effects of changes in environment on allocation, unless the allocation parameters are altered. In this paper a crop model with a dynamic allocation parameter for dry matter between shoots and roots is described. The basis of the model is that a plant allocates dry matter such that its growth is maximized. Consequently, the demand and supply of carbon, nitrogen, and water is maintained in balance. This model supports the hypothesis that a functional equilibrium exists between shoots and roots.This paper explains the mathematical computation procedure of the crop model. Moreover, an analysis was made of the ability of a crop model to simulate plant dry matter production and allocation of dry matter between plant organs. The model was tested using data from a greenhouse experiment in which spring wheat (Triticum aestivum L.) was grown under different soil moisture and nitrogen (N) levels.Generally, the model simulations agreed well with data recorded for total plant dry matter. For validation data the coefficient of determination (r²) between simulated and measured shoot dry weight was 0.96. For the validation treatments r² was slightly lower, 0.94. In addition to dry matter production the model succeeded satisfactorily in simulating the dry weight of different plant organs. The response of simulated root to shoot ratio to the level of soil moisture was mainly in accordance with the measured data. In contrast, the simulated ratio seemed to be insensitive to the changes in the levels soil N concentration used in the experiment.The data used in the present study were not extensive, and more data are needed to validate the model. However, the results showed that the model responses to the changes in soil N and water level were realistic and mostly agreed with the data. Thus, we suggest that the model and the method employed to allocate dry matter between roots and shoots are useful when modelling the growth of crops under N and water limited conditions.     

Marker-Based Estimation of Heritability in Immortal Populations

Heritability is a central parameter in quantitative genetics, from both an evolutionary and a breeding perspective. For plant traits heritability is traditionally estimated by comparing within- and between-genotype variability. This approach estimates broad-sense heritability and does not account for different genetic relatedness. With the availability of high-density markers there is growing interest in marker-based estimates of narrow-sense heritability, using mixed models in which genetic relatedness is estimated from genetic markers. Such estimates have received much attention in human genetics but are rarely reported for plant traits. A major obstacle is that current methodology and software assume a single phenotypic value per genotype, hence requiring genotypic means. An alternative that we propose here is to use mixed models at the individual plant or plot level. Using statistical arguments, simulations, and real data we investigate the feasibility of both approaches and how these affect genomic prediction with the best linear unbiased predictor and genome-wide association studies. Heritability estimates obtained from genotypic means had very large standard errors and were sometimes biologically unrealistic. Mixed models at the individual plant or plot level produced more realistic estimates, and for simulated traits standard errors were up to 13 times smaller. Genomic prediction was also improved by using these mixed models, with up to a 49% increase in accuracy. For genome-wide association studies on simulated traits, the use of individual plant data gave almost no increase in power. The new methodology is applicable to any complex trait where multiple replicates of individual genotypes can be scored. This includes important agronomic crops, as well as bacteria and fungi.     

Simulation of developmental changes in action potentials with ventricular cell models

During cardiomyocyte development, early embryonic ventricular cells show spontaneous activity that disappears at a later stage. Dramatic changes in action potential are mediated by developmental changes in individual ionic currents. Hence, reconstruction of the individual ionic currents into an integrated mathematical model would lead to a better understanding of cardiomyocyte development. To simulate the action potential of the rodent ventricular cell at three representative developmental stages, quantitative changes in the ionic currents, pumps, exchangers, and sarcoplasmic reticulum (SR) Ca²⁺ kinetics were represented as relative activities, which were multiplied by conductance or conversion factors for individual ionic systems. The simulated action potential of the early embryonic ventricular cell model exhibited spontaneous activity, which ceased in the simulated action potential of the late embryonic and neonatal ventricular cell models. The simulations with our models were able to reproduce action potentials that were consistent with the reported characteristics of the cells in vitro. The action potential of rodent ventricular cells at different developmental stages can be reproduced with common sets of mathematical equations by multiplying conductance or conversion factors for ionic currents, pumps, exchangers, and SR Ca²⁺ kinetics by relative activities.     

Stability analysis and optimal vaccination of an SIR epidemic model

Almost all mathematical models of diseases start from the same basic premise: the population can be subdivided into a set of distinct classes dependent upon experience with respect to the relevant disease. Most of these models classify individuals as either a susceptible individual S, infected individual I or recovered individual R. This is called the susceptible-infected-recovered (SIR) model. In this paper, we describe an SIR epidemic model with three components; S, I and R. We describe our study of stability analysis theory to find the equilibria for the model. Next in order to achieve control of the disease, we consider a control problem relative to the SIR model. A percentage of the susceptible populations is vaccinated in this model. We show that an optimal control exists for the control problem and describe numerical simulations using the Runge-Kutta fourth order procedure. Finally, we describe a real example showing the efficiency of this optimal control.     

Spatiotemporal variation in predispersal seed predation intensity

The effect of predispersal seed predation by Bruchus atomarius (Bruchidae, Coleoptera) on individual performance and population dynamics of the perennial forest herb, Lathyrus vernus (Leguminosae), was investigated in 11 permanent plots over 4 years. Seed predation and parameters describing intra-specific neighbour distance, plant size, inflorescence size, flowering phenology and current and previous herbivore damage were measured on all plants. In addition, demographic information from all plots was analysed using transition matrix population models in order to estimate the influence of seed predation on population growth rates. Predispersal seed predation rates differed significantly among years. Plot averages ranged from 0 to 83.7%. However, most of the variation occurred among individuals. Within individuals there was no consistency in predation rates among years. Exposure to herbivory, plant size and flowering phenology did not affect predation rates but individuals with larger inflorescences suffered from significantly higher predation. Seed predation in L. vernus was not influenced by neighbour distances of individual plants but it was positively correlated with the average density of seeds within plots, suggesting that seed predation is density dependent at the patch level. The reduction in population growth rate due to seed predation ranged from 0 to 7.6%. The sensitivity of population growth rate to reductions in seed production varied considerably among years and plots. This variation was mainly due to differences in the reproductive value of seeds and seedlings. The intensity of seed predation over the range found was not correlated with changes in population growth rate. The results of this study suggest that the influence of external factors, like seed predation, on population growth rate largely depends on the demographic transition rates in the investigated population.     

Growth models of cultures with two liquid phases. VI. Parameter estimation and statistical analysis

Parameter estimation studies have been conducted employing mathematical models developed previously by the investigators and experimental data collected by the last author. A batch fermentation process in which Candida lipolytica were cultured on n-hexadecane dissolved in dewaxed gas oil was employed to obtain the experimental data. The kinetic data from a number of batch experiments conducted at different initial substrate concentrations and different dispersed phase volume fractions were analyzed assuming that, the basic model parameters (maximum specific growth rate, saturation constant, substrate phase equilibrium constant, adsorption constant, desorption constant, etc.) did not change from experiment to experiment. The Gauss-Newton method with modification by Greenstadt, Eisenpress, Bard, and Carroll was used to minimize the conventional sum of squares criterion on the IBM 300/50 computer. The individual confidence intervals were obtained for each individual parameter. Tin- models were compared employing the F-test for equality of variances and an analysis of residuals. For the two best models, the estimated parameter values were compared with available experimental information. The results showed good agreement between the experimental data and the values predicted by the mathematical models. The results presented in this work did suggest that growth on small segregated drops may be more important than continuous phase growth on dissolved substrate.     

Neighborhood models of plant population dynamics. 2. Multi-species models of annuals

Models are developed for the dynamics of multi-species communities of annual plants that lack seed dormancy. These models explicitly include plastic plant growth, the spatial distribution of individuals, and the fact that individuals interact primarily with nearby individuals. Because the models are based on submodels of individual plants (fecundity, survivorship and dispersal, and how these are affected by inter-individual interactions), they provide explanations of community-level phenomena in terms of the biology of individuals. All model parameters and functional forms may be estimated from data obtained in simple experiments of a single years's duration. The models are used to examine the community-level consequences of some types of inter-individual interactions that have been reported in the ecological literature. In addition, the models are used to demonstrate that dispersal may markedly influence the outcome of competition among plant species, even in a physically homogeneous environment, due to an effect of dispersal on the spatial distribution of individuals.     

Stochastic population dynamics of clonal plants: Numerical experiments with ramet and genet models

Dynamics of ramer and genet populations were analyzed by use of stochastic matrix models. Based on field data, population development and extinction rates during 50 simulated years were estimated for ramet populations of three speciesPotentilla anserina, Rubus saxatilis andLinnaea borealis. Only small initial populations (below 125–250 ramets), experienced a detectable risk of extinction within this time interval. ForP. anserina andR. saxatilis, population increase occurred in some simulations despite negative average growth rates. A model for stochastic genet dynamics was constructed by combining field data and hypothesized parameter values. Growth rate and population structure were insensitive to variation in disturbance intensity and frequency, whereas variation in recruitment affected population structure but only to a minor extent growth rate. Decreasing recruitment causes extinction of genet populations, but the time-scale for the decline is in the magnitude of centuries for initial genet populations of about 1000 individuals. Dynamics of genets in clonal plants thus incorporate processes occurring on widely different scales. Some implications of the results for models of population dynamics in long-lived clonal plants are discussed.     

Effects of intensity and duration of infection by a hemiparasitic plant, Rhinanthus serotinus, on growth and reproduction of a perennial grass, Agrostis capillaris

Arising from annual variation in parasitic plant population densities, substantial yearly changes may occur in the parasitic load of an individual perennial host. We conducted two two-year greenhouse pot experiments to examine the effects of varying intensities and duration of infection by an annual root hemiparasitic plant. Rhinanthus serotinus, on the growth and reproduction of its perennial host grass. Agrostis capillaris. In the first experiment, one host plant was growing either alone or under a load of 1 or 3 root hemiparasitic plants for one growing season, and during the next season all hosts continued their life free of hemiparasites. In the second experiment, the host plants either grew alone or were parasitised by 1 or 2 root hemiparasitic plants either during the first growing season only or during two successive seasons (the parasitic load being the same in the two seasons). In both experiments, the root hemiparasites markedly reduced the growth and reproduction of their perennial hosts. In the first experiment, the negative effects of parasites on host performance increased with the increase in intensity of parasitic infection from one to three parasites. The harmful effects of hemiparasitim were carried over to the following season; hosts parasitised during the previous season with one or three parasites produced significantly less biomass than those without parasites. In addition, hosts parasitised by three parasites during the first season produced significantly less panicles in the second season than those parasitised by one parasite and those without parasites. The second experiment showed that the production of biomass of A. capillaris during the second season was, but the production of panicles was not affected by the duration of parasitic infection. In addition, in this experiment, the second season biomass of A. capillaris depended on the intensity of infection (1 vs 2 parasites), but the production of panicles was unaffected by the number of parasites.     

Growth,yield and reproduction of dwarf tomato grown under simulated microgravity conditions

Abstract

A closed hydroponic system combined with a horizontal uniaxial clinostat has been used to grow tomato plants (Solanum lycopersicum L.) under simulated microgravity conditions. The study was carried out to evaluate the quanti-qualitative traits (growth, yield and quality) of the dwarf tomato variety ‘Micro-Tom’ grown under simulated microgravity conditions and to determine if tomato plants would complete their life cycle (‘seed-to-seed’). Morphological and growth characteristics of ‘Micro-Tom’ were modified during clinorotation treatment. The ‘Micro-Tom’ plants grown under simulated microgravity exhibited a spreading growth and an increasing of the internode length. Total fruit yield, small fruit yield, leaf area, leaf dry weight, fruit dry weight, total dry weight and shoot – root ratio were lower in the clinorotated tomato plants than those grown in the control treatment. Foliar amount of carotenoids, and chlorophyll a and b were also substantially reduced under simulated microgravity conditions. Quality parameters (total soluble solids and fruit dry matter) of tomato plants were also negatively affected by clinorotation. The number of flowers per plant was increased by 32% in clinorotated plants versus controls. Fruit setting was reduced by 46% under clinorotation, while no significant difference was recorded for the pollen fertility and the seed number in small and large fruits. Clinorotation-exposed and control seeds were used in a germination trial in order to evaluate whether the seeds so formed were viable and if subsequent generations might be obtained in microgravity. Seeds formed under simulated microgravity proved to be biologically and functionally complete (germination = 78.6%) showing that ‘Micro-Tom’ plants could realize complete ontogenesis, from seed to seed in microgravity.     

Consistent pollen nutritional intake drives bumble bee (Bombus impatiens) colony growth and reproduction across different habitats

Foraging behavior is a critical adaptation by insects to obtain appropriate nutrients from the environment for development and fitness. Bumble bees (Bombus spp.) form annual colonies which must rapidly increase their worker populations to support rearing reproductive individuals before the end of the season. Therefore, colony growth and reproduction should be dependent on the quality and quantity of pollen resources in the surrounding landscape. Our previous research found that B. impatiens foraging preferences to different plant species were shaped by pollen protein:lipid nutritional ratios (P:L), with foragers preferring pollen species with a ~5:1 P:L ratio. In this study, we placed B. impatiens colonies in three different habitats (forest, forest edge, and valley) to determine whether pollen nutritional quality collected by the colonies differed between areas that may differ in resource abundance and diversity. We found that habitat did not influence the collected pollen nutritional quality, with colonies in all three habitats collecting pollen averaging a 4:1 P:L ratio. Furthermore, there was no difference in the nutritional quality of the pollen collected by colonies that successfully reared reproductives and those that did not. We found however, that “nutritional intake,” calculated as the colony‐level intake rate of nutrient quantities (protein, lipid, and sugar), was strongly related to colony growth and reproductive output. Therefore, we conclude that B. impatiens colony performance is a function of the abundance of nutritionally appropriate floral resources in the surrounding landscape. Because we did not comprehensively evaluate the nutrition provided by the plant communities in each habitat, it remains to be determined how B. impatiens polylectic foraging strategies helps them select among the available pollen nutritional landscape in a variety of plant communities to obtain a balance of key macronutrients.     

Neighbourhood size,dispersal distance and the complex dynamics of the spatial Ricker model

Amongst the most frequently made assumptions in simple population models are that individuals interact equally with every other individual and that dispersal occurs with equal likelihood to any location. This is especially true for models of a single population (as opposed to a patchy population or metapopulation). For many species of animals and probably for all plant species these assumptions are unlikely to hold true. Here one much-studied population model—the Ricker model—is reformulated such that interactions occur only between individuals located within a certain distance of each other and dispersal distance is finite. Two alternative reformulations are presented. Results demonstrate that both limiting the interaction neighbourhood and reducing dispersal distance tend to stabilise the global population dynamics, although the extent to which this occurs depends upon the reformulation used. Spatial pattern formation is a feature of the simulated population. At lower intrinsic rates of growth (r) these patterns tend to be static, while for higher r, they are dynamic. Both the stabilisation of global dynamics and spatial pattern formation are well-described features of metapopulation models. Here, similar effects are shown to occur on a single contiguous patch of habitat.     

基于器官生物量构建植株形态的玉米虚拟模型

探讨了基于玉米器官生物量模拟其形态的方法,并应用2000年田间试验数据提取了玉米节间、叶鞘和叶片的形态构建参数。基于玉米虚拟模型生物量分配模块模拟的器官生物量积累和建立的形态构建方法与提取的参数,模拟了2001年玉米不同生长阶段的器官形态,模拟结果与田间试验数据吻合较好。应用本模型实现了玉米生长过程中植株各个器官形态变化以及植株高度、叶面积动态的模拟,并实现了植株形态的可视化。     

Alternative spatial sampling in studies of plant demography: consequences for estimates of population growth rate

Ecologists commonly use matrix models to study the population dynamics of plants. Most studies of plant demography use plot-based methods to collect data, in part, because mapped individuals are easier to relocate in subsequent surveys and survey methods can be standardized among sites. However, there is tremendous variation among studies, both in terms of plot arrangement and the total area sampled. In addition, there has been little discussion of how alternative sampling arrangements influence estimates of population growth rates (λ) calculated with matrix models. We surveyed the literature to determine what sampling designs are most used in studies of plant demography using matrix models. We then used simulations of three common sampling techniques—using a single randomly placed plot, multiple randomly placed plots, and systematically distributed plots—to evaluate how these alternative strategies influenced the precision of estimates of λ. These simulations were based on long-term demographic data collected on 13 populations of the Amazonian understory herb Heliconia acuminate (Heliconiaceae). We found that the method used to collect data did not affect the bias or precision of estimates in our system—a surprising result, since the advantage in efficiency that is gained from systematic sampling is a well-known result from sampling theory. Because the statistical advantage of systematic sampling is most evident when there is spatial structure in demographic vital rates, we attribute this result to the lack of spatially structured vital rates in our focal populations. Given the likelihood of spatial autocorrelation in most ecological systems, we advocate sampling with a systematic grid of plots in each study site, as well as that researchers ensure that enough area is sampled—both within and across sites—to encompass the range of spatial variation in plant survival, growth, and reproduction.     

A simultaneous saccharification and fermentation model for dynamic growth environments

Many mathematical models by researchers have been formulated for Saccharomyces cerevisiae which is the common yeast strain used in modern distilleries. A cybernetic model that can account for varying concentrations of glucose, ethanol and organic acids on yeast cell growth dynamics does not exist. A cybernetic model, consisting of 4 reactions and 11 metabolites simulating yeast metabolism, was developed. The effects of variables such as temperature, pH, organic acids, initial inoculum levels and initial glucose concentration were incorporated into the model. Further, substrate and product inhibitions were included. The model simulations over a range of variables agreed with hypothesized trends and to observations from other researchers. Simulations converged to expected results and exhibited continuity in predictions for all ranges of variables simulated. The cybernetic model did not exhibit instability under any conditions simulated.