Modelling the growth of Trichoderma virens with limited sampling of digital images

AIMS: Using limited digital image sampling, a model of fungal growth in soil that considers both hyphal production and lysis was constructed for two strains of Trichoderma virens over a range of four temperatures. MATERIALS AND METHODS: A growth model was developed by fitting the radial cross sectional data with a modified form of the Ratkowsky equation to determine maximum growth rate and a modified Arrhenius equation to determine maximal rate of decrease in area covered by mycelia. The parameters obtained from a combined equation were then verified by using the data obtained from the whole colony to determine the appropriateness of the model. CONCLUSIONS: Using a limited data set and a combination of the Ratkowsky and Arrhenius equations, the mycelial coverage of the T. virens colony was determined, relating microscopic hyphal growth to macroscopic colony growth. This model was sufficiently robust to predict growth across four temperatures for a genetically modified and wild-type strain of T. virens. SIGNIFICANCE AND IMPACT OF STUDY: By using simple assumptions for the increase and eventual decline in fungal growth on a resource-limited medium, this model constructs an initial framework onto which additional parameters such as nutrient consumption could be incorporated for prediction of fungal growth.     

On the lag phase and initial decline of microbial growth curves

The lag phase is generally thought to be a period during which the cells adjust to a new environment before the onset of exponential growth. Characterizing the lag phase in microbial growth curves has importance in food sciences, environmental sciences, bioremediation and in understanding basic cellular processes. The goal of this work is to extend the analysis of cell growth curves and to better estimate the duration of the lag phase. A non-autonomous model is presented that includes actively duplicating cells and two subclasses of non-duplicating cells. The growth curves depend on the growth and death rate of these three subpopulations and on the initial proportion of each. A deterministic and a stochastic model are both developed and give the same results. A notable feature of the model is the decline of cells during the early stage of the growth curve, and the range of parameters when this decline occurs is identified. A limited growth model is also presented that accounts for the lag, exponential growth and stationary phase of microbial growth curves.     

Effect of the population heterogeneity on growth behavior and its estimation

Different types of the Logistic model are constructed based on a simple assumption that the microbial populations are all composed of homogeneous members and consequently, the condition of design for the initial value of these models has to be rather limited in the case of N(t ₀)=N ₀. Therefore, these models cannot distinguish the dynamic behavior of the populations possessing the same N ₀ from heterogeneous phases. In fact, only a certain ratio of the cells in a population is dividing at any moment during growth progress, termed as θ, and thus, dN / dt not only depends on N, but also on θ. So θ is a necessary element for the condition design of the initial value. Unfortunately, this idea has long been neglected in widely used growth models. However, combining together the two factors (N ₀ and θ) into the initial value often leads to the complexity in the mathematical solution. This difficulty can be overcome by using instantaneous rates (V _inst) to express growth progress. Previous studies in our laboratory suggested that the V _inst curve of the bacterial populations all showed a Guassian function shape and thus, the different growth phases can be reasonably distinguished. In the present study, the Gaussian distribution function was transformed approximately into an analytical form ( Y_i = ae^{[ - 0.5( fracx_i - x₀ b )2 ]} Y_i = alpha e^{left[ { - 0.5left( {frac{{x_i - x_0 }}{b}} right)^2 } right]} ) that can be conveniently used to evaluate the growth parameters and in this way the intrinsic growth behavior of a bacterial species growing in heterogeneous phases can be estimated. In addition, a new method has been proposed, in this case, the lag period and the double time for a bacterial population can also be reasonably evaluated. This approach proposed could thus be expected to reveal important insight of bacterial population growth. Some aspects in modeling population growth are also discussed.     

The limited importance of size-asymmetric light competition and growth of pioneer species in early secondary forest succession in Vietnam

It is generally believed that asymmetric competition for light plays a predominant role in determining the course of succession by increasing size inequalities between plants. Size-related growth is the product of size-related light capture and light-use efficiency (LUE). We have used a canopy model to calculate light capture and photosynthetic rates of pioneer species in sequential vegetation stages of a young secondary forest stand. Growth of the same saplings was followed in time as succession proceeded. Photosynthetic rate per unit plant mass (P(mass): mol C g(-1) day(-1)), a proxy for plant growth, was calculated as the product of light capture efficiency [Phi(mass): mol photosynthetic photon flux density (PPFD) g(-1) day(-1)] and LUE (mol C mol PPFD(-1)). Species showed different morphologies and photosynthetic characteristics, but their light-capturing and light-use efficiencies, and thus P (mass), did not differ much. This was also observed in the field: plant growth was not size-asymmetric. The size hierarchy that was present from the very early beginning of succession remained for at least the first 5 years. We conclude, therefore, that in slow-growing regenerating vegetation stands, the importance of asymmetric competition for light and growth can be much less than is often assumed.     

一类自催化反应扩散模型正解的唯一性与稳定性

主要考虑了一类三分子自催化反应扩散系统．在齐次Dirichlet和Robin边界条件下,当反应率c适当小,系统没有共存态;当c适当大,系统至少有一个共存态;当c充分大,系统有唯一渐近稳定的共存态．特别地,在一维空间上共存态是唯一的．在齐次Neumann边界条件下系统是一个简单系统．     

Generalized aphid population growth models with immigration and cumulative-size dependent dynamics

Mechanistic models in which the per-capita death rate of a population is proportional to cumulative past size have been shown to describe adequately the population size curves for a number of aphid species. Such previous cumulative-sized based models have not included immigration. The inclusion of immigration is suggested biologically as local aphid populations are initiated by migration of winged aphids and as reproduction is temperature-dependent. This paper investigates two models with constant immigration, one with continuous immigration and the other with restricted immigration. Cases of the latter are relatively simple to fit to data. The results from these two immigration models are compared for data sets on the mustard aphid in India.     

Plant population growth and competition in a light gradient: a mathematical model of canopy partitioning

Can a difference in the heights at which plants place their leaves, a pattern we call canopy partitioning, make it possible for two competing plant species to coexist? To find out, we examine a model of clonal plants living in a nonseasonal environment that relates the dynamical behavior and competitive abilities of plant populations to the structural and functional features of the plants that form them. This examination emphasizes whole plant performance in the vertical light gradient caused by self-shading. This first of three related papers formulates a prototype single species Canopy Structure Model from biological first principles and shows how all plant properties work together to determine population persistence and equilibrium abundance. Population persistence is favored, and equilibrium abundance is increased, by high irradiance, high maximum photosynthesis rate, rapid saturation of the photosynthetic response to increased irradiance, low tissue respiration rate, small amounts of stem and root tissue necessary to support the needs of leaves, and low density of leaf, stem, and root tissues. In particular, equilibrium abundance decreases as mean leaf height increases because of the increased cost of manufacturing and maintaining stem tissue. All conclusions arise from this formulation by straightforward analysis. The argument concludes by stating this formulation's straightforward extension, called a Canopy Partitioning Model, to two competing species.     

Size-asymmetric competition and size-asymmetric growth in a spatially explicit zone-of-influence model of plant competition

Size-asymmetric competition among plants is usually defined as resource pre-emption by larger individuals, but it is usually observed and measured as a disproportionate size advantage in the growth of larger individuals in crowded populations (“size-asymmetric growth”). We investigated the relationship between size-asymmetric competition and size-asymmetric growth in a spatially explicit, individual-based plant competition model based on overlapping zones of influence (ZOI). The ZOI of each plant is modeled as a circle, growing in two dimensions. The size asymmetry of competition is reflected in the rules for dividing up the overlapping areas. We grew simulated populations with different degrees of size-asymmetric competition and at different densities and analyzed the size dependency of individual growth by fitting coupled growth functions to individuals. The relationship between size and growth within the populations was summarized with a parameter that measures the size asymmetry of growth. Complete competitive symmetry (equal division of contested resources) at the local level results in a very slight size asymmetry in growth. This slight size asymmetry of growth did not increase with increasing density. Increased density resulted in increased growth asymmetry when resource competition at the local level was size asymmetric to any degree. Size-asymmetric growth can be strong evidence that competitive mechanisms are at least partially size asymmetric, but the degree of size-asymmetric growth is influenced by the intensity as well as the mode of competition. Intuitive concepts of size-asymmetric competition among individuals in spatial and nonspatial contexts are very different.     

Tree growth and competition in a post-logging Quercus mongolica forest on Mt. Sobaek, South Korea

Secondary woodlands in South Korea cover most mountains from low to middle elevations. While general patterns of forest succession are well understood, little is known about mechanisms of stand recovery after disturbance. We examined the spatio-temporal variations in establishment, growth, size inequality, and mode of competition among trees in a 50-year-old post-logging Quercus mongolica-dominated stand. We further compared the growth and stem allometry of single trees, presumably of seed origin, with multi-stemmed trees resprouting from stumps. Q. mongolica formed the upper canopy 16–22 m tall, 88.3% of total stand basal area, and 36.2% of total stem density, with most trees established during the first post-logging decade (51.2% were resprouts). During the first three decades, the Q. mongolica recruits grew exponentially, and disproportionately more in diameter than few older reserved trees left after the last cutting. This substantially decreased size inequality. The reverse trend was observed from 1994 to 2004: larger trees grow more, indicating an increasing asymmetry of competition for light. Neighborhood analysis revealed that when target trees had more or larger neighbors, their exponential phase of growth was reduced and maximum size was decreased. After the 50 years of stand development, more than 70% of Q. mongolica showed growth decline as a result of competitive stress, and mortality was about 30%, concentrated in smaller size classes. Compared to single stems, resprouts within clones do not seem to compete less asymmetric as might be expected based on studies of clonal herbaceous plants and physiological integration within genets. As Q. mongolica was also negatively affected by competition from woody species currently prevailing in the lower tree stratum (Tilia amurensis, Acer mono, Fraxinus rhynchophylla, Acer pseudosieboldianum), we predict the stand will become increasingly dominated by these more shade-tolerant trees.     

Bioclimate and growth history affect beech lifespan in the Italian Alps and Apennines

When site factors reduce growth rates, tree lifespan tends to increase. This study investigates processes leading to such inverse relationship in Fagus sylvatica stands distributed along two elevation gradients, with an emphasis on climatic response, suppression periods, and growth trends. Dendrochronological records from old‐growth beech populations sampled at different elevations within two different bioclimatic regions (Alps vs. Apennines), were used to investigate factors that control tree lifespan. Differences between old‐growth (12) and nearby managed (15) stands were used to assess effects of silvicultural practices on maximum age. Logging reduced tree lifespan not only by removing older trees, but also by reducing the number of years beech individuals spent in the shaded understory. Tree lifespan and growth rates were affected by climate (spring–summer temperature) and were inversely related to one another along elevation gradients. The greatest lifespan was observed in old‐growth high‐mountain populations, and was related not only to slower growth due to a shorter growing season, but also to multidecadal periods of growth suppression during the initial development stages in the understory (i.e., slower growth rates at the youngest cambial ages). Past unfavorable climatic periods (in this case, the Little Ice Age) also helped increase tree lifespan. Using a linear model, we estimated a reduction in beech lifespan of 23 ± 5 years for each degree of warming. Basal area increment of trees with the maximum observed lifespan showed an increasing trend over time. Because growth of old (>300 years) trees has increased in the Alps, while it has recently declined in the Apennines, different bioclimatic regions can have opposite responses to global climatic change. In the next decades, if warming continues, beech lifespan could be reduced in the Alps by faster growth and in the Apennines by drought‐induced mortality.     

Stature of sub-arctic birch in relation to growth rate, lifespan and tree form

BACKGROUND AND AIMS: Sub-arctic mountain birch Betula pubescens var. pumila communities in the North Atlantic region are of variable stature, ranging from prostrate scrubs to forests with trees up to 12 m high. Four hypotheses were tested, relating growth and population characteristics of sub-arctic birch woodland and scrub to tree stature; i.e. the variable stature of birch woods is due to differences in (1) the mean growth rate; (2) the age-related patterns of growth rate; (3) the life expectancy of stems; or (4) the tree form. Methods: A stratified random sample of 300 birch trees was drawn from the total population of indigenous birch woodlands and scrub in Iceland, yielding 286 valid sample genets. The population was divided into three sub-populations with dominant trees 0-2, 2-4 and 4-12 m tall, referred to as birch scrub, birch scrub-woodland and birch forest, respectively. KEY RESULTS: Trees in the scrub population were of more contorted growth form than birch in the scrub-woodland and forest populations. Mean growth rates, mean age and median life expectancies increased significantly with sub-population of greater tree stature. At the population level, annual increment and longevity of birch stems was apparently interrelated as the stems in vigorously growing birch sub-populations had a longer life expectancy than those of slower growth. However, no difference was observed between sub-populations in age-related patterns of extension growth rate. CONCLUSIONS: The results were consistent with hypotheses (1), (3) and (4), but hypothesis (2) was rejected. Hence, mountain birch of more vigorous growth attains a greater stature than birch of lesser increment due to faster extension growth rate and a longer lifespan. In addition, the more contorted stem form of scrub populations contributes to their low stature.     

The impact of dietary restriction, intermittent feeding and compensatory growth on reproductive investment and lifespan in a short-lived fish

While dietary restriction usually increases lifespan, an intermittent feeding regime, where periods of deprivation alternate with times when food is available, has been found to reduce lifespan in some studies but prolong it in others. We suggest that these disparities arise because in some situations lifespan is reduced by the costs of catch-up growth (following the deprivation) and reproductive investment, a factor that has rarely been measured in studies of lifespan. Using three-spined sticklebacks, we show for the first time that while animals subjected to an intermittent feeding regime can grow as large as continuously fed controls that receive the same total amount of food, and can maintain reproductive investment, they have a shorter lifespan. Furthermore, we show that this reduction in lifespan is linked to rapid skeletal growth rate and is due to an increase in the instantaneous risk of mortality rather than in the rate of senescence. By contrast, dietary restriction caused a reduction in reproductive investment in females but no corresponding increase in longevity. This suggests that in short-lived species where reproduction is size dependent, selection pressures may lead to an increase in intrinsic mortality risk when resources are diverted from somatic maintenance to both growth and reproductive investment.     

Spatial competition with Lactococcus lactis in mixed-species continuous-flow biofilms inhibits Listeria monocytogenes growth

Surfaces in industrial settings provide a home for resident biofilms that are likely to interact with the attachment, growth and survival of pathogens such as Listeria monocytogenes. Experimental results have indicated that L. monocytogenes cells were inhibited by the presence of a model resident flora (Lactococcus lactis) in dual-species continuous flow-biofilms, and are spatially restricted to the lower biofilm layers. Using a new, simplified individual-based model (IBM) that simulates bacterial cell growth in a three-dimensional space, the spatial arrangements of the two species were reconstructed and their cell counts successfully predicted. This model showed that the difference in generation times between L. monocytogenes and L. lactis cells during the initial stages of dual-species biofilm formation was probably responsible for the species spatialization observed and the subsequent inhibition of growth of the pathogen.     

Modeling linear and variable growth in phosphate limited suspension cultures of Opium poppy

In examining the growth kinetics of cell suspensions of opium poppy (Papaver somniferum), the increase in biomass with time was observed to be linear over the entire batch growth period of up to 20 days. Although batch growth profiles were reproducible utilizing the same inoculum, growth rates varied tremendously when experiments were inoculated with cells from different flasks. Both of these phenomena are difficult to explain with conventional batch growth models. In a series of a experiments, phosphate was determined to be the growth-rate-limiting substrate. By expressing growth rate in terms of the intracellular reserves of phosphorus, a growth model which expresses kinetics in terms of the intracellular phosphorus contents of the cells is shown to predict both linear growth character and inoculum dependent variability in growth. The stationary phase phosphate content of seven plant suspension cultures of different plant species was found to be comparable to phosphorus levels of phosphate-starved poppy cells, which suggests that phosphate limitation may be common for plant tissue culture. The applicability of this model to other biological systems which display similar batch growth patterns when subjected to inorganic nutrient deprivation is discussed.     

凉拌豆制品中单核细胞增生李斯特菌生长模型建立的研究

单核细胞增生李斯特菌是凉拌豆制品中检出率较高的一种致病菌。本研究考察了温度(4℃、15℃、25℃、30℃和37℃)对凉拌豆制品中单核细胞增生李斯特菌生长的影响,并采用SGompertz和SLogistic模型对不同温度下单核细胞增生李斯特菌的生长数据进行拟合;在此基础上,以拟合度(R2)、准确因子(A_f)和偏差因子(B_f)为指标,比较并建立了凉拌豆制品中单核细胞增生李斯特菌的二级生长模型。结果表明,SGompertz模型能更好的拟合凉拌豆制品中单核细胞增生李斯特菌在不同温度下的生长数据,平方根模型能够较准确地预测凉拌豆制品中单核细胞增生李斯特菌的生长状况,因此依次选择此两种模型作为单核细胞增生李斯特菌在凉拌豆制品中的一级和二级生长模型,且模型具有可靠性。研究结果可为凉拌豆制品中单核细胞增生李斯特菌的定量风险评估提供依据。     

Iron uptake and iron limited growth of Escherichia coli K-12

Cells of Escherichia coli K-12 could grow aerobically at an iron concentration as low as 0.05 M without any of the known iron ionophores present. The growth rate increased between 0.05 and 2 M iron. Supplementation with the iron ligands ferrichrome and citrate resulted in optimal growth already at 0.05 M iron. Under certain conditions iron uptake preceded growth of cells by more than an hour. During logarithmic growth the rate of iron uptake matched the growth rate. The radioactive tracer method revealed a cellular iron content of 4 nmol/mg dry weight.After consumption of the iron in the medium cells continued to grow with high rate for 1–2 generations. The iron uptake activity was increased during iron starvation.     

Biological and mathematical description of the growth pattern of Fusarium oxysporum in a sterilized soil

Abstract The population dynamics of 4 F. oxysporum strains incubated in sterilized soil have been studied for 35 days. Enumeration of fungal propagules was carried out by the soil dilution plate technique. The qualitative variations of the populations were viewed by epifluorescent microscopy after staining the fungal propagules in soil with Calcofluor. A logistic model was used to describe population dynamic parameters. The predominant mode of growth of F. oxysporum in sterilized soil involved abundant production of conidia during the exponential phase. The increase of the propagules resulting from mycelial development during the lag phase was not taken into account by the logistic model. By determining the density of the population at the end of the lag phase, growth parameters of different F. oxysporum strains have been identified allowing the saprophytic competence of each strain to be characterized.