Probable effects of algal bloom on the growth ofPhragmites australis (Cav.) Trin. ex Steud.

The effects of blue-green algal blooms on an emergent reed plant,Phragmites australis (Cav.) Trin. ex Steud., were investigated in a eutrophic lake in central Japan. The plants showed conspicuous withering of bottom leaves in spring of 1982, after an early occurrence of the bloom. In June, the plants in the area of algal infestation had about half the shoot length and dry weight of normalP. australis without the algal infestation. Reductions in water transparency, dissolved oxygen in bottom water and redox potentials of surface soil corresponded to the presence of algal bloom and plant damage.     

Fermentation process diagnosis using a mathematical model

Summary Intriguing physiology of a solvent-producing strain ofClostridium acetobutylicum led to the synthesis of a mathematical model of the acetone-butanol fermentation process. The model presented is capable of describing the process dynamics and the culture behavior during a standard and a substandard acetone-butanol fermentation. In addition to the process kinetic parameters, the model includes the culture physiological parameters, such as the cellular membrane permeability and the number of membrane sites for active tansport of sugar. Computer process simulation studies for different culture conditions used the model, and quantitatively pointed out the importance of selected culture parameters that characterize the cell membrane behaviour and play an important role in the control of solvent synthesis by the cell. The theoretical predictions by the new model were confirmed by experimental determination of the cellular membrane permeability.     

Simulation of field data by a basic three-dimensional model of interactive root growth

Published field data for lupins grown in a deep sandy soil in the wheatbelt of south-western Australia were used to test the predictive ability of a model of three-dimensional root growth. The model has the capacity to simulate the growth of individual root sections in response to the supply and demand for water and nitrate. N mineralisation was not modelled explicitly, but was accounted for through the use of a seasonally variable mineralisation input derived from the field data. Simulated nitrogen and water contents and root length densities in the soil profile agreed well with observed profiles, although all were slightly under-predicted. A sensitivity analysis revealed that model predictions were most sensitive to the drained upper limit values (v/v) and the mineralisation rates (gN m^–3 s^–1) incorporated as external inputs to the model, along with the unit rate of N₂ fixation (mol nodule^–1 s^–1) and unit root growth rates (m mol^–1 s^–1) which are physiological parameters previously calibrated for lupins. The amount of nitrate leached was predicted well. Spatial plots of nitrate leaching were a close inverse of the root length density plots, with the highest nitrate leaching below the inter-plant zones, and the least nitrate leaching directly below each plant. These results suggest that the root distribution of a legume species such as lupin can have an effect on the leaching of nitrate to depth. It may thus be possible to reduce the total amount of nitrate leached under lupin crops by investigating factors such as the spatial deployment of roots, planting densities and intercropping.     

A mathematical study of a two-regional population growth model

The paper provides a mathematical study of a model of urban dynamics, adjusting to an ecological model proposed by Lotka and Volterra. The model is a system of two first-order non-linear ordinary differential equations. The study proposed here completes the original proof by using the main tools such as a Lyapunov function.     

A mathematical framework for estimating pathogen transmission fitness and inoculum size using data from a competitive mixtures animal model

We present a method to measure the relative transmissibility (transmission fitness) of one strain of a pathogen compared to another. The model is applied to data from competitive mixtures experiments in which animals are co-infected with a mixture of two strains. We observe the mixture in each animal over time and over multiple generations of transmission. We use data from influenza experiments in ferrets to demonstrate the approach. Assessment of the relative transmissibility between two strains of influenza is important in at least three contexts: 1) Within the human population antigenically novel strains of influenza arise and compete for susceptible hosts. 2) During a pandemic event, a novel sub-type of influenza competes with the existing seasonal strain(s). The unfolding epidemiological dynamics are dependent upon both the population's susceptibility profile and the inherent transmissibility of the novel strain compared to the existing strain(s). 3) Neuraminidase inhibitors (NAIs), while providing significant potential to reduce transmission of influenza, exert selective pressure on the virus and so promote the emergence of drug-resistant strains. Any adverse outcome due to selection and subsequent spread of an NAI-resistant strain is exquisitely dependent upon the transmission fitness of that strain. Measurement of the transmission fitness of two competing strains of influenza is thus of critical importance in determining the likely time-course and epidemiology of an influenza outbreak, or the potential impact of an intervention measure such as NAI distribution. The mathematical framework introduced here also provides an estimate for the size of the transmitted inoculum. We demonstrate the framework's behaviour using data from ferret transmission studies, and through simulation suggest how to optimise experimental design for assessment of transmissibility. The method introduced here for assessment of mixed transmission events has applicability beyond influenza, to other viral and bacterial pathogens.     

Response ofPhragmites australis,Glyceria maxima,andTypha latifolia to additions of piggery sewage in a flooded sand culture

One-year-old clones ofPhragmites australis, Glyceria maxima, andTypha latifolia were subjected to different doses of piggery sewage added in flooded sand cultures for one growing season.Phragmites responded to increasing sewage doses by an increase in the shoot biomass and a decrease in root porosity and carbohydrate levels in rhizomes;Glyceria responded by a decrease in the biomass and depth penetration of the root system, and carbohydrate levels in rhizomes. In contrast,Typha increased both root porosity and carbohydrate levels in rhizomes. These findings are discussed in relationship to plant performance in sewage-polluted wetlands.     

Subconductance states of Cx30 gap junction channels: data from transfected HeLa cells versus data from a mathematical model

Human HeLa cells expressing mouse connexin30 were used to study the electrical properties of gap junction channel substates. Experiments were performed on cell pairs using a dual voltage-clamp method. Single-channel currents revealed discrete levels attributable to a main state, a residual state, and five substates interposed, suggesting the operation of six subgates provided by the six connexins of a gap junction hemichannel. Substate conductances, gamma(j,substate), were unevenly distributed between the main-state and the residual-state conductance (gamma(j,main state) = 141 pS, gamma(j,residual state) = 21 pS). Activation of the first subgate reduced the channel conductance by approximately 30%, and activation of subsequent subgates resulted in conductance decrements of 10-15% each. Current transitions between the states were fast (<2 ms). Substate events were usually demarcated by transitions from and back to the main state; transitions among substates were rare. Hence, subgates are recruited simultaneously rather than sequentially. The incidence of substate events was larger at larger gradients of V(j). Frequency and duration of substate events increased with increasing number of synchronously activated subgates. Our mathematical model, which describes the operation of gap junction channels, was expanded to include channel substates. Based on the established V(j)-sensitivity of gamma(j,main state) and gamma(j,residual state), the simulation yielded unique functions gamma(j,substate) = f(V(j)) for each substate. Hence, the spacing of subconductance levels between the channel main state and residual state were uneven and characteristic for each V(j).     

Methane flux in Peltandra virginica (Araceae) wetlands: comparison of field data with a mathematical model

We present a mathematical model of the diffusive flux of methane through Peltandra virginica. Data on the diurnal changes in both the petiolar [CH₄] gradient and the values of the radial bulk exchange coefficient, E_r, are entirely consistent with this model and the assertion that changes in stomatal conductance regulate the rate of methane efflux in P. virginica. The differences between the values of E_r calculated for daytime and nighttime conditions are -40% for the submerged condition and -54% for the emergent condition. The axial diffusivity of CH₄ through the petiole of P. virginica is estimated in vitro to be 0.771 cm² min^-1. Using our model, we estimate the equilibrium rate of methane efflux under daytime (97 ng CH₄ min ¹ petiole^-1) and nighttime (65 ng CH₄ min^-1 petiole^-1) emergent conditions. Numerical solutions of the model equations in the time domain offer a way of providing a dynamic model of the gas exchange responses of P. virginica to changing environmental conditions.     

Analysis of a mathematical model for the growth of tumors

 In this paper we study a recently proposed model for the growth of a nonnecrotic, vascularized tumor. The model is in the form of a free-boundary problem whereby the tumor grows (or shrinks) due to cell proliferation or death according to the level of a diffusing nutrient concentration. The tumor is assumed to be spherically symmetric, and its boundary is an unknown function r=s(t). We concentrate on the case where at the boundary of the tumor the birth rate of cells exceeds their death rate, a necessary condition for the existence of a unique stationary solution with radius r=R ₀ (which depends on the various parameters of the problem). Denoting by c the quotient of the diffusion time scale to the tumor doubling time scale, so that c is small, we rigorously prove that (i) lim inf _t→∞ s(t)>0, i.e. once engendered, tumors persist in time. Indeed, we further show that (ii) If c is sufficiently small then s(t)→R ₀ exponentially fast as t→∞, i.e. the steady state solution is globally asymptotically stable. Further, (iii) If c is not “sufficiently small” but is smaller than some constant γ determined explicitly by the parameters of the problem, then lim sup _t→∞ s(t)<∞; if however c is “somewhat” larger than γ then generally s(t) does not remain bounded and, in fact, s(t)→∞ exponentially fast as t→∞. Received: 25 February 1998 / Revised version: 30 April 1998     

The age and growth of perch (Perca fluviatilis L.) in two Scottish lochs

This study is concerned with the age and growth of perch ( Perca fluviatilis L. ) in two contrasting Scottish lochs-the Dubh Lochan and Loch Lomond. Age and back-calculated growth were determined from annual rings in the opercular bones, and during the 2-year project 470 perch from the Dubh Lochan and 796 from Loch Lomond were examined. Growth in length in the two lochs, though similar for the first 2 years, differed thereafter, the average length at 8 years in the Dubh Lochan being less than 15 cm, that in Loch Lomond more than 23 cm at the same age. In neither locality did the growth of perch follow the Von Bertalanffy growth formula. Reasons for differential growth rates are discussed and comparisons made with the growth of perch in other waters in Europe and North America.     

A mathematical model of tumour-induced capillary growth

The corneal limbal vessels of an animal host respond to the presence of a source of Tumour Angiogenesis Factor (TAF) implanted in the cornea by the formation of new capillaries which grow towards the source. This neovasculature can be easily seen and studied and this paper describes a mathematical model of some of the important features of the growth. The model includes the diffusion of TAF, the formation of sprouts from pre-existing vessels and models the movement of these sprouts to form new capillaries as a chemotactic response to the presence of TAF. Numerical results are produced for various values of the parameters which characterize the model and it is suggested that the model might form the framework for further theoretical work on related phenomena such as wound healing or to develop strategies for the investigation of anti-angiogenesis.     

A simplified mathematical model of tumor growth

A one-dimensional model of tumor tissue growth is presented in which the source of mitotic inhibitor is nonuniformly distributed within the tissue (in contrast to many earlier models). As a result, stable and unstable regimes of growth become significantly modified from the uniform-source case, indicating that the model, schematic though it is, is very sensitive to the type of source term assumed, and this has implications for experimental and theoretical comparisons in more realistic geometries.     

Describing force-induced bone growth and adaptation by a mathematical model

This work proposes a mathematical model that qualitative describes the process of mechanically force-induced bone growth and adaptation. The mathematical model includes osteocytes as the key interfacing layer connecting tissue, cellular and molecular signaling levels. Specifically, in the presence of an increase in the mechanical stimuli, osteocytes respond by mechano-transduction releasing the local factors nitric oxide (NO) and prostaglandin E(2) (PGE(2)). These local factors act as the signaling recruitment signals for bone cells progenitors and influence the coupling activity among osteoblasts and osteoclasts during the process of bone remodeling. The model is in agreement with qualitative observations found in the literature concerning the process of bone adaptation and the cellular interactions during a local bone remodeling cycle induced by mechanical stimulation.     

Observations on the colonization of a young polder area in the netherlands with special reference to the clonal expansion ofPhragmites australis

In 1968, the polder Zuidelijk Flevoland was reclaimed in the Netherlands. Observations on species succession were made during a period of seven years in an area later known as the nature reserve Oostvaardersplassen. Directly after reclamation, a large number of plant species were recruited. Here, only the dynamics of the three dominant species will be discussed, i.e. the annual mudflat speciesSenecio congestus, and the long-lived emergent macrophytesTypha latifolia andPhragmites australis. Small differences in elevation had a large impact on seedling recruitment. Overall,S. congestus dominated in the first year after reclamation, andT. latifolia prevailed during the second and third year. Thereafter,P. australis became dominant, despite fewer seedlings. In the first three years after reclamation, clones ofP. australis grew very slowly, afterwards they showed a constant expansion rate of ca. 4 m/yr. However, close to pools waterfowl grazing slowed down the expansion of clones. The observed spatial and temporal variation in the colonization of this young polder area can be explained by species differences in life history traits, resource capture, as well as in the susceptibility to stem-boring insects and waterfowl grazing.     

A mathematical model for the determination of steady-state cardiolipin remodeling mechanisms using lipidomic data

Technical advances in lipidomic analysis have generated tremendous amounts of quantitative lipid molecular species data, whose value has not been fully explored. We describe a novel computational method to infer mechanisms of de novo lipid synthesis and remodeling from lipidomic data. We focus on the mitochondrial-specific lipid cardiolipin (CL), a polyglycerol phospholipid with four acyl chains. The lengths and degree of unsaturation of these acyl chains vary across CL molecules, and regulation of these differences is important for mitochondrial energy metabolism. We developed a novel mathematical approach to determine mechanisms controlling the steady-state distribution of acyl chain combinations in CL . We analyzed mitochondrial lipids from 18 types of steady-state samples, each with at least 3 replicates, from mouse brain, heart, lung, liver, tumor cells, and tumors grown in vitro. Using a mathematical model for the CL remodeling mechanisms and a maximum likelihood approach to infer parameters, we found that for most samples the four chain positions have an independent and identical distribution, indicating they are remodeled by the same processes. Furthermore, for most brain samples and liver, the distribution of acyl chains is well-fit by a simple linear combination of the pools of acyl chains in phosphatidylcholine (PC), phosphatidylethanolamine (PE), and phosphatidylglycerol (PG). This suggests that headgroup chemistry is the key determinant of acyl donation into CL, with chain length/saturation less important. This canonical remodeling behavior appears damaged in some tumor samples, which display a consistent excess of CL molecules having particular masses. For heart and lung, the "proportional incorporation" assumption is not adequate to explain the CL distribution, suggesting additional acyl CoA-dependent remodeling that is chain-type specific. Our findings indicate that CL remodeling processes can be described by a small set of quantitative relationships, and that bioinformatic approaches can help determine these processes from high-throughput lipidomic data.     

A model to predict the thermal reaction norm for the embryo growth rate from field data

The incubation of eggs is strongly influenced by temperature as observed in all species studied to date. For example, incubation duration, sexual phenotype, growth, and performances in many vertebrate hatchlings are affected by incubation temperature. Yet it is very difficult to predict temperature effect based on the temperature within a field nest, as temperature varies throughout incubation. Previous works used egg incubation at constant temperatures in the laboratory to evaluate the dependency of growtProd. Type: FTPh rate on temperature. However, generating such data is time consuming and not always feasible due to logistical and legislative constraints. This paper therefore presents a methodology to extract the thermal reaction norm for the embryo growth rate directly from a time series of incubation temperatures recorded within natural nests. This methodology was successfully applied to the nests of the marine turtle Caretta caretta incubated on Dalyan Beach in Turkey, although it can also be used for any egg-laying species, with some of its limitations being discussed in the paper. Knowledge about embryo growth patterns is also important when determining the thermosensitive period for species with temperature-dependent sex determination. Indeed, in this case, sexual phenotype is sensitive to temperature only during this window of embryonic development.     

A mathematical model of a crocodilian population using delay-differential equations

The crocodilia have multiple interesting characteristics that affect their population dynamics. They are among several reptile species which exhibit temperature-dependent sex determination (TSD) in which the temperature of egg incubation determines the sex of the hatchlings. Their life parameters, specifically birth and death rates, exhibit strong age-dependence. We develop delay-differential equation (DDE) models describing the evolution of a crocodilian population. In using the delay formulation, we are able to account for both the TSD and the age-dependence of the life parameters while maintaining some analytical tractability. In our single-delay model we also find an equilibrium point and prove its local asymptotic stability. We numerically solve the different models and investigate the effects of multiple delays on the age structure of the population as well as the sex ratio of the population. For all models we obtain very strong agreement with the age structure of crocodilian population data as reported in Smith and Webb (Aust. Wild. Res. 12, 541-554, 1985). We also obtain reasonable values for the sex ratio of the simulated population.