Steady-state Population Density Research Articles

Modelling the Dynamics of Outbreak Species: The Case of Ditrupa arietina (O.F. Müller), Gulf of Lions, NW Mediterranean Sea

An outbreak species exhibits extreme, rapid population fluctuations that can be qualified as discrete events within a continuous dynamic. When outbreaks occur they may appear novel and disconcerting because the limiting factors of their dynamics are not readily identifiable. We present the first population hybrid dynamic model that combines continuous and discrete processes, designed to simulate marine species outbreaks. The deterministic framework was tested using the case of an unexploited benthic invertebrate species: the small, serpulid polychaete Ditrupa arietina. This species is distributed throughout the northeast Atlantic Ocean and Mediterranean Sea; it has a life cycle characterised by a pelagic dispersive larval stage, while juveniles and adults are sedentary. Sporadic reports of extremely high, variable densities (from <10 to >10,000 ind.m−2) have attracted attention from marine ecologists for a century. However, except for one decade-long field study from the Bay of Banyuls (France, Gulf of Lions, Mediterranean Sea), observations are sparse. Minimal formulations quantified the processes governing the population dynamics. Local population continuous dynamics were simulated from a size-structured model with a null immigration–emigration flux balance. The mathematical properties, based on the derived hybrid model, demonstrated the possibilities of reaching an equilibrium for the population using a single number of recruits per reproducer. Two extrapolations were made: (1) local population dynamics were simulated over 180 years using North Atlantic Oscillation indices to force recruitment variability and (2) steady-state population densities over the Gulf of Lions were calculated from a connectivity matrix in a metapopulation. The dynamics reach a macroscopic stability in both extrapolations, despite the absence of density regulating mechanisms. This ensures the persistence of D. arietina, even when strong, irregular oscillations characteristic of an outbreak species are observed. The hybrid model suggests that a macroscopic equilibrium for a population with variable recruitment conditions can only be characterised for time periods which contain several outbreak occurrences distributed over a regional scale.

COVID-19 CT image denoising algorithm based on adaptive threshold and optimized weighted median filter

CT image of COVID-19 is disturbed by impulse noise during transmission and acquisition. Aiming at the problem that the early lesions of COVID-19 are not obvious and the density is low, which is easy to confuse with noise. A median filtering algorithm based on adaptive two-stage threshold is proposed to improve the accuracy for noise detection. In the advanced stage of ground-glass lesion, the density is uneven and the boundary is unclear. It has similar gray value to the CT images of suspected COVID-19 cases such as adenovirus pneumonia and mycoplasma pneumonia (reticular shadow and strip shadow). Aiming at the problem that the traditional weighted median filter has low contrast and fuzzy boundary, an adaptive weighted median filter image denoising method based on hybrid genetic algorithm is proposed. The weighted denoising parameters can adaptively change according to the detailed information of lung lobes and ground-glass lesions, and it can adaptively match the cross and mutation probability of genetic combined with the steady-state regional population density, so as to obtain a more accurate COVID-19 denoised image with relatively few iterations. The simulation results show that the improved algorithm under different density of impulse noise is significantly better than other algorithms in peak signal-to-noise ratio (PSNR), image enhancement factor (IEF) and mean absolute error (MSE). While protecting the details of lesions, it enhances the ability of image denoising.

Beyond the pair approximation: Modeling colonization population dynamics.

The process of range expansion (colonization) is one of the basic types of biological dynamics, whereby a species grows and spreads outwards, occupying new territories. Spatial modeling of this process is naturally implemented as a stochastic cellular automaton, with individuals occupying nodes on a rectangular grid, births and deaths occurring probabilistically, and individuals only reproducing onto unoccupied neighboring spots. In this paper we derive several approximations that allow prediction of the expected range expansion dynamics, based on the reproduction and death rates. We derive several approximations, where the cellular automaton is described by a system of ordinary differential equations that preserves correlations among neighboring spots (up to a distance). This methodology allows us to develop accurate approximations of the population size and the expected spatial shape, at a fraction of the computational time required to simulate the original stochastic system. In addition, we provide simple formulas for the steady-state population densities for von Neumann and Moore neighborhoods. Finally, we derive concise approximations for the speed of range expansion in terms of the reproduction and death rates, for both types of neighborhoods. The methodology is generalizable to more complex scenarios, such as different interaction ranges and multiple-species systems.

Population dynamics of chemotrophs in anaerobic conditions where the metabolic energy acquisition per redox reaction is limited

We present a new model of microbial population growth that focuses on the acquisition of metabolic energy through chemosynthesis and how this depends on the concentration of resources and byproducts. Due to entropy effects, organisms extract the greater energy (i.e., they produce the greater amount of adenosine triphosphate) when they use resources that are abundant and generates byproducts that are rare. This effect, which we call the “abundant resource premium,” has been neglected in traditional models of microbial growth because the total metabolic energy acquisition is generally far greater than this premium. This term, however, cannot be neglected for many microbes, such as sulfate reducers, iron oxidizers, and methanogens, which live under conditions of low-energy availability. Our model showed qualitatively different behaviors from those observed in traditional microbial population growth models, such as the Monod model. For example, the steady-state population density was maximum at an intermediate resource-utilizing ability, suggesting that high substrate acquisition is not always advantageous for a microbial population when the availability of metabolic energy is low. We discuss possible implications for evolutionary and ecosystem sciences.

Pump wavelength dependence of ASE and SBS in single-frequency EYDFAs.

In this Letter, the pump wavelength dependence of the amplified spontaneous emission (ASE) and the threshold of stimulated Brillouin scattering (SBS) in a typical single-frequency continuous wave Er3+:Yb3+-codoped fiber amplifier is investigated numerically. The Er3+:Yb3+ system is modeled as coupled two- and three-level systems, linked by a Förster resonance energy transfer process and described by the corresponding rate equations. The evolution of the pump and signal power along the fiber is modeled by differential equations, taking into account the steady-state population densities. Since the absorption at 976nm can exceed the Yb3+-to-Er3+ energy transfer rate in high-power operation, unsaturated gain at around 1.0μm can generate excessive ASE. Off-peak pumping with commercially available pump diodes at 915 or 940nm spatially distributes the energy over a longer distance. For the studied amplifier configuration, energy transfer bottlenecking is prevented without the onset of SBS.

A stabilized microbial ecosystem of self-limiting bacteria using synthetic quorum-regulated lysis.

Microbial ecologists are increasingly turning to small, synthesized ecosystems1–5 as a reductionist tool to probe the complexity of native microbiomes6,7. Concurrently, synthetic biologists have gone from single-cell gene circuits8–11 to controlling whole populations using intercellular signaling12–16. The intersection of these fields is giving rise to new approaches in waste recycling,17 industrial fermentation18, bioremediation19, and human health16,20. These applications share a common challenge7 well known in classical ecology21,22; stability of an ecosystem cannot arise without mechanisms that prohibit the faster growing species from eliminating the slower. Here, we combine orthogonal quorum sensing systems and a population control circuit with diverse self-limiting growth dynamics in order to engineer two ‘ortholysis’ circuits capable of maintaining a stable co-culture of metabolically competitive strains in microfluidic devices. While no successful co-cultures are observed in a two-strain ecology without synthetic population control, the ‘ortholysis’ design dramatically increases the co-culture rate from 0% to approximately 80%. Agent-based and deterministic modeling reveal that our system can be adjusted to yield different dynamics, including phase-shifted, anti-phase or synchronized oscillations as well as stable steady-state population densities. The ‘ortholysis’ approach establishes a paradigm for constructing synthetic ecologies by developing stable communities of competitive microbes without the need for engineered codependency.

Striated populations in disordered environments with advection

Growth in static and controlled environments such as a Petri dish can be used to study the spatial population dynamics of microorganisms. However, natural populations such as marine microbes experience fluid advection and often grow up in heterogeneous environments. We investigate a generalized Fisher-Kolmogorov-Petrovsky-Piscounov (FKPP) equation describing single species population subject to a constant flow field and quenched random spatially inhomogeneous growth rates with a fertile overall growth condition. We analytically and numerically demonstrate that the non-equilibrium steady-state population density develops a flow-driven striation pattern. The striations are highly asymmetric with a longitudinal correlation length that diverges linearly with the flow speed and a transverse correlation length that approaches a finite velocity-independent value. Linear response theory is developed to study the statistics of the steady states. Theoretical predictions show excellent agreement with the numerical steady states of the generalized FKPP equation obtained from Lattice Boltzmann simulations. These findings suggest that, although the growth disorder can be spatially uncorrelated, correlated population structures with striations emerge naturally at sufficiently strong advection.

Energy-Transfer-Upconversion Models, Their Applicability and Breakdown in the Presence of Spectroscopically Distinct Ion Classes: A Case Study in Amorphous Al2O3:Er3+

The influence of energy migration and energy-transfer upconversion (ETU) among neighboring Er3+ ions on luminescence decay and steady-state population densities in Al2O3:Er3+ thin films is investigated by means of photoluminescence decay measurements under quasi-CW excitation. The experimental results are analyzed by several models. As expected from the basic physical assumptions made by these models, only Zubenko’s microscopic model provides good agreement with the experimental data, while other donor−acceptor treatments found in the literature are unsuccessful and the macroscopic rateequation approach provides meaningful results only when misinterpreting the intrinsic lifetime as a free fit parameter. Furthermore, a fast quenching process induced by, e.g., active ion pairs and clusters, undesired impurities, or host material defects such as voids, that is not revealed by any particular signature in the luminescence decay curves because of negligible emission by the quenched ions under quasi-CW excitation, is verified by pump-absorption experiments. This quenching process strongly affects device performance as an amplifier. Since Zubenko’s microscopic model treats all ions equally, it is unable to describe a second, spectroscopically distinct class of ions involving a fast quenching process. The model is extended to take into account the fraction of quenched ions. This approach finally leads to excellent agreement between the luminescence-decay, pump-absorption, and small-signal-gain experiments within the frame of a single theoretical description.

Space-propagation model of Tm-doped fiber laser

In this paper, we propose the space-propagation model for the Tm-doped fiber laser. This model builds the space-propagation equations for the population densities at different energy levels as well as the pump and laser powers. Compared to the conventional models, this model has significant advantage in reducing the computing time significantly when the steady-state population density rate equations cannot be solved analytically. On the basis of the model, the power characteristic and optimization for the Tm-doped fiber laser are investigated. Excellent agreements are achieved between the numerical simulation and experimental results.

Modeling population patterns of chemotactic bacteria in homogeneous porous media

The spatio-temporal distribution of subsurface microorganisms determines their efficiency in providing essential ecosystem services such as the degradation of organic matter, the remineralization of carbon and nitrogen, or the remediation of anthropogenic contaminants. Populations of motile, chemotactic bacteria have been shown to be capable of pattern formation even in the absence of environmental heterogeneities. Focusing on the water saturated domain of the subsurface ( e.g., aquatic sediments, porous aquifers), we analyze this innate capability of bacterial populations in an idealized model of a homogeneous, saturated porous medium. Considering a linear array of connected, identical microhabitats populated by motile, chemotactic bacterial cells, we identify prerequisites for pattern formation, analyze types of patterns, and assess their impact on substrate utilization. In our model, substrate supplied to the microhabitats facilitates bacterial growth, and microbial cells can migrate between neighboring microhabitats due to (i) random motility, (ii) chemotaxis towards substrate, and (iii) self-attraction. A precondition for inhomogeneous population patterns is analytically derived, stating that patterns are possible if the self-attraction exceeds a threshold defined by the random motility and the steady state population density in the microhabitats. An individual-based implementation of the model shows that static and dynamic population patterns can unfold. Degradation efficiency is highest for homogeneous bacterial distributions and decreases as pattern formation commences. If during biostimulation efforts the carrying capacity of the microhabitats is successively increased, simulation results show that degradation efficiency can unexpectedly decrease when the pattern formation threshold is crossed.

A negative feedback loop involving small RNAs accelerates Vibrio cholerae’s transition out of quorum-sensing mode

Quorum sensing is a cell-to-cell communication process that allows bacteria to measure their population numbers and to synchronously alter gene expression in response to changes in cell population density. At the core of the Vibrio cholerae quorum-sensing signal transduction pathway lie four redundant small RNAs (sRNAs), named the Quorum Regulatory RNAs (Qrr1-4). Expression of qrr1-4 is cell population density-dependent due to a requirement for the quorum-sensing controlled phosphorylated response regulator LuxO-P, which is abundant only at low cell population density. When expressed, Qrr1-4 repress translation of HapR, the "master" quorum-sensing transcription factor. Here we show a negative feedback loop in which HapR activates transcription of the qrr genes, which indirectly leads to hapR repression. Efficient feedback activation of the qrr genes requires the simultaneous presence of LuxO-P (present only at low cell population density) and HapR (present only at high cell population density). For this reason, the feedback loop does not influence quorum sensing at steady-state low or high cell population density. However, LuxO-P and HapR are simultaneously present immediately following the switch from high to low cell density conditions. In this state, the HapR feedback loop dramatically accelerates V. cholerae's transition from the high to the low cell density mode.

THE IMPORTANCE OF FUNCTIONAL FORM IN OPTIMAL CONTROL SOLUTIONS OF PROBLEMS IN POPULATION DYNAMICS

Optimal control theory is finding increased application in both theoretical and applied ecology, and it is a central element of adaptive resource management. One of the steps in an adaptive management process is to develop alternative models of system dynamics, models that are all reasonable in light of available data, but that differ substan- tially in their implications for optimal control of the resource. We explored how the form of the recruitment and survival functions in a general population model for ducks affected the patterns in the optimal harvest strategy, using a combination of analytical, numerical, and simulation techniques. We compared three relationships between recruitment and pop- ulation density (linear, exponential, and hyperbolic) and three relationships between survival during the nonharvest season and population density (constant, logistic, and one related to the compensatory harvest mortality hypothesis). We found that the form of the component functions had a dramatic influence on the optimal harvest strategy and the ultimate equi- librium state of the system. For instance, while it is commonly assumed that a compensatory hypothesis leads to higher optimal harvest rates than an additive hypothesis, we found this to depend on the form of the recruitment function, in part because of differences in the optimal steady-state population density. This work has strong direct consequences for those developing alternative models to describe harvested systems, but it is relevant to a larger class of problems applying optimal control at the population level. Often, different func- tional forms will not be statistically distinguishable in the range of the data. Nevertheless, differences between the functions outside the range of the data can have an important impact on the optimal harvest strategy. Thus, development of alternative models by iden- tifying a single functional form, then choosing different parameter combinations from extremes on the likelihood profile may end up producing alternatives that do not differ as importantly as if different functional forms had been used. We recommend that biological knowledge be used to bracket a range of possible functional forms, and robustness of conclusions be checked over this range.

Generalized model for all-optical light modulation in bacteriorhodopsin

We present a generalized model for the photochemical cycle of bacteriorhodopsin (bR) protein molecule. Rate equations have been solved for the detailed light-induced processes in bR for its nine states: B→K↔L↔MI→MII↔N↔O↔P→Q→B. The complete steady-state intensity-induced population densities in various states of the molecule have been computed to obtain a general, exact, and analytical expression for the nonlinear absorption coefficient for multiple modulation pump laser beams. All-optical light modulation of different probe laser beam transmissions by intensity induced population changes due to one and two modulation laser beams has been analyzed. The proposed model has been shown to accurately model experimental results.

Dynamics of the output of heavily Tm-doped double-clad silica fiber lasers

The relaxation oscillations that are present in the output of a high-power free-running diode-pumped Tm-doped silica fiber laser are characterized and modeled. The laser operates on the 3H4→3H6 quasi-three-level transition and operates efficiently from ∼1.9 to ∼2.0 µm. From the measurements of the 3F4→3H4 fluorescence after 1.98-µm pumping of a separate, heavily Tm-doped silica fiber, it is established that the 3H4, 3H4→3H6, 3F4 upconversion process is significant in heavily Tm-doped silica fibers. This process causes the saturable absorption that is indicated by the presence of the relaxation oscillations. A detailed theoretical model that describes the ion-pair dynamics relevant to the Tm-doped silica system is presented. Equations for the steady-state intracavity photon density and for the steady-state population densities of the isolated and paired ions are derived. A linear stability analysis and numerical analysis are also carried out. It is established that, for large emission-to-absorption cross-section ratios that are relevant to Tm-doped silica and for pump rates for which stable output is predicted, the oscillations are weakly damped before the steady state is reached. Best agreement between the experimental and model results is achieved when all the Tm3+ ions within the present fiber are considered paired.

POPULATION DYNAMICS OF LIGHT-LIMITED PHYTOPLANKTON: MICROCOSM EXPERIMENTS

This paper investigates the extent to which the predictions of an elementary model for light-limited growth are matched by laboratory experiments with light-limited phytoplankton. The model and experiments link the population dynamics of phytoplankton species with changes in the light gradient caused by phytoplankton shading. The model predicts that a phytoplankton population should continue to grow until, at steady state, the light intensity at the bottom of the water column equals its critical light intensity. The experimental results were in good agreement with the theoretical predictions: (1) the steady-state population density increased with an increase of the incident light intensity, (2) the steady-state population density (per unit volume) was inversely proportional to mixing depth, (3) the steady-state population size (per unit area) decreased linearly with mixing depth, (4) the critical light intensity decreased with an increase of the incident light intensity, (5) the critical light intensity was approximately the same at each mixing depth, and (6) the time courses predicted by the model were in line with the observed time courses of population density and light penetration. Implications for phytoplankton ecology and aquatic production biology are discussed.

CRYSTALLIZATION KINETICS AND PRODUCT PURITY OF α-GLUTAMIC ACID CRYSTAL

Abstract A continuous mixed-suspension mixed-product removal lpar;CMSMPR) crystallizer was used to study the crystallization kinetics and product purity of glutamic acid crystal in pure solution and impure solution with L-phenylanaline as the impurity. Under the assumption that the crystal growth rate was a function of crystal size, the population balance equation was solved to give the crystal growth and nucleation rates by use of the steady-state population density data. The crystal growth and nucleation rates were suppressed by the presence of impurity. The impurity contents in the crystal products, which were analyzed by a HPLC pre-column method, were found to be related to crystal size, supersaturation, and impurity concentration of solution

Sensitivity analysis of a simple model food chain

Parameter sensitivities of steady-state population densities of a simple Lotka-Volterra food chain are studied analytically. It is shown that a high percentage of parameter sensitivities is zero, and that the distribution of zero sensitivities along the food chain exhibits a characteristically regular pattern. The pattern implies that the sensitivity of a given population with respect to parameters of another population depends non-monotonically upon the distance of the two populations within the chain. Moreover, the complete sensitivity structure depends drastically on whether the total number of populations in the food chain is odd or even. The sensitivity pattern is shown to be identical to that of the inverse of the community matrix of the food chain. These results provide characterisation of the model food chain in addition to that in terms of steady states and their stability properties.

Saha decrements and collisional-radiative recombination and ionization coefficients for a nonequilibrium oxygen plasma

Using a time-dependent approach, a collisional-radiative model is developed for an oxygen plasma. Effective recombination and ionization coefficients are calculated for two specific cases, optically thin and optically thick in bound-bound u.v. radiation. The steady-state population densities for neutral and ionic states are presented in terms of their deviations from Saha equilibrium predictions. These results show the approach of the plasma to a state of local thermodynamic equilibrium (LTE) as a function of electron temperature and density. The computations are for temperatures between 1.0 and 3.0 eV and electron densities between 10 16 and 10 19 cm -3.

Saha decrements and collisional-radiative recombination and ionization coefficients for a nonequilibrium nitrogen plasma

Using a time-dependent approach, a collisional-radiative model is developed for a nitrogen plasma. Effective recombination and ionization coefficients are calculated for optically thin and optically thick cases in bound-bound u.v. radiation. The steady-state population densities for neutral and ionic states are presented in terms of their deviations from Saha equilibrium predictions. These results show the approach of the plasma to local thermodynamic equilibrium (LTE) as a function of electron temperature and density. The computations focus on temperatures between 1.0 and 3.0 eV and electron densities between 10 16 and 10 19 cm −3.

A method for the regulation of microbial population density during continuous culture at high growth rates.

A method for the continuous culture of microorganisms is described which employs growth-dependent pH changes to control the rate of addition of fresh medium to a culture vessel. The apparatus (the "phauxostat") supports, at constant pH, long-term continuous culture at rates near or at the maximum of which the organisms are capable. The buffering capacity of the inflowing medium determines the steady-state population density of the culture, but the rate of growth is independent of the buffering capacity. The fundamental theory of operation is tested and some basic parameters of growth are estimated using Escherichia coli B growing continuously in media containing glucose, glycerol or DL-lactate.