scholarly journals Empirically based minimalistic model for representing seasonal phytoplankton dynamics

2020 ◽  
Vol 640 ◽  
pp. 63-77
Author(s):  
SH Piltz ◽  
PG Hjorth ◽  
Ø Varpe
Keyword(s):  
Differential Equation ◽  
Primary Production ◽  
Equation Model ◽  
Trophic Levels ◽  
Model Parameters ◽  
Division Rate ◽  
The North ◽  
Approximate Bayesian ◽  
Relative Change

Supported by chl a satellite data in the North Atlantic (and phytoplankton division rates computed from that data), the disturbance-recovery hypothesis for the initiation of phytoplankton blooms posits that the change in chl a concentration is proportional to the relative change in the phytoplankton division rate. We used this hypothesis, introduced by Behrenfeld, as a principal model assumption and constructed a non-autonomous ordinary differential equation model for seasonally varying chl a concentrations. Our quantitative comparison between model simulations and in situ measurements of chl a and primary production collected from a Swedish fjord was 2-fold: first, using approximate Bayesian computations, we found distributions of values for the 3 model parameters that best described the chl a data. Then, we validated our model by comparing the simulated (not fitted) division rate to the division rate determined from the data. Our minimalistic model was able to capture (1) the yearly trend in the chl a concentration, (2) the pattern of growth and decline in the phytoplankton division rate, and (3) the decreasing trend in the relative change of the division rate exhibited in the data for several individual years. Moreover, the modeling efficiency was positive (between 0.3 and 0.9 with an average of 0.63) for all 11 yr included in this study. We conclude that the change in chl a concentration being proportional to the relative change in the division rate is a possible explanation for the bloom dynamics in the Gullmar fjord. In addition, our work provides a simple and empirically based differential equation for representing yearly dynamics of primary production, e.g. for generating ecological hypotheses using models of other trophic levels.

A stochastic differential equation model of diurnal cortisol patterns

2001 ◽  
Vol 280 (3) ◽  
pp. E450-E461 ◽  
Author(s):  
Emery N. Brown ◽  
Patricia M. Meehan ◽  
Arthur P. Dempster
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Plasma Cortisol ◽  
Equation Model ◽  
Plasma Cortisol Level ◽  
Model Parameters ◽  
Kinetic Properties ◽  
Simulation Studies ◽  
Physiological Factors ◽  
Diurnal Patterns

Circadian modulation of episodic bursts is recognized as the normal physiological pattern of diurnal variation in plasma cortisol levels. The primary physiological factors underlying these diurnal patterns are the ultradian timing of secretory events, circadian modulation of the amplitude of secretory events, infusion of the hormone from the adrenal gland into the plasma, and clearance of the hormone from the plasma by the liver. Each measured plasma cortisol level has an error arising from the cortisol immunoassay. We demonstrate that all of these three physiological principles can be succinctly summarized in a single stochastic differential equation plus measurement error model and show that physiologically consistent ranges of the model parameters can be determined from published reports. We summarize the model parameters in terms of the multivariate Gaussian probability density and establish the plausibility of the model with a series of simulation studies. Our framework makes possible a sensitivity analysis in which all model parameters are allowed to vary simultaneously. The model offers an approach for simultaneously representing cortisol's ultradian, circadian, and kinetic properties. Our modeling paradigm provides a framework for simulation studies and data analysis that should be readily adaptable to the analysis of other endocrine hormone systems.

Combined analyses reveal environmentally driven changes in the North Sea ecosystem and raise questions regarding what makes an ecosystem model’s performance credible?

2014 ◽  
Vol 71 (1) ◽  
pp. 31-46 ◽  
Author(s):  
Steven Mackinson
Keyword(s):  
Primary Production ◽  
North Sea ◽  
Ecosystem Model ◽  
Ecosystem Approach ◽  
Trophic Levels ◽  
Fish Stock ◽  
Supporting Evidence ◽  
Sea Temperature ◽  
The North ◽  
The North Sea

When an ecosystem model of the North Sea is calibrated to data from multiple trophic levels, the model estimated the primary production required to support the food web correlates temporally with observed changes in sea temperature and nutrient levels, supporting evidence from empirical analyses. However, a different result is given from an alternative calibration using fish stock data only. The inference taken from the emergent primary production – temperature relationship and empirical data are that, on balance, there is stronger overall evidence to support the calibration constrained at multiple trophic levels. Two important implications of the findings are (i) that the relative importance of fishing and environmental effects is likely to be interpreted differently depending on the calibration approach and (ii) the contrasting model calibrations would give different responses to fishing policies. It raises questions regarding how to judge the performance (and credibility) of an ecosystem model and the critical importance of conducting empirical and modelling analyses in parallel. Adopting a combined approach to ecosystem modelling is an important step in the pursuit of operational and defensible tools to support the ecosystem approach to management.

scholarly journals Detection of regional scale sea-to-air oxygen emission related to spring bloom near Japan by using in-situ measurements of the atmospheric oxygen/nitrogen ratio

2008 ◽  
Vol 8 (12) ◽  
pp. 3325-3335 ◽  
Author(s):  
H. Yamagishi ◽  
Y. Tohjima ◽  
H. Mukai ◽  
K. Sasaoka
Keyword(s):  
Primary Production ◽  
North Pacific ◽  
Spring Bloom ◽  
Atmospheric Oxygen ◽  
Regional Scale ◽  
Japan Sea ◽  
In Situ Monitoring ◽  
Back Trajectory ◽  
The North

Abstract. We have been carrying out in-situ monitoring of atmospheric O2/N2 ratio at Cape Ochi-ishi (COI; 43°10' N, 145°30' E) in the northern part of Japan since March 2005 by using a modified gas chromatography/thermal conductivity detector (GC/TCD). The standard deviation of the O2/N2 ratio is estimated to be about ±14 per meg (≈3 ppm) with intervals of 10 minutes. Thus, the in-situ measurement system has a 1σ precision of ± 6 per meg (≈1.2 ppm) for one-hour mean O2/N2 ratio. Atmospheric potential oxygen (APO≈O2+1.1 CO2), which is conserved with respect to terrestrial photosynthesis and respiration but reflects changes in air-sea O2 and CO2 fluxes, shows large variabilities from April to early July 2005. Distribution of satellite-derived marine primary production indicates occurrences of strong bloom in the Japan Sea and the latitudinal band between 30° and 40° N in the western North Pacific in April and in the Okhotsk Sea and northeastern region near Hokkaido Island in the North Pacific in June. Back trajectory analysis of air masses indicates that high values of APO, which last for several hours or several days, can be attributed to the oxygen emission associated with the spring bloom of active primary production.

scholarly journals Primary Production, an Index of Climate Change in the Ocean: Satellite-Based Estimates over Two Decades

2020 ◽  
Vol 12 (5) ◽  
pp. 826 ◽  
Author(s):  
Gemma Kulk ◽  
Trevor Platt ◽  
James Dingle ◽  
Thomas Jackson ◽  
Bror F. Jönsson ◽  
...  
Keyword(s):  
Primary Production ◽  
Environmental Variables ◽  
Linear Trend ◽  
In Situ Measurements ◽  
Marine Phytoplankton ◽  
Initial Slope ◽  
Model Parameters ◽  
Photosynthetic Parameters ◽  
Photosynthetic Response

Primary production by marine phytoplankton is one of the largest fluxes of carbon on our planet. In the past few decades, considerable progress has been made in estimating global primary production at high spatial and temporal scales by combining in situ measurements of primary production with remote-sensing observations of phytoplankton biomass. One of the major challenges in this approach lies in the assignment of the appropriate model parameters that define the photosynthetic response of phytoplankton to the light field. In the present study, a global database of in situ measurements of photosynthesis versus irradiance (P-I) parameters and a 20-year record of climate quality satellite observations were used to assess global primary production and its variability with seasons and locations as well as between years. In addition, the sensitivity of the computed primary production to potential changes in the photosynthetic response of phytoplankton cells under changing environmental conditions was investigated. Global annual primary production varied from 38.8 to 42.1 Gt C yr − 1 over the period of 1998–2018. Inter-annual changes in global primary production did not follow a linear trend, and regional differences in the magnitude and direction of change in primary production were observed. Trends in primary production followed directly from changes in chlorophyll-a and were related to changes in the physico-chemical conditions of the water column due to inter-annual and multidecadal climate oscillations. Moreover, the sensitivity analysis in which P-I parameters were adjusted by ±1 standard deviation showed the importance of accurately assigning photosynthetic parameters in global and regional calculations of primary production. The assimilation number of the P-I curve showed strong relationships with environmental variables such as temperature and had a practically one-to-one relationship with the magnitude of change in primary production. In the future, such empirical relationships could potentially be used for a more dynamic assignment of photosynthetic rates in the estimation of global primary production. Relationships between the initial slope of the P-I curve and environmental variables were more elusive.

scholarly journals Daily to annual net primary production in the North Sea determined using autonomous underwater gliders and satellite Earth observation

2021 ◽  
Author(s):  
Benjamin Loveday ◽  
Timothy Smyth ◽  
Anıl Akpinar ◽  
Tom Hull ◽  
Mark Inall ◽  
...  
Keyword(s):  
Time Series ◽  
Primary Production ◽  
North Sea ◽  
Large Scale ◽  
Net Primary Production ◽  
Earth Observation ◽  
Small Scale ◽  
The North ◽  
The North Sea

Abstract. Shelf-seas play a key role in both the global carbon cycle and coastal marine ecosystems through the drawn-down and fixing of carbon, as measured through phytoplankton net primary production (NPP). Measuring NPP in situ, and extrapolating this to the local, regional and global scale presents challenges however because of limitations with the techniques utilised (e.g. radiocarbon isotopes), data sparsity and the inherent biogeochemical heterogeneity of coastal and open-shelf waters. Here, we introduce a powerful new technique based on the synergistic use of in situ glider profiles and satellite Earth Observation measurements which can be implemented in a real-time or delayed mode system. We apply this system to a fleet of gliders successively deployed over a 19-month time-frame in the North Sea, generating an unprecedented fine scale time-series of NPP in the region (Loveday and Smyth, 2020). At the large-scale, this time-series gives close agreement with existing satellite-based estimates of NPP for the region and previous in situ estimates. What has not been elucidated before is the high-frequency, small-scale, depth-resolved variability associated with bloom phenology, mesoscale phenomena and mixed layer dynamics.

A Numerical Model for Determining Integral Primary Production and its Application to Lake Michigan

1973 ◽  
Vol 30 (10) ◽  
pp. 1447-1468 ◽  
Author(s):  
Everett J. Fee
Keyword(s):  
Primary Production ◽  
Lake Michigan ◽  
Model Parameters ◽  
Time Interval ◽  
Actual Distribution ◽  
In Situ Experiments ◽  
Routine Basis ◽  
Computer Based ◽  
Large Water

A computer-based model for determining production by phytoplankton, integrated over depth and over an arbitrary time interval, is described. The solution incorporates light inhibition and uses the actual distribution of surface irradiance for the time interval of interest, since it is not possible to predict the detailed nature of cloudiness. Statistical procedures for estimating the model parameters from experimental data relating the rate of carbon uptake to irradiance are described. The model is applied to data collected from May 27, 1970 through February 3, 1971 from Lake Michigan.Integral primary production was bimodal at inshore and offshore stations with minimum production in midsummer and winter. There was great daily variability of integral production, due solely to variation of light. From this it is inferred that occasional in situ measurements would give a very poor knowledge of true seasonal trends.The model output was verified by performing two in situ experiments. The agreement was better than 95% on both dates. The model makes it possible to estimate integral primary production on a routine basis in large water bodies with well-mixed photic zones.

CMEMS Primary production from satellite remote sensing: spatial and temporal evolution and comparison with other products

2020 ◽  
Author(s):  
Marine Bretagnon ◽  
Philippe Garnesson ◽  
Antoine Mangin
Keyword(s):  
Primary Production ◽  
Carbon Sink ◽  
Global Scale ◽  
Trophic Levels ◽  
Economic Resources ◽  
In Situ Data ◽  
Basin Scale ◽  
Carbon Pump ◽  
Satellite Estimate

<p>Half of the global primary production is produced in the ocean by phytoplankton and the reaction of photosynthesis. For the marine environment, primary production is at the basis for the food web, by the supply of energy for higher trophic levels. Monitor primary production appears therefore to be a guideline to reach sustainable fisheries. In addition to its role on the trophic web, primary production is also important for its role on CO<sub>2</sub> fluxes. Indeed, while phytoplankton creates matter from nutrients and CO<sub>2</sub>. The produced matter can be grazed by higher trophic levels or sink towards sediment. Amount of carbon sequestrated and exported out of the productive layer give some clues efficiencies of the oceanic biological carbon pump. Primary production is therefore important not only for economic resources, but also for climatic studies, to investigate if the ocean is a carbon sink or sources.</p><p>A strategy of algorithm validation / inter-comparison was used as part as the CMEMS project to identify most accurate primary production algorithm among the most used in the literature.</p><p>Primary production validation is based on the commonly used comparison with in situ data, as well as the frequency and the intensity of the annual bloom in different basin. Inter-comparison with model were performed at the basin scale of the Mediterranean Sea to assess the robustness and the consistency of different type of estimates.</p><p>Satellite estimate of primary production, as proposed by CMEMS, give now access to an archive of 21 years for user community, to investigate evolution of primary production at the global scale or in specific basin.</p><p> </p>

scholarly journals Evaluation of the Number of Visits to Chinese Medical Institutions Using a Logistic Differential Equation Model

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Xiaoxia Zhao ◽  
Wei Li ◽  
Yanyang Wang ◽  
Lihong Jiang
Keyword(s):  
Differential Equation ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Equation Model ◽  
Positive Equilibrium ◽  
Model Parameters ◽  
Unknown Parameters ◽  
Differential Equation Model ◽  
Number Of Visits ◽  
Positive Equilibrium Point

In this study, we established a two-dimensional logistic differential equation model to study the number of visits in Chinese PHCIs and hospitals based on the behavior of patients. We determine the model's equilibrium points and analyze their stability and then use China medical services data to fit the unknown parameters of the model. Finally, the sensitivity of model parameters is evaluated to determine the parameters that are susceptible to influence the system. The results indicate that the system corresponds to the zero-equilibrium point, the boundary equilibrium point, and the positive equilibrium point under different parameter conditions. We found that, in order to substantially increase visits to PHCIs, efforts should be made to improve PHCI comprehensive capacity and maximum service capacity.

A Bayes Regularized Ordinary Differential Equation Model for the Inference of Gene Regulatory Networks

2010 ◽  
pp. 139-168
Author(s):  
Nicole Radde ◽  
Lars Kaderali
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Regulatory Networks ◽  
Quantitative Description ◽  
Simulated Data ◽  
Equation Model ◽  
Model Parameters ◽  
Ordinary Differential Equation Model ◽  
Differential Equation Model ◽  
Stochastic Framework

Differential equation models provide a detailed, quantitative description of transcription regulatory networks. However, due to the large number of model parameters, they are usually applicable to small networks only, with at most a few dozen genes. Moreover, they are not well suited to deal with noisy data. In this chapter, we show how to circumvent these limitations by integrating an ordinary differential equation model into a stochastic framework. The resulting model is then embedded into a Bayesian learning approach. We integrate the-biologically motivated-expectation of sparse connectivity in the network into the inference process using a specifically defined prior distribution on model parameters. The approach is evaluated on simulated data and a dataset of the transcriptional network governing the yeast cell cycle.

scholarly journals Calibrating models of cancer invasion: parameter estimation using approximate Bayesian computation and gradient matching

2021 ◽  
Vol 8 (6) ◽  
pp. 202237
Author(s):  
Yunchen Xiao ◽  
Len Thomas ◽  
Mark A. J. Chaplain
Keyword(s):  
Measurement Error ◽  
Approximate Bayesian Computation ◽  
Additive Model ◽  
Simulated Data ◽  
Cancer Invasion ◽  
Enzyme Concentration ◽  
Equation Model ◽  
Model Parameters ◽  
Bayesian Computation ◽  
Approximate Bayesian

We present two different methods to estimate parameters within a partial differential equation model of cancer invasion. The model describes the spatio-temporal evolution of three variables—tumour cell density, extracellular matrix density and matrix degrading enzyme concentration—in a one-dimensional tissue domain. The first method is a likelihood-free approach associated with approximate Bayesian computation; the second is a two-stage gradient matching method based on smoothing the data with a generalized additive model (GAM) and matching gradients from the GAM to those from the model. Both methods performed well on simulated data. To increase realism, additionally we tested the gradient matching scheme with simulated measurement error and found that the ability to estimate some model parameters deteriorated rapidly as measurement error increased.

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