Solving Differential Equations in R

Soetaert, Karline; Cash, J. R.; Mazzia, Francesca

doi:10.1007/978-3-642-28070-2

Cited by 348 publications

(347 citation statements)

References 1 publication

(3 reference statements)

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“…In our model, we represent the stroma and mitochondria as a single volume assuming a mitochondria-to-stroma volume ratio of 0.03 m 3 m 23 (Tholen and Zhu, 2011). the R library deSolve (Soetaert et al, 2010). Specifically, the diffusive flux of CO 2 through the stomatal boundaries, intercellular airspace, and mesophyll cells was described by:…”

Section: Leaf Geometry Materials Properties and Boundary Conditionsmentioning

confidence: 99%

Excess Diffuse Light Absorption in Upper Mesophyll Limits CO₂ Drawdown and Depresses Photosynthesis

et al. 2017

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Section: Leaf Geometry Materials Properties and Boundary Conditionsmentioning

confidence: 99%

Excess Diffuse Light Absorption in Upper Mesophyll Limits CO₂ Drawdown and Depresses Photosynthesis

et al. 2017

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“…Simulations were performed with the deSolve package (ver. 1.10.8; Soetaert et al 2010), using the lsoda adaptive solver. After simulation, the last 5,000 time units were retained and split into two time series of 2,500 time units each.…”

Section: Analysis Of Ecological Resiliencementioning

confidence: 99%

Nonhierarchical Dispersal Promotes Stability and Resilience in a Tritrophic Metacommunity

Pedersen

Marleau

Granados

et al. 2016

The American Naturalist

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Community interactions (e.g., predation, competition) can be characterized by two factors: their strengths and how they are structured between and within species. Both factors play a role in determining community dynamics. In addition to trophic interactions, dispersal acts as an interaction between separate populations. As with other interactions, the structure of dispersal can affect the stability of a system. However, the primary structure that has been studied in consumer-resource models has been hierarchical dispersal, where between-patch dispersal rates increase with trophic level. Here we use analytical, numerical, and simulation approaches on a two-patch, three-species metacommunity model to investigate the relationship between structure and community stability and resilience. We show that metacommunity stability is greater in systems with both weak and strong dispersal rates. Our system is stabilized by the formation of patterns when predators disperse frequently and herbivores disperse rarely, and via asynchrony when both predators and herbivores disperse infrequently. Our results show how interaction strengths within both trophic and spatial networks shape metacommunity stability.

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“…The liquid in the abomasum then emptied at a constant fractional rate. Ordinary differential equations were solved using the package deSolve in the R software (Soetaert et al, 2010) and parameters of the model (x: proportion of the milk replacer provided via the bucket that entered in the rumen owing to leakage during drinking and constant fractional emptying rates from the rumen and the abomasum) were estimated for each calf to minimize the sum of squared differences between actual and predicted AMV (Nelder and Mead, 1965). Volumes of the contents of the rumen and abomasum before feeding were based on volumes measured at slaughter in Experiment 3 and equaled 9300 and 100 ml, respectively for Experiment 2 and 10 000 and 100 ml, respectively, for Experiment 3.…”

Section: Calculationsmentioning

confidence: 99%

Estimation of milk leakage into the rumen of milk-fed calves through an indirect and repeatable method

Labussière

Berends

Gilbert

et al. 2014

Animal

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In milk-fed calves, quantification of the milk that enters the rumen (ruminal milk volume, RMV) because of malfunction of the esophageal groove reflex may explain part of the variability observed between animals in their growth performance. The RMV can directly be quantified by adding an indigestible marker to the diet and measuring its recovery in the rumen at slaughter, but this technique cannot be repeated in time in the same animal. The objective of the study was to evaluate three indirect methods for estimating RMV. The first method was based on the assumption that ruminal drinking delays and limits acetaminophen appearance in blood after ingestion of milk supplemented with acetaminophen. The second method was based on a negative linear relationship between RMV and urinary recovery of non-metabolizable monosaccharides (3-O-methylglucose, L-rhamnose and D-xylose) added to the milk, owing to rumen fermentation. In the third method, RMV was calculated as the difference between total milk intake and the increase in abomasal milk volume (AMV) at feeding, measured through ultrasonography shortly after feeding, or estimated from the mathematical extrapolation of AMV to feeding time, based on consecutive measurements. These methods were tested in three experiments where calves (n = 22, 10 and 13) were bucket fed or partly tube fed (i.e. by inserting milk replacer into the rumen via a tube to mimic ruminal drinking). In addition, Co-EDTA and Cr-EDTA were used as an indigestible marker in one experiment to trace bucket-fed or tube-fed milk replacer, respectively, to measure RMV. The relationship between AMV measured by ultrasonography and AMV measured at slaughter improved when kinetics of AMV were extrapolated to the time of slaughter by mathematical modeling (error between predicted and measured AMV equaled 0.49 l). With this technique, RMV during feeding averaged 17% and 24% of intake in Experiments 2 and 3, respectively. Plasma acetaminophen kinetics and recovery of non-metabolizable monosaccharides in urine were partly associated with ruminal drinking, but these techniques are not considered quantitatively accurate without further information of rumen degradation and absorption. The recovery of indigestible marker measured at slaughter gave a quantitative estimate of RMV (2% in Experiment 3), but improper measurement of emptying rate of fluid from the rumen may lead to underestimation. In conclusion, measuring changes in AMV by ultrasonography, in response to milk feeding, was the most promising indirect method to quantify RMV in veal calves.

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Solving Differential Equations in R

Cited by 348 publications

References 1 publication

Excess Diffuse Light Absorption in Upper Mesophyll Limits CO₂ Drawdown and Depresses Photosynthesis

Excess Diffuse Light Absorption in Upper Mesophyll Limits CO₂ Drawdown and Depresses Photosynthesis

Nonhierarchical Dispersal Promotes Stability and Resilience in a Tritrophic Metacommunity

Estimation of milk leakage into the rumen of milk-fed calves through an indirect and repeatable method

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Solving Differential Equations in R

Cited by 348 publications

References 1 publication

Excess Diffuse Light Absorption in Upper Mesophyll Limits CO2 Drawdown and Depresses Photosynthesis

Excess Diffuse Light Absorption in Upper Mesophyll Limits CO2 Drawdown and Depresses Photosynthesis

Nonhierarchical Dispersal Promotes Stability and Resilience in a Tritrophic Metacommunity

Estimation of milk leakage into the rumen of milk-fed calves through an indirect and repeatable method

Contact Info

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Excess Diffuse Light Absorption in Upper Mesophyll Limits CO₂ Drawdown and Depresses Photosynthesis

Excess Diffuse Light Absorption in Upper Mesophyll Limits CO₂ Drawdown and Depresses Photosynthesis