The document presents an argument that affinity is a superior metric to half-saturation constant (Ks) for describing nutrient uptake rates. It shows that affinity (a) and the Michaelis-Menten constant (Ks) are mathematically related through the maximum uptake rate (Vmax), and that using affinity removes trade-offs seen when using Ks. Plots of uptake rates using the affinity-based and Michaelis-Menten equations show that the affinity formulation is less sensitive to changes in Vmax, improving parameter tuning. Data transformed from a previous study to use affinity rather than Ks shows all data points falling on a straight line with no trade-off, in contrast to the original analysis. The document concludes K
Affinity: the meaningful trait-based alternative to the half-saturation constantLanimal
1) The document discusses two common equations used to model nutrient uptake rates: the affinity-based equation and the Michaelis-Menten/Monod equation.
2) While the equations appear different, they actually describe the same curve relationship between uptake rate and nutrient concentration.
3) The key difference is that the affinity-based equation defines competitive ability using the parameter "a", whereas the Michaelis-Menten equation uses the "Ks" parameter. However, "a" and "Ks" are mathematically related.
Apresentação do professor Pedro Grande, da seção UFRGS do Instituto Nacional de Engenharia de Superfície. Palestra convidada do Simpósio Engenharia de Superfície do X Encontro da SBPMAT. Realizada no dia 26 de setembro de 2011 em Gramado (RS).
Phylogeny and uncertainty in analyses of life spanOwen Jones
This document summarizes a study that analyzed lifespan data for over 200 bird species while accounting for various issues with the data. The study developed a state-space regression model that uses Markov chain Monte Carlo methods to simultaneously estimate coefficients, phylogenetic signal, true lifespans accounting for censoring and truncation in the data, and the degree of sample size effects. The results showed that the maximum observed lifespan data from the British Trust for Ornithology underestimates lifespan for many species, with the degree of underestimation increasing with greater reproductive effort.
Death and uncertainty: Bayesian modeling of the association between life span...Owen Jones
This document summarizes a study that used Bayesian modeling to analyze the relationship between lifespan and reproductive investment in birds while accounting for phylogenetic relationships and data issues. The study developed a state-space model that estimates coefficients, phylogenetic signal, true responses, and error using MCMC. The model found lifespan is moderately associated with body weight and reproductive effort. It also found BTO data underestimates lifespan for many species and that the method of phylogenetic correction is important.
Study of Metadynamic Recrystallization Phenomena in Coarse Grained Nb Microal...Pello Uranga
This study examines metadynamic recrystallization in coarse-grained Nb microalloyed austenite steel. There is a transition between static and metadynamic recrystallization between the critical strain εc and transition strain εT = 2.2εc. Below εc only static recrystallization occurs. Between εc and εT both static and metadynamic recrystallization contribute to softening. Above εT only metadynamic recrystallization occurs. A new model was developed that considers the contributions of both static and metadynamic recrystallization between εc and εT. The model predictions matched experimental validations
This document provides an overview of regression analysis and the steps involved in building a regression model to predict property values. It discusses the history of regression, uses of regression, and key components like the dependent and independent variables. The document walks through exploring the data, specifying the model, running regression, and interpreting the results. It shows how adding additional relevant variables like size, land size, age, and quality can improve the predictive power of the model. Transforming categorical variables is also discussed. The goal is to create a model that explains as much of the variation in sales prices as possible.
TALAT Lecture 3802: Physical Mechanism of SuperplasticityCORE-Materials
This lecture describes in general the physical mechanism of superplasticity and the microstructural changes which accompany superplastic forming. General background in production engineering and material science is assumed.
Affinity: the meaningful trait-based alternative to the half-saturation constantLanimal
1) The document discusses two common equations used to model nutrient uptake rates: the affinity-based equation and the Michaelis-Menten/Monod equation.
2) While the equations appear different, they actually describe the same curve relationship between uptake rate and nutrient concentration.
3) The key difference is that the affinity-based equation defines competitive ability using the parameter "a", whereas the Michaelis-Menten equation uses the "Ks" parameter. However, "a" and "Ks" are mathematically related.
Apresentação do professor Pedro Grande, da seção UFRGS do Instituto Nacional de Engenharia de Superfície. Palestra convidada do Simpósio Engenharia de Superfície do X Encontro da SBPMAT. Realizada no dia 26 de setembro de 2011 em Gramado (RS).
Phylogeny and uncertainty in analyses of life spanOwen Jones
This document summarizes a study that analyzed lifespan data for over 200 bird species while accounting for various issues with the data. The study developed a state-space regression model that uses Markov chain Monte Carlo methods to simultaneously estimate coefficients, phylogenetic signal, true lifespans accounting for censoring and truncation in the data, and the degree of sample size effects. The results showed that the maximum observed lifespan data from the British Trust for Ornithology underestimates lifespan for many species, with the degree of underestimation increasing with greater reproductive effort.
Death and uncertainty: Bayesian modeling of the association between life span...Owen Jones
This document summarizes a study that used Bayesian modeling to analyze the relationship between lifespan and reproductive investment in birds while accounting for phylogenetic relationships and data issues. The study developed a state-space model that estimates coefficients, phylogenetic signal, true responses, and error using MCMC. The model found lifespan is moderately associated with body weight and reproductive effort. It also found BTO data underestimates lifespan for many species and that the method of phylogenetic correction is important.
Study of Metadynamic Recrystallization Phenomena in Coarse Grained Nb Microal...Pello Uranga
This study examines metadynamic recrystallization in coarse-grained Nb microalloyed austenite steel. There is a transition between static and metadynamic recrystallization between the critical strain εc and transition strain εT = 2.2εc. Below εc only static recrystallization occurs. Between εc and εT both static and metadynamic recrystallization contribute to softening. Above εT only metadynamic recrystallization occurs. A new model was developed that considers the contributions of both static and metadynamic recrystallization between εc and εT. The model predictions matched experimental validations
This document provides an overview of regression analysis and the steps involved in building a regression model to predict property values. It discusses the history of regression, uses of regression, and key components like the dependent and independent variables. The document walks through exploring the data, specifying the model, running regression, and interpreting the results. It shows how adding additional relevant variables like size, land size, age, and quality can improve the predictive power of the model. Transforming categorical variables is also discussed. The goal is to create a model that explains as much of the variation in sales prices as possible.
TALAT Lecture 3802: Physical Mechanism of SuperplasticityCORE-Materials
This lecture describes in general the physical mechanism of superplasticity and the microstructural changes which accompany superplastic forming. General background in production engineering and material science is assumed.
Affinity: the meaningful trait-based alternative to the obsolete obfuscation ...Lanimal
1) The document presents an argument that affinity, represented by the variable "a", is a superior metric to the half-saturation constant "Ks" for modeling nutrient uptake kinetics in aquatic systems. Affinity separates the traits relevant for uptake at high versus low nutrient concentrations in a clearer way.
2) Analysis of multiple data sets shows relationships between maximum uptake rate (Vmax) and affinity, but these relationships do not necessarily indicate a physiological trade-off as relationships between Vmax and Ks had been interpreted. In some cases there was a strong positive correlation between Vmax and affinity.
3) Adopting affinity over Ks allows models to be more easily tuned and better reveals relationships between kinetic parameters,
The document summarizes a presentation on optimality-based modeling of plankton. It discusses using evolutionary principles like natural selection and fitness optimization to build dynamic models of plankton populations. These models assume plankton are well-adapted via traits that maximize growth rates. The presentation notes successes in modeling plankton foraging and primary production in this way. It also discusses challenges like incorporating both short-term acclimation and long-term evolutionary adaptation. Overall, the presentation argues that optimality-based models provide a way to account for the adaptive capacity of plankton in Earth system models.
This document discusses an organization and its members. It mentions veterans, military members, and others working together towards a goal. The document expresses optimism and enthusiasm for cooperation between the group.
Lan\'s Presentation at the Ocean Sciences Meeting 2010Lanimal
First, I briefly review of selected recent studies which have improved our understanding of phytoplankton through the concept of optimality. Then, I present my most recent study of the combined effects of temperature and nutrient concentrations on the rates of nutrient uptake by phytoplankton. The point is that our assumptions about the fundamental dependencies affect our interpretation of the patterns observed in field experiments.
1. The document describes a study comparing two models - one using optimal uptake kinetics (SPONGE) and one using Michaelis-Menten kinetics - in simulating a multi-element ecosystem in an iron-enrichment experiment.
2. The SPONGE model allows phytoplankton to dynamically allocate their internal nutrients between uptake sites and enzymes in response to nutrient availability, while the Michaelis-Menten model uses fixed uptake parameters.
3. Both models were able to fit the in-patch data from the iron-enrichment experiment similarly well but the SPONGE model was better able to capture changes in nutrient uptake rates and ratios observed during the transition from iron-
1) Optimal uptake kinetics can explain variations in half-saturation constants (Ks) observed in field experiments better than traditional Michaelis-Menten kinetics. According to optimal uptake kinetics, all phytoplankton acclimate their physiology to ambient nutrient concentrations in the same way.
2) When incorporated into an Earth system climate model, optimal uptake kinetics produced significantly different primary production dynamics compared to Michaelis-Menten kinetics, with more primary production in subtropical gyres and less in upwelling regions.
3) Optimal uptake kinetics provides a more accurate and predictive framework for modeling nutrient uptake and primary production than traditional Michaelis-Menten kinetics, which does not account for phytop
Affinity: the meaningful trait-based alternative to the obsolete obfuscation ...Lanimal
1) The document presents an argument that affinity, represented by the variable "a", is a superior metric to the half-saturation constant "Ks" for modeling nutrient uptake kinetics in aquatic systems. Affinity separates the traits relevant for uptake at high versus low nutrient concentrations in a clearer way.
2) Analysis of multiple data sets shows relationships between maximum uptake rate (Vmax) and affinity, but these relationships do not necessarily indicate a physiological trade-off as relationships between Vmax and Ks had been interpreted. In some cases there was a strong positive correlation between Vmax and affinity.
3) Adopting affinity over Ks allows models to be more easily tuned and better reveals relationships between kinetic parameters,
The document summarizes a presentation on optimality-based modeling of plankton. It discusses using evolutionary principles like natural selection and fitness optimization to build dynamic models of plankton populations. These models assume plankton are well-adapted via traits that maximize growth rates. The presentation notes successes in modeling plankton foraging and primary production in this way. It also discusses challenges like incorporating both short-term acclimation and long-term evolutionary adaptation. Overall, the presentation argues that optimality-based models provide a way to account for the adaptive capacity of plankton in Earth system models.
This document discusses an organization and its members. It mentions veterans, military members, and others working together towards a goal. The document expresses optimism and enthusiasm for cooperation between the group.
Lan\'s Presentation at the Ocean Sciences Meeting 2010Lanimal
First, I briefly review of selected recent studies which have improved our understanding of phytoplankton through the concept of optimality. Then, I present my most recent study of the combined effects of temperature and nutrient concentrations on the rates of nutrient uptake by phytoplankton. The point is that our assumptions about the fundamental dependencies affect our interpretation of the patterns observed in field experiments.
1. The document describes a study comparing two models - one using optimal uptake kinetics (SPONGE) and one using Michaelis-Menten kinetics - in simulating a multi-element ecosystem in an iron-enrichment experiment.
2. The SPONGE model allows phytoplankton to dynamically allocate their internal nutrients between uptake sites and enzymes in response to nutrient availability, while the Michaelis-Menten model uses fixed uptake parameters.
3. Both models were able to fit the in-patch data from the iron-enrichment experiment similarly well but the SPONGE model was better able to capture changes in nutrient uptake rates and ratios observed during the transition from iron-
1) Optimal uptake kinetics can explain variations in half-saturation constants (Ks) observed in field experiments better than traditional Michaelis-Menten kinetics. According to optimal uptake kinetics, all phytoplankton acclimate their physiology to ambient nutrient concentrations in the same way.
2) When incorporated into an Earth system climate model, optimal uptake kinetics produced significantly different primary production dynamics compared to Michaelis-Menten kinetics, with more primary production in subtropical gyres and less in upwelling regions.
3) Optimal uptake kinetics provides a more accurate and predictive framework for modeling nutrient uptake and primary production than traditional Michaelis-Menten kinetics, which does not account for phytop
Affinity: the meaningful trait-based alternative to the obsolete obfuscation known as the half-saturation constant
1. ASLO Aquatic Sciences Meeting 2012 Lake Biwa, Japan
Affinity: a clearly superior alternative
to the obsolete obfuscation known as the
‘half-saturation constant’
S. Lan Smith
Environmental Biogeochemical Cycles Research Program
Research Institute for Global Change
Japan Agency for Marine-Earth Science & Technology
Yokohama, Japan
S. Lan Smith Aquatic Sciences Meeting, July 9, 2012
2. Two Equations for the Same Curve
Affinity-based Michaelis-Menten / Monod
(Button & Robertson 1989, (Michaelis & Menten 1913,
Aksnes & Egge 1991) Monod 1942, Dugdale 1967)
VmaxaS VmaxS
VAff = VMM =
Vmax + aS Ks + S
Vmax Vmax
VMM
VA
Ks
α Concentration, S Concentration, S
a is just the initial slope, Ks defines the concentration at
which rate is half-saturated.
which is determines competitive
ability at low nutrient concentrations Vmax is the maximum uptake rate.
(Healey. Micrbial Ecology 1980).
S. Lan Smith p. 2 Aquatic Sciences Meeting, July 9, 2012
3. They’re really the same shape.
Affinity-based Michaelis-Menten/ Monod
VmaxaS VmaxS
VAff = VMM =
Vmax + aS Ks + S
Affinity and Ks are related:
a = Vmax
Ks
the initial slope of the MM eq.
is a better measure of competitive
ability than either Vmax or Ks alone
(Button Deep-Sea Res. 25, 1978;
Healey Microb. Ecol. 5, 1980).
S. Lan Smith p. 3 Aquatic Sciences Meeting, July 9, 2012
4. What difference does this make?
Effect of varying only Vmax
Affinity-based equation MM / Monod equation
1.5 1.5
Rate (d-1)
Rate (d-1)
1.0 1.0
0.5 0.5
0.0 0.0
fractional difference
fractional difference
0.4
0.4
0.2 0.2
0.0 0.0
−0.2 −0.2
−0.4 −0.4
0 5 10 15 0 5 10 15
nutrient concentration (mol m-3) nutrient concentration (mol m-3)
S. Lan Smith p. 4 Aquatic Sciences Meeting, July 9, 2012
5. What difference does this make?
Effect of varying only Vmax
Affinity-based equation MM / Monod equation
1.5 1.5
Rate (d-1)
Rate (d-1)
1.0 1.0
0.5 0.5
0.0 0.0
fractional difference
fractional difference
0.4
0.4
Changing Vmax has no effect at low Changing Vmax has the same effect at
0.2
nutrient concentrations. low & 0.2
high nutrient concentrations.
0.0
Model response is comparatively less Model0.0
response is more sensitive
sensitive to Vmax.
−0.2 to Vmax.
−0.2
=> Vmax & a can be tuned separately.
−0.4 => after tuning Vmax must tune Ks too.
−0.4
Easier to tune models. 10
0 5 15 This may 0 also cause poor perfor-
5 10 15
nutrient concentration (mol m-3) -3
mance nutrient concentration (mol m )
for some data assimilation
alogirthms.
S. Lan Smith p. 5 Aquatic Sciences Meeting, July 9, 2012
6. Trade-off or Not Trade-off?
from Litchman et al. (Ecology Letters 10, 2007)
per cell basis vs. per mol C basis
Fig. 1a,b of Litchman et al. (Ecol. Lett. 10:1170-1181, 2007)
But does a positive Vmax vs. Ks relationship reveal a trade-off?
Affinity, not Ks, quantifies competitive ability at low nutrients.
So, let’s transform the data: a = Vmax
Ks
S. Lan Smith p. 6 Aquatic Sciences Meeting, July 9, 2012
7. There is no Trade-off!
Positive relationship between Vmax and a
per cell basis per mol C basis
0.001 10
Vmax (μmol (μmol C)-1 d-1)
r2 = 0.92, r2 = 0.80,
Vmax (μmol cell-1 d-1) p < 0.001 1
p < 0.001
1e−05
0.1
1e−07
0.01
1e−09 0.001
1e−08 1e−06 1e−04 1e−04 0.01 1
α (L cell-1 d-1) α (L (μmol C)-1 d-1)
Data from Litchman et al. (EL 2007, Fig. 1ab),
transformed to affinity.
This constrasts with the following from Litchman et al. (2007):
“Significant positive correlations between ... Vmax and K found in our data analysis
imply inherent physiological trade-offs between these physiological traits.”
Ks is NOT a physiological trait.
S. Lan Smith p. 7 Aquatic Sciences Meeting, July 9, 2012
8. Mathematical relationship implies correlations
Vmax (μmol (μmol C)-1 d-1)
0.001 10
red dots
Vmax (mmol cell-1 d-1)
log-log 1
generated as
slope = 0.66 1e−05 independent
less steep than 0.1 Gaussian
in the data, 1e−07
variables,
slope = 2.3 0.01 same mean &
s.d. as data
1e−09 0.001
0.1 1.0 10 0.1 1.0 10
Kn (μmol L-1) Kn (μmol L-1)
red dots Vmax
transformed
a=
Kn
Vmax (μmol (μmol C)-1 d-1)
0.001 10
Vmax (mmol cell-1 d-1)
red dots log-log
generated as 1e−05
1
slope = 0.76
independent
the same as for data,
Gaussian
0.1
slope = 0.71 +/- 0.09
variables, 1e−07
0.01
same mean &
s.d. as data 1e−09 0.001
1e−08 1e−06 1e−04 1e−04 0.01 1
α (L cell-1 d-1) α (L (μmol C)-1 d-1)
S. Lan Smith p. 8 Aquatic Sciences Meeting, July 9, 2012
9. An independent data set
Dauta (Ann. Limnol. 18:263–292,1982)
measured nitrate uptake parameters for 8 species, each at various temperatures
Vmax (μg atoms N (109 cells h)-1)
200 No overall relationship between
100 Vmax & Ks
50
20
10 Anabaena cylindrica
Only 2 significant intra-species rels.
Coelastrum microsporum
5 Dictyosphaerium pulchellum
Fragillaria bidens
Transforming
Pediastrum boryanum
2 Monoraphidium minutum
Scenedesmus crassus
1 Scenedesmus quadricauda as before to
0.5 1.0
Kn (mmol
2.0
m-3)
5.0
affinity.
Vmax (μg atoms N (109 cells h)-1)
200
r2 = 0.89, Strong overall relationship between
100
p < 0.001 Vmax & a
50
Vmax
20
a=
10 Kn 4 significant intra-species rels.,
5
all positive
2
1
0.2 0.5 2.0
α
5.0 20.0 50.0
No Trade-off.
(m3 μg atoms N (mmol 109 cells h)-1)
S. Lan Smith p. 9 Aquatic Sciences Meeting, July 9, 2012
10. What does this mean in terms of the response?
Rate vs. Concentration Response
100
80
Species that compete better at low
60
nutrient concentrations also tend to
Rate
40
20
compete better at higher concentra-
0
tions.
nutrient concentration
Vmax (μg atoms N (10 cells h) )
-1
200
Strong overall relationship between
100
Vmax & a
50
9
Here the log-log slope = 0.57
20
10
5
r2 = 0.89,
2 p < 0.001
1
0.2 0.5 2.0 5.0 20.0 50.0
α No Trade-off.
(m3 μg atoms N (mmol 109 cells h)-1)
S. Lan Smith p. 10 Aquatic Sciences Meeting, July 9, 2012
11. But, Optimal Uptake kinetics is based on a trade-off : Vmax vs. a
This does NOT imply a OU kinetics predicts a shape-changing
universal negative relation- response in short-term expts., i.e., MM param-
ship between Vmax & a. eters that depend on nutrient concentration.
Trade-off Adaptive Response
This physiological 1.0
trade-off was postulated 0.8
Uptake
Rate
0.6
specifically for accli-
Vmax
0.4
0.2
mation (or adaptation) 0.0
0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000
to ambient nutrient NO3 in incubation expts.
concentrations. α
0
-1
log KNO3
-2
Low Nutrient Conc. High Nutrient Conc. n = 61 data pts.
-3
-2.5 -1.0 0.0
Smith et al. (MEPS 2009) log NO3 (in seawater)
S. Lan Smith p. 11 Aquatic Sciences Meeting, July 9, 2012
12. Conclusions
Affinity-based kinetics clearly separates the traits relevant at high
vs. low nutrient concentrations.
This makes it easier to tune models & interpret results,
compared to MM/Monod kinetics using Ks.
A postive relationship between Vmax & Ks does NOT necessarily
identify a trade-off.
Analyses in terms of Ks have ‘found’ trade-offs where none exist.
Affinity, a, as a trait-based quantity, more clearly and simply
reveals relationships between kinetic parameters.
Affinity is a better choice for modeling trade-offs and their impact
on large-scale biodiversity & biogeochemistry, as in e.g.,
Follows & Dutkiewicz (Ann. Rev. Mar. Sci. 2011) & Smith et al. (L&O 2011).
Ks
S. Lan Smith p. 12 Aquatic Sciences Meeting, July 9, 2012