phytoplankton, microcosms, ode's, r.€¦ · ecology ode’s rodeo desolve shiny!...

Ecology ODE’s rodeo deSolve Shiny!

Phytoplankton, Microcosms, ODE’s, R.

Andrew M. Dolman

useR-Aalborg 01 July 2015

Andrew M. DolmanPhytoplankton, Microcosms, ODE’s, R.


Ecology



Eutrophication

+N +P



Bioassays

Davis et al (2015)

N limitation

Ctrl +N +P +NPC

hl. a

µg

L-1

Kolzau et al (2014)



Standard statistics

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−0.5

0.0

0.5

0.25 1 2.6 10 20 30DIN:TP

RR

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P−limitationCo−limitationN−limitation

Kolzau et al (2014)RR = log(Presponse/Nresponse)



ODE’s



Simulate the microcosm with ODE’s





Phytoplankton (Cphy) + 1 resource (Nphy and DIN)

dCphydt =

Cphy INmax

(1−

Cphy INminNphy

)INmax −INmin

dNphydt =

Cphy

(INmax −

NphyCphy

)Nupmax DIN

(INmax −INmin) (DIN+KNup)

dDINdt = −

Cphy

(INmax −

NphyCphy

)Nupmax DIN

(INmax −INmin) (DIN+KNup)

Use numerical solvers to step forward in time from initial conditions.




Technical challenges

I No standard implementationI Sharing (communication between modellers) is difficultI Re-use is difficultI No standard = hard to get started

I Theory and code entangledI Poor documentationI Collaboration with non-modellers is difficult



rodeo



Definition in tables + Code generation





rodeo - David Kneis

https://github.com/dkneis/rodeo





Identifiers

1

2

3

4

5

6

7

8

9

10

name

C_phy

N_phy

DIN

r_max

IN_max

IN_min

UN_max

K_Nup

uptake

droop

type

v

v

v

p

p

p

p

p

f

f

unit

µgC/L

µgN/L

µgN/L

1/day

gN/gC

gN/gC

gN/gC/day

µgN/L

µg/µgC/d

µgC/µgC/d

description

Cellular C

Cellular N

External dissolved inorganic N

Max phytoplankton growth rate

Max internal N:C ratio

Min internal N:C ratio

Max N uptake rate

Half sat. for N uptake

uptake rate for N

realised growth rate of phytoplankton

tex

C_{phy}

N_{phy}

DIN

r_{max}

IN_{max}

IN_{min}

UP_{max}

K_{Nup}

uptake

droop

html

C_phy

N_phy

DIN

r_max

IN_max

IN_min

UN_max

K_Nup

uptake

droop




Processes

1

2

name

Growth

U_DIN

unit

µgC/d

µgN/d

description

Growth

Uptake of DIN

expression

r_max * droop(IN_max, IN_min, N_phy/C_phy)

uptake(UN_max, IN_max, IN_min, K_Nup, DIN, N_phy/C_phy)




Stoichiometry

1

2

3

variable

C_phy

N_phy

DIN

process

Growth

U_DIN

U_DIN

expression

C_phy

C_phy

−C_phy




Define functions

uptake <- function(Umax, Qmax, Qmin, K_half, Ext, Int){Umax*((Ext*(Qmax-Int))/((K_half+Ext)*(Qmax-Qmin)))}

droop <- function(Qmax, Qmin, Int){(Qmax / (Qmax - Qmin)) * (1 - (Qmin / Int))}



Neat documentation

Neat documentation



Neat documentation

State variables

Symbol Unit DescriptionCphy µgC/L Cellular CNphy µgN/L Cellular NDIN µgN/L External dissolved inorganic N



Neat documentation

Parameters

Symbol Unit Descriptionrmax 1/day Max phytoplankton growth rateINmax gN/gC Max internal N:C ratioINmin gN/gC Min internal N:C ratioUPmax gN/gC/day Max N uptake rateKNup µgN/L Half sat. for N uptake



Code generation

Code generation



Code generation

Instantiate model object

model <- new("rodeo", vars=subset(identifiers,type=="v"), pars=subset(identifiers,type=="p"), funs=subset(identifiers,type=="f"), pros=processes, stoi=stoichiometry)



Code generation

Generate code

R or Fortran95

code <- model$generate(name="derivs",lang="r")derivs <- eval(parse(text=code))



Code generation

Provide parameter and starting values

pars <- list(r_max=1, K_Nup=100, UN_max=0.2, IN_max=0.13 * (14/12), IN_min=0.05 * (14/12))

init_C_phy <- 2000init_DIN <- 80

vars <- list(C_phy=init_C_phy, DIN=init_DIN, N_phy=(2*pars[["IN_min"]])*init_C_phy)

p <- model$arrangePars(pars)v <- model$arrangeVars(vars)



Code generation

Test the derivative function

derivs(time, v, p, NLVL = 1)

## $dydt## [1] 1625.00000 66.66667 -66.66667#### $pro## [1] 0.81250000 0.03333333



deSolve



Solve the ODE system





Pass parameters and starting values at runtime

t <- seq(0, 5, length.out=100)

system.time({out_R1 <- ode(y=v, times=t, func=derivs

, parms=p, NLVL=1)})

## user system elapsed## 0.06 0.00 0.08




Plot output

0 1 2 3 4 5

2000

3500

5000

C_phy

time0 1 2 3 4 5

240

260

280

300

N_phy

time0 1 2 3 4 5

020

4060

80

DIN

time



Shiny!



More ecology

I N or P limit growth rateI Effect of light (I) is multiplicative

dCphydt = f (I) ·min{f (N), f (P)}



Shiny app demonstration



Packages

I rodeo (David Kneis) https://github.com/dkneis/rodeoI Standard definition of ODE’s in tablesI Definition is the documentationI Code generation in R or F95 (250x faster)

I deSolve (Soetaert, Petzoldt, Setzer)I Numeric solvers for DE

I Shiny (Chang, Cheng, Allaire, Xie and McPherson)




AcknowledgmentsI David Kneis rodeo @TU Dresden

I https://github.com/dkneis/rodeo

I Thomas Petzoldt @TU DresdenI Sebastian Kolzau, Jacqueline Rücker, Claudia Wiedner @BTUI Nitrolimit www.nitrolimit.deI BMBF FONA 033L041A and 0033W015AN




Petersen matrix

(Cphy Nphy DINGrowth Cphy 0 0U DIN 0 Cphy −Cphy

) Rate expressions

f (NphyCphy

, INmax , INmin)

f (DIN,NphyCphy

, Nupmax , . . . )



Literature cited

I Davis, T.W., Bullerjahn, G.S., Tuttle, T., McKay, R.M. &Watson, S.B. (2015) Effects of Increasing Nitrogen andPhosphorus Concentrations on Phytoplankton CommunityGrowth and Toxicity During Planktothrix Blooms in SanduskyBay, Lake Erie. Environmental Science & Technology, 49,7197–7207.

I Karline Soetaert, Thomas Petzoldt, R. Woodrow Setzer (2010).Solving Differential Equations in R: Package deSolve Journalof Statistical Software, 33(9), 1–25. URLhttp://www.jstatsoft.org/v33/i09/.


http://www.jstatsoft.org/v33/i09/


I Kolzau, S., Wiedner, C., Rücker, J., Köhler, J., Köhler, A. &Dolman, A.M. (2014) Seasonal patterns of nitrogen andphosphorus limitation in four German lakes and thepredictability of limitation status from ambient nutrientconcentrations. PLoS ONE, 9, e96065.


phytoplankton, microcosms, ode's, r.€¦ · ecology ode’s rodeo desolve shiny!...

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