Dynamic Energy Budget - DEB

Table of Contents:

• Dynamic Energy Budget - DEB
• Concept figure
• DEB equations
  • basics - reserve dynamics
  • allocation of pC
• Existing models
  • MATLAB tools (original DEB)
  • NicheMapR (Habitat modeling)
  • FABM, FABM-DEB (Hydrodynamic coupling)
  • Population models
    • IBM (Individual-Based-Model)
    • EBT
    • CPM
• Useful web interfaces
• Acquire parameters
  • From AmP collection
    • In MATLAB
    • In R
  • Parameter estimation with literature/experimental data
    • Better-to-have data
    • parameter estimation preparation
    • Parameter estimation procedure
• Further DEB modeling - State Variables - ODE In standard DEB model (std) - DEB model can be coupled

Concept figure

DEB website

DEB equations

basics - reserve dynamics

(refer to graph above, from top to bottom, left to right)

• food ingestion rate $\dot{p_X}$ $$\dot{p_X} = \dot{{p_{Xm}}}f(X)L^2$$
• assimilation flux $\dot{p_A}$ $$\dot{p_A} = \dot{{p_{Am}}} f(X) L^2$$
• Reserve $E$ $$\frac{dE}{dt} = \dot{p_A} - \dot{p_C}$$
• Reserve density $E/V$ $$\frac{d[E]}{dt} = \dot{[p_A]} - \dot{[p_C]} - [E]\dot{r}$$
• mobilization flux $\dot{p_C}$
  $$\dot{p_C} = E (\frac{\dot{v}}{L} - \dot{r})$$ $$\dot{[p_C]} = [E](\frac{\dot{v}}{L} - \dot{r})$$

allocation of pC

$$\dot{p_C} = \textcolor{blue}{\dot{p_S} + \dot{p_G} }+ \textcolor{red}{\dot{p_J} + \dot{p_R}}$$

fraction $\color{blue}\kappa$ --> $\color{blue}\dot{p_S}$ and $\color{blue}\dot{p_G}$,

fraction $\color{red}1-\kappa$ --> $\color{red}\dot{p_J}$ and $\color{red}\dot{p_R}$

• somatic maintenance $\color{blue}\dot{p_S}$ $$\dot{p_S} = \dot{[p_M]} L^2 + \dot{{p_T}} L^3$$

• energy allocated to growth $\color{blue}\dot{p_G}$ $$\dot{p_G} = \kappa\dot{p_C} - \dot{p_S} $$ $$\dot{p_G} = [E_G] \frac{dV}{dt}$$

• specific growth rate $\color{blue}\dot{r}$ $$\dot{r} = \frac{1}{V}\frac{dV}{dt}$$ OR? $$\dot{r} = \frac{d}{dt}lnV$$ OR? $$\dot{r} = \frac{\dot{[p_G]} }{[E_G]}$$

• maturity maintenance $\color{red}\dot{p_J}$ $$\dot{p_J} = \dot{k_J} * E_H$$

• maturation (embryo-juvenile) $\color{red}\dot{p_R}$ $$\dot{p_R} = (1 - \kappa) \dot{p_C} - \dot{p_J} $$ $$\frac{dE_H}{dt} = \dot{p_R}$$

• reproduction (adult) $\color{red}\dot{p_R}$ $$\dot{p_R} = (1 - \kappa) \dot{p_C} - \dot{p_J}$$ $$\frac{dE_R}{dt} = \kappa_R \dot{p_R}$$

MORE DERIVATIONS for equations

Existing models

some of these packages are required to run the scripts in code_pu (or src)

MATLAB tools (original DEB)

DEBtool

DEBtool illustrate some implications of the DEB theory

AmPtool

AmPtool analyses patterns in DEB parameters

install and configuration: Need MATLAB. In MATLAB, Home >> set path and direct to the source code

NicheMapR (Habitat modeling)

NicheMapR package

NicheMapR is written by Michael Kearney. It includes Microclimates, Ectotherms, Endotherms, Plants, Dynamic Energy Budgets modules that can be coupled together to do habitat and behavioral modeling

install and configuration: install package from github tutorial

FABM, FABM-DEB (Hydrodynamic coupling)

FABM

FABM-DEB (it is a population model)

FABM couples hydrodynamic models with biogeochemical models. There is a FABM-DEB model constructed by Jorn Bruggeman

installation and configuration

# >>>>>> install and compile FABM-DEB with 0d driver
FABMDIR="~/src/fabm" 	# Path to FABM source code
GOTMDIR="~/src/GOTM6" 	# Path to GOTM source code 
compiler="/opt/homebrew/bin/gfortran" 	# fortran compiler on this computer

mkdir -p ~/build/fabm-0d && cd ~/build/fabm-0d

cmake $FABMDIR/src/drivers/0d -DGOTM_BASE=$GOTMDIR -DCMAKE_Fortran_COMPILER=$compiler -DFABM_INSTITUTES="akvaplan;au;bb;csiro;ersem;examples;gotm;iow;jrc;msi;niva;pclake;pml;selma;su;uhh;deb" -DFABM_DEB_BASE=~/src/fabm-deb

make install

# >>>>>> generate yaml files >>>>>>>
https://github.com/fabm-model/fabm/wiki/Setting-up-a-simulation

# >>>>>> run fabm0d coupled with deb >>>>>>>
cd /Users/tongyaop/test_funcs_local/fabm-deb/0d_deb_test
~/local/fabm/0d/bin/fabm0d -y ./fabm-deb.yaml

Or use pydeb:

# >>>>>> run deb in pydeb >>>>>>>

# python packages : NumPy, Python, Jupyter, plotly

# install pydeb:
PYDEB_DIR=~/src/pydeb
python -m pip install $PYDEB_DIR --user

# run a deb model:
# go to $PYDEB_DIR/examples

Population models

IBM (Individual-Based-Model)

installation and configuration

1. Install NetLogo

2. set path in .bash_profile for MacOS

cd
vim .bash_profile
export JAVA_HOME=/Library/Internet\ Plug-Ins/JavaAppletPlugin.plugin/Contents/Home
export EBTPATH=/Applications/EBTtool.app/Contents/Resources
export PATH=${JAVA_HOME}/bin:/Applications/NetLogo\ 6.2.0/app:/Applications/EBTtool.app/Contents/MacOs:$PATH

3. To run: use IBM() function in MATLAB (from DEBtool)

    [txNL23W, info] = IBM('Daphnia_magna', [], [], [], [], [], [], 80, 1);

EBT

installation and configuration Need fortran compiler and MATLAB

To run: use EBT() function in MATLAB (from DEBtool).

[txNL23W, info] = EBT('Daphnia_magna', [], [], [], [], [], 80);

CPM

EXPLAIN

Useful web interfaces

• AmP (Add my pet) portal

• NicheMapR shiny apps: Online habitat and DEB modeling

• Debber: Estimates DEB parameters and provide confidence interval ranges.

This could be a documentation for the DEBtool github. Instead of just linking https://bio.vu.nl/thb/deb/deblab/ in the github readme file (That's could be where the frustrating, because you are getting back to where you came from), maybe explain a little bit about how to work with the code.

Acquire parameters

From AmP collection

Even a species exist in the collection, it can be improved

AmP website

This website should get a top-left figure to click on to go back to the home page

COLLECTION > AmPdata.zip

In MATLAB

1. Put AmPdata to MATLAB path
2. In MATLAB,

load AmPdata

In R

(copied from NicheMapR tutorial)

install.packages('R.matlab')
library(R.matlab)

allStat <- readMat('allStat.mat') # this will take a few minutes
save(allStat, file = 'allstat.Rda') # save it as an R data file for faster future loading
library(knitr) # this packages has a function for producing formatted tables.

load('allStat.Rda')

allDEB.species<-unlist(labels(allStat$allStat)) # get all the species names
allDEB.species<-allDEB.species[1:(length(allDEB.species)-2)] # last two elements are not species names
kable(head(allDEB.species))
Nspecies <- length(allStat$allStat)
Nspecies

species <- "Eulamprus.quoyii"
species.slot <- which(allDEB.species == species)
par.names <- unlist(labels(allStat$allStat[[species.slot]]))

for(i in 1:length(par.names)){
 assign(par.names[i], unlist(allStat$allStat[[species.slot]][i]))
}

Parameter estimation with literature/experimental data

Better-to-have data

Data to be collected	Common symbol
length-weight relationship
length at first feeding (birth)	$L_b$
length at puberty	$L_p$
max mass	$L_m$
max reproduction rate	$R_i$
time from conception to first feeding (birth)	$a_b$
time from first feeding (birth) to puberty	$a_p$
life span	$a_m$
*metamorphasis info
*other types of weight
*growth data from birth to death
*any forms of rate
*reproduction
*temperature dependence

Better to be under known constant temperature, saturated food conditions (f = 1). This is not a hard requirement.

Start working on all the available data and then reduce the weight of some data if they are uncertain and provides bad estimations

❗ Provide an univariate dataset here in txt/xlsx file form.

parameter estimation preparation

1. Create directory Taeniopygia_guttata_test

2. In MATLAB, change directory to Taeniopygia_guttata_test, then run AmPeps in the command window. The following window will pop up

   

3. Type in corresponding information:

   species	Taeniopygia_guttata_test
   ecoCode	climate: Af
   	ecozone: TPi, TA
   	habitat: 0iTh, 0iTi, 0iTs, 0iTg, 0iTa
   	embryo: Tnsf, Tnpf
   	migrate:
   	food: biCi, biHs
   	gender: Dg
   	reprod: O
   T_typical	42°C

   Add to 0-var data

   	Value	Reference
   age at birth	15 d	Wiki
   time since birth at puberty	300 d	Wiki
   life span	4360 d	voliere
   wet weight at birth	0.8 g	Wiki
   ultimate wet weight	11.7 g	AnAge
   maximum reproduction rate	0.0137	Wiki

   You can also add to 1-var data

   Add the reference list to biblist

   Add author (your name)

   Add curator (this will not send the information directly)

   Add data completeness

   If finishes, click pause/save > quit AmPgui, continue with AmPeps

4. AmPeps will then generate four MATLAB scripts. Edit accordingly

   • mydata_*.m includes observational data you just typed in. You can add to this by typing or using MATLAB functions (e.g. load, readmatrix). Code up corresponding temperature/food if they vary with time.
   • pars_init_*.m don't need to be edited at this stage.
   • predict_*.m includes prediction models for observational data. Add in your own model if the auto-generated one is not ideal.
   • run_*.m specifies estimation options and run the parameter estimation process.

predict model examples can be searched in AmP website > COLLECTION > search for relevant models (e.g. t-L (time-length), T-F(temperature-filtration rate)), click into the species with these models, look at their predict_ file and get inspired

Parameter estimation procedure

AmPestimation

Open the run_*.m script, you will see:

close all; 
global pets 

pets = {'Taeniopygia_guttata'}; 
check_my_pet(pets); 

estim_options('default');  % initialize estimation options
estim_options('max_step_number', 5e2); % maximum 
estim_options('max_fun_evals', 5e3); 

estim_options('pars_init_method', 2); 
estim_options('results_output', 3); 
estim_options('method', 'no'); 

estim_pars; 

The parameter estimation procedure compares observational data in mydata_*.m with DEB model described in predict_*.m using parameters defined in pars_init_*.m

The comparison result is evaluated with loss function.

By running run_*.m in MATLAB, this procedure is repeated for many times (until max_step_number), or until the minimum of the loss function is found.

If the minimum of loss function is not found (did not converge), edit pars_init_method to 1 (now reading parameters from previous-procedure-generated results_*.mat); then run run_*.m again in MATLAB until convergence is reached.

In the MATLAB command window, type mat2pars_init. This will rewrite the estimated parameter sets to the pars_init_*.m file.

❗ Make sure to look at the generated .html page, evaluate if the predicted data is physical, and look at if MRE is small. If not, you might want to fix a certain parameter or set less weight to the questionable observational dataset.

To fix a parameter: open pars_init_*.m, change par.** based on your best guess, and set free.** = 0.

To set dataset weight, open mydata_*.m, in the %% set weights for all real data section, change/type weights.** = 0 if you don't want this data to affect parameter estimation, or weights.** = 5 if you feel the dataset is of great importance.

Further DEB modeling

Extract the estimated parameters, and use that in a designated models (e.g. self-coded DEB model, NicheMapR, other coupling modules, population models). Sometimes a full-set of ODE (ordinary differential equation) is needed to simulate the influence of time-varying temperature or food concentration.

State Variables

Variables to be modeled. Typical DEB state variables:

	Variable	Dynamics
Reserve	$E$	$\frac{dE}{dt} = \dot{p_A} - \dot{p_C}$
Structure	$V$	$\frac{dV}{dt} = \frac{\dot{p_G}}{[E_G]}$
Maturity	$E_H$	$\frac{dE_H}{dt} = \dot{p_R}$ (before maturation)
Reproduction	$E_R$	$\frac{dE_R}{dt} = \dot{p_R}$ (after maturation)

Where $\dot{p_A}$ is assimilation flux. $\dot{p_C}$, $\dot{p_G}$, and $\dot{p_R}$ are fluxes, all links to the reserve dynamics which can be expressed explicitly. Since all the dynamics of the state variables can be expressed explicitly, the dynamics can be solved with ODE (ordinary differential equation) solver.

ODE In standard DEB model (std)

The ODEs are constructed by the dynamic equations above. Here is one coding example. This pieces of code generates 4-vector with state variabels ELHR, correspond to time t

GIVE A CODING EXAMPLE, Maybe AmPtools/trajectory/>std model

DEB model can be coupled

DEB has the potential to be coupled with physical environmental models, population dynamic models, ecological models etc.