animal
runs a demo for the standard model, after editing parameter values in
pars_animal
:
shmics
:
temp correction, embryo weights, reproduction, reserve residence times shtime_animal
:
length, reprod, weight, survival shphase
:
phase diagram shflux
:
fluxes of compounds shflux_struc
:
structurespecific fluxes shflux_weight
:
weightspecific fluxes shratio
:
Repiration, Watering, Urination Quotients shpower
:
powers and specific powers shscale
:
variables versus species' max body weight shssd_iso
:
population characteristics versus functional response
The animal (or other organism) is decomposed in:
structure (V) and reserve (E)
Organic compounds:
X = food, V = structure, E = reserve, P = faeces
Mineral compounds:
C = carbon dioxide, H = water, O = dioxygen, N = nitrogen waste
The animal develops through an embryonic, juvenile and adult phase.
Assimilation is switched on at birth
Allocation to maturation is redirected to reproduction at puberty
Uptake is proportional to surface area, which is taken to be proportional to the structural volume^(2/3): isomorph
The heating length (this is the volumetric length reduction due to the energy drain that goes into heating or osmotic work) is set to a fixed length in this implementation. The DEB theory has a module on the water balance, with implications for the costs of heating. These implications make the heating length a function of other variables.
All lengths refer to volumetric lengths. Lengths should be divided by a shape coefficients to arrive at shapespecific lengths.
Script shtraject runs a simulation of the stochastic variant, where food searching is a timeinhomogeneous Poisson process.
DEB theory quantifies aging directly in terms of the hazard rate, so for the aging process no deterministic equivalent is available.
The scripts plot variables as function of scaled time since birth.
Function shphase
presents phase diagrams, which indicate how reserve and structure chnage relative to each other.
Script statistics
computes quantities that depend on food density,
while script parscomp
computes quantities that are independent of food density,
so functions of parameters, called compound parameters.
Function
shpower
plots the various powers as function of scaled length.
It is based on
scaled_power
.
It is similar to
shflux
for mass fluxes and
shflux_struc
for structurespecific mass fluxes and
shflux_weight
for body weightspecific mass fluxes.
Likewise
shratio
plots ratio's of mineral fluxes.
Maturity is, at constant food density, found from length by functions
maturity
,
maturity_j
,
maturity_s
.
The functions relate to nonacceleration, tyupe M acceleration and delayed type M acceleration.
They can be applied for the full life cycle (although maturity remains constant for adults).
Since food denisity trajectories uniquely determine state trajectories, the inverse mapping also exists:
from states trajectories to trajectories of scaled functional response.
The pair of functions
f2o
and
o2f
is and example for (fish) otoliths, where otoliths are considered to be products,
with contributions from assimilations, dissipation and growth.
See section 4.11.4 of the DEB book.
Isotops, their dynamics is discussed in Section 4.7, add to the reconstruction to include temperature trajectories as well.
See function isotope
get_ue0
for eggs and
get_ue0_foetus
for foetusses.
The latter amounts to the cumulative energy investment till birth.
The functions
initial_scaled reserve
and
initial_scaled reserve_foetus
are shells around these function for vectorarguments and they are not scaled down to dimensionless quantities.
Scaled maturity at birth should not exceed a threshold that is computed in
get_vHb
.
The scaled length at birth is computed by
get_lb
,
get_lb1
,
get_lb2
, and
get_lb3
.
The functions differ in numerical method, from fast and dirty to slow and robust.
Use function get_lb_foetus
for foetal development.
The scaled time at birth is computed by
get_tb
,
get_tb1
and
get_tb_foetus
.
These functions also compute scaled length at birth.
Age, reserve, length (and maturity) at birth is produced by
get_ael
,
get_aulh
,
get_tul
and
get_tul_i
for egg development and
get_ael_f
and
get_aulh_f
for foetal development.
The results are obtained by integration and can to used to check the results of other embryofunctions.
The numerical methods differ between these functions.
The scaled reserve density at which growth and/or maturition ceases at birth is computed by
get_eb_min_G
,
get_eb_min_R
and
get_eb_min
.
The levels can be seen as minimum levels to reach birth.
The cumulative energy investment to the various endpoints at birth can be obtained numerically with functions
get_EMJHG
and
get_EMJHG_foetus
,
and graphically with functions
birth_pie
and
birth_pie_foetus
.
get_tx
and
start acceleration
get_ts
and
metamorphosis
get_tj
and
get_tj_foetus
and puberty
get_tp
and
get_tp_foetus
are computed in combination with other scaled times and scaled lengths at life history events.
If you only need scaled lengths, it is more economic to use the corresponding get_l*
functions:
get_ls
,
get_lj
,
get_lj_foetus
,
get_lp
,
get_lp_foetus
.
If you only need states at birth, see under embryo
The scaled reserve density at which growth and maturition ceases at puberty is computed by
get_ep_min
without acceleration,
get_ep_min_metam
with acceleration.
Scaled functional response is reconstructed from scaled length by functions
l2f
and
l2f1
.
They apply to the juvenile and adult stages.
The reserve residence time as function of length is computed by
res_time
and fluxes of masses for parameters and states by
flux
.
It applies to the juvenile and adult stages.
reprod_rate
and
reprod_rate_foetus
.
In case of type M acceleration, use functions
reprod_rate_j
or
reprod_rate_s
.
Likewise, the cumulative reproduction as function of time can be obtained with function
cum_reprod
.
In case of type M acceleration, use functions
cum_reprod__j
or
cum_reprod_s
.
The cumulative energy investment in milk production (most by mammals) from birth to weaning is computed by
milk
.
The median age at death due to ageing is computed by
get_t50_s
for short growth periods.
The scaled mean age at death due to aging is computed by
get_tm_s
for short growth periods and for arbitrary growth periods by
get_tm
and
get_tm_foetus
.
Functions
get_evh
and
get_leh
get state variables as functions of time over the whole life cycle.
get_pars_*
obtain compound DEB parameters from easytoobserve quantities and the functions iget_pars_*
do the reverse, which can be used for checking.
The theory is discussed in KooySous2008.
The heating length L_{T} is assumed to be zero in all get_pars_*
functions.
An example of use is given in mydata_get_pars
.
The routines are organized as follows:
get_pars  iget_pars  

food level  one  several  one  several  
constraint  k_{J} = k_{M}  k_{J} != k_{M}  k_{J} = k_{M}  k_{J} = k_{M}  k_{J} != k_{M}  k_{J} = k_{M} 
growth  get_pars_g 
get_pars_h 
get_pars_i 
iget_pars_g 
iget_pars_h

iget_pars_i 
growth & reprod  get_pars_ 
get_pars_s 
get_pars_t 
iget_pars_r 
iget_pars_s 
iget_pars_s 
elas_pars_g
and
elas_pars_r
give elasticity coefficients.
Function get_pars_u
converts compound parameters into unscaled primary parameters at abundant food.
Another group of get_pars
functions obtain primary (rather than compound) parameters from data at abundant food.
This strategy comes with assumptions about particular (chemical) parameter values (chemical potentials and the like).
Again, all functions assume absence of surfacearea linked maintenance.
They don't make use of the assumption k_J = k_M, but assume that k_J is known.
By increasing the number of known parameters, we can decrease the amount of data that is needed to get the remaining parameters, as reflected in the different get_par
s varieties:
get_pars_9
,
get_pars_8
,
get_pars_7
,
get_pars_6
,
get_pars_6a
,
get_pars_5
,
get_pars_4
,
get_pars_3
,
get_pars_2
,
get_pars_2a
.
Functions
iget_pars_9
and
iget_pars_8
are inverse functions, from parameters to data.
Functions get_pars_9_foetus
and
iget_pars_9_foetus
are for foetal development.
One strategy to set values of "known" parameters is to use the generalized animal settings of Table 8.1 in the DEBbook.
The maximum number of parameters than can be obtained at abundant food only is 9.
Functions
filter_pars_9
and
filter_data_9
filter allowable parameter and data combinations in the case of 9 parameters (including type M acceleration).
Functions
filter_pars_8
and
filter_data_8
filter allowable parameter and data combinations in the case of 8 parameters (no acceleration).
sgr_iso
,
sgr_iso_foetus
and
sgr_iso_metam
.
The latter accounts for type M accleration.
Likewise, the mean age, length, squared and cubed length in the population at constant food density is computed by
ssd_iso
,
ssd_iso_foetus
and
ssd_iso_metam
.
The scaled functional response at which the specific population growth rate is zero is found by
f_ris0
.
Population characteristics are plotted against scaled functional response by
shssd_iso
.
scale
obtains ecophysiological qantities as function of the zoomfactor and function
shscale
plots these quanties against maximum body weight, which itself is just one such quantity.