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The covariation method of estimation Add_my_pet

The covariation method of estimation Add_my_pet. Dina Lika Dept of Biology. UNIVERSITY OF CRETE. Texel, 15/4/2013. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A. Contents. The covariation method for parameter estimation DEB parameters

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The covariation method of estimation Add_my_pet

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  1. The covariation method of estimationAdd_my_pet Dina Lika Dept of Biology UNIVERSITY OF CRETE Texel, 15/4/2013 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAA

  2. Contents • The covariation method for parameter estimation • DEB parameters • Auxiliary theory • Real & pseudo data • Zero & variate data • Estimation criteria • Numerical implementation • Evaluation of the estimation

  3. The standard DEB model 1 food type, 1 reserve, 1 structure, isomorph Extended: V1-morphic early juvenile stage variables • structure, reserve, maturity, density of damage inducing compounds, and density of damage compounds parameters • Core parameters • Control changes of the state variables • Linked to the concepts on which the model is based on • Auxiliary parameters • Convert measurement (e.g. from dry to wet mass, length to volume etc.) • Quantify effects of temperature on rates and time • Primary parameters • Connected to a single underlying process • Compound parameters • Depend on several underlying processes

  4. Core parameters assimilation {pAm} max surface-specific assim rate  Lm ( 22.5z J cm-2 d-1) feeding {Fm} surface- specific searching rate (6.5 l d-1 cm-2) digestionκX digestion efficiency (0.8) product formationκXP defecation efficiency (0.1) mobilisation v energy conductance (0.02 cm d-1) allocation  allocation fraction to soma (0.8) reproduction R reproduction efficiency (0.95) turnover,activity [pM] volume-specific somatic maint. costs ( 18 d-1cm-3) heating,osmosis {pT} surface-specific somatic maint. costs (0 d-1cm-2) development kJ maturity maintenance rate coefficient (0.002 d-1) Growth [EG] specific growth for structure (2800 J cm-3) life cycle EHb maturity at birth (0.275z3 J) life cycle EHj maturity at metamorphosis ( z3 J) life cycle EHp maturity at puberty (166z3 J) aging ha Weibul aging acceleration (10-6z d-2) aging sG Gompertz stress coefficient (0.01) z zoom factor z=Lm / Lmref, with Lmref =1 maximum length Lm =  {pAm} / [pM]

  5. Auxiliary parameters Conversion parameters δM shape coefficient(-) dO =(dX, dV, dE, dP) specific densities (g/cm3) μO =(μX, μV, μE, μP) chemical potentials (J/mol) μM=(μC, μH, μO, μN) chemical potentials (J/mol) nO =(nX, nV, nE, nP)chemical indices (-) nM=(nC, nH, nO, nN) chemical indices (-) wO=(12 1 16 14) nO molecular weights (-) Temperature parameters Tref reference temperature (273 K) TA Arrhenius temperature (8000 K) TL, TH temperature tolerance range (277 K, 318 K) TAL, TAH Arrhenius temperatures for transitions to inert state (20 kK, 190kK)

  6. Assumptions of auxiliary theory • A well-chosen physical length  (volumetric) structural length for isomorphs • Physical lengthLw is the actual length of a body, defined for a particular shape • Structural lengthL is the volumetric length of structure, where the individual is assumed to consist of structure, reserve and the reproduction buffer. δM = L/ Lw • Volume, wet/dry weight have contributions from structure, reserve, reproduction buffer • Constant specific mass & volume of structure, reserve, reproduction buffer • Constant chemical composition of juvenile growing at constant food

  7. Data • Real-data Empirical observations of physiological process • zero-variate • uni-variate • Pseudo-data Prior knowledge of a selection of parameter values • zero-variate

  8. Zero-variate data Life history events: hatching, birth, metamorphosis, puberty, death Real data: age, length, dry-, wet-weight at life history events max rates: reproduction, respiration, feeding, growth Modified by food, temperature

  9. Pseudo-data Typical parameter values of the generalized animal Species specific parameters should not be included as pseudo-data (e.g., z, δM, EHb, EHp) Growth efficiencyκGvary less than the specific cost for structure [EG], and should be preferred for pseudo-data [EG] = μV [MV] / κG with [MV] =dV /wV Typical values for the ash-free-dry-weight over wet-weight ratio. Scyphomedusa 0.04 Ctenophora 0.04 Ascidia 0.06 Ectoprocta 0.07 Priapulida 0.07 Cheatognata 0.07 Actinaria 0.08 Bivalvia 0.09 Echinodermata 0.09 Porifera 0.11 Sipuncula 0.11 Gastropoda 0.15 Polychaeta 0.16 Crustacea 0.17 Cephalopoda 0.21 Pisces 0.22 Turbellaria 0.25 Aves 0.28 Reptilia 0.30 Mammalia 0.30

  10. Uni-variate data • length, weight, reproduction, respiration, feeding • as functions of time, temperature, food • incubation time, juvenile period, life span • as functions of time, temperature, food • weight as function of length • egg number as function of weight/length

  11. Completeness of Real-data Each level includes all lower levels

  12. Abstract World Auxiliary Parameters Core Primary Parameters [pM] [EG] f {pAm}  ... δM dV yEV v ... Mapping Functions Lm = {pAm}/[pM] ref =  [Em] = {pAm}/v rB = 1/(3/ [pM]/[EG] + 3 * f * Lm/ v) Wm = Lm3dV(1+fyEV [Em]/[EG]) prediction estimation LWm = Lm/δM Lw(t)= Lwm - (Lwm - Lwb) exp(-rBt) Wm maximum dry mass (g) t (time, days) LW (body lenght,cm) [pM]ref vref [EG]ref ref LWm maximum body length (cm) t1 LW(t1) rb von Bertalanffy growth rate (1/day) t2 LW(t2) ... Zero-variate Pseudo-data t3 LW(t3) ... Zero-variate Observations Uni-variate Observations Real World Lika et al., 2011 J. Sea Research 22:270-277

  13. The covariation method Estimates all parameters simultaneously using all data: single-step-procedure Independently normally distributed error with constant variation coefficient Estimation criteria • Weighted Least Square (WLS) • Maximum Likelihood (ML)

  14. WLS criterion Minimization of a weighted sum of squared deviations between observations yijand predictions fij The weight coefficients : wij / yij2 account for differences in units of the various data The dimensionless weight factorwij account for the certainty of the individual data point

  15. ML criterion For independently normally distributed dependent variables, the ln-likelihood function is The ML estimator for thesquared variation coeff The ML estimates minimize

  16. Numerical implementation Reflection Expansion Nelder-Mead method A simplex method for finding a local minimum of a function of several variables For 2 variables, a simplex is a triangle The function is evaluated at the vertices of the triangle. The worst vertex xh , where f is largest, is rejected and replaced with a new vertex xC obtained via a sequence oftransformations (reflect, expand or contract) or shrink the triangle towards the best. Does not require any derivative info Contraction outside Contraction inside Shrinking

  17. Numerical implementation Nelder-Mead simplex method debtool/lib/regr/nmregr (WLS) debtool/lib/regr/nmvcregr (ML)

  18. Numerical implementation Newton-Raphson A method for finding successively the roots of anequation f(x)=0. The iteration scheme: debtool/lib/regr/nrregr (WLS) debtool/lib/regr/nrvcregr (ML) Source wikipedia

  19. Evaluation of the estimation • Effects of pseudo-data • Elasticity coefficients θa core parameter to be estimated estimate ofθ given the pseudo data θ0 αpercentage increase in pseudo-value estimate ofθ given the pseudo data θ0(1+α)

  20. Evaluation of the estimation • Goodness of fit • Mean relative error for the real data FIT =10 (1-MRE)

  21. Parameter identifiability κdata on growth and reproduction and size at birth and puberty are required simultaneously z, δMzero-variate data and growth data, while additional uni-variate data reduce the standard deviation of the estimate. κΧ, {Fm}feeding data kJ, EHp,κRreproduction at several food levels ha mean life span sGsurvival as a function of age Kooijman et al. 2008 Biol. Rev., 83:533-552. Lika et al., 2011 J. Sea Research 22:278-288

  22. Properties of the covariation method estimation of parameter κ The effect ofthe pseudo-value κis reduced only when there is information for both growth and reproduction estimation of parameter theeffectof the pseudo-valueisreducedonly wheninformation on age at birth and puberty is given estimation of parameter [pM] the effects of the pseudo-value [pM] are reduced as information on real data increases the least effect is obtained when information on respiration is included the estimation of [EG] the effects of the pseudo-data κG are reduced as information on real data increases estimation of the parameter kJ the pseudo-value for kJ does not play significant role

  23. The covariation method for parameter estimation • Estimation of all parameters of the standard DEB model simultaneously • Real-data and pseudo-data, exploiting the rules for the covariation of parameter values among species implied by the standard DEB model • The least required information is the maximum size, but the pseudo-data fully control the result • Increasing the number of type of data decreases the role of pseudo data

  24. Add_my_pet collection 2011 : ~ 60 species 2013 : 240 species

  25. Max specific assimilation rate Before acceleration After acceleration Kooijman, 2013 Oikos 122:348-357

  26. Maturity levels

  27. Energy conductance Before acceleration After acceleration

  28. Thank you for your attention

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