%% iget_pars_9 % Obtains 9 data points from 9 DEB parameters at abundant food %% function data = iget_pars_9(par, fixed_par, chem_par) % created 2013/07/08 by Bas Kooijman; modified 2013/09/26 %% Syntax % data = <../iget_pars_9.m *iget_pars_9*>(par, fixed_par, chem_par) %% Description % Obtains 9 data points from 9 DEB parameters at abundant food % % Input % % * par: 9-vector with DEB parameters % % p_Am: J/d.cm^2, {p_Am}, max specific assimilation rate % v: cm/d, energy conductance % kap: -, allocation fraction to soma % p_M: J/d.cm^3, [p_M], specific somatic maintenance costs % E_G: J/cm^3, [E_G] specific cost for structure % E_Hb: J, E_H^b, maturity at birth % E_Hj: J, E_H^j, maturity at metamorphosis % E_Hp: J, E_H^p, maturity at puberty % h_a: 1/d^2, ageing acceleration % % * fixed_par: optional 4 vector with k_J, s_G, kap_R, kap_G % * chem_par: optional 4 vector with w_V, w_E, mu_V, mu_E % % Output % % * data: 9-vector with zero-variate data % % d_V: g/cm^3 specific density of structure % a_b: d, age at birth % a_p: d, age at puberty % a_m: d, age at death due to ageing % W_b: g, wet weight at birth % W_j: g, wet weight at metamorphosis % W_p: g, wet weight at puberty % W_m: g, maximum wet weight % R_m: #/d, maximum reproduction rate %% Remarks % The theory behind this mapping is discussed in % . % See for the inverse mapping %% Example of use % See <../mydata_get_pars_9.html *mydata_get_pars_9*> % assumptions: % abundant food (f=1) % a_b, a_p, a_m and R_m are temp-corrected to T_ref = 293 K p_T = 0; % J/d, {p_T} = 0 J/d.cm^2, surf-spec som maint if exist('fixed_par','var') == 0 k_J = 0.002; % 1/d, maturity maintenance rate coefficient s_G = 1e-4; % -, Gopertz stress coefficient (= small) kap_R = 0.95; % -, reproduction efficiency kap_G = 0.8; % -, growth efficiency else k_J = fixed_par(1); % 1/d, maturity maintenance rate coefficient s_G = fixed_par(2); % -, Gopertz stress coefficient (= small) kap_R = fixed_par(3); % -, reproduction efficiency kap_G = fixed_par(4); % -, growth efficiency end if exist('chem_par', 'var') == 0 % C:H:O:N = 1:1.8:0.5:0.15 w_V = 23.9; % g/C-mol, molecular weight of structure w_E = 23.9; % g/C-mol, molecular weight of reserve mu_V = 5E5; % J/C-mol, chemical potential of structure mu_E = 5.5E5; % J/C-mol, chemical potential of reserve else w_V = chem_par(1); w_E = chem_par(2); mu_V = chem_par(3); mu_E = chem_par(4); end % unpack par p_Am = par(1); % J/d.cm^2, {p_Am}, max specific assimilation rate v = par(2); % cm/d, energy conductance kap = par(3); % -, allocation fraction to soma p_M = par(4); % J/d.cm^3, [p_M], specific somatic maintenance costs E_G = par(5); % J/cm^3, [E_G], specific cost for structure E_Hb = par(6); % J, E_H^b, maturity level at birth E_Hj = par(7); % J, E_H^j, maturity level at metamorphosis E_Hp = par(8); % J, E_H^p, maturity level at puberty h_a = par(9); % 1/d^2, ageing acceleration % compound pars k_M = p_M/ E_G; % 1/d, somatic maintenance rate coefficient k = k_J/ k_M; % -, maintenance ratio d_V = kap_G * E_G * w_V/ mu_V; % g/cm^3, specific density of structure E_m = p_Am/ v; % J/cm^3, [E_m] reserve capacity g = E_G/ kap/ E_m; % -, energy investment ratio w = E_m * w_E/ d_V/ mu_E; % -, contribution of reserve to weight L_m = v/ k_M/ g; % cm, maximum structural length L_T = p_T/ p_M; % cm, heating length (also applies to osmotic work) l_T = L_T/ L_m; % -, scaled heating length % maturity at birth U_Hb = E_Hb/ p_Am; % cm^2 d, scaled maturity at birth V_Hb = U_Hb/ (1 - kap); % cm^2 d, scaled maturity at birth v_Hb = V_Hb * g^2 * k_M^3/ v^2; % -, scaled maturity at birth % maturity at metamorphosis U_Hj = E_Hj/ p_Am; % cm^2 d, scaled maturity at metamorphosis V_Hj = U_Hj/ (1 - kap); % cm^2 d, scaled maturity at metamorphosis v_Hj = V_Hj * g^2 * k_M^3/ v^2; % -, scaled maturity at metamorphosis % maturity at puberty U_Hp = E_Hp/ p_Am; % cm^2 d, scaled maturity at puberty V_Hp = U_Hp/ (1 - kap); % cm^2 d, scaled maturity at puberty v_Hp = V_Hp * g^2 * k_M^3/ v^2; % -, scaled maturity at puberty % obtain predictions pars_tj = [g; k; l_T; v_Hb; v_Hj; v_Hp]; % compose parameter vector for get_tj [t_j t_p t_b l_j l_p l_b l_i] = get_tj(pars_tj, 1); a_b = t_b/ k_M; % d, age at birth % a_j = t_j/ k_M % d, age at metamorphosis a_p = t_p/ k_M; % d, age at puberty L_b = l_b * L_m; % cm, structural length at birth L_j = l_j * L_m; % cm, structural length at metamorphosis L_p = l_p * L_m; % cm, structural length at puberty L_i = l_i * L_m; % cm, ultimate structural length Ww_b = L_b^3 * (1 + w); % g, wet weight at birth Ww_j = L_j^3 * (1 + w); % g, wet weight at metamorphosis Ww_p = L_p^3 * (1 + w); % g, wet weight at puberty Ww_m = L_i^3 * (1 + w); % g, ultimate wet weight pars_Rm = [kap; kap_R; g; k_J; k_M; L_T; v; U_Hb; U_Hj; U_Hp]; % compose par vector R_m = reprod_rate_j(L_i, 1, pars_Rm); % #/d, maximum reprod rate pars_tm = [g; l_T; h_a/ k_M^2; s_G]; % compose parameter vector t_m = get_tm_s(pars_tm, 1); % -, scaled mean life span a_m = t_m/ k_M; % d, mean life span at T % pack data data = [d_V; a_b; a_p; a_m; Ww_b; Ww_j; Ww_p; Ww_m; R_m];