%% iget_pars_9_foetus % %% function data = iget_pars_9_foetus (par, t_0, fixed_par, chem_par, T, T_A) % created 2014_06_16 by Bas Kooijman %% Syntax % data = <../iget_pars_9_foetus.m *iget_pars_9_foetus*> (par, t_0, T, T_A) %% Description % Obtains 9 data points from 9 DEB parameters at abundant food fro foetal development. % No acceleration. Time at start development is an extra parameter. % % 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_Hx, J, E_H^x, maturity at weaning % E_Hp, J, E_H^p, maturity at puberty % h_a, 1/d^2, ageing acceleration % % * t_0: scalar with delay till start development: a_b = t_b - t_0 % * 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 % * T: optional scalar with body temperature (default 293.15 K) % * T_A: optional scalar with Arrhenius temperature (default 8000 K) % % Output % % * data: 9-vector with zero-variate data % % d_V, g/cm^3 specific density of structure % t_b, d, time at birth % t_x, d, time since birth at weaning % t_p, d, time since birth at puberty % t_m, d, time since birth at death due to ageing % W_b, g, wet weight at birth % W_x, g, wet weight at weaning % W_m, g, maximum wet weight % R_m, #/d, maximum reproduction rate %% Remarks % The theory behind iget_pars_9 is discussed in % . % See for inverse mapping. % See for egg development. %% Example of use % See <../mydata_get_pars_9_foetus.m *mydata_get_pars_9_foetus*> % assumptions: % abundant food (f=1) 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 = 0.5; % -, 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_Hx = par(7); % J, E_H^x, maturity level at weaning E_Hp = par(8); % J, E_H^p, maturity level at puberty h_a = par(9); % 1/d^2, ageing acceleration % correct for temperature using T_ref = 293.15; % K, reference temperature if ~exist('T', 'var') T = T_ref; % K, body temperature end if ~exist('T_A', 'var') T_A = 8e3; % K, Arrhenius temperature end TC = tempcorr(T, T_ref, T_A); p_Am = p_Am * TC; v = v * TC; p_M = p_M * TC; h_a = h_a * TC^2; % 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 l_i = 1 - l_T; % -, scaled ulitmate 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 weaning U_Hx = E_Hx/ p_Am; % cm^2 d, scaled maturity at weaning V_Hx = U_Hx/ (1 - kap); % cm^2 d, scaled maturity at weaning v_Hx = V_Hx * g^2 * k_M^3/ v^2; % -, scaled maturity at weaning % 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_tx = [g; k; l_T; v_Hb; v_Hx; v_Hp]; % compose parameter vector for get_tj [t_p t_x t_b l_p l_x l_b] = get_tx(pars_tx, 1); a_b = t_b/ k_M; % d, age at birth a_x = t_x/ k_M; % d, age at weaning a_p = t_p/ k_M; % d, age at puberty L_b = l_b * L_m; % cm, structural length at birth L_x = l_x * L_m; % cm, structural length at weaning %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_x = L_x^3 * (1 + w); % g, wet weight at weaning %Ww_p = L_p^3 * (1 + w); % g, wet weight at puberty Ww_m = L_i^3 * (1 + w); % g, ultimate wet weight u_E0 = (1 + g + l_b * 3/ 4) * l_b^3/ g; % -, scaled initial reserve R_m = (1 - kap) * kap_R * k_M * (1 - k * v_Hp)/ u_E0; 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 h_G = s_G * k_M * g; % 1/d, Gompertz aging rate a_m = fzero(@fnget_am, a_m, [], h_G, s_G^3 * g^2 * k_M^2/ h_a); t_b = a_b + t_0; % d, time at birth t_x = a_x - a_b; % d, time since birth at weaning t_p = a_p - a_b; % d, time since birth at puberty t_m = a_m - a_b; % d, time since birth at death % pack data data = [d_V; t_b; t_x; t_p; t_m; Ww_b; Ww_x; Ww_m; R_m]; end % subfunctions function f = fnget_am(a_m, h_G, t_W) t_G = a_m * h_G; f = 1 - exp(t_G) + t_G + t_G^2/2 + t_W * log(2); end