BYOM function derivatives.m (the model in ODEs)
Syntax: dX = derivatives(t,X,par,c)
This function calculates the derivatives for the model system. It is linked to the script files byom_debkiss_no_egg.m. As input, it gets:
- t is the time point, provided by the ODE solver
- X is a vector with the previous value of the states
- par is the parameter structure
- c is the external concentration (or scenario number)
Time t and scenario name c are handed over as single numbers by call_deri.m (you do not have to use them in this function). Output dX (as vector) provides the differentials for each state at t.
function dX = derivatives(t,X,par,c)
global glo % allow for global parameters in structure glo
The state variables enter this function in the vector X. Here, we give them a more handy name.
WV = X(1); % state 1 is the structural body mass cR = X(2); % state 2 is the cumulative reproduction (not used in this function) WB = 0; % no egg phase, so egg buffer is empty
The parameters enter this function in the structure par. The names in the structure are the same as those defined in the byom script file. The 1 between parentheses is needed as each parameter has 5 associated values.
dV = glo.dV; % dry weight density of structure delM = glo.delM; % shape correction coefficient (if needed) % delM is used to allow Lwp as a parameter instead of WVp sJAm = par.sJAm(1); % specific assimilation rate sJM = par.sJM(1); % specific maintenance costs WB0 = par.WB0(1); % initial weight of egg Lwp = par.Lwp(1); % shell length at puberty yAV = par.yAV(1); % yield of assimilates on volume (starvation) yBA = par.yBA(1); % yield of egg buffer on assimilates yVA = par.yVA(1); % yield of structure on assimilates (growth) kap = par.kap(1); % allocation fraction to soma f = par.f(1); % scaled food level fB = par.fB(1); % scaled food level for the embryo Lwf = par.Lwf(1); % half-saturation length for initial food limitation if glo.len ~= 0 % only if the switch is set to 1 or 2! % Translate shell length at puberty to body weight WVp = glo.dV*(Lwp * glo.delM).^3; % initial length to initial dwt WVf = glo.dV*(Lwf * glo.delM).^3; % initial length to initial dwt end
Calculate the derivatives
This is the actual model, specified as a system of ODEs. Note: some unused fluxes are calculated because they may be needed for future modules (e.g., respiration and ageing).
L = (WV/dV)^(1/3); % volumetric length % select what to do with maturity maintenance if glo.mat == 1 sJJ = sJM * (1-kap)/kap; % add specific maturity maintenance with the suggested value else sJJ = 0; % or ignore it end WVb = WB0 *yVA * kap; % body mass at birth if WB > 0 % if we have an embryo f = fB; % assimilation at different rate else if WVf > 0 f = f / (1+WVf/WV); % hyperbolic relationship for f with body weight end end JA = f * sJAm * L^2; % assimilation JM = sJM * L^3; % somatic maintenance JV = yVA * (kap*JA-JM); % growth if WV < WVp % below size at puberty JR = 0; % no reproduction JJ = sJJ * L^3; % maturity maintenance flux % JH = (1-kap) * JA - JJ; % maturation flux (not used!) else JJ = sJJ * (WVp/dV); % maturity maintenance JR = (1-kap) * JA - JJ; % reproduction flux end % starvation rules may override these fluxes if kap * JA < JM % allocated flux to soma cannot pay maintenance if JA >= JM + JJ % but still enough total assimilates to pay both maintenances JV = 0; % stop growth if WV >= WVp % for adults ... JR = JA - JM - JJ; % repro buffer gets what's left else % JH = JA - JM - JJ; % maturation gets what's left (not used!) end elseif JA >= JM % only enough to pay somatic maintenance JV = 0; % stop growth JR = 0; % stop reproduction % JH = 0; % stop maturation for juveniles (not used) JJ = JA - JM; % maturity maintenance flux gets what's left else % we need to shrink JR = 0; % stop reproduction JJ = 0; % stop paying maturity maintenance % JH = 0; % stop maturation for juveniles (not used) JV = (JA - JM) / yAV; % shrink; pay somatic maintenance from structure end end % we do not work with a repro buffer here, so a negative JR does not make % sense; therefore, minimise to zero JR = max(0,JR); % Calcululate the derivatives dWV = JV; % change in body mass dcR = yBA * JR / WB0; % continuous reproduction flux if WB > 0 % for embryos ... dWB = -JA; % decrease in egg buffer else dWB = 0; % for juveniles/adults, no change end if WV < WVb/4 && dWB == 0 % dont shrink below quarter size at birth dWV = 0; % simply stop shrinking ... end dX = [dWV;dcR]; % collect both derivatives in one vector