BYOM function call_deri.m (calculates the model output)

Syntax: [Xout TE] = call_deri(t,par,X0v)

This function calls the ODE solver to solve the system of differential equations specified in derivatives.m, or the explicit function(s) in simplefun.m. It is linked to the model in the directory 'simple_compound'. As input, it gets:

The output Xout provides a matrix with time in rows, and states in columns. This function calls derivatives.m. The optional output TE is the time at which an event takes place (specified using the events function). The events function is set up to catch discontinuities. It should be specified according to the problem you are simulating. If you want to use parameters that are (or influence) initial states, they have to be included in this function.

Copyright (c) 2012-2019, Tjalling Jager, all rights reserved.
This source code is licensed under the MIT-style license found in the
LICENSE.txt file in the root directory of BYOM.

Contents

Start

function [Xout TE] = call_deri(t,par,X0v)
global glo   % allow for global parameters in structure glo
global zvd   % global structure for zero-variate data

Initial settings

This part extracts optional settings for the ODE solver that can be set in the main script (defaults are set in prelim_checks). The useode option decides whether to calculate the model results using the ODEs in derivatives.m, or the analytical solution in simplefun.m. Using eventson=1 turns on the events handling. Also modify the sub-function at the bottom of this function! Further in this section, initial values can be determined by a parameter (overwrite parts of X0), and zero-variate data can be calculated. See the example BYOM files for more information.

useode   = glo.useode; % calculate model using ODE solver (1) or analytical solution (0)
eventson = glo.eventson; % events function on (1) or off (0)
stiff    = glo.stiff; % set to 1 to use a stiff solver instead of the standard one

% Unpack the vector X0v, which is X0mat for one scenario
X0 = X0v(2:end); % these are the intitial states for a scenario

% if needed, extract parameters from par that influence initial states in X0
% start from specified initial size in a model parameter
L0 = par.L0(1); % initial body length (mm) is a parameter
X0(glo.locL) = L0; % put this estimate in the correct location of the initial vector

Calculations

This part calls the ODE solver (or the explicit model in simplefun.m) to calculate the output (the value of the state variables over time). There is generally no need to modify this part. The solver ode45 generally works well. For stiff problems, the solver might become very slow; you can try ode15s instead.

c  = X0v(1); % the concentration (or scenario number)
t  = t(:);   % force t to be a row vector (needed when useode=0)

% specify options for the ODE solver
options = odeset; % start with default options
if eventson == 1
    options = odeset(options, 'Events',@eventsfun); % add an events function
end
options = odeset(options, 'RelTol',1e-4,'AbsTol',1e-7); % specify tightened tolerances
options = odeset(options,'InitialStep',(t(end)-t(1))/1000,'MaxStep',(t(end)-t(1))/100); % specify smaller stepsize
% This small time step will make the simulations considerably slower.
% However, this extra precision is needed for time-varying concentrations,
% time-varying food levels, and possibly also for starvation. You can
% comment out this option setting for extra speed, if you know what you're
% doing.

TE = 0; % dummy for time of events

if useode == 1 % use the ODE solver to calculate the solution
    % call the ODE solver (use ode15s for stiff problems, especially for pulses)
    if isempty(options.Events) % if no events function is specified ...
        switch stiff
            case 0
                [~,Xout] = ode45(@derivatives,t,X0,options,par,c);
            case 1
                [~,Xout] = ode113(@derivatives,t,X0,options,par,c);
            case 2
                [~,Xout] = ode15s(@derivatives,t,X0,options,par,c);
        end
    else % with an events functions ... additional output arguments for events:
        % TE catches the time of an event, YE the states at the event, and IE the number of the event
        switch stiff
            case 0
                [~,Xout,TE,YE,IE] = ode45(@derivatives,t,X0,options,par,c);
            case 1
                [~,Xout,TE,YE,IE] = ode113(@derivatives,t,X0,options,par,c);
            case 2
                [~,Xout,TE,YE,IE] = ode15s(@derivatives,t,X0,options,par,c);
        end
    end
else % alternatively, use an explicit function provided in simplefun!
    Xout = simplefun(t,X0,par,c);
end

if isempty(TE) || all(TE == 0) % if there is no event caught
    TE = +inf; % return infinity
end

Output mapping

Xout contains a row for each state variable. It can be mapped to the data. If you need to transform the model values to match the data, do it here.

if glo.len == 2 % when animal cannot shrink in length (but does on weight!)
    L = Xout(:,glo.locL); % take correct state for body lenght
    maxL = 0; % initialise value for max size achieved
    for i = 1:length(L) % run through length data
        maxL = max([maxL;L(i)]); % new max is max of old max and previous size
        L(i) = maxL; % replace value in output vector
    end
    Xout(:,glo.locL) = L; % replace body weight by physical body length
end

% % To obtain the output of the derivatives at each time point. The values in
% % dXout might be used to replace values in Xout, if the data to be fitted
% % are the changes (rates) instead of the state variable itself.
% % dXout = zeros(size(Xout)); % initialise with zeros
% for i = 1:length(t) % run through all time points
%     dXout(i,:) = derivatives(t(i),Xout(i,:),par,c);
%     % derivatives for each stage at each time
% end

Events function

Modify this part of the code if eventson=1. This subfunction catches the 'events': in this case, this one catches when the scaled internal concentration exceeds one of the NECs, and catches the switch at puberty.

Note that the eventsfun has the same inputs, in the same sequence, as derivatives.m.

function [value,isterminal,direction] = eventsfun(t,X,par,c)

global glo
Lp = par.Lp(1); % length at puberty (mm)
zb = par.zb(1); % effect threshold for the energy budget
zs = par.zs(1); % effect threshold for survival

nevents = 3; % number of events that we try to catch

value    = zeros(nevents,1); % initialise with zeros
value(1) = X(glo.locD) - zb; % follow when scaled damage exceeds the effect threshold for the energy budget
value(2) = X(glo.locD) - zs; % follow when scaled damage exceed the effect threshold for survival
value(3) = X(glo.locL) - Lp; % follow when body length exceeds length at puberty

isterminal = zeros(nevents,1); % do NOT stop the solver at an event
direction  = zeros(nevents,1); % catch ALL zero crossing when function is increasing or decreasing