## Code for Figure 10.14

### main.m

```
## comparing intrinsic growth rate dispersion to growth dependent dispersion
## jbr 10/5/04

nhalf = 5;
npart = 2*nhalf;

k = 10;

rand('seed',0)
randn('seed',0)

## particles have a distribution of growth rates
g0 = 1;
std = 0.1;
size0 = 10;
ntime = 15;
time = (0:ntime-1)';
x(:,1) = size0*ones(npart,1);
g = std*randn(npart,1) + g0;

for i = 1:ntime-1
x(:,i+1) = x(:,i) + g;
end

## particles have same growth rate; choose which one grows at random
## particle increases size by increment delta

delta = 0.1;
nsim = 1500;
ipart = fix(rand(nsim,1)*npart)+1;
xran = size0*ones(npart,1);
simtim = (0:nsim-1)';
tau(1) = 0;

for i = 1:nsim-1
tau(i+1) = tau(i) -log(rand)/(k*npart);
part = ipart(i);
xran(:,i+1) = xran(:,i);
xran(part,i+1) = xran(part,i) + delta;
end

##sort the particles by size; split into two groups, large and small,
##and grow them again

[size, label] = sort(x(:,ntime));

y1(:,1) = x(label(1:nhalf),ntime);
g1 = g(label(1:nhalf));
y2(:,1) = x(label(nhalf+1:npart),ntime);
g2 = g(label(nhalf+1:npart));

for i = 1:ntime-1
y1(:,i+1) = y1(:,i) + g1;
y2(:,i+1) = y2(:,i) + g2;
end

[size, label] = sort(xran(:,nsim));
y1ran(:,1) = xran(label(1:nhalf),nsim);
y2ran(:,1) = xran(label(nhalf+1:npart),nsim);
simtim = (0:(nsim-1)/2)';
tau1(1) = 0;
tau2(1) = 0;

ipart1 = fix(rand(nsim,1)*nhalf)+1;
ipart2 = fix(rand(nsim,1)*nhalf)+1;
for i = 1:(nsim-1)/2
tau1(i+1) = tau1(i) -log(rand)/(k*npart)*2;
tau2(i+1) = tau2(i) -log(rand)/(k*npart)*2;
part1 = ipart1(i);
part2 = ipart2(i);
y1ran(:,i+1) = y1ran(:,i);
y2ran(:,i+1) = y2ran(:,i);
y1ran(part1,i+1) = y1ran(part1,i) + delta;
y2ran(part2,i+1) = y2ran(part2,i) + delta;
end

table1 = [time,x'];
table2 = [tau',xran'];

% save -ascii dispmodel1.dat table1
% save -ascii dispmodel2.dat table2

save dispmodel.dat table1 table2;

figure(1);
plot (table1(:,1), table1(:,2:10));
title ('Figure 10.14')

figure(2);
plot (table2(:,1), table2(:,2:10));
title ('Figure 10.14')
```

## Data files

### dispmodel.dat

```# Created by Octave 3.6.4, Sat Nov 23 16:40:47 2013 CST
# name: table1
# type: matrix
# rows: 15
# columns: 11
0 10 10 10 10 10 10 10 10 10 10
1 10.78461410999298 10.83132467269897 10.96634800136089 11.09037248492241 11.00534181408584 11.03744063675404 10.96175577640533 11.01738204360008 11.0490690946579 11.03897350132465
2 11.56922821998596 11.66264934539795 11.93269600272179 12.18074496984482 12.01068362817168 12.07488127350807 11.92351155281067 12.03476408720017 12.0981381893158 12.07794700264931
3 12.35384232997894 12.49397401809692 12.89904400408268 13.27111745476723 13.01602544225753 13.11232191026211 12.885267329216 13.05214613080025 13.1472072839737 13.11692050397396
4 13.13845643997193 13.3252986907959 13.86539200544357 14.36148993968963 14.02136725634337 14.14976254701615 13.84702310562134 14.06952817440033 14.19627637863159 14.15589400529861
5 13.92307054996491 14.15662336349487 14.83174000680447 15.45186242461204 15.02670907042921 15.18720318377018 14.80877888202667 15.08691021800042 15.24534547328949 15.19486750662327
6 14.70768465995789 14.98794803619385 15.79808800816536 16.54223490953445 16.03205088451505 16.22464382052422 15.77053465843201 16.1042922616005 16.29441456794739 16.23384100794792
7 15.49229876995087 15.81927270889282 16.76443600952625 17.63260739445686 17.03739269860089 17.26208445727825 16.73229043483734 17.12167430520058 17.34348366260529 17.27281450927257
8 16.27691287994385 16.65059738159179 17.73078401088715 18.72297987937927 18.04273451268674 18.29952509403229 17.69404621124268 18.13905634880066 18.39255275726319 18.31178801059723
9 17.06152698993683 17.48192205429077 18.69713201224804 19.81335236430168 19.04807632677258 19.33696573078632 18.65580198764801 19.15643839240075 19.44162185192109 19.35076151192188
10 17.84614109992981 18.31324672698975 19.66348001360893 20.90372484922408 20.05341814085842 20.37440636754036 19.61755776405334 20.17382043600083 20.49069094657899 20.38973501324654
11 18.63075520992279 19.14457139968872 20.62982801496982 21.99409733414649 21.05875995494426 21.41184700429439 20.57931354045867 21.19120247960091 21.53976004123689 21.42870851457119
12 19.41536931991577 19.9758960723877 21.59617601633071 23.0844698190689 22.0641017690301 22.44928764104843 21.54106931686401 22.208584523201 22.58882913589478 22.46768201589585
13 20.19998342990875 20.80722074508667 22.5625240176916 24.17484230399131 23.06944358311594 23.48672827780246 22.50282509326934 23.22596656680108 23.63789823055268 23.5066555172205
14 20.98459753990173 21.63854541778565 23.5288720190525 25.26521478891372 24.07478539720179 24.52416891455649 23.46458086967467 24.24334861040116 24.68696732521058 24.54562901854516

# name: table2
# type: matrix
# rows: 1500
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```