8/12/2019 Levinson A

1/6

MATLAB code to produce the following model:

%Andrew Levinson%April 28, 2009%ompeting species!"red#tor$"re Model

%&et up p#r#meters for vector field

'(,)* + meshgrid0:-.:2-/, 0:-.:2-/1.+(-3.-/$-/3($)14.+)-32$)$.-.2/3(12+(-3.$-/3)142+)-3$-2/$-/3(1w#rning off #ll%Begin simul#tionfor #lp+0:-0.:. figure1hold on%re#te new figure +.$#lp3.5#lp321

4+.$#lp34.5#lp3421 L+s6rt-7254-721 6uiver(,), -!L,4-!L,-/%plot vector field #is e6u#l

%"h#se plot e6u#tion +t,'.$#lp3.3.-/$-/3.$25#lp3.3.$-/321.$#lp3232$2$.-.2/3.5#lp323$-2/$-/3.*1 for #+$2:-2/:2%"h#se plot loop for ;+$2:-2/:2 't,#*+ode minutes to run on # 2->> ?h@ ntel% entrio uo with 2 ?B of CAM running MATLAB C200D#

8/12/2019 Levinson A

2/6

At E+0 the model is purel competing species- There #re critic#l points #t 0,0

#nd .,.- This model reflects # point in time when there #re two species competing fo

the s#me suppl of food- All the possi;le initi#l v#lues tend tow#rds # line th#t runs

#pproim#tel from 0,2 to >,0- This would ;e ;efore #n of either species #d#pted

to ;e #;le to ill #nd consume the other for food- The ph#se portr#it shows no signs of

inw#rd curl th#t is # tr#it of the pred#tor$pre model-

8/12/2019 Levinson A

3/6

At this point E+-> #nd the pred#tor$pre model is ;eginning to t#e over the

competing species model- The critic#l point #t .,. h#s shifted up #nd to the left #nd

is now #t -

8/12/2019 Levinson A

4/6

At E+-/ the model is evenl split ;etween competing species #nd pred#tor$pre-

The critic#l point #t .,. initi#ll h#s now shifted to the $#is- This signifies # point in

evolution when # h#lf of the pred#tor popul#tion h#s #d#pted to e#t its one time

competitor #s # source of food- The tr#it h#s not ;een ;red into the entire pred#tor

popul#tion #nd will still t#e time ;efore evolution is complete- There is now much less

competition for the origin#l food source #s the pred#tor popul#tion no longer re6uires

#s much of it to survive #nd there #re less cre#tures over#ll who need it for

nourishment- The ph#se portr#it #t this time is ;eginning to ;e domin#ted ; thepred#tor pre model #s it now h#s signific#nt inw#rd curl-

8/12/2019 Levinson A

5/6

At E+ -D the pred#tor$pre model h#s #lmost completel overwhelmed the

competing species model- The critic#l point th#t h#d ;een shifted to the $#is h#s

now shifted down the $#is to 0,.-2/- The model now simul#tes # point in time

where # signific#nt portion of the pred#tor species h#s evolved to ;e #;le to e#t its

former competitor for food, ;ut there is some competition for food still #s the rest of the

pred#tor species still relies on the initi#l food source #s well #s the pre- The ph#se

portr#it is ;eginning to weed out the competing species model #s it onl influences the

#re# immedi#tel #round the origin-

8/12/2019 Levinson A

6/6

At E+. the model is purel pred#tor$pre- The critic#l point th#t h#d ;een on the

$#is h#s ;een elimin#ted- This model reflects the point in time where the pred#tor

species h#s evolved completel #nd no longer competes for the initi#l food source-

The pre still relies on the food source, ;ut the pred#tor relies solel on the former

competitor- The ph#se portr#it is th#t of # pure pred#tor$pre model-