python

python

1 python

” 12 1212 276 ”

t N_t N_t+1

N_t+1=N_t+r*N_t*(1-N_t/K)

r

python

python

t Nt 1.0r 1.5K 100

T 30Nt

TNt Nt+r*Nt*(1.0-Nt/K)

Nt

python

IDLE

IDLE File New WindowRun

Run module

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Nt=1.0r=1.5K=100T=30print("0"+"\t"+str(Nt))for  i  in  range(T):        Nt=  Nt+r*Nt*(1.0-­‐Nt/K)        print(str(i+1)+"\t"+str(Nt))

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python

python matplotlibEPD Free matplotlib

matplotlib

matplotlib

matplotlib pyplot plt.

1 import  matplotlib.pyplot  as  plt<br> ?

x, ypython x

y dataX, dataYpython

2 printx 0 y Nt

0 Nt=1.0

for i 0 T-1

for

plt.plot dataX x dataY y

12

dataX=[]dataY=[]

12

dataX.append(0)dataY.append(Nt)

12

dataX.append(i+1)dataY.append(Nt)

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plt.plot(dataX,  dataY)plt.xlabel("time")plt.ylabel("population  size")plt.show()

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?

?

?

r

(a) (b)(c)

r

python def python python C

return( )x y

python

K, r, T N_t N_0 x ydo_logistic_growth

return return(fdataX, fdataY) dataX,dataY= return

dataX datax dataY datay dataX, dataY plot

python

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import  matplotlib.pyplot  as  plt  def  do_logistic_growth(k,  r,  n0,  t):        nt=  n0        datax=[]        datay=[]          datax.append(0)        datay.append(nt)          for  i  in  range(t):                nt=  nt+r*nt*(1.0-­‐nt/k)                datax.append(i+1)                datay.append(nt)          return(datax,  datay)    dataX,  dataY=  do_logistic_growth(100.0,  1.5,  1.0,  20)plt.plot(dataX,  dataY)  plt.xlabel("time")plt.ylabel("population  size")plt.show()

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(a) (b) (c) a: -> b: -> c: r 0<=r<=3 20

K=100, N_0 Nt =1.0r

show plot

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dataX,  dataY=  do_logistic_growth(パラメータ設定１)plt.plot(dataX,  dataY)  dataX,  dataY=  do_logistic_growth(パラメータ設定２)plt.plot(dataX,  dataY)  ...

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r r251 300 50 N_t

K=100, r 1.0 3.0 0.01

plt.plot "."

plt.plot(dataX, dataY, '.')

bifX bifYbifX: [1.0, 1.0, 1.0, ..., 1.0 (50 ), 1.01, 1.01, ..., 1.01 (50 ), ..., 3.0, ..., 3.0 (50 )]bifY: ["r=1.0 251 Nt", "r=1.0 252 Nt", ..., "r=1.0 300 Nt", "r=1.01 251 Nt", "r=1.01 252 Nt", ..., "r=1.01 300 Nt", ..., "r=3.0 251 Nt", "r=3.0 252 Nt", ..., "r=3.0 300 Nt"]

bifX bifY, rdataX[251:301] dataY[251:301] bifX, bifY

x a b x[a:b+1]x y x+y x=[x1, x2] y=[y1, y2] x+y [x1, x2, y1, y2]

a b x x= [b] * a x [b, b, ..., b] ba

21 t N1t 2

N2t 1 2 r K

1 2

12 d(0<=d<=1)

d

K=100 1

2 NA_t NB_t

r_A r_B A B d_A d_B A B X Q

X d

Q

”Yoshida T, Ellner SP, Jones LE, Bohannan BJM, Lenski RE, et al. (2007)Cryptic population dynamics: Rapid evolution masks trophic interactions. PLoS Biol 5(9): e235.”

B Ad_B<d_A r_B<r_A

P PNA NB NA+NB

” ”