File:Assumed development of population of precolumbian tiwanaku 1.png

   Erik J. Marsh ,
   Alexei Vranich,
   Deborah Blom,
   Maria Bruno,
   Katharine Davis,
   Jonah Augustine,
   Nicole C. Couture,
   Santiago Ancapichún,
   Kelly J. Knudson,
   Danijela Popović,
   Gianni Cunietti

PLOS

   Published: November 22, 2023
   https://doi.org/10.1371/journal.pone.0288798 

1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 3
2. 2. Tiwanaku population growth , python3, based on simple assumptions
4. 31.12.2023 0000.0000

1. 1. A mathematical model for the Andean Tiwanaku civilization collapse: Climate variations

import math import numpy as np import scipy

import matplotlib.pyplot as plt

from matplotlib.offsetbox import AnchoredText

def calcu_t2_r(t1,t2,p1,p2): td1=abs(t2-t1) pd1=p2/p1 r1=math.log(pd1)/td1 tt2=math.log(2)/r1 return(r1,tt2)

def calcu_population(pop0, r0, deltat, tas1, tas2,populimit1,shrinkt1, shrinkr1, collapset1, collapsefrac1):

rangelen1=int((tas2-tas1)/deltat) taa1=tas1 tb1=0 r1=r0 p1=pop0 taa1=tas1 tees=[] pops=[] nuna=0

for n in range(0,rangelen1): tb1=tb1+deltat taa1=taa1+deltat p2=p1*math.exp(tb1*r1) #print(taa1,p2) if(p2>populimit1): p2=populimit1 r1=1e-4 if(taa1>shrinkt1): r1=shrinkr1 tb1=0 p1=p2 #print(r1,p1) nuna=nuna+1 #print(shrinkt1, collapset1) print(taa1,p2,r1) #if(nuna>2): quit(-1)

if(taa1>collapset1): #print("Collapse") p2=p2*collapsefrac1 r1=-1

tees.append(taa1) pops.append(p2) #print(taa1,tb1,p2) print(taa1,p2)

tees=np.array(tees) pops=np.array(pops)

return(tees, pops)

1. 1. population growth calcu times

p1=2000 ## p2=45000 ## tiwanaku

ta1=150 ## ta2=800

1. 1. rendder times

te1=150 te2=1200

deltat=5 ## time step

1. 1. growth rate
2. r1=0.0031

1. r1=0.00225
2. r1=1e-3 ## often in ancient cultures

rc1,tc_two1=calcu_t2_r(ta1,ta2,p1,p2)

print(" r  %",rc1)

print(" T2 ",int(tc_two1))

tee2=900 deetee2=tee2-ta1

r1=rc1 t_two=tc_two1

pee2=math.exp(r1*deetee2)*p1

print(pee2)

collapsepros1=2000/45000

1. 1. assumed pop collapse to 5%

tees0, pops0=calcu_population(p1/4, r1, deltat, te1, te2, 100000, 800, -r1, 1020,collapsepros1) tees1, pops1=calcu_population(p1/2, r1, deltat, te1, te2, 100000, 800, -r1, 1020,collapsepros1) tees2, pops2=calcu_population(p1, r1, deltat, te1, te2, 100000, 800, -r1, 1020,collapsepros1) tees3, pops3=calcu_population(p1*2, r1, deltat, te1, te2, 100000, 800, -r1, 1020,collapsepros1) tees4, pops4=calcu_population(p1*3, r1, deltat, te1, te2, 100000, 800, -r1, 1020,collapsepros1)

plt.plot(tees0,pops0, lw=2, color="violet", linestyle=":", label="500") plt.plot(tees1,pops1, lw=3, color="blue", linestyle="--", label="1000") plt.plot(tees2,pops2, lw=5, color="green", label="2000") plt.plot(tees3,pops3, lw=3, linestyle=":", color="orange", label="4000")

plt.legend(title="Initial population")

SMALL_SIZE = 16 MEDIUM_SIZE = 18 BIGGER_SIZE = 20

plt.rcParams.update({'font.size': MEDIUM_SIZE,}) plt.tick_params(labelsize=MEDIUM_SIZE)

plt.rc('font', size=SMALL_SIZE) # controls default text sizes plt.rc('xtick', labelsize=MEDIUM_SIZE) # fontsize of the tick labels plt.rc('ytick', labelsize=MEDIUM_SIZE)

plt.suptitle("Assumed Tiwanaku population") plt.title("Constant growth rate, shrink, sudden collapse") plt.xlabel("Year BC/AD", size=MEDIUM_SIZE) plt.ylabel("Population, estimated", size=MEDIUM_SIZE)

plt.grid()

1. annot1="Initial population at "+str(ta1)+ " BC "+str(p1)

1. annot2="Population at "+str(ta2)+ " AD "+str((p2+10)/1000000)+" million"

annot3="Growth rate "+str(round(r1*10000)/100)+ " %" annot4="Duplication time "+str(int(round(t_two)))+ " yr"

1. plt.text(-10000, 4.0e6, "Assumptions", fontsize=12)

1. plt.text(-10000, 3.5e6, annot1, fontsize=12)
2. plt.text(-10000, 3.25e6, annot2, fontsize=12)

plt.text(200, 8.0e4, annot3, fontsize=20) plt.text(200, 7.0e4, annot4, fontsize=20)

plt.show()