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coupled model
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# Coding manuscript 1
#the coupled model
# Python version 3.4.3
# -*- coding: utf-8 -*-
"""
Created on Fri Apr 1 15:40:42 2016
@author: jrhillae
"""
import itertools
import numpy as np
import scipy.stats as sp
import random as rnd
import math
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
import sys
import timeit
class Write_Weights:
def __init__(self,
Title,
Number,
sample_ind):
self.sample_weights = open((str(Number) + 'Sample_weights' + Title + '.txt'), 'w')
self.sample_weights.write('%20s'%'AdultWeights [kg]'+ '\n')
for a in sample_ind:
self.sample_weights.write('%20s'%str(a.AdultWeight) + '\n')
#closing file
self.sample_weights.close()
class Write_Files:
def __init__(self,
Title,
Summary,
sample_ind,
ResDist,
ConDist,
landscape,
grid,
Variability,
Locations,
Fst,
O):
'''Writing out the values within summary into text files'''
#create output file for the summary values
self.summary = open('Summary' + Title + '.txt', 'w')
self.sample_weights = open('Sample_weights' + Title + '.txt', 'w')
self.cell_specific_data= open ('Cell_specific_data' + Title + '.txt', 'w')
self.variability=open('Variability'+Title+'.txt', 'w')
self.locations=open('Locations_' + Title + '.txt', 'w')
self.fst=open('Fst_'+ Title + '.txt', 'w')
#headings
self.summary.write('%20s'%'Time' + '\t'+ \
'%20s'%'MeanR[J/cell]' + '\t'+ \
'%20s'%'VarR' + '\t'+ \
'%20s'%'TotalAmountR'+'\t'+ \
'%20s'%'TotalAdults'+'\t'+\
'%20s'%'TotalLarvae'+'\t'+ \
'%20s'% 'AWeightAverage[kg]'+'\t'+ \
'%20s'% 'AWeightVariance'+'\t'+ \
'%20s'% 'AWeightSkewness'+'\t'+ \
'%20s'% 'AWeightKurtosis'+'\t'+ \
'%20s'% 'AWeightCV'+'\t'+ \
'%20s'% 'AWeightLower[kg]'+'\t'+ \
'%20s'% 'AWeightUpper[kg]'+'\n')
self.sample_weights.write('%20s'%'AdultWeights [kg]' + '%20s'%'CurrentWeights [kg]' + '\t' + '%20s'%'Neutral gene' +'\n')
self.cell_specific_data.write(self.Cell_specific_data(ResDist, ConDist, landscape, grid))
self.variability.write(self.Calculate_variability(Variability))
#writing out values in both files
for time in Summary['Time']:
self.summary.write('%20s'%str(time) + '\t'+ \
'%20s'%str(Summary['MeanR'][time]) + '\t'+ \
'%20s'%str(Summary['VarR'][time]) + '\t'+ \
'%20s'%str(Summary['TotalAmountR'][time])+'\t'+ \
'%20s'%str(Summary['TotalAdults'][time])+'\t'+\
'%20s'%str(Summary['TotalLarvae'][time])+'\t'+ \
'%20s'%str(Summary['AWeightAverage'][time])+'\t'\
'%20s'%str(Summary['AWeightVariance'][time])+'\t'\
'%20s'%str(Summary['AWeightSkewness'][time])+'\t'\
'%20s'%str(Summary['AWeightKurtosis'][time])+'\t'\
'%20s'%str(Summary['AWeightCV'][time])+'\t'\
'%20s'%str(Summary['AWeightLower'][time])+'\t'\
'%20s'%str(Summary['AWeightUpper'][time])+'\n')
for a in sample_ind:
self.sample_weights.write('%20s'%str(a.AdultWeight)+'\t'+'%20s'%str(a.Weight)+'\t'+'%20s'%str(a.neutral)+'\n')
for item in Locations.keys():
self.locations.write(str(item))
for loc in Locations[item]:
self.locations.write(' '+ str(loc))
self.locations.write('\n')
for item in Fst:
self.fst.write(str(item)+'\t')
self.fst.write('\n')
for item in O:
self.fst.write(str(item)+'\t')
#closing files
self.summary.close()
self.sample_weights.close()
self.cell_specific_data.close()
self.variability.close()
self.locations.close()
self.fst.close()
def Cell_specific_data(self, ResDist, ConDist, landscape, grid):
content= ''
content+='%20s'% 'y'+'\t'+ \
'%20s'% 'x'+'\t'+ \
'%20s'% 'Nind'+'\t'+ \
'%20s'% 'MeanAW_cell'+'\t'+ \
'%20s'% 'VarAW_cell'+'\t'+ \
'%20s'% 'MeanCW_cell'+'\t'+ \
'%20s'% 'VarCW_cell'+'\t'+ \
'%20s'% 'Resources'+'\n'
for y in range (grid[0]):
for x in range (grid[1]):
if landscape[y,x]==1:
Nind= (len(ConDist['Larvae'][y][x]) + len(ConDist['Adults'][y][x]))
if Nind>0:
Adult_weights= [ind.AdultWeight for stage in ConDist for ind in ConDist[stage][y][x]]
Current_weights=[ind.Weight for stage in ConDist for ind in ConDist[stage][y][x]]
MeanAW= np.mean(Adult_weights)
VarAW= np.var(Adult_weights)
MeanCW=np.mean(Current_weights)
VarCW=np.var(Current_weights)
R= ResDist[y,x]
else: MeanAW, MeanCW, VarAW,VarCW, R= \
'None', 'None','None','None', ResDist[y,x]
content+='%20s'%str(y)+'\t'\
'%20s'%str(x)+'\t'\
'%20s'%str(Nind)+'\t'\
'%20s'%str(MeanAW)+'\t'\
'%20s'%str(VarAW)+'\t'\
'%20s'%str(MeanCW)+'\t'\
'%20s'%str(VarCW)+'\t'\
'%20s'%str(R)+'\n'
return content
def Calculate_variability (self, Variability):
a=np.cov(Variability)
x=0
for i in range (len(Variability)):
x+=math.sqrt(a[i,i])
muM= sum([np.mean(b) for b in Variability])
alpha= (x/muM)**2
y=0
for e in range (len(Variability)):
for f in range (len(Variability)):
y+=a[e,f]
gamma= y/(muM**2)
beta1=alpha/gamma
beta2=alpha-gamma
solution = '%20s'%str(alpha)+'\t'\
'%20s'%str(beta1)+'\t'\
'%20s'%str(beta2)+'\t'\
'%20s'%str(gamma)
return solution
class Plot_Visual:
def __init__(self, Title,
summary,
Maxtime,
MaxAmountR,
sample_ind):
'''Creating plots with values of summary'''
#create 3 graphs in 1 image:
#Plot of the Amount of Resources
plt.figure(figsize=(10,10))
plt.subplot(311)
plt.ylabel('Average amount of resources')
plt.ylim((0, MaxAmountR))
plt.title('Resources')
plt.plot(summary['Time'],summary['MeanR'])
#Plot of the amount of Adults and Larvae
plt.subplot(312)
plt.ylabel('Total number')
plt.title('Consumer')
plt.plot(summary['Time'], summary['TotalAdults'], 'b-', label= 'Adults')
plt.plot(summary['Time'], summary['TotalLarvae'], 'r-', label= 'Larvae')
lg1=plt.legend(loc='upper left')
lg1.draw_frame(False)
#PLot of the average weight of the Adults
plt.subplot(313)
plt.xlabel('Time')
plt.ylabel('Weight [kg]')
plt.title('Evolution of weight')
plt.plot(summary['Time'], summary['AWeightLower'], '--', color=(0.5,0.5,0.9))
plt.plot(summary['Time'], summary['AWeightUpper'], '--', color=(0.5,0.5,0.9))
plt.plot(summary['Time'], summary['AWeightAverage'], 'b-', label= 'AdultWeight')
lg2=plt.legend(loc='upper left')
lg2.draw_frame(False)
#Save the 3 graphs as 1 PNG file
plt.savefig(('FigurSummary' + Title + '.png'), bbox_edges='tight')
#Delete the active figure
#plt.clf()
#Create a histogram of the weights of Adults in final population, and save it as a PNG file
if len(sample_ind)>0:
plt.figure()
plt.hist([ind.AdultWeight for ind in sample_ind], label=['AdultWeight'])
plt.xlabel('Weight [kg]')
plt.ylabel('Total number')
plt.title('Distribution of weight')
lg3=plt.legend(loc='upper right')
lg3.draw_frame(False)
plt.savefig(('Histogram' + Title + '.png'), bbox_edges='tight')
#Delete the active figure
#plt.clf()
#plt.show()
class ConInd:
def __init__(self,
AdultWeight, #kg
neutral,
Gene_Fst,
t,
Weight = 0, #kg
Energy = 0, #J
DevelAge = 0): #day
'''Creating a consumer individual'''
#Weight when maturity is reached or potential maximal weight
self.AdultWeight = AdultWeight
#The current weight of an individual
self.Weight = Weight
# m0 (start weight): egg size for young
self.InitialWeight = Weight
#Energy reservoir for BMR, dispersion, growth and reproduction
self.Energy = Energy
# an individual's neutral marker for determining origin of variation
self.neutral = neutral
#an individuals developmental age according to the growth curve of West et al. (2001)
self.DevelAge = DevelAge
#Neutral gene used to calculte Fst value
self.gene_fst=Gene_Fst
#time of introduction, immigration or birth
self.t=t
def ConsumeCI(self, TimeC, Assim_Frac=1, Res= 1, Sum=1):
'''Replenish an individual's energy reservoir with a
fraction of the consumed energy'''
#Ingestation rate (Watts) of carnivorous poikilotherms
#(carnivorous, copepods, benthic detrivores):
#2W ^ 0.80 (Peters 1983)
return Assim_Frac * TimeC *2.0 * (self.Weight**0.80)*(Res/Sum)
def BMR_Move_CI(self,SP,TimeD,y,x,grid,p):
'''Expenditure of energy on daily basal metabolism
Returning an array of foraging area or 'Death' or 'No' (in case an individual does not move).
This function is written for a squared landscape!!!'''
#Basal metabolic rate: 0.14W ^ 0.751 (Peters 1983) [J/s]
#Energy expended on basal metabolic processes throughout the entire day
#Cost of movement already includes cost of BMR
BMRDay = 0.14 * (self.Weight**0.751) *24 * 3600#[J/day]
#Energy for basal metabolic processes extracted from energy reservoir
self.Energy -= BMRDay
if self.Energy <0:
return 'Death'
if rnd.random()<p:
#Cost of movement(J/s): 0.17W (kg) ^ 0.75 + 3.4W (kg) (Peters 1983 p96)
CostPerSec = (0.17 * (self.Weight**0.75)) + (3.4 * self.Weight) -0.14 * (self.Weight**0.751)#[J/s]
#determining tm: time invested in movement at day t
tm= self.Energy / CostPerSec if (self.Energy / CostPerSec) <TimeD else TimeD
#Energy expended on movement is removed from the energy reservoir
self.Energy -= CostPerSec*tm
#Speed of walking insects(m/s): 0.3W (kg) ^ 0.29 (Buddenbrock 1934)
#dmax: total covered distance at time t
dmax = 0.30 * (self.Weight**0.29)*tm#[m]
perc_range=0.096989967 + (301.0033444816 *self.Weight)#[m]
#Here, r is the radius of a circle representing the foraging area of an individual during one day.
#Within this foraging area, an individual will move towards the cell with the highest amount of resources.
r = math.sqrt(((2*dmax*perc_range)+ (math.pi *perc_range**2))/math.pi) + rnd.uniform (-0.5*SP,0.5*SP)#[m/day]
#When individual able to move outside patch
if (r/SP) > 0.5:
#creating mask array (0: cell which will not be masked, 1: cells which will be masked)
#Foraging_Area (name of mask array)initially only contains 1
# 1) determine square of suitable cells=> these become 0
# 2) this square is minimized starting from the corners (cells become 1 again)
# until area of unmasked cells approximates area of circle.
Foraging_Area = np.zeros((grid)) + 1
#Dimension of the landscape (landscape must be squared!!!)
dim=grid[0]
#Surface of Perfect Circle representing Foraging Area
Circle = math.pi * (r ** 2) #[m]
#Surface of Square approximating Foraging Area
Surface_square = (((np.ceil((r/SP)-0.5)*2)+1)*SP) ** 2 #[m]
#Radius of circle expressed in number of cells
l = (np.ceil((r/SP)-0.5))#[cells]
#3 possible cases:
#1)Surfaces of circle and square (representing
#foraging area) are smaller than total landscape surface
if (Circle<(dim*SP)**2) and (Surface_square<(dim*SP)**2):
#Borders of the Square of Foraging Area
D, U, L, R =(y-l)%dim, (y+l+1)%dim,\
(x-l)%dim, (x+l+1)%dim #[coordinates]
#The square doesn't exceed borders of grid
if D < U and L < R:
Foraging_Area[D:U, L:R] = 0
#The square does exceed borders of grid
#3 possibilities:
elif D > U and L > R:
Foraging_Area[D:, L:] = 0
Foraging_Area[:U, L:] = 0
Foraging_Area[D:, :R] = 0
Foraging_Area[:U, :R] = 0
elif D > U:
Foraging_Area[D:, L:R] = 0
Foraging_Area[:U, L:R] = 0
else: #L<R
Foraging_Area[D:U, L:] = 0
Foraging_Area[D:U, :R] = 0
#Trying to recreate a circular foraging area
#by cutting corners of square
i = 1
Surface=Surface_square
while Surface > Circle:
Surface -= (4 * i * (SP ** 2))
if Surface > Circle:
#decrease the number of unmasked patches in foraging area
diff=[item for item in zip(range(0,i), range(i-1,-1,-1))]
for d1,d2 in diff:
for tup in itertools.product([(D+d1)%dim, (U-1-d1)%dim],\
[(L+d2)%dim, (R-1-d2)%dim]):
Foraging_Area[tup] = 1
i+=1
#2) Surface of circle (representing foraging area) is smaller
#than total landscape surface but square's surface exceeds it
elif (Circle<(dim*SP)**2) and (Surface_square>=(dim*SP)**2):
#Complete foraging range is unmasked
Foraging_Area -= 1
#Square's surface equals landscape' s surface
Surface_square = (dim*SP)**2 #[m]
#Borders of the Square of Foraging Area
D, U, L, R = y-l, y+l, x-l, x+l #[coordinates]
#Try to recreate a circular foraging area
#by cutting the corners of square
Surface_A = Surface_square
A=set()
i=1
#The square is decreasing in surface up to the point where an
#extra cut would result in a square which is smaller than
#the circle. As such, the surface of the square
#is never smaller than the surface of the circle!
while Surface_A >= Circle:
B=A.copy()
diff=[item for item in zip(range(0,i), range(i-1,-1,-1))]
for d1,d2 in diff:
for tup in itertools.product([(D+d1)%dim, (U-d1)%dim],\
[(L+d2)%dim, (R-d2)%dim]):
A.add(tup)
Surface_A=Surface_square-(len(A)*(SP**2))
i+=1
for tup in B:
Foraging_Area[tup]=1
#3) Surfaces of circle and square (representing foraging area)
#do exceed total landscape surface
else: #Circle >= (dim*SP)**2
#The entire landscape is considered foraging area
Foraging_Area-=1
return Foraging_Area
else:
return 'NO' #Individual does move but only within its cell.
else:
return 'NO'
def GrowthCI(self,
a,
TimeC,
AssimFrac):
'''Updating the actual size of an individual according to West et al. (2001)'''
#Calculating the proportion of the total metabolic power/available energy devoted to growth (West et al. 2001)
#R = (1 - r) = 1 - (m/M) ^0.25
#Threshold for growth = a proportion R of the maximum amount of energy that an individual can ingest in one day
R=(1-(self.Weight/self.AdultWeight)**0.25)
DeltaGrowth = self.Energy / ( R*AssimFrac * 2.0 * (self.Weight**0.80) * TimeC)#[J]
if DeltaGrowth > 1:DeltaGrowth=1
#energy used for growth is deleted from storage
self.Energy -= (DeltaGrowth*R * AssimFrac * 2.0 * (self.Weight**0.80) * TimeC)
#organism grows
self.DevelAge += DeltaGrowth
# m = M * {1 - [1 - (m0 / M) ^ 1/4] * e ^ [ -at / (4M) ^ 1/4]} ^ 4
#(West et al. 2001) with weights expressed in gram
#term1 : (m0 / M) ^ 1/4
#term2 : e ^ [ -at / 4 * (M) ^ 1/4]
# m = M * {1 - [1 - term1] * term2 } ^ 4
self.Weight = ((self.AdultWeight*1000) * (
(1 -
((1 - (self.InitialWeight*1000/(self.AdultWeight*1000))**(0.25) )
* math.exp((-a * self.DevelAge) /(4 * ((self.AdultWeight*1000)**(0.25))))
)) ** 4))/1000#[kg]
def MatureCI(self, NumberofEggs, TimeC, TimeD, AssimFrac):
'''checking whether an individual has reached maturity'''
if not self.Weight >= 0.99 * self.AdultWeight:
return False
#Clutch size for aquatic poikilotherms:
#0.158W ^ 0.92 (RECALCULATED from Blueweiss et al. 1978)
ClutchSize = 0.158 * (self.Weight ** 0.92)#[kg]
#Energy per kilogram of insect
EnergyKgInsect = 7000000#[J/kg]
#Weight of individual egg
self.EggSize = ClutchSize / NumberofEggs#[kg]
#Amount of energy given to egg for survival of its first day:
#Basal metabolic processes Cost + Total Movement Cost + Cost devoted to Growth
self.EggEnergy = ((0.14 * (self.EggSize**0.751)) * ((24 * 3600) - TimeD)) + \
((0.17 * (self.EggSize**0.75) + (3.4 * self.EggSize))* TimeD) + \
((1 - ((self.EggSize/self.AdultWeight)**0.25)) * \
(AssimFrac * (2.0 * (self.EggSize**0.80)) * TimeC))#[J]
#Threshold for reproduction: Amount of Energy necessary for clutch +
#Amount of Energy for every egg to survive one day
self.ThresholdR =(ClutchSize * EnergyKgInsect) + (NumberofEggs * self.EggEnergy)#[J]
return True
def ReproduceCI(self, NumberOfEggs, MinWeight, MaxWeight, Mutationrate, TimeC, t):
'''Returns list of offspring in case an individual has gathered enough energy to produce it. '''
if self.Energy >= self.ThresholdR:
Offspring, neutral = [], self.neutral
#create total number of eggs
for _ in range(NumberOfEggs):
#mutation rate
if rnd.random() < Mutationrate:
NewAdultWeight= self.AdultWeight + rnd.uniform(-0.5*self.AdultWeight, 0.5*self.AdultWeight)
neutral= 'mutation'
if NewAdultWeight<max(self.EggSize,(10**MinWeight)):
NewAdultWeight=max(self.EggSize,(10**MinWeight))
elif NewAdultWeight> (10**MaxWeight):
NewAdultWeight= (10**MaxWeight)
else:
NewAdultWeight=self.AdultWeight
if rnd.random() < 0.0001:
Gene_Fst=rnd.randint(0,999)
else: Gene_Fst= self.gene_fst
#create new larvae in population
egg=ConInd(#variation in maximum size of consumer
NewAdultWeight,
neutral,
Gene_Fst,
t,
Weight = self.EggSize,
Energy = self.EggEnergy
)
Offspring.append(egg)
sumimax= NumberOfEggs *egg.ConsumeCI(TimeC)
return sumimax, Offspring
else: return None
class ConSpec:
def __init__(self,
Startpop,
MinWeight,
MaxWeight,
TimeC,
TimeD,
AssimFrac,
landscape,
grid,
NumberofEggs,
Resource,
t,
IPD):
'''Initializing a consumer species'''
self.landscape = landscape
self.MinWeight = MinWeight
self.MaxWeight = MaxWeight
self.TimeC = TimeC
self.TimeD = TimeD
self.AssimFrac = AssimFrac
self.totaladults = Startpop
self.totallarvae = 0
self.grid=grid
self.NumberofEggs= NumberofEggs
#empty dictionary with individual lists for adults and larvae
self.ConDist = {'Adults': [[
[] for _ in line]
for line in self.landscape],
'Larvae': [[
[] for _ in line]
for line in self.landscape]
}
self.sumimax=np.zeros(grid, dtype = np.float)
#add initial amount of consumers at random places in the grid
for _ in range(Startpop):
#Initial variation
AdultWeight =(10**(rnd.uniform(self.MinWeight, self.MaxWeight)))
Gene_Fst=rnd.randint(0,999)
y = rnd.randint(0,grid[0] - 1)#randint: boundaries included => -1
x = rnd.randint(0,grid[1] - 1)
#no consumers should be introduced in non-suitable cells
while self.landscape[y, x] == 0:
y = rnd.randint(0,grid[0] - 1)
x = rnd.randint(0,grid[1] - 1)
#add individual adult to list
EnergyCon = (((0.14 * (AdultWeight**0.751)) * ((24 * 3600) - self.TimeD)) + \
((0.17 * (AdultWeight**0.75) + (3.4 * AdultWeight)) * self.TimeD))
NewInd=ConInd(AdultWeight,'OriginalPop',Gene_Fst,t, Weight = AdultWeight,Energy= EnergyCon, DevelAge = 'startpop')
NewInd.MatureCI(self.NumberofEggs, TimeC, TimeD, AssimFrac)
self.ConDist['Adults'][y][x].append(NewInd)
self.sumimax[y,x]+=NewInd.ConsumeCI(self.TimeC)
'''Going over all individuals and letting them consume with maximum
ingestion rate depending on an individual's size. Competition is scramble.'''
# every consumer has the chance to consume every time step
#only consumption in suitable patches with consumers
for y in range(0, 50+IPD*50, IPD+1):
for x in range(0, 50+IPD*50, IPD+1):
if self.landscape[y,x]==1 and self.sumimax[y,x]>0:
#scramble competition
AmResLeft = Resource.ResDist[y, x]#J
Sumimax=self.sumimax[y,x]
#When AmresLeft>=Sumimax, all individuals are able to eat
if AmResLeft >= Sumimax:
AmResLeft, Sumimax= 1,1
for indiv in self.ConDist['Adults'][y][x]:
indiv.Energy += indiv.ConsumeCI(self.TimeC, Assim_Frac= self.AssimFrac,
Sum=Sumimax, Res=AmResLeft)
Resource.ResDist -= self.sumimax
np.place(Resource.ResDist, Resource.ResDist<0, 0)
def New_consumer(self, t):
'''Introduction of single consumer every 10 time steps'''
#Initial variation
AdultWeight = (10**(rnd.uniform(self.MinWeight, self.MaxWeight)))
Gene_Fst=rnd.randint(0,999)
x = rnd.randint(0,self.grid[1] - 1)#randint: boundaries included => -1
y = rnd.randint(0,self.grid[0] - 1)
#no consumers should be introduced in non-suitable cells
while self.landscape[y, x] == 0:
x = rnd.randint(0,self.grid[1] - 1)
y = rnd.randint(0,self.grid[0] - 1)
#Energy level sufficient to survive a full day
EnergyCon = (((0.14 * (AdultWeight**0.751)) * ((24 * 3600) - self.TimeD)) + \
((0.17 * (AdultWeight**0.75) + (3.4 * AdultWeight)) * self.TimeD))
#add individual adult to list
NewInd=ConInd(AdultWeight,'immigrant', Gene_Fst, t, Weight = AdultWeight,Energy = EnergyCon,DevelAge = 'intro')
NewInd.MatureCI(self.NumberofEggs, self.TimeC, self.TimeD, self.AssimFrac)
self.ConDist['Adults'][y][x].append(NewInd)
self.sumimax[y,x]+=NewInd.ConsumeCI(self.TimeC)
def BMR_Move_CS(self, SizePatch, ResDist, locations, id_set,IPD):
'''Managing all individual's expenditure on basal metabolism'''
'''Going over all individuals and letting them move randomly but INFORMED.
The movement distance is dependent on an individual's size.'''
new_pop = {'Adults': [[
[] for _ in line]
for line in self.landscape],
'Larvae': [[
[] for _ in line]
for line in self.landscape]
}
for y in range(0, 50+IPD*50, IPD+1):
for x in range(0, 50+IPD*50, IPD+1):
if len(self.ConDist['Larvae'][y][x])>0 or len(self.ConDist['Adults'][y][x])>0:
#Calculating probability of leaving cell
assert (self.sumimax[y,x]>0), 'self.sumimax negative'
p= 1- (ResDist[y,x]/self.sumimax[y,x])
for lifestage in self.ConDist:
for indiv in self.ConDist[lifestage][y][x]:
#check for enough energy to move & cost of BMR
ForArea = indiv.BMR_Move_CI(SizePatch,self.TimeD,y,x,self.grid, p)
if ForArea != 'Death':
if ForArea == 'NO':
#individual stays in same patch
new_pop[lifestage][y][x].append(indiv)
if str(id(indiv))+ str(indiv.t) in id_set:
locations[str(id(indiv))+ str(indiv.t)].append((y,x))
else:
#informed movement
##Mask the array of the Resource distribution with the foraging area
R_Area = np.ma.masked_array(ResDist, ForArea)
#acquire the patches with maximum amount of resources in the foraging area
(new_y, new_x) = np.ma.where(R_Area == R_Area.max())
#select random patch out of all patches with maximum resources
value = rnd.choice(range(len(new_y)))
#consumer moves to random patch and doesn't die
new_pop[lifestage][new_y[value]][new_x[value]].append(indiv)
if str(id(indiv))+ str(indiv.t) in id_set:
locations[str(id(indiv))+ str(indiv.t)].append((new_y[value],new_x[value]))
else:
if str(id(indiv))+ str(indiv.t)in id_set:
id_set.remove(str(id(indiv))+ str(indiv.t))
locations[str(id(indiv))+ str(indiv.t)].append('D' + ' ' + str(indiv.AdultWeight))
self.ConDist = new_pop
self.sumimax*=0
def Growth_Mature_Reprod_Cons_CS(self, a, Mutationrate, Resource,id_set,locations, sampling, t,IPD):
'''Only larvae can grow if they have enough available energy'''
'''Those Larvae which approach (99%) of their adult size become mature
and do no longer grow but invest their energy in reproduction.'''
#Adults no longer grow
#create new list for population after maturation
new_pop = {'Adults': [[
[] for _ in line]
for line in self.landscape],
'Larvae': [[
[] for _ in line]
for line in self.landscape]
}
if sampling:
all_eggs=[]
for y in range(0, 50+IPD*50, IPD+1):
for x in range(0, 50+IPD*50, IPD+1):
for indiv in self.ConDist['Larvae'][y][x]:
# larvae grow and mature
if indiv.Energy > 0:
indiv.GrowthCI(a, self.TimeC, self.AssimFrac)
#when larva is mature, add it to the adult population
if indiv.MatureCI(self.NumberofEggs, self.TimeC, self.TimeD, self.AssimFrac):
new_pop['Adults'][y][x].append(indiv)
else:
new_pop['Larvae'][y][x].append(indiv)
else:
new_pop['Larvae'][y][x].append(indiv)
self.sumimax[y][x]+=indiv.ConsumeCI(self.TimeC)
#adults reproduce in case habitat is suitable
if self.landscape[y, x]!= 0:
for indiv in self.ConDist['Adults'][y][x]:
#check ability for reproduction
Offspring = indiv.ReproduceCI(self.NumberofEggs, self.MinWeight, self.MaxWeight,
Mutationrate, self.TimeC, t)
#after reproduction, consumer dies
if Offspring:
self.sumimax[y][x]+= Offspring[0]#sumimax
new_pop['Larvae'][y][x] += Offspring[1]#list of Offspring
if str(id(indiv))+ str(indiv.t) in id_set:
id_set.remove(str(id(indiv))+ str(indiv.t))
locations[str(id(indiv))+ str(indiv.t)].append('R'+ ' ' + str(indiv.AdultWeight))
if sampling:
for egg in Offspring[1]:
all_eggs.append((egg, y, x))
else:
#not reproducing adults stay in the population
new_pop['Adults'][y][x].append(indiv)
self.sumimax[y][x]+=indiv.ConsumeCI(self.TimeC)
else:
#no reproduction in non-suitable patches, so adults stay in population
for indiv in self.ConDist['Adults'][y][x]:
new_pop['Adults'][y][x].append(indiv)
self.sumimax[y][x]+=indiv.ConsumeCI(self.TimeC)
'''Going over all individuals and letting them consume with maximum
ingestion rate depending on an individual's size. Competition is scramble.'''
# every consumer has the chance to consume every time step
#only consumption in suitable patches with consumers
if (len(new_pop['Adults'][y][x])>0 or len(new_pop['Larvae'][y][x])>0):
assert(self.sumimax[y,x]>0), 'problems with calculating sumimax'
if self.landscape[y,x]==1 and self.sumimax[y,x]>0:
#scramble competition
AmResLeft = Resource.ResDist[y, x]#J
Sumimax=self.sumimax[y,x]
#When AmresLeft>=Sumimax, all individuals are able to eat
if AmResLeft >= Sumimax:
AmResLeft, Sumimax= 1,1
for lifestage in new_pop:
for indiv in new_pop[lifestage][y][x]:
assert(indiv.Energy>=-0.000000000001), 'Energy negative'
indiv.Energy += indiv.ConsumeCI(self.TimeC, Assim_Frac= self.AssimFrac,
Sum=Sumimax, Res=AmResLeft)
self.ConDist = new_pop
Resource.ResDist -= self.sumimax
np.place(Resource.ResDist, Resource.ResDist<0, 0)
if sampling:
return all_eggs
def CountingCS(self):
'''Going over all individuals counting the amount of adults and larvae'''
self.totaladults=sum([len(location)
for row in self.ConDist['Adults']
for location in row])
self.totallarvae=sum([len(location)
for row in self.ConDist['Larvae']
for location in row])
def ListAllInd(self):
'''Return a list of ALL (adults and larvae) individuals.'''
AllInd=[indiv
for lifestage in self.ConDist
for row in self.ConDist[lifestage]
for location in row
for indiv in location
]
rnd.shuffle(AllInd)
return AllInd
def Summary_Weights(self, allind):
'''Calculate the average and its variance of the actual weight
and AdultWeight of ALL individuals. '''
AdultWeights=[Ind.AdultWeight for Ind in allind]
AdultWeights.sort()
if len(AdultWeights)>1:
return (sp.describe(AdultWeights,ddof=0),#number of obs, mean, var, skewnesss, kurtosis
sp.variation(AdultWeights),#coefficient of variation
AdultWeights[int(round(len(AdultWeights)*0.025))],
AdultWeights[int(round(len(AdultWeights)*0.975))-1])
else:
return ([None]*6,None,None,None)
class Resource:
def __init__(self,
IniNumR,
MaxAmountR,
Enc,
landscape):
'''Initiate the resource class with ResDist (a distribution of all
resources in the landscape)being the most important state variable.'''
self.landscape = landscape
self.mask= (self.landscape -1)**2
self.MaxAmountR = MaxAmountR
self.Enc = Enc*landscape
self.ResDist = IniNumR * self.landscape
def GrowResources(self,
GrowthspeedR):
'''Each time step resources grow within one cell according to a
logistic growth function'''
#logistic growth of resources dN/dt = rN * (K - N / K)
self.ResDist+=self.Enc
self.ResDist += (GrowthspeedR * (self.ResDist)) * ((
self.MaxAmountR - self.ResDist) / (
self.MaxAmountR))
self.ResDist-=self.Enc
#when no resources left, add small percentage to reinitiate growth of resources
def MeanVarR(self):
'''Determine the average amount of resources within the landscape.'''
Resources_only = np.ma.masked_array(self.ResDist, self.mask)
return (np.ma.mean(Resources_only), np.ma.var(Resources_only))
def TotalAmountR(self):
'''Return the entire amount of resources in the landscape.'''
return np.sum(self.ResDist)
class Simulation:
def __init__(self,Maxtime,IniNumR,GrowthspeedR,MaxAmountR,Enc,
SizePatch,TimeC,TimeD,a,AssimFrac,MinWeight,
MaxWeight,Mutationrate,NumberofEggs,IPD, replicate):
'''Defining the most important variables of the simulation and
defining the order of events during one day'''
print(IPD, ' ', GrowthspeedR, 'O')
t=0
Fst_lijst, O_lijst= [], []
Title='O_'+'IPD'+ str(IPD) + 'replicate'+ str(replicate)+'r'+str(GrowthspeedR)
grid=(50+IPD*50,50+IPD*50)
self.landscape = np.zeros(grid)
for y in range(0, 50+IPD*50, IPD+1):
for x in range(0, 50+IPD*50, IPD+1):
self.landscape[y,x]=1
Summary={'Time':[],
'MeanR':[],
'VarR':[],
'TotalAmountR':[],
'TotalAdults':[],
'TotalLarvae':[],
'AWeightAverage':[],
'AWeightVariance':[],
'AWeightSkewness':[],
'AWeightKurtosis':[],
'AWeightCV':[],
'AWeightLower':[],
'AWeightUpper':[]
}
#create class resources
self.Resources = Resource(IniNumR, MaxAmountR, Enc, self.landscape)
#Mean density of Startpop:2 individuals per suitable cell
Startpop = 1000
#create consumer species 1
self.ConSpec1 = ConSpec(Startpop,MinWeight, MaxWeight, TimeC, TimeD,
AssimFrac,self.landscape,grid, NumberofEggs, self.Resources, t,IPD)
print (self.ConSpec1)
#calculating alpha, beta and gamma variability
suitable_patches=np.where(self.landscape==1.0)
samples=[d for d in range (len(suitable_patches[0]))]
rnd.shuffle(samples)
variability_dict={}
for b in range (100):
variability_dict[str(suitable_patches[0][samples[b]])+\
'-'+str(suitable_patches[1][samples[b]])]=[]
samples_time_st=[Maxtime-f for f in range (0,110,10)]
#tracking 1000 individuals within the landscape during their lifetime
locations=dict()
id_set=set()
N_traced_eggs=0
samples_time_m=[Maxtime-s for s in range (300,600,10)]
while ((self.ConSpec1.totaladults + self.ConSpec1.totallarvae) > 0) and (t < Maxtime):
print ('Time', t)
print('Adults: ',self.ConSpec1.totaladults,
'Larvae ',self.ConSpec1.totallarvae,
'Resources: ',self.Resources.MeanVarR()[0] )
if t%10 == 0:
self.ConSpec1.New_consumer(t)
self.Resources.GrowResources(GrowthspeedR)
sampling=False
#tracking 1000 individuals within the landscape during their lifetime
if (t in samples_time_m) and (N_traced_eggs<1000):
sampling=True
self.ConSpec1.BMR_Move_CS(SizePatch, self.Resources.ResDist, locations, id_set,IPD)
all_eggs=self.ConSpec1.Growth_Mature_Reprod_Cons_CS(a, Mutationrate, self.Resources, id_set, locations, sampling, t,IPD)
#tracking 1000 individuals within the landscape during their lifetime
if sampling:
if len(all_eggs)>100:
rnd.shuffle(all_eggs)
for position in range(100):
locations[str(id(all_eggs[position][0]))+str(all_eggs[position][0].t)]=[(all_eggs[position][1],all_eggs[position][2])]
id_set.add(str(id(all_eggs[position][0]))+str(all_eggs[position][0].t))
N_traced_eggs+=100
else:
for egg in all_eggs:
locations[str(id(egg[0]))+ str(egg[0].t)]=[(egg[1],egg[2])]
id_set.add(str(id(egg[0]))+ str(egg[0].t))
N_traced_eggs+=1
#Determining number of adults and larvae in population at time t
self.ConSpec1.CountingCS()
#Collecting data of population at time t within dictionary 'Summary'
all_ind=self.ConSpec1.ListAllInd()
P4, PCV, PL, PU =self.ConSpec1.Summary_Weights(all_ind)
MeanR, VarR= self.Resources.MeanVarR()
Summary['Time'].append(t)
Summary['MeanR'].append(MeanR)
Summary['VarR'].append(VarR)
Summary['TotalAmountR'].append(self.Resources.TotalAmountR())
Summary['TotalAdults'].append(self.ConSpec1.totaladults)
Summary['TotalLarvae'].append(self.ConSpec1.totallarvae)
Summary['AWeightAverage'].append(P4[2])
Summary['AWeightVariance'].append(P4[3])
Summary['AWeightSkewness'].append(P4[4])
Summary['AWeightKurtosis'].append(P4[5])
Summary['AWeightCV'].append(PCV)
Summary['AWeightLower'].append(PL)
Summary['AWeightUpper'].append(PU)
t+=1
#Writing out adult weight of 50000 individuals during simulation (checking for equilibrium)
if t%500 == 0 and 0<t<Maxtime:
Write_Weights(Title,
t,
all_ind[:50000])
if t in samples_time_st:
#calculating alpha, beta and gamma variability
for key in variability_dict.keys():
coo_y, coo_x=key.split('-')
variability_dict[key].append(sum([ind.Weight
for stage in self.ConSpec1.ConDist
for ind in self.ConSpec1.ConDist[stage][int(coo_y)][int(coo_x)]
]))
#defining occupancy (O)
full_patches=[]
for y in range (0, 50+IPD*50, IPD+1):
for x in range(0,50+IPD*50, IPD+1):
if (len(self.ConSpec1.ConDist['Larvae'][y][x])>0) or (len(self.ConSpec1.ConDist['Adults'][y][x])>0):
full_patches.append((y,x))
O_lijst.append(len(full_patches)/2500)
#calculating genetic differentation between patches within landscape (Fst)
#suitable_patches=np.where(self.landscape==1.0)
#samples=[a for a in range (len(suitable_patches[0]))]
rnd.shuffle(full_patches)
w=100 if len(full_patches)>=100 else len(full_patches)
sample_ind_Fst=[[]for _ in range(w)]
for patch_number in range (w):
all_ind_patch=[indiv
for stage in self.ConSpec1.ConDist
for indiv in self.ConSpec1.ConDist[stage][full_patches[patch_number][0]][full_patches[patch_number][1]]]
rnd.shuffle(all_ind_patch)
sample_ind_Fst[patch_number]=all_ind_patch[:100]
#calculate Fst based on sampling
list_haploid_div=[]
gene_freq_pop = np.array([0 for _ in range (1000)])
for patch_number in range (w):
present_alleles=set([i.gene_fst for i in sample_ind_Fst[patch_number]])
gene_freq_patch= np.array([0 for _ in range (1000)])