README.md

QFASA

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Overview

Accurate estimates of the diets of predators are required in many areas of ecology, but for many species current methods are imprecise, limited to the last meal, and often biased. The diversity of fatty acids and their patterns in organisms, coupled with the narrow limitations on their biosynthesis, properties of digestion in monogastric animals, and the prevalence of large storage reservoirs of lipid in many predators, led us to propose the use of quantitative fatty acid signature analysis (QFASA) to study predator diets.

Installing

Via GitHub

devtools::install_github('justinkamerman/QFASA')

Via CRAN

install.packages('QFASA')

Load Package

library(QFASA)

Modeling Inputs

Prior to starting make sure that:

Distance Measure

Choose from one of three distance measures: 1=KL (Kullback-Leibler) || 2=AIT (Aitchison) || 3=CSD (Chi-Squared)

dist.meas=1

Fatty Acid Set

data(FAset)
fa.set = as.vector(unlist(FAset))

Matrix of Predator FA signatures

data(predatorFAs)
tombstone.info = predatorFAs[,1:4]
predator.matrix = predatorFAs[,5:(ncol(predatorFAs))]

# number of predator FA signatures this is used to create the matrix of CC values (see section 6 below)
npredators = nrow(predator.matrix)

Matrix of Prey FA signatures

#full file
data(preyFAs)

#extract prey FA only from data frame and subset them for the FA set designated above
prey.sub=(preyFAs[,4:(ncol(preyFAs))])[fa.set]

#renormalize over 1
prey.sub=prey.sub/apply(prey.sub,1,sum) 

#extract the modelling group names from the full file
group=as.vector(preyFAs$Species)

#add modelling group names to the subsetted and renormalized FAs
prey.matrix=cbind(group,prey.sub)

#create an average value for the FA signature for each designated modelling group
prey.matrix=MEANmeth(prey.matrix) 

Prey Lipid Content

#numbers are the column which identifies the modelling group, and the column which contains the lipid contents
FC = preyFAs[,c(2,3)] 
FC = as.vector(tapply(FC$lipid,FC$Species,mean,na.rm=TRUE))

Calibration Coefficients

data(CC)
cal.vec = CC[,2]
cal.mat = replicate(npredators, cal.vec)

Run QFASA

Q = p.QFASA(predator.matrix, prey.matrix, cal.mat, dist.meas, gamma=1, FC, start.val=rep(1,nrow(prey.matrix)), fa.set)

p.QFASA Output

The QFASA output is a list with 2 components:

Diet Estimates

This is a matrix of the diet estimate for each predator (by rows, in the same order as the input file) by the modelling groups (by column, in the same order as the prey.matrix file). The estimates are expressed as a proportion (they will sum to 1). In the code below the Diet Estimate matrix is extracted from the QFASA output and the modelling group identities and predator tombstone data (created above) are added to the matrix:

DietEst = Q$'Diet Estimates'

#estimates changed from proportions to percentages
DietEst = round(DietEst*100,digits=2)
colnames(DietEst) = (as.vector(rownames(prey.matrix)))
DietEst = cbind(tombstone.info,DietEst)
knitr::kable(DietEst)

|SampleCode |AnimalCode |SampleGroup |Biopsy | capelin| coho| eulachon| herring| mackerel| pilchard| pollock| sandlance| squid| surfsmelt_lg| surfsmelt_s| |:----------|:----------|:-----------|:------|-------:|----:|--------:|-------:|--------:|--------:|-------:|---------:|-----:|------------:|-----------:| |3-01A |P031 |T |A | 35.30| 0| 0| 44.90| 9.25| 2.36| 0| 8.19| 0| 0.00| 0| |3-01B |P031 |T1 |B | 43.06| 0| 0| 44.79| 3.72| 4.25| 0| 4.18| 0| 0.00| 0| |3-01C |P031 |T1 |C | 50.15| 0| 0| 34.34| 6.14| 3.97| 0| 5.40| 0| 0.00| 0| |3-02A |P032 |T |A | 37.80| 0| 0| 47.14| 1.42| 5.04| 0| 8.60| 0| 0.00| 0| |3-02B |P032 |T1 |B | 39.86| 0| 0| 45.50| 3.69| 5.77| 0| 5.18| 0| 0.00| 0| |3-02C |P032 |T1 |C | 47.99| 0| 0| 35.59| 4.47| 5.39| 0| 6.55| 0| 0.00| 0| |3-04A |P034 |T |A | 41.29| 0| 0| 46.33| 8.24| 2.65| 0| 1.49| 0| 0.00| 0| |3-04B |P034 |T2 |B | 31.96| 0| 0| 28.00| 2.95| 2.40| 0| 34.70| 0| 0.00| 0| |3-04C |P034 |T2 |C | 21.07| 0| 0| 14.45| 0.27| 2.00| 0| 37.03| 0| 25.17| 0| |3-05A |P035 |T |A | 28.91| 0| 0| 63.50| 0.00| 3.93| 0| 3.66| 0| 0.00| 0|

Additional Measures

This is a list of lists where each list (one per predator) is itself a list of four outputs:

# plyr package
library(plyr)
Add.meas = ldply(Q$'Additional Measures', data.frame)
knitr::kable(Add.meas)

| ModFAS.c14.0| ModFAS.c16.0| ModFAS.c16.1w7| ModFAS.c16.2w6| ModFAS.c16.2w4| ModFAS.c16.3w6| ModFAS.c17.0| ModFAS.c16.3w4| ModFAS.c16.4w3| ModFAS.c16.4w1| ModFAS.c18.0| ModFAS.c18.1w9| ModFAS.c18.1w7| ModFAS.c18.2w6| ModFAS.c18.2w4| ModFAS.c18.3w6| ModFAS.c18.3w4| ModFAS.c18.3w3| ModFAS.c18.3w1| ModFAS.c18.4w3| ModFAS.c18.4w1| ModFAS.c20.1w11| ModFAS.c20.1w9| ModFAS.c20.1w7| ModFAS.c20.2w6| ModFAS.c20.3w6| ModFAS.c20.4w6| ModFAS.c20.3w3| ModFAS.c20.4w3| ModFAS.c20.5w3| ModFAS.c22.1w11| ModFAS.c22.1w9| ModFAS.c22.1w7| ModFAS.c21.5w3| ModFAS.c22.4w6| ModFAS.c22.5w6| ModFAS.c22.4w3| ModFAS.c22.5w3| ModFAS.c22.6w3| DistCont.c14.0| DistCont.c16.0| DistCont.c16.1w7| DistCont.c16.2w6| DistCont.c16.2w4| DistCont.c16.3w6| DistCont.c17.0| DistCont.c16.3w4| DistCont.c16.4w3| DistCont.c16.4w1| DistCont.c18.0| DistCont.c18.1w9| DistCont.c18.1w7| DistCont.c18.2w6| DistCont.c18.2w4| DistCont.c18.3w6| DistCont.c18.3w4| DistCont.c18.3w3| DistCont.c18.3w1| DistCont.c18.4w3| DistCont.c18.4w1| DistCont.c20.1w11| DistCont.c20.1w9| DistCont.c20.1w7| DistCont.c20.2w6| DistCont.c20.3w6| DistCont.c20.4w6| DistCont.c20.3w3| DistCont.c20.4w3| DistCont.c20.5w3| DistCont.c22.1w11| DistCont.c22.1w9| DistCont.c22.1w7| DistCont.c21.5w3| DistCont.c22.4w6| DistCont.c22.5w6| DistCont.c22.4w3| DistCont.c22.5w3| DistCont.c22.6w3| PropDistCont.c14.0| PropDistCont.c16.0| PropDistCont.c16.1w7| PropDistCont.c16.2w6| PropDistCont.c16.2w4| PropDistCont.c16.3w6| PropDistCont.c17.0| PropDistCont.c16.3w4| PropDistCont.c16.4w3| PropDistCont.c16.4w1| PropDistCont.c18.0| PropDistCont.c18.1w9| PropDistCont.c18.1w7| PropDistCont.c18.2w6| PropDistCont.c18.2w4| PropDistCont.c18.3w6| PropDistCont.c18.3w4| PropDistCont.c18.3w3| PropDistCont.c18.3w1| PropDistCont.c18.4w3| PropDistCont.c18.4w1| PropDistCont.c20.1w11| PropDistCont.c20.1w9| PropDistCont.c20.1w7| PropDistCont.c20.2w6| PropDistCont.c20.3w6| PropDistCont.c20.4w6| PropDistCont.c20.3w3| PropDistCont.c20.4w3| PropDistCont.c20.5w3| PropDistCont.c22.1w11| PropDistCont.c22.1w9| PropDistCont.c22.1w7| PropDistCont.c21.5w3| PropDistCont.c22.4w6| PropDistCont.c22.5w6| PropDistCont.c22.4w3| PropDistCont.c22.5w3| PropDistCont.c22.6w3| MinDist| |------------:|------------:|--------------:|--------------:|--------------:|--------------:|------------:|--------------:|--------------:|--------------:|------------:|--------------:|--------------:|--------------:|--------------:|--------------:|--------------:|--------------:|--------------:|--------------:|--------------:|---------------:|--------------:|--------------:|--------------:|--------------:|--------------:|--------------:|--------------:|--------------:|---------------:|--------------:|--------------:|--------------:|--------------:|--------------:|--------------:|--------------:|--------------:|--------------:|--------------:|----------------:|----------------:|----------------:|----------------:|--------------:|----------------:|----------------:|----------------:|--------------:|----------------:|----------------:|----------------:|----------------:|----------------:|----------------:|----------------:|----------------:|----------------:|----------------:|-----------------:|----------------:|----------------:|----------------:|----------------:|----------------:|----------------:|----------------:|----------------:|-----------------:|----------------:|----------------:|----------------:|----------------:|----------------:|----------------:|----------------:|----------------:|------------------:|------------------:|--------------------:|--------------------:|--------------------:|--------------------:|------------------:|--------------------:|--------------------:|--------------------:|------------------:|--------------------:|--------------------:|--------------------:|--------------------:|--------------------:|--------------------:|--------------------:|--------------------:|--------------------:|--------------------:|---------------------:|--------------------:|--------------------:|--------------------:|--------------------:|--------------------:|--------------------:|--------------------:|--------------------:|---------------------:|--------------------:|--------------------:|--------------------:|--------------------:|--------------------:|--------------------:|--------------------:|--------------------:|---------:| | 0.0547664| 0.1853966| 0.0701887| 0.0009476| 0.0017854| 0.0069045| 0.0056682| 0.0052232| 0.0013693| 0.0093276| 0.0232666| 0.1480562| 0.0370854| 0.0096465| 0.0015922| 0.0012739| 0.0008316| 0.0047609| 0.0007809| 0.0141435| 0.0014503| 0.0178365| 0.0650470| 0.0040928| 0.0017300| 0.0007539| 0.0061731| 0.0004931| 0.0038550| 0.1147319| 0.0820286| 0.0074502| 0.0022416| 0.0040179| 0.0003608| 0.0011030| 0.0004209| 0.0110993| 0.0920990| 0.0088791| 0.0150925| 0.0001173| 6.05e-05| 0.0002396| 0.0000650| 0.0003814| 0.0002666| 0.0000305| 0.0005486| 0.0001031| 0.0183438| 0.0000862| 0.0000401| 2.07e-05| 2.0e-07| 0.0001591| 0.0000213| 0.0000010| 0.0013139| 7.90e-06| 0.0031149| 0.0155393| 0.0003308| 0.0001363| 4.91e-05| 0.0001160| 0.0001174| 0.0000440| 0.0006008| 0.0212495| 0.0000001| 0.0035884| 0.0002199| 1.26e-05| 0.0001506| 0.0001160| 0.0057975| 0.0147840| 0.0794585| 0.1350617| 0.0010495| 0.0005416| 0.0021443| 0.0005815| 0.0034132| 0.0023854| 0.0002733| 0.0049093| 0.0009225| 0.1641565| 0.0007714| 0.0003593| 0.0001856| 1.60e-06| 0.0014239| 0.0001909| 0.0000086| 0.0117581| 0.0000703| 0.0278749| 0.1390601| 0.0029605| 0.0012198| 0.0004395| 0.0010377| 0.0010502| 0.0003934| 0.0053766| 0.1901595| 0.0000006| 0.0321122| 0.0019676| 0.0001128| 0.0013478| 0.0010383| 0.0518812| 0.1323003| 0.1117455| | 0.0550460| 0.1841167| 0.0720054| 0.0009930| 0.0016304| 0.0070830| 0.0053360| 0.0056322| 0.0012572| 0.0104616| 0.0233679| 0.1478895| 0.0367106| 0.0093263| 0.0016973| 0.0013089| 0.0008664| 0.0043575| 0.0007758| 0.0138342| 0.0015588| 0.0142726| 0.0682818| 0.0042321| 0.0016245| 0.0007779| 0.0061654| 0.0004480| 0.0038504| 0.1163810| 0.0814998| 0.0076830| 0.0022185| 0.0041182| 0.0003539| 0.0010787| 0.0004058| 0.0119736| 0.0893801| 0.0063032| 0.0171896| 0.0036939| 2.20e-06| 0.0003432| 0.0002371| 0.0004968| 0.0003633| 0.0000041| 0.0010276| 0.0000137| 0.0178350| 0.0001426| 0.0005043| 1.04e-05| 2.2e-06| 0.0002163| 0.0001160| 0.0000737| 0.0011233| 9.90e-06| 0.0023613| 0.0139278| 0.0003984| 0.0000013| 7.77e-05| 0.0003517| 0.0000505| 0.0002181| 0.0000005| 0.0244185| 0.0000336| 0.0032871| 0.0001371| 5.53e-05| 0.0001587| 0.0001128| 0.0064767| 0.0121005| 0.0553518| 0.1509500| 0.0324377| 0.0000191| 0.0030137| 0.0020822| 0.0043629| 0.0031900| 0.0000363| 0.0090237| 0.0001206| 0.1566182| 0.0012518| 0.0044287| 0.0000910| 1.94e-05| 0.0018996| 0.0010187| 0.0006473| 0.0098644| 0.0000866| 0.0207353| 0.1223068| 0.0034983| 0.0000115| 0.0006822| 0.0030885| 0.0004436| 0.0019155| 0.0000041| 0.2144305| 0.0002949| 0.0288652| 0.0012042| 0.0004860| 0.0013933| 0.0009902| 0.0568754| 0.1062608| 0.1138759| | 0.0560279| 0.1789890| 0.0723739| 0.0009591| 0.0017444| 0.0067273| 0.0049163| 0.0053720| 0.0012702| 0.0101304| 0.0228679| 0.1378388| 0.0355206| 0.0096423| 0.0016793| 0.0012881| 0.0008372| 0.0043167| 0.0008086| 0.0137151| 0.0015843| 0.0152122| 0.0732648| 0.0046766| 0.0016630| 0.0007612| 0.0059978| 0.0004516| 0.0039308| 0.1163864| 0.0861903| 0.0086955| 0.0022833| 0.0040713| 0.0003448| 0.0010633| 0.0004023| 0.0123792| 0.0936161| 0.0017016| 0.0107110| 0.0061674| 6.90e-06| 0.0004523| 0.0002586| 0.0004484| 0.0004357| 0.0000136| 0.0008326| 0.0000424| 0.0126327| 0.0000073| 0.0009051| 1.39e-05| 1.7e-06| 0.0000459| 0.0001008| 0.0000944| 0.0012928| 3.40e-06| 0.0029103| 0.0144433| 0.0007050| 0.0000070| 1.93e-05| 0.0000384| 0.0000488| 0.0002088| 0.0004433| 0.0285698| 0.0000262| 0.0046912| 0.0000356| 1.12e-05| 0.0000781| 0.0000473| 0.0052183| 0.0080927| 0.0167216| 0.1052544| 0.0606055| 0.0000674| 0.0044448| 0.0025410| 0.0044065| 0.0042818| 0.0001335| 0.0081813| 0.0004165| 0.1241387| 0.0000720| 0.0088944| 0.0001370| 1.68e-05| 0.0004512| 0.0009907| 0.0009272| 0.0127039| 0.0000333| 0.0285992| 0.1419305| 0.0069274| 0.0000687| 0.0001898| 0.0003778| 0.0004791| 0.0020517| 0.0043557| 0.2807480| 0.0002577| 0.0460989| 0.0003498| 0.0001098| 0.0007675| 0.0004645| 0.0512792| 0.0795249| 0.1017630| | 0.0549324| 0.1886819| 0.0713946| 0.0010226| 0.0017054| 0.0071749| 0.0053501| 0.0058160| 0.0012653| 0.0109474| 0.0243862| 0.1504301| 0.0368751| 0.0092908| 0.0017885| 0.0013530| 0.0008909| 0.0046221| 0.0008388| 0.0148194| 0.0016100| 0.0128313| 0.0632252| 0.0039940| 0.0016646| 0.0007920| 0.0063065| 0.0004683| 0.0040066| 0.1192530| 0.0750986| 0.0069816| 0.0021633| 0.0042342| 0.0003746| 0.0011081| 0.0004206| 0.0121530| 0.0897284| 0.0130936| 0.0188271| 0.0015858| 4.30e-05| 0.0002297| 0.0000408| 0.0005260| 0.0001712| 0.0000203| 0.0002750| 0.0005548| 0.0239421| 0.0000178| 0.0000801| 1.40e-06| 9.1e-06| 0.0001440| 0.0002830| 0.0000192| 0.0001850| 1.30e-05| 0.0016961| 0.0158307| 0.0005330| 0.0001075| 0.00e+00| 0.0000122| 0.0000066| 0.0001355| 0.0012861| 0.0139420| 0.0000800| 0.0025324| 0.0002661| 1.00e-07| 0.0001324| 0.0001049| 0.0080911| 0.0131539| 0.1109885| 0.1595887| 0.0134418| 0.0003643| 0.0019472| 0.0003454| 0.0044584| 0.0014508| 0.0001722| 0.0023313| 0.0047031| 0.2029459| 0.0001513| 0.0006794| 0.0000121| 7.71e-05| 0.0012205| 0.0023990| 0.0001630| 0.0015682| 0.0001103| 0.0143772| 0.1341896| 0.0045183| 0.0009115| 0.0000000| 0.0001030| 0.0000559| 0.0011484| 0.0109018| 0.1181795| 0.0006784| 0.0214662| 0.0022555| 0.0000010| 0.0011227| 0.0008889| 0.0685845| 0.1114991| 0.1179728| | 0.0551564| 0.1860906| 0.0718531| 0.0010309| 0.0016327| 0.0072122| 0.0052826| 0.0059086| 0.0012421| 0.0113276| 0.0241941| 0.1489066| 0.0369172| 0.0092367| 0.0018067| 0.0013635| 0.0009050| 0.0044098| 0.0008202| 0.0144234| 0.0016661| 0.0139787| 0.0644588| 0.0040255| 0.0016226| 0.0008094| 0.0063120| 0.0004537| 0.0040279| 0.1191223| 0.0771774| 0.0072574| 0.0021436| 0.0042723| 0.0003667| 0.0010828| 0.0004133| 0.0126588| 0.0884308| 0.0075153| 0.0150745| 0.0012235| 2.24e-05| 0.0003131| 0.0002711| 0.0006123| 0.0003867| 0.0000006| 0.0008265| 0.0002306| 0.0167278| 0.0000755| 0.0004254| 3.30e-06| 1.1e-06| 0.0002367| 0.0001534| 0.0000901| 0.0008256| 2.25e-05| 0.0018837| 0.0120798| 0.0005337| 0.0000055| 3.60e-06| 0.0002554| 0.0000568| 0.0001010| 0.0000000| 0.0186703| 0.0000472| 0.0022597| 0.0002001| 1.65e-05| 0.0001432| 0.0000487| 0.0077364| 0.0103954| 0.0755503| 0.1515409| 0.0122994| 0.0002253| 0.0031475| 0.0027254| 0.0061557| 0.0038871| 0.0000064| 0.0083088| 0.0023185| 0.1681610| 0.0007593| 0.0042765| 0.0000331| 1.09e-05| 0.0023794| 0.0015418| 0.0009061| 0.0082998| 0.0002260| 0.0189360| 0.1214356| 0.0053647| 0.0000554| 0.0000359| 0.0025671| 0.0005709| 0.0010153| 0.0000000| 0.1876884| 0.0004741| 0.0227160| 0.0020120| 0.0001655| 0.0014394| 0.0004898| 0.0777722| 0.1045025| 0.0994748| | 0.0560505| 0.1817995| 0.0723815| 0.0010029| 0.0017353| 0.0068926| 0.0048537| 0.0056954| 0.0012426| 0.0110586| 0.0237688| 0.1398926| 0.0357112| 0.0094975| 0.0017979| 0.0013444| 0.0008776| 0.0043657| 0.0008541| 0.0143584| 0.0016866| 0.0138687| 0.0694806| 0.0044664| 0.0016535| 0.0007911| 0.0061452| 0.0004535| 0.0040879| 0.1193432| 0.0810038| 0.0081787| 0.0022098| 0.0042271| 0.0003589| 0.0010720| 0.0004093| 0.0130023| 0.0923806| 0.0023871| 0.0087871| 0.0021140| 5.80e-06| 0.0003958| 0.0003019| 0.0005416| 0.0003837| 0.0000211| 0.0005778| 0.0004160| 0.0114337| 0.0000748| 0.0007350| 6.00e-06| 3.7e-06| 0.0000521| 0.0001235| 0.0002417| 0.0008650| 2.36e-05| 0.0018387| 0.0112123| 0.0005756| 0.0000040| 2.06e-05| 0.0000082| 0.0000061| 0.0000562| 0.0005961| 0.0189813| 0.0000657| 0.0036601| 0.0000206| 5.07e-05| 0.0000651| 0.0000114| 0.0064457| 0.0064989| 0.0299852| 0.1103792| 0.0265544| 0.0000726| 0.0049721| 0.0037927| 0.0068028| 0.0048198| 0.0002655| 0.0072581| 0.0052258| 0.1436248| 0.0009394| 0.0092332| 0.0000759| 4.70e-05| 0.0006548| 0.0015511| 0.0030362| 0.0108653| 0.0002962| 0.0230963| 0.1408430| 0.0072303| 0.0000503| 0.0002586| 0.0001032| 0.0000768| 0.0007066| 0.0074877| 0.2384340| 0.0008247| 0.0459761| 0.0002588| 0.0006369| 0.0008178| 0.0001431| 0.0809679| 0.0816362| 0.0796084| | 0.0547001| 0.1817555| 0.0715331| 0.0009510| 0.0015960| 0.0070167| 0.0056379| 0.0053222| 0.0013040| 0.0095083| 0.0224540| 0.1486681| 0.0371563| 0.0094265| 0.0015574| 0.0012542| 0.0008343| 0.0043098| 0.0007035| 0.0130305| 0.0014459| 0.0174640| 0.0699567| 0.0042452| 0.0016257| 0.0007582| 0.0060870| 0.0004500| 0.0036742| 0.1126239| 0.0867604| 0.0079380| 0.0022620| 0.0039682| 0.0003395| 0.0010656| 0.0003999| 0.0112330| 0.0889833| 0.0047755| 0.0174695| 0.0036603| 6.00e-06| 0.0001590| 0.0001289| 0.0007356| 0.0004164| 0.0000281| 0.0012425| 0.0003970| 0.0201024| 0.0002863| 0.0000133| 3.82e-05| 6.6e-06| 0.0001921| 0.0000508| 0.0000030| 0.0010064| 5.00e-07| 0.0032654| 0.0156070| 0.0005452| 0.0000089| 2.14e-05| 0.0001790| 0.0000451| 0.0000147| 0.0000077| 0.0291126| 0.0000320| 0.0045975| 0.0001798| 4.68e-05| 0.0001565| 0.0001103| 0.0093666| 0.0164309| 0.0366090| 0.1339216| 0.0280598| 0.0000456| 0.0012191| 0.0009878| 0.0056393| 0.0031924| 0.0002151| 0.0095252| 0.0030435| 0.1541055| 0.0021948| 0.0001017| 0.0002928| 5.09e-05| 0.0014730| 0.0003898| 0.0000228| 0.0077150| 0.0000035| 0.0250325| 0.1196438| 0.0041797| 0.0000683| 0.0001644| 0.0013720| 0.0003457| 0.0001125| 0.0000588| 0.2231776| 0.0002455| 0.0352442| 0.0013786| 0.0003587| 0.0012000| 0.0008454| 0.0718042| 0.1259598| 0.1304458| | 0.0563824| 0.1968077| 0.0671719| 0.0009391| 0.0026376| 0.0061370| 0.0047962| 0.0048937| 0.0015236| 0.0090623| 0.0264545| 0.1343605| 0.0343480| 0.0105995| 0.0018357| 0.0013559| 0.0008015| 0.0063743| 0.0011786| 0.0189172| 0.0015480| 0.0120723| 0.0547957| 0.0042769| 0.0021356| 0.0007097| 0.0062515| 0.0006337| 0.0046436| 0.1262907| 0.0638349| 0.0066688| 0.0022629| 0.0042235| 0.0004413| 0.0012529| 0.0004936| 0.0113655| 0.1095215| 0.0036647| 0.0099124| 0.0014762| 3.04e-05| 0.0003230| 0.0000780| 0.0000663| 0.0001142| 0.0000072| 0.0000934| 0.0000010| 0.0132954| 0.0001011| 0.0004996| 3.46e-05| 5.0e-07| 0.0001643| 0.0010005| 0.0000480| 0.0002908| 1.76e-05| 0.0015343| 0.0150237| 0.0002299| 0.0000085| 2.14e-05| 0.0000647| 0.0000328| 0.0003402| 0.0000457| 0.0094349| 0.0005935| 0.0038285| 0.0002098| 4.90e-06| 0.0000490| 0.0001888| 0.0051552| 0.0066288| 0.0491150| 0.1328495| 0.0197849| 0.0004070| 0.0043294| 0.0010451| 0.0008882| 0.0015309| 0.0000971| 0.0012514| 0.0000134| 0.1781888| 0.0013554| 0.0066959| 0.0004638| 7.10e-06| 0.0022024| 0.0134090| 0.0006430| 0.0038974| 0.0002360| 0.0205638| 0.2013518| 0.0030816| 0.0001140| 0.0002874| 0.0008667| 0.0004402| 0.0045593| 0.0006120| 0.1264499| 0.0079545| 0.0513105| 0.0028117| 0.0000660| 0.0006569| 0.0025302| 0.0690916| 0.0888414| 0.0746140| | 0.0560089| 0.1993966| 0.0621763| 0.0009045| 0.0036597| 0.0054941| 0.0043480| 0.0044963| 0.0017555| 0.0084072| 0.0311406| 0.1224158| 0.0334652| 0.0108072| 0.0020314| 0.0015495| 0.0007844| 0.0073389| 0.0016374| 0.0207108| 0.0015147| 0.0085509| 0.0418152| 0.0056803| 0.0024959| 0.0007186| 0.0086272| 0.0007766| 0.0050396| 0.1375296| 0.0454824| 0.0066172| 0.0024761| 0.0043525| 0.0006707| 0.0021301| 0.0005243| 0.0122009| 0.1342687| 0.0019381| 0.0035051| 0.0027773| 1.35e-05| 0.0004209| 0.0000144| 0.0008635| 0.0000194| 0.0001671| 0.0000288| 0.0003219| 0.0082416| 0.0010711| 0.0015401| 3.05e-05| 1.5e-06| 0.0000059| 0.0015270| 0.0001205| 0.0012847| 4.43e-05| 0.0010478| 0.0105549| 0.0004779| 0.0000206| 1.00e-07| 0.0001562| 0.0000012| 0.0005087| 0.0002161| 0.0046874| 0.0002321| 0.0035418| 0.0000906| 9.70e-06| 0.0001440| 0.0001202| 0.0026136| 0.0019608| 0.0385154| 0.0696546| 0.0551910| 0.0002689| 0.0083636| 0.0002852| 0.0171597| 0.0003853| 0.0033203| 0.0005718| 0.0063978| 0.1637800| 0.0212859| 0.0306061| 0.0006069| 2.94e-05| 0.0001174| 0.0303453| 0.0023954| 0.0255310| 0.0008809| 0.0208233| 0.2097509| 0.0094974| 0.0004101| 0.0000025| 0.0031035| 0.0000240| 0.0101087| 0.0042948| 0.0931494| 0.0046122| 0.0703841| 0.0018012| 0.0001924| 0.0028619| 0.0023879| 0.0519379| 0.0389659| 0.0503210| | 0.0536044| 0.1916365| 0.0711010| 0.0010240| 0.0015210| 0.0075065| 0.0059829| 0.0058547| 0.0012665| 0.0105092| 0.0239668| 0.1617185| 0.0383445| 0.0089801| 0.0016851| 0.0013215| 0.0008915| 0.0045276| 0.0007313| 0.0140701| 0.0014783| 0.0133808| 0.0611832| 0.0036268| 0.0016014| 0.0007879| 0.0063729| 0.0004538| 0.0037150| 0.1157722| 0.0753060| 0.0062637| 0.0021495| 0.0041354| 0.0003677| 0.0011093| 0.0004140| 0.0110648| 0.0845737| 0.0112392| 0.0103927| 0.0061986| 7.60e-05| 0.0002106| 0.0000047| 0.0007563| 0.0000227| 0.0000918| 0.0001002| 0.0001074| 0.0177674| 0.0001146| 0.0000145| 4.05e-05| 1.6e-06| 0.0001552| 0.0001715| 0.0002282| 0.0002335| 4.50e-06| 0.0014146| 0.0124359| 0.0001925| 0.0014653| 3.50e-06| 0.0001069| 0.0000219| 0.0000435| 0.0022707| 0.0075854| 0.0000000| 0.0030467| 0.0001723| 1.50e-06| 0.0000405| 0.0000800| 0.0059879| 0.0092741| 0.1220660| 0.1128721| 0.0673211| 0.0008259| 0.0022876| 0.0000508| 0.0082139| 0.0002463| 0.0009975| 0.0010880| 0.0011666| 0.1929665| 0.0012449| 0.0001579| 0.0004397| 1.74e-05| 0.0016857| 0.0018630| 0.0024789| 0.0025355| 0.0000494| 0.0153636| 0.1350625| 0.0020904| 0.0159142| 0.0000380| 0.0011607| 0.0002380| 0.0004725| 0.0246620| 0.0823833| 0.0000000| 0.0330888| 0.0018716| 0.0000159| 0.0004396| 0.0008686| 0.0650327| 0.1007230| 0.0920750|



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QFASA documentation built on June 15, 2019, 1:03 a.m.