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Demographic data of Hypericum cumulicola in "Florida rosemary scrub at" Archbold Biological Station (FL, USA). Life cycle, experimental design and data are described in Quintana-Ascencio & Menges (2003). Data contains a subset of individuals from population "bald 1" and annual period "1997-1998". Full dataset can be obtained upon request to the authors ([email protected]).

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The format is: chr "dataIPMpackHypericum"

data-frame with headings:

- id: unique plant id (this file contains only a subset of all individuals)

- bald: population (this subset contains only one population)

- year: transition from t to t+1 (this subset contains only data for 1997-1998)

- size: length of longest stem in individual (cm) in time t

- ontogeny: recruits vs established individuals in time t (1 = individual was recruited in time t, 0 = already established individual prior to time t, NA = individual not yet recruited in time t)

- fec0: probability of reproduction (0= no flowering, 1 = individual was flowering in time t, NA = individual not alive in year t)

- fec1: number of fruits per plant (NA if fec0 = 0)

- surv: survival (0 = dead, 1= alive, NAs if not yet recruited or past dead)

- sizeNext: length of longest stem in individual (cm) in time t+1

- ontogenyNext: recruits vs established individuals in time t+1 (1 = individual was recruited in time t+1, 0 = already established individual prior to time t+1, NA = individual not yet recruited or dead in t+1)

Pedro Quintana Ascencio & Eric Menges

Quintana-Ascencio, Menges & Weekley. 2003. A fire-explicit population viability analyses of Hypericum cumulicola in Florida Rosemary scrub. Conservation Biology 17, p433-449.

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#Access data from the long-term censuses on Hypericum cumulicula
# carried out by Eric Menges, Pedro Quintana-Ascencio and coworkers
# at Archbold Biological Station. Here only a subset of individuals
# from population 'bald 1' and for the annual transition '1997-1998' are shown.
data("dataIPMpackHypericum")
d<-dataIPMpackHypericum
#Variables are:
#id: unique identifier for each individual
#bald: population. Here only bald 1
#year: annual transition of the long-term data. Here only 1997-1998
#surv: survival (1) or not (0) of individuals between 1997 and 1998
#size: maximum height of the stems of each individual
#ontogeny: because the demography of Hypericum is very dynamic
# (turnover is very high) the experimental design described
# in Quintana-Ascencio et al. (2003) consists on establishing
# new permanent plots every year at each population,
# in addition to censusing old plots. Here we differentiate
# between individuals that appear for the first time in time t
# because they were recruits (1) and those that, not being new
# recruits, where measured for the first time in t because they
# were in a new permanent plot.
#fec0: probability of flowering (1) or not (0)
#fec1: number of fruits per individual
#sizeNext: same as "size" above, for t+1
#stageNext: same as "stage" above, for t+1
#Due to the sampling design described above, here we consider only
# individual with a certain recruit origin:
d <- subset(d,is.na(d$size)==FALSE | d$ontogenyNext==1)
#Side-experiments revealed that the following vital rates are size-independent
# and equal to:
#Number of seeds produced per fruit
fec2<-13.78
#Probability of seedling establishment
fec3<-0.001336
#Probability of seedling survival half a year after germinating,
# corresponding to the next annual census
fec4<-0.14
#Probability of a seed going into the seed bank
goSB<-0.08234528
#Probability of a seed staying in the seed bank
staySB<-0.672
#Note that the aforementioned vital rates are function of time since last fire,
#but because here we are only dealing with one population and one year
#transition, we treat them as constants. See Quintana-Ascencio et al (2003)
#for more information.
#A simple re-organization of the data, getting rid of non-critical information
d<-d[,c("surv","size","sizeNext","fec0","fec1")]
#The following states the continuous (max height of individual plant)
#part of the IPM. Note that the IPM to be constructed here contains a
#discrete stage: seedbank.
d$stageNext<-d$stage<-"continuous"
d$stage[is.na(d$size)]<-NA
#If individual did not survive, it is labelled as dead to t+1.
d$stageNext[d$surv==0]<-"dead"
#Adds probability of seeds going into (continuous -> seedbank),
#staying (seedbank -> seedbank) and leaving (continuous -> seedbank)
#the discrete stage.
d$number<-1
d$stage<-as.factor(d$stage)
d$stageNext<-as.factor(d$stageNext)
#Carry out comparisons to establish the best survival model
testSurv <- survModelComp(d, expVars = c(surv~1, surv~size,
surv~size + size2), testType = "AIC",makePlot = TRUE,legendPos = "bottomleft")
#Carry out comparisons to establish the best growth model
testGrow <- growthModelComp(d,expVars = c(sizeNext~1, sizeNext~size,
sizeNext~size + size2), regressionType = "constantVar",
testType = "AIC", makePlot = TRUE, legendPos = "bottomright")
#Create survival object using regression model indicated by testSurv
so <- makeSurvObj(d, Formula = surv~size + size2)
picSurv(d,so)
#Create growth object using regression model indicated by testGrown
go<-makeGrowthObj(d, Formula = sizeNext~size)
picGrow(d,go)
abline(a=0,b=1,lty=2)
#Create fecundity object using regression models
fo <- makeFecObj(d, Formula=c(fec0~size, fec1~size),
Family=c("binomial","poisson"),
Transform=c("none", "none"),
meanOffspringSize=mean(d[is.na(d$size)==TRUE &
is.na(d$sizeNext)==FALSE,"sizeNext"]),
sdOffspringSize=sd(d[is.na(d$size)==TRUE &
is.na(d$sizeNext)==FALSE,"sizeNext"]),
fecConstants=data.frame(fec2=fec2,fec3=fec3,fec4=fec4),
offspringSplitter=data.frame(seedbank=goSB,
continuous=(1-goSB)),
vitalRatesPerOffspringType=data.frame(seedbank=c(1,1,1,0,0),
continuous=c(1,1,1,1,1),
row.names=c("fec0","fec1",
"fec2","fec3","fec4")))
#Define discrete transition matrix
dto<-makeDiscreteTrans(d,
discreteTrans = matrix(c(staySB,(1-staySB)*fec3*fec4,
(1-staySB)*(1-fec3*fec4),0,
sum(d$number[d$stage=="continuous"&d$stageNext=="continuous"],
na.rm=TRUE),sum(d$number[d$stage=="continuous"&d$stageNext=="dead"],
na.rm=TRUE)),ncol=2,nrow=3,
dimnames=list(c("seedbank","continuous","dead"),
c("seedbank","continuous"))),
meanToCont = matrix(mean(d$sizeNext[is.na(d$stage)&
d$stageNext=="continuous"]),ncol=1,nrow=1,dimnames=list(c("mean"),
c("seedbank"))),
sdToCont = matrix(sd(d$sizeNext[is.na(d$stage)&
d$stageNext=="continuous"]),ncol=1,nrow=1,dimnames=list(c(""),
c("seedbank"))))
#choose number of bins for discretization in the IPM
nBigMatrix <- 100
#Create the P matrix describing growth-survival transitions
# The argument correction="discretizeExtremes" places parts of the
# growth distribution that fall
# below minSize or above maxSize into the first and last bin
#
Pmatrix<-makeIPMPmatrix(growObj=go,survObj=so,discreteTrans=dto,
minSize=0,maxSize=80,nBigMatrix=nBigMatrix,
correction="discretizeExtremes")
#Create the F matrix descributing fecundity transitions
# The argument correction="discretizeExtremes" places parts of the
# continuous offspring distribution that fall
# below minSize or above maxSize into the first and last bin
#
Fmatrix<-makeIPMFmatrix(fecObj=fo,
minSize=0,maxSize=80,nBigMatrix=nBigMatrix,
correction="discretizeExtremes")
#Build a P matrix reflecting only the continuous part of the model
# and check that binning, etc is adequate
PmatrixContinuousOnly <- makeIPMPmatrix(growObj=go,
survObj=so,minSize=0,maxSize=70,nBigMatrix=nBigMatrix,
correction="discretizeExtremes")
diagnosticsPmatrix(PmatrixContinuousOnly,growObj=go,
survObj=so,dff=d, correction="discretizeExtremes")
#Form the IPM as a result of adding the P and F matrices
IPM <- Pmatrix + Fmatrix
#Population growth rate for the whole life cycle of Hypericum is
eigen(IPM)$value[1]
#Population growth rate excluding the seed bank stage is
eigen(IPM[2:(nBigMatrix+1),2:(nBigMatrix+1)])$value[1]
``` |

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