r.marked.egg.fraction {ConnMatTools}  R Documentation 
Estimates of fraction of eggs marked accounting for variability in reproductive output
Description
This function estimates the fraction of eggs "marked" at a site (where the "mark" could be microchemical or genetic) taking into account uncertainty in female (and potentially male in the case of dual genetic mark transmission) reproductive output. It generates a set of potential values for the fraction of eggs marked assuming that reproductive output of each marked or unmarked mature individual is given by a random variable drawn from a single probability distribution with known mean and standard deviation (or equivalently coefficient of variation) and that the numbers of marked and unmarked individuals are large enough that the central limit theorem applies and, therefore, their collective reproductive outputs are reasonably well described by a gamma distribution whose mean and standard deviation are appropriately scaled based on the number of individual reproducers. The function also returns the total egg production corresponding to each fraction of marked eggs, needed for estimating absolute connectivity values (i.e., elements of the connectivity matrix needed for assessing population persistence).
Usage
r.marked.egg.fraction(
n,
n.females,
n.marked.females = round(n.females * p.marked.females),
mean.female = 1,
cv.female,
dual = FALSE,
male.uncert = FALSE,
n.males = n.females,
n.marked.males = tryCatch(round(n.males * p.marked.males), error = function(e)
n.marked.females),
mean.male = mean.female,
cv.male = cv.female,
p.marked.females,
p.marked.males = p.marked.females
)
Arguments
n 
Number of random values to estimates 
n.females 
Total number of mature females in the population 
n.marked.females 
Number of marked females in population 
mean.female 
Mean egg production of each mature female. Defaults to 1. 
cv.female 
Coefficient of variation of reproductive output of an individual mature female 
dual 
Logical variable. If 
male.uncert 
Logical variable. If 
n.males 
Total number of mature males in the population. Only used if

n.marked.males 
Number of marked males in population. Only used if

mean.male 
Mean sperm production of each mature male. Only used if

cv.male 
Coefficient of variation of reproductive output of an
individual mature male. Only used if 
p.marked.females 
Fraction of marked females in population. Can be
supplied instead of 
p.marked.males 
Fraction of marked males in population. Can be supplied
instead of 
Value
A list with the following elements:
 p
Vector of length
n
with estimates for fraction of marked eggs eggs
Vector of length
n
with estimates for total egg production marked.eggs
Vector of length
n
with estimates for total number of marked eggs produced sperm
Only returned if
dual=TRUE
. Ifmale.uncert=FALSE
, then a scalar equal ton.males
. Otherwise, a vector of lengthn
with estimates for total sperm production marked.sperm
Only returned if
dual=TRUE
. Ifmale.uncert=FALSE
, then a scalar equal ton.marked.males
. Otherwise, a vector of lengthn
with estimates for total marked sperm production
Author(s)
David M. Kaplan dmkaplan2000@gmail.com
References
Kaplan DM, Cuif M, Fauvelot C, Vigliola L, NguyenHuu T, Tiavouane J and Lett C (in press) Uncertainty in empirical estimates of marine larval connectivity. ICES Journal of Marine Science. doi:10.1093/icesjms/fsw182.
See Also
Other connectivity estimation:
d.rel.conn.beta.prior()
,
d.rel.conn.dists.func()
,
d.rel.conn.finite.settlement()
,
d.rel.conn.multinomial.unnorm()
,
d.rel.conn.multiple()
,
d.rel.conn.unif.prior()
,
dual.mark.transmission()
,
optim.rel.conn.dists()
Examples
library(ConnMatTools)
n.females < 500
n.marked.females < 100
p.marked.females < n.marked.females/n.females
mn < 1
cv < 1
# Numbers of males and marked males and variance in male sperm production
# assumed the same as values for females
# Random values from distribution of pure female mark transmission
F=r.marked.egg.fraction(1000,n.females=n.females,n.marked.females=n.marked.females,
mean.female=mn,cv.female=cv)
# Random values from distribution of dual femalemale mark transmission, but
# fraction of marked eggs only depends on fraction of marked males
Fm=r.marked.egg.fraction(1000,n.females=n.females,n.marked.females=n.marked.females,
mean.female=mn,cv.female=cv,dual=TRUE,male.uncert=FALSE)
# Random values from distribution of dual femalemale mark transmission, with
# fraction of marked eggs depending on absolute marked and unmarked sperm output
FM=r.marked.egg.fraction(1000,n.females=n.females,n.marked.females=n.marked.females,
mean.female=mn,cv.female=cv,dual=TRUE,male.uncert=TRUE)
# Plot of pure female mark transmission
hist(F$p,50,main="Female mark transmission",
xlab="Fraction of marked eggs",
ylab="Frequency")
# Female+male mark transmission, but no variability in male mark transmission
h < hist(Fm$p,50,main="Female+male mark transmission, no male uncert.",
xlab="Fraction of marked eggs",
ylab="Frequency")
hh < hist((1p.marked.females)*F$p + p.marked.females,
breaks=c(Inf,h$breaks,Inf),plot=FALSE)
lines(hh$mids,hh$counts,col="red")
# Plot of pure female mark transmission
h < hist(FM$p,50,plot=FALSE)
hh < hist(Fm$p,
breaks=c(Inf,h$breaks,Inf),plot=FALSE)
plot(h,ylim=c(0,1.1*max(hh$counts,h$counts)),
main="Female+Male mark transmission, male uncert.",
xlab="Fraction of marked eggs",
ylab="Frequency")
lines(hh$mids,hh$counts,col="red")