Nothing

```
ettersonEq14 <- function(s,f,J){
#This function calculates the function gfe in Eq. 14 of Etterson, M.
#Hidden Markov models for estimating animal mortality from anthropogenic
#hazards. Ecological Applications, 23(8), 2013, pp. 1915-1925
#
#original Inputs:
# pr = estimated daily scavenging rate
pr <- 1-s
# pd = estimated per-search discovery rate
pd <- f
# J = row-vector of intervals between searches
#
#Outputs:
# gf0 = function related to the probability of sampling a carcass
# killed between the first and last searches. See ms for details.
#
# Note: this function requires expm
#
q_d <- 1-pd;
q_r <- 1-pr;
n <- length(J);
Svec <- c(q_r,pr,0,0,1,0,0,0,1);
S <- matrix( Svec, ncol=3, byrow=TRUE )
Dvec <- c(q_d,0,pd,0,1,0,0,0,1);
D <- matrix( Dvec, ncol=3, byrow=TRUE )
gfe <- 0;
V1<- matrix( c(1,0,0), ncol=3, byrow=TRUE)
V3<- matrix( c(0,0,1), ncol=3, byrow=TRUE)
for (k in 1:(n-1)){
dk <- J[k];
A <- diag(3);
for (m in (k+1):n){
dm = J[m];
A = A %*% (S %^%dm) %*% D;
}
for (h in 1:dk){
A1 <- (S %^% h) %*% D;
gfe <- gfe + V1 %*% A1 %*% A %*% t(V3);
}
}
dn <- J[n];
for (h in 1:dn){
A1 <- (S %^% h) %*% D;
gfe <- gfe + V1 %*% A1 %*% t(V3);
}
# original output: return(gfe)
# transpose to probability of finding a carcass during the study period (n*d time intervals)
p <- gfe/sum(J)
return(p)
}
```

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