Here is a clean version. I did this with nls and  it works (see below), but
I need to  do it with optim. Keun-Hyung

# optim
vol<-rep(c(0.03, 0.5, 2, 4, 8, 16, 32), 3)
time<-rep(c(2,4,8),each=7)
p.mated<-c(0.47, 0.48, 0.43, 0.43, 0.26, 0.23, NA, 0.68, 0.62, 0.64, 0.58,
0.53, 0.47,
0.24, 0.8, 0.79, 0.71, 0.56, 0.74, 0.8, 0.47)
eury<-data.frame(vol=vol, time=time, p.mated=p.mated)
eury<-na.omit(eury); eury

p0<- c(f=0.87, b=0.1, d=10)
eury.fit <- function (f, time, vol)
{
            f<-p[1]; b<-p[2]; d<-p[3]
            p.mated = p[1] * ( (1 -
exp(-p[2]*time))-(p[2]/(p[2]-(p[3]/vol)))
                           * (exp(-p[3]/vol*time)-exp(-p[2]*time)))
}
eury.opt<- optim(p0, fn=eury.fit, NULL, method = "BFGS", hessian = TRUE)

# I received the following error message.
Error in fn(par, ...) : argument "time" is missing, with no default

##  done with nls - this  works
eury.newfit1 <- nls(p.mated ~ f * ( 1 -
exp(-b*time)-(b/(b-d/vol))*(exp(-d/vol*time)-exp(-b*time))),
                                            data=eury, start=list(f=.87,
b=0.1, d=10))
v <- log10(range(eury$vol))
y <- expand.grid(vol=10^seq(min(v), max(v), length=100), time=c(2,4,8))
y$pred.mate.new <- predict(eury.newfit1,y)

plot (eury$vol, eury$p.mated, type="n", log="x",  xlab="Volume L", ylab =
"Fraction Mating")
for (i in c(2, 4, 8))
{
         points(eury$vol[eury$time==i], eury$p.mated[eury$time==i], pch=16,
col=(i/2)+1)
         lines(y$vol[y$time==i], y$pred.mate.new[y$time==i], lwd=3, col=i)
}
legend(.005,.2, c(" 2h","4h","8h"), col=c(2,4,8), lwd=3)

	[[alternative HTML version deleted]]

