fr_typeI: Type I Response

Description

A generic type-I (linear) response.

Usage

typeI_fit(data, samp, start, fixed, boot=FALSE, windows=FALSE)
    typeI_nll(a, T, X, Y)
    typeI(X, a, T)

Arguments

data: A dataframe containing X and Y.
samp: A vector specifying the rows of data to use in the fit. Provided by boot() or manually, as required.
start: A named list. Starting values for items to be optimised. Usually 'a'.
fixed: A names list. 'Fixed data' (not optimised). Usually 'T'.
boot: A logical. Is the function being called for use by boot()?
windows: A logical. Is the operating system Microsoft Windows?
a: The capture rate
T: T: Total time available
X: The X variable. Usually prey density.
Y: The Y variable. Usually the number of prey consumed.

Author

Daniel Pritchard

Details

This implements a simple type-I, or linear functional response. This is helpful when the response is known (or suspected) to be handling time independent. It is implemented as:

$$N_e = a N_0 T$$

where a is the capture rate, T is the total time available and $N_0$ (== X) is the initial prey density.

None of these functions are designed to be called directly, though they are all exported so that the user can call them directly if desired. The intention is that they are called via frair_fit, which calls them in the order they are specified above.

typeI_fit does the heavy lifting and also pulls double duty as the statistic function for bootstrapping (via boot() in the boot package). The windows argument if required to prevent needless calls to require(frair) on platforms that can manage sane parallel processing.

The core fitting is done by mle2 from the bbmle package and users are directed there for more information. mle2 uses the typeI_nll function to optimise typeI.

Further references and recommended reading can be found on the help page for frair_fit.

Examples

Run this code

datx <- rep(1:60, times=5)
r1 <- rnorm(60*5, mean = 0.25, sd = 0.1)
r2 <- rnorm(60*5, mean = 0.75, sd = 0.1)
r1[r1>1] <- 1
r2[r2>1] <- 1
daty1 <- abs(round(r1*datx, 0))
daty2 <- abs(round(r2*datx, 0))
dat <- data.frame(datx,daty1,daty2)

TI1 <- frair_fit(daty1~datx, data=dat, response='typeI', 
        start=list(a=0.5), fixed=list(T=1))
TI2 <- frair_fit(daty2~datx, data=dat, response='typeI', 
        start=list(a=0.5), fixed=list(T=1))

plot(c(0,60), c(0,60), type='n', xlab='Density', ylab='No. Eaten')
points(TI1)
points(TI2, col=4)
lines(TI1)
lines(TI2, col=4)

# Test with frair_compare
frair_compare(TI1, TI2)

if (FALSE) {
# Test with a big stick
TI1b <- frair_boot(TI1)
TI2b <- frair_boot(TI2)
confint(TI1b)
confint(TI2b)

plot(c(0,60), c(0,60), type='n', xlab='Density', ylab='No. Eaten')
drawpoly(TI1b, col=1)
drawpoly(TI2b, col=4)
points(TI1b, pch=20)
points(TI2b, pch=20, col=4)
}