frair (version 0.5.100)

fr_hollingsII: Holling's Original Type II Response

Description

Holling's Type II predator-prey function.

Usage

hollingsII_fit(data, samp, start, fixed, boot=FALSE, windows=FALSE)
    hollingsII_nll(a, h, T, X, Y)
    hollingsII(X, a, h, 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' and 'h'.

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, h

Capture rate and handling time. Usually items to be optimised.

T

T, the 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 the Hollings original type-II functional response, otherwise known as the 'disc equation'. An important assumption of this equation is that prey density remains constant (i.e. a 'replacement' experimental design). In practice this is often not the case and often the Roger's 'random predator' equation may be more appropriate (see rogersII).

In Holling's original formulation the number of prey eaten (Ne) follows the relationship:

$$N_e=\frac{a N_0 T}{1+a N_0 h}$$

Where \(N_0\) is the initial number of prey and a, h and T are the capture rate, handling time and the total time available, receptively. It is implemented internally in FRAIR as:

Ne <- (a*X*T)/(1+a*X*h)

where \(X = N_0\).

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.

rogersII_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 rogersII_nll function to optimise rogersII.

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

References

Bolker BM (2008) Ecological Models and Data in R. Princeton University Press, Princeton, NJ.

See Also

frair_fit.

Examples

datx <- rep(c(1,2,3,4,6,12,24,50,100), times=10)
daty1 <- round(hollingsII(X=datx, 
            a=0.75*rnorm(length(datx), mean=1, sd=0.1), 
            h=0.1*rnorm(length(datx), mean=1, sd=0.1), 
            T=1),0)
daty2 <- round(hollingsII(X=datx, 
            a=0.75*rnorm(length(datx), mean=1, sd=0.1), 
            h=0.01*rnorm(length(datx), mean=1, sd=0.1), 
            T=1),0)
dat <- data.frame(datx,daty1,daty2)

hollII_1 <- frair_fit(daty1~datx, data=dat, response='hollingsII', 
        start=list(a=1, h=0.1), fixed=list(T=1))
hollII_2 <- frair_fit(daty2~datx, data=dat, response='hollingsII', 
        start=list(a=1, h=0.01), fixed=list(T=1))

plot(c(0,100), c(0,40), type='n', xlab='Density', ylab='No. Eaten')
points(hollII_1)
points(hollII_2, col=4)
lines(hollII_1)
lines(hollII_2, col=4)

frair_compare(hollII_1, hollII_2)