drift: Sink Rate Modelling

In farcego/slimmingDive: Flexible, Hierarchical Selection of Drift Dives

Sink Rate Modelling

Description

GLM family object to fit mass models to observed sink rate data.

Usage

drift(M0, V0, a, Vm = 1.11, p = 1/2, link = c("dragp", "drag0"))

Arguments

M0	initial mass of animal
V0	initial volume of animal
a	a proportionality constant.
Vm	the volume per unit mass of the accreted mass
p	the power in the V/A relation for the dragp link
link	the link function

Details

This function provides a family object for modelling sink rates of animals of varying condition.

The terminal or free settling velocity of a sinking object of density \rho, volume V and cross-sectional area A is

v = -\left ( \frac{2g V}{C_{d} A} (\rho-1) \right )^{1/2}

The volume V is modelled in terms of mass M, an initial mass M_{0} and volume V_{0}, and the volume V_{m} per unit mass of the accreted mass

V = V_{0} + V_{m}(M-M_{0})

.

The expression for free settling velocity is rewritten as

v = -a \left ( R(V/V_{0})(M/V-1) \right )^{1/2}

where R(V)= k V/A and R(1)=1 and a and k are constants.

The family provides two links that relate the expected sink rate to the mass of the animal. The "dragp" link corresponds to R(z) = z^p, and the "drag0" link corresponds to R(z) = 1.

If the animal grows as a sphere as it gains condition, then area scales as radius squared and volume as radius cubed, so V/A \propto V^{1/3} and p=1/3. If the animal grows as a cyclinder of constant length as it gains condition, then area scales with radius and volume as radius squared, so V/A \propto V^{1/2} and p=1/2. The p=0 case corresponds to an animal that grows only in one dimension as gains condition.

Value

an object of class family. Essential a gaussian family with a link function that relates the animal's mass to expected drift rate.

farcego/slimmingDive documentation built on April 14, 2024, 8:24 a.m.