Geoscience Reference
In-Depth Information
include density-dependent competition, prey-seeking and predator-avoiding
movements. Abiotic processes that may influence the structure of the size
spectrum and interact with or override biotic processes include turbulence and
tidal mixing. Abiotic processes are expected to have relatively greater effects on
smaller individuals (e.g.
MacKenzie et al., 1994; Smayda, 1970
).
Ideal free distribution theory (IFD;
Fretwell and Lucas, 1970
) has been
used to predict the biotic movements of all individuals in relation to their
prey, since the theory predicts that individuals seek to maximise their fitness
(usually via food intake or growth rates) by moving to locations where their
per capita consumption rates are higher. Individuals, therefore, move into
areas with high food availability but away from areas with high densities
of competitors and predators. The consequences of these movements are
captured with the IFD, where all individuals ultimately have the same
profitability and all predators have the same consumption rate. Realisation
of the IFD requires that all individuals are free to move and have ideal
knowledge of profitability. IFD theory has been used to model equilibrium
spatial distributions of fish populations and may describe observed patterns
(
Blanchard et al., 2005b, 2008; Fisher and Frank, 2004; MacCall, 1990
).
Here, we develop a spatially explicit dynamic size-spectrummodel that allows
individuals to move to maximise some measure of fitness, but where movement
is based on local rather than 'ideal' knowledge of the fitness landscape. We use
the model to predict how individuals grow, die and move through space and
time in a size-structured community. The growth of individuals is predation
based and competition results in individuals of similar size moving away from
one another. Prey-seeking behaviour involves individuals of a given sizemoving
locally towards areas that contain high concentrations of their favoured prey.
Predator-avoiding behaviour involves prey moving away from areas of high
predator density. We also incorporate passive transport for the smallest size
classes to represent the effects of turbulent mixing of plankton. The model
allows us to explore the effects of biotic and abiotic processes and their interac-
tions on community size composition, to understand how local sources of
production are propagated through the food web and to estimate the scale of
sampling that may be needed to describe the size spectrum.
II. METHODS
A. Model Development
The independent variables used are time t, a spatial vector
x
and m, where m
is the natural logarithm of the mass M of an individual. We derive an
expression for n(m, t,
x
), the spatial distribution of the number of individuals
with respect to m.
