Chapter 4
Numerical models: the standard form of theory in
pelagic ecology
Well before the advent of readily available computers for solving complex systems of
difference equations, Riley (1946, also Riley et al. 1949) had introduced numerically
solved rate-equation models of pelagic ecosystem dynamics representing the
interactions among physical factors and several trophic levels. With the development
of accessible computers in the 1960s and with improvements since, numerical models
have become the basis of most theory in biological oceanography. Such theory is so
pervasive that modeling is now a specialty within the field, much as theoretical and
observational physics are done by different people. Models are indispensable in ocean
ecology; almost whatever we do, we work back and forth between model populations
or ecosystems and field observations. Just as important, models facilitate thought
experiments about processes too widespread or too small to observe. We model
effects of possible future events, like doubling atmospheric CO 2 , that cannot be
experimentally determined. There are benthic ecosystem models, fishery models,
population-dynamical models for whales, and more. A standard problem, causal
explanation of the spring phytoplankton bloom and other seasonal cycles, is a
motivation for some of this theory, the part we will review. There are now models of
every system and process that the imagination can isolate within the world’s oceans,
but very often the basic mechanics are those examined here.
(^) Pelagic ecosystem models are often numerical approximations to the solutions of
systems of differential equations. Not enough is known to include the full complexity
of ecosystem processes, but what we do not know, we “parameterize” (guess, cover
over by lumping categories, or some other strategy). The models often generate
convincing simulations of our concepts of ecological processes. In what follows, we
will examine several rather old, but easy to follow, pelagic ecosystem models. After
reviewing seasonal cycling in temperate, coastal, pelagic ecosystems and a primer on
difference-equation modeling, we will work toward simulating the processes
generating and terminating (in places preventing) spring blooms.