Foreword to the First Edition
A mathematical model is a caricature, a deliberate oversimplification of reality.
As such, its weaknesses may be transparent, its limitations obvious. This is not so,
perhaps, with the invisible model a decision-maker or researcher must inevitably
use. But some form of model must be implicit in informed decision-making, lest
those decisions become random acts of whimsy; and some form of model similarly
guides any experimental design. For all of the limitations of any model, the
likelihood is that the explicit consideration of assumptions is a step in the direction
of better understanding and better decision-making. One goal of this book is to
develop that thesis and to provide the reader the tools to become a better decisionmaker or better scientist. A more general goal is simply to make the power of
dynamical simulation models available to the widest possible audience of
researchers, as aids to exploring the dynamics of ecosystems.
The use of dynamic mathematical models in ecology is not new; indeed, it has a
rich and glorious history. In the early part of the twentieth century, the brilliant
mathematician, Vito Volterra, challenged by his son-in-law Umberto D’Ancona to
explain the oscillations of the Adriatic fisheries, formulated a simple but
now-classic pair of differential equations to show how the interaction between
predator and prey could drive sustained oscillations. More sophisticated models,
incorporating historical effects via Volterra’s own specialty, integral equations,
were explored; but it was the simplicity of the ordinary differential equation models
that captured the attention of later generations. Indeed, the power of simple models
as tools for understanding is also a central theme of this book.
Volterra was not alone in laying out the foundations of today’s mathematical
ecology. Alfred Lotka, an actuary and part-time genius, developed similar equations, as did the Russian V.I. Kostitzin. Generations of mathematicians explored the
complexities of these apparently simple equations; and even today, new and
esoteric discoveries about bifurcations and chaos are being made. But this research
has largely been the domain of mathematicians, and at times has made little contact
with biological fact or application. It is time, in the words of the authors, for a
“democratization of modeling,” driven by their conviction that modeling is too
important and too much fun to be left to mathematicians. It is also the case that
v
A mathematical model is a caricature, a deliberate oversimplification of reality.
As such, its weaknesses may be transparent, its limitations obvious. This is not so,
perhaps, with the invisible model a decision-maker or researcher must inevitably
use. But some form of model must be implicit in informed decision-making, lest
those decisions become random acts of whimsy; and some form of model similarly
guides any experimental design. For all of the limitations of any model, the
likelihood is that the explicit consideration of assumptions is a step in the direction
of better understanding and better decision-making. One goal of this book is to
develop that thesis and to provide the reader the tools to become a better decisionmaker or better scientist. A more general goal is simply to make the power of
dynamical simulation models available to the widest possible audience of
researchers, as aids to exploring the dynamics of ecosystems.
The use of dynamic mathematical models in ecology is not new; indeed, it has a
rich and glorious history. In the early part of the twentieth century, the brilliant
mathematician, Vito Volterra, challenged by his son-in-law Umberto D’Ancona to
explain the oscillations of the Adriatic fisheries, formulated a simple but
now-classic pair of differential equations to show how the interaction between
predator and prey could drive sustained oscillations. More sophisticated models,
incorporating historical effects via Volterra’s own specialty, integral equations,
were explored; but it was the simplicity of the ordinary differential equation models
that captured the attention of later generations. Indeed, the power of simple models
as tools for understanding is also a central theme of this book.
Volterra was not alone in laying out the foundations of today’s mathematical
ecology. Alfred Lotka, an actuary and part-time genius, developed similar equations, as did the Russian V.I. Kostitzin. Generations of mathematicians explored the
complexities of these apparently simple equations; and even today, new and
esoteric discoveries about bifurcations and chaos are being made. But this research
has largely been the domain of mathematicians, and at times has made little contact
with biological fact or application. It is time, in the words of the authors, for a
“democratization of modeling,” driven by their conviction that modeling is too
important and too much fun to be left to mathematicians. It is also the case that
v