3
Predator-Prey Dynamics
Matthias Ruth and James Lindholm
Pod after spouting pod of whales, the great ones together with the lesser
kinds, surge through waters everywhere a-ripple with living tides of
fishes.
Farley Mowat, from Sea of Slaughter
In this chapter you will:
• Interpret, modify and make use of Lotka-Volterra equations to model
predator-prey relations ;
• Learn how to translate a mathematical model into a STELLA model ;
• Scale graphical output, generate numeric displays, and run individual
sub models of a larger model in isolation of each other
3.1. Humpback Whales and Sand Lance
Historically, many of the models of the natural world , both marine and terrestrial, have involved only a single species, conceptually separating the
species of interest from its environment. In fact, species are in continuous
contact with other organisms and their physical environment. The models
we address in this book all involve relationships between marine organisms
and between organisms and their surrounding physical environment. Several of the relationships will reflect some form of predator-prey interaction-sea birds preying upon horseshoe crabs, sea otters on sea urchins ,
fish on fish, and ultimately, humans on fish.
The Lotka-Volterra equations (Lotka 1925, Volterra 1926) for capturing
predator-prey interaction are often used in ecology to describe interaction
between two species. The equations are :
dW
.
--=W=P*A*W*S-Q*W
dt
(1)
and
dS =S=R * S - A * W * S.
dt
(2)
In equation (1), dWldt denotes a change in the predator population Wthat
occurs over an infinitesimally small time interval dt. Similarly, in equation
43
M. Ruth et al. (Eds.), Dynamic Modeling for Marine Conservation
© Springer-Verlag New York, Inc. 2002
Predator-Prey Dynamics
Matthias Ruth and James Lindholm
Pod after spouting pod of whales, the great ones together with the lesser
kinds, surge through waters everywhere a-ripple with living tides of
fishes.
Farley Mowat, from Sea of Slaughter
In this chapter you will:
• Interpret, modify and make use of Lotka-Volterra equations to model
predator-prey relations ;
• Learn how to translate a mathematical model into a STELLA model ;
• Scale graphical output, generate numeric displays, and run individual
sub models of a larger model in isolation of each other
3.1. Humpback Whales and Sand Lance
Historically, many of the models of the natural world , both marine and terrestrial, have involved only a single species, conceptually separating the
species of interest from its environment. In fact, species are in continuous
contact with other organisms and their physical environment. The models
we address in this book all involve relationships between marine organisms
and between organisms and their surrounding physical environment. Several of the relationships will reflect some form of predator-prey interaction-sea birds preying upon horseshoe crabs, sea otters on sea urchins ,
fish on fish, and ultimately, humans on fish.
The Lotka-Volterra equations (Lotka 1925, Volterra 1926) for capturing
predator-prey interaction are often used in ecology to describe interaction
between two species. The equations are :
dW
.
--=W=P*A*W*S-Q*W
dt
(1)
and
dS =S=R * S - A * W * S.
dt
(2)
In equation (1), dWldt denotes a change in the predator population Wthat
occurs over an infinitesimally small time interval dt. Similarly, in equation
43
M. Ruth et al. (Eds.), Dynamic Modeling for Marine Conservation
© Springer-Verlag New York, Inc. 2002