Roberts, David C.

English

Research Papers in Economics

Biological, Technological, and Economic Relationships between 
Predator and Prey
David C. Roberts, Assistant Professor, 
North Dakota State University
Introduction
Brander and Taylor (1998) developed a bioeconomic model to describe the dynamics of a 
Lotka-Volterra predator-prey system when the prey is an open-access resource. They apply 
their model specifically to explain the rapid rise and collapse of human civilization on Easter 
Island. They propose that socio-economic collapse was caused by unsustainable harvest—and 
eventual extinction—of the palm trees essential to the economic prosperity of ancient Easter 
Islanders. Elimination of this resource reduced the carrying capacity of the island and standard 
of living for the remaining inhabitants because other forms of natural capital, such as reeds and 
bushes, were only weakly substitutable for palm trees in the production of shelter and fishing 
vessels. Brander and Taylor (1998) clearly illustrate the forces that lead to market failure in the 
presence of open-access resources, and discover the set of starting parameters that could lead 
to stable equilibrium populations of both predator and prey. However, they assume no change 
in predatory efficiency over time. 
Coevolution—the process by which predator and prey species adapt responsively through 
natural selection—has the tendency to keep predator and prey populations at stable 
equilibrium levels, assuming sufficient numbers of susceptible and unsusceptible prey upon the 
introduction of a new predator (Saloneimi, 1993). However, it is possible that all potential prey 
animals would be susceptible to predation by a novel predator. For example, the introduction 
of rats to Pacific islands has led to the extinction of several seabird species (Jones et al., 2007). 
The biological fitness of the introduced predator relative to a prey species may be what leads 
introduced species to become “invasive.”
The global spread of humans is partially due to biological and technological innovations, 
such as weapons for hunting large game and technologies for efficient extraction of marine 
resources. Advanced technology allows humans to inhabit virtually any climate and exploit any 
useful resource. Human predation has led to the extinction of Steller’s sea cow, the great auk 
and others (Vermeij, 1992). Currently, many high valued fish stocks have drastically declined 
due to over-fishing (Fromentin and Powers, 2005; Rose, 2004).
This research assumes two types of technological innovations exist: 1) those that improve 
extractive efficiency, and 2) those that improve use-efficiency.
Objectives
1. To describe the effects of technological and biological fitness of predators relative to prey 
on the population dynamics of the bioeconomic system.
2. To determine the effects of technological innovation on the long-run success of potentially 
invasive species
Methods
The model used is based on Brander and Taylor (1998). However, we assume that harvested 
units of the resource based do not directly satisfy the wants of the predator, but are 
transformed into consumption goods through some technological process. The model is as 
follows:
V = population of the prey resource
K = carrying capacity of the prey resource
r = prey population growth rate
τ = extractive efficiency
β = utility function parameter
ρ= fertility function
θ =  use efficiency
d = predator death rate, absent useful output
0
2000
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10000
12000
0 100 200 300 400 500
Time (Decades)
P
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P
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Prey Population
Predator Population
Results
Because improvements in extractive efficiency and use-efficiency have the effect of reducing 
the price of useful output from the resource sector, it is determined that both types of 
technological advancement will ultimately increase the demand for the resource good through 
population growth, unless the fertility function decreases sufficiently as real income levels rise. 
Without a sufficient decrease in fertility rates, population collapse and reduced standards of 
living may be inevitable.
0
2000
4000
6000
8000
10000
12000
0 100 200 300 400 500
P
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p
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Time (Decades)
Prey Population
Predator Population
0
5000
10000
15000
20000
25000
30000
35000
40000
45000
50000
0 100 200 300 400 500
Time (Decades)
P
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P
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,
 
P
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Predator 
Population
Prey 
Population
Conclusions
Improved resource use efficiency does not automatically counteract increased extractive 
efficiency in terms of taking pressure off a natural resource base. In fact, technological 
advancement may put increasing pressure on natural resources unless fertility decreases 
sufficiently to counteract the forces of technological change.
References
Brander, J.A., and Taylor, M.S. 1998. “The Simple Economics of Easter Island: A Ricardo-Malthus 
Model of Renewable Resource Use.” The American Economic Review 88(1):119-138.
Fromentin, J., and Powers, J.E. 2005. “Atlantic Bluefin Tuna: Population Dynamics, Ecology, 
Fisheries and Management.” Fish and Fisheries 6(4):281-306.
Jones, H.P., Tershy, B.R., Zavaleta, E.S., Croll, D.A, Keitt, B.S., Finkelstein, M.E., and Howald, G.R. 
2007. “Severity of the Effects of Invasive Rats on Seabirds: A Global Review.” Conservation 
Biology 22(1):16-26.
Lueck, D. 2002. “The Extermination and Conservation of the American Bison.” The Journal of 
Legal Studies 31(2,2):S609-S652.
Rose, G.A. 2004. “Reconciling Overfishing and Climate Changewith Stock Dynamics of Atlantic 
Cod (Gadus morhua) over 500 Years.” Canadian Journal of Fisheries and Aquatic Sciences
61(9):1553-1557.
Saloneimi, I. 1993. “A Coevolutionary Predator-Prey Model with Quantitative Characters.” The 
American Naturalist 141(6):880-896.
Vermeij, G.J. 1992. “Biogeography of Recently Extinct Marine Species: Implications for 
Conservation.” Conservation Biology 7(2):391-397.

Atlantic Bluefin Tuna: Population Dynamics,

Biological, Technological, and Economic Relationships between Predator and Prey

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