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12
Can Individual-Based Models
Yield a Better Assessment of
Population Variability?
Yiannis G. Matsinos, Wilfried F. Wolff, and Donald L. DeAngelis
Introduction
The variability of a population is one of the key attributes influencing its ability to
persist over a long period of time. Thus, population variability and the sources of
that variability are of great interest to conservation biologists and to population
ecologists in general. The central questions biologists want to answer are, can the
factors controlling the variability in a population be identified, and, once identified, can they be included in a model of the population that can be used to predict
changes in the population in response to those factors? We contrast two modeling
approaches to this problem, the state variable approach and the individual-based
approach.
Population variability is determined by the temporal variabilities of both reproduction and survival in a population. Part of this variability is a result of demographic stochasticity; the fact that, to some extent, births and deaths are influenced
by factors that are effectively stochastic. The remainder of the variability is
determined by temporal variability in the environment that changes the average
survivorship and reproduction through time.
State Variable Models
The state variable approach, in which state variables are used to represent population sizes, is the most common approach in modeling populations. This approach
is more appropriate for numerically large than small populations. In such populations, demographic stochasticity will generally not cause large excursions of the
population size away from the mean value that the state variable represents.
Often, one state variable is used to represent the size of the total population, but
in structured models, a set of state variables represents the numbers of individuals
in various age, stage, or size classes within a population (e.g., the Leslie matrix
model [Caswell 1989] or the McKendrick-von Foerster equation [Metz and Diekmann 1986]).
12
Can Individual-Based Models
Yield a Better Assessment of
Population Variability?
Yiannis G. Matsinos, Wilfried F. Wolff, and Donald L. DeAngelis
Introduction
The variability of a population is one of the key attributes influencing its ability to
persist over a long period of time. Thus, population variability and the sources of
that variability are of great interest to conservation biologists and to population
ecologists in general. The central questions biologists want to answer are, can the
factors controlling the variability in a population be identified, and, once identified, can they be included in a model of the population that can be used to predict
changes in the population in response to those factors? We contrast two modeling
approaches to this problem, the state variable approach and the individual-based
approach.
Population variability is determined by the temporal variabilities of both reproduction and survival in a population. Part of this variability is a result of demographic stochasticity; the fact that, to some extent, births and deaths are influenced
by factors that are effectively stochastic. The remainder of the variability is
determined by temporal variability in the environment that changes the average
survivorship and reproduction through time.
State Variable Models
The state variable approach, in which state variables are used to represent population sizes, is the most common approach in modeling populations. This approach
is more appropriate for numerically large than small populations. In such populations, demographic stochasticity will generally not cause large excursions of the
population size away from the mean value that the state variable represents.
Often, one state variable is used to represent the size of the total population, but
in structured models, a set of state variables represents the numbers of individuals
in various age, stage, or size classes within a population (e.g., the Leslie matrix
model [Caswell 1989] or the McKendrick-von Foerster equation [Metz and Diekmann 1986]).