199
13
Potential of Branching
Processes as a Modeling Tool
for Conservation Biology
Fr´ ed´ eric Gosselin and Jean-Dominique Lebreton
Deterministic theory in population ecology thus seems to be of little help in providing a
framework for probability theory. We had better not adhere too much to our deterministic
concepts and ideas, but start afresh.
—J. Reddingius (1971)
Introduction
Reaching some predictive ability is a long-term purpose in many applied scientific
fields. Conservation biology is no exception to the rule, because land managers
dealing with endangered species frequently expect predictive evaluations of alternative management plans. Such predictions, often developed in the framework of
population viability analysis (PVA), generally rely on some kind of modeling
(Boyce 1992). In such a multidisciplinary endeavor and in the context of the
strong social pressure presently typical of many environmental problems, it is not
surprising that a variety of modeling tools has been used with, in general, an
emphasis on biological relevance. Simulation is frequently used without any
mathematical analysis, and many models exist only as computer programs (e.g.,
Woolfenden and Fitzpatrick 1991; Stacey and Taper 1992). This state of the art is
summarized by Boyce (1992), who says of PVA, “Any attempt is qualified that
involves some simulation or analysis with the intent of projecting future populations, or estimating some extinction or persistence parameter.”
The priority afforded to extinction implies the need to account for stochastic
events in the models to represent adequately the possibility of extinction. For
instance, within the more restrictive framework of minimum viable population
(MVP) estimation (Gilpin and Soul´ e 1986), frequent use is made of densitydependent stochastic models. Even within this narrower focus, the variety of
model structures in the literature and the absence of a backbone theory for extinction models are striking. There is therefore a clear need for a class of models with,
simultaneously, enough biological relevance and enough mathematical tractability to be useful in solving problems (Reddingius 1971; Chesson 1978).
What are the features that should be considered in such canonical extinction
models? Despite the diversity of modeling approaches used until now, there is a
clear consensus on three structural characteristics:
13
Potential of Branching
Processes as a Modeling Tool
for Conservation Biology
Fr´ ed´ eric Gosselin and Jean-Dominique Lebreton
Deterministic theory in population ecology thus seems to be of little help in providing a
framework for probability theory. We had better not adhere too much to our deterministic
concepts and ideas, but start afresh.
—J. Reddingius (1971)
Introduction
Reaching some predictive ability is a long-term purpose in many applied scientific
fields. Conservation biology is no exception to the rule, because land managers
dealing with endangered species frequently expect predictive evaluations of alternative management plans. Such predictions, often developed in the framework of
population viability analysis (PVA), generally rely on some kind of modeling
(Boyce 1992). In such a multidisciplinary endeavor and in the context of the
strong social pressure presently typical of many environmental problems, it is not
surprising that a variety of modeling tools has been used with, in general, an
emphasis on biological relevance. Simulation is frequently used without any
mathematical analysis, and many models exist only as computer programs (e.g.,
Woolfenden and Fitzpatrick 1991; Stacey and Taper 1992). This state of the art is
summarized by Boyce (1992), who says of PVA, “Any attempt is qualified that
involves some simulation or analysis with the intent of projecting future populations, or estimating some extinction or persistence parameter.”
The priority afforded to extinction implies the need to account for stochastic
events in the models to represent adequately the possibility of extinction. For
instance, within the more restrictive framework of minimum viable population
(MVP) estimation (Gilpin and Soul´ e 1986), frequent use is made of densitydependent stochastic models. Even within this narrower focus, the variety of
model structures in the literature and the absence of a backbone theory for extinction models are striking. There is therefore a clear need for a class of models with,
simultaneously, enough biological relevance and enough mathematical tractability to be useful in solving problems (Reddingius 1971; Chesson 1978).
What are the features that should be considered in such canonical extinction
models? Despite the diversity of modeling approaches used until now, there is a
clear consensus on three structural characteristics: