computational limitations have prompted the development of new analytical and computational methods (particularly on parallel processors) that
are discussed later in this chapter.
Other approaches to spatial optimization include the combinatorial interchange technique to minimize spatial fragmentation (Loehle 1999) that
extends the stochastic search algorithms of Bettinger et al. (1997). This
approach cannot readily link to dynamic models to predict population
responses to fragmentation, but it is computationally efficient compared to
mixed-integer programming methods. A Markov-decision approach can be
applied to optimize landscapes for metapopulations (Tuck and Possingham
2000). This method allows simple dynamics of localized patches to be
included, but the size of the problem increases exponentially with the
number of states allowed. Other algorithms have been applied to attempt
to specify optimal spatial-reserve patterns for biodiversity conservation
(Csuti et al. 1997; Pressey et al. 1997), although they ignore population
dynamics.
8.3.1.6 New Methods for Developing Statistical Models
New techniques are also being developed to improve our ability to produce
ecological statistical models and to handle increasingly large data sets.
Traditional multivariate linear-regression tools are useful for finding global
effects, especially with sparse data sets. For data mining (finding previously
unknown, significant relationships between variables in large data sets),
there is no need to assume global structure. Local data can refine global
rules by adding conditions to global rules. The resulting regression is
thereby determined by local conditions. Classification and regression tree
analysis (RTA) uses iterative splitting of the data to develop empirical relationships between response and predictor variables without the restrictive
distribution assumptions of classical regression analysis. This approach
creates models that are fitted by binary recursive partitioning, in which a
data set is successively split into increasingly homogeneous subsets (Clark
and Pregibon 1992). Regression tree analysis is much more flexible than
classic statistical methods in uncovering structure in data with variables that
are hierarchical, nonlinear, nonadditive, or categorical in nature. Regression
tree analysis is useful as a means of devising prediction rules for rapid and
repeated evaluation, as a screening method for variables, as a diagnostic
technique to assess the adequacy of linear models, and for summarizing
large multivariate data sets (Clark and Pregibon 1992; Iverson et al.
1999).
Multivariate adaptive-regression splines (MARS) is a multivariate,
nonparametric regression procedure that builds flexible regression models
by fitting separate splines (or basis functions) to distinct intervals of
the predictor variables (Friedman 1991). The variables and interactions
to use and the endpoints of the intervals for each variable are optimized
8. Evolving Approaches and Technologies
147
are discussed later in this chapter.
Other approaches to spatial optimization include the combinatorial interchange technique to minimize spatial fragmentation (Loehle 1999) that
extends the stochastic search algorithms of Bettinger et al. (1997). This
approach cannot readily link to dynamic models to predict population
responses to fragmentation, but it is computationally efficient compared to
mixed-integer programming methods. A Markov-decision approach can be
applied to optimize landscapes for metapopulations (Tuck and Possingham
2000). This method allows simple dynamics of localized patches to be
included, but the size of the problem increases exponentially with the
number of states allowed. Other algorithms have been applied to attempt
to specify optimal spatial-reserve patterns for biodiversity conservation
(Csuti et al. 1997; Pressey et al. 1997), although they ignore population
dynamics.
8.3.1.6 New Methods for Developing Statistical Models
New techniques are also being developed to improve our ability to produce
ecological statistical models and to handle increasingly large data sets.
Traditional multivariate linear-regression tools are useful for finding global
effects, especially with sparse data sets. For data mining (finding previously
unknown, significant relationships between variables in large data sets),
there is no need to assume global structure. Local data can refine global
rules by adding conditions to global rules. The resulting regression is
thereby determined by local conditions. Classification and regression tree
analysis (RTA) uses iterative splitting of the data to develop empirical relationships between response and predictor variables without the restrictive
distribution assumptions of classical regression analysis. This approach
creates models that are fitted by binary recursive partitioning, in which a
data set is successively split into increasingly homogeneous subsets (Clark
and Pregibon 1992). Regression tree analysis is much more flexible than
classic statistical methods in uncovering structure in data with variables that
are hierarchical, nonlinear, nonadditive, or categorical in nature. Regression
tree analysis is useful as a means of devising prediction rules for rapid and
repeated evaluation, as a screening method for variables, as a diagnostic
technique to assess the adequacy of linear models, and for summarizing
large multivariate data sets (Clark and Pregibon 1992; Iverson et al.
1999).
Multivariate adaptive-regression splines (MARS) is a multivariate,
nonparametric regression procedure that builds flexible regression models
by fitting separate splines (or basis functions) to distinct intervals of
the predictor variables (Friedman 1991). The variables and interactions
to use and the endpoints of the intervals for each variable are optimized
8. Evolving Approaches and Technologies
147