Final Technical Report: - Southwest Fisheries Science Center - NOAA

“number of individuals” as the response variable and 2) deriving density from a two-step process
in which the probability of a species being present in a given habitat is multiplied by the
expected number of individuals given favorable habitat. The primary reason we decided to use
separate models to predict encounter rate and group size is that this approach breaks the process
down into ecologically meaningful quanta: differences in distribution may arise from variability
in group size or number of groups in a given region, with potentially different environmental
factors affecting the variability in each model. The two-step process of computing the
probability of presence and then multiplying by the expected number of individuals does not
have this flexibility because environmental effects on encounter rate and group size are
confounded in a single model.
GAMs are commonly used to relate characteristics of a species, such as distribution or
abundance, to environmental characteristics. A GAM may be represented as
(Hastie and Tibshirani 1990). The function g(μ) is known as the link function, and it relates the
mean of the response variable given the predictor variables =E(Y|X1,…,Xp) to the additive
predictor jfj(Xj). GAMs are nonparametric extensions of generalized linear models (GLMs).
The components fj(Xj) in the additive predictor of a GAM may include nonparametric smooth
functions of the predictor variables, whereas a GLM is composed of a linear predictor, jjXj,
in which the terms j are constants. This difference between the additive and linear predictor
allows GAMs to be more flexible than GLMs.
Model Comparison Analysis
When working with ecological data, it is often difficult to distinguish meaningful signals
from noise arising from the unexplainable variability and complex interactions inherent in
ecological systems. Even in the absence of noise, relationships among ecological variables
rarely can be explained by simple mathematical equations. Working within the framework of
generalized additive models may be useful for analyzing ecological data because the
nonparametric model structure of GAMs provides flexibility in model building and fitting, often
allowing GAMs to exhibit more fidelity to the data than alternative model structures.
Nevertheless, there are disadvantages to GAMs. For example, if appropriate model building and
selection methods are not used, the resulting GAM may overfit the data, reliably reproducing the
data upon which the model was built at the cost of sacrificing accuracy when predicting on novel
data. In addition, GAMs may be difficult to interpret because they cannot always be defined by
a simple formula comprised of a constant coefficient tied to each explanatory variable that
indicates the strength, magnitude, and direction of the covariate’s effect on the response variable.
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