Geoscience Reference
In-Depth Information
11
Models for
Trend Analysis
Timothy Robinson and Jennifer Brown
11.1 Introduction
Previous chapters of this topic have focused on various strategies for sam-
pling ecological populations to estimate parameters such as the population
size or density. Often, environmental managers require information not only
on the current status of a population but also on the changes in the popula-
tion over time. For example, interest may be in monitoring a special area such
as national parks (e.g., Fancy et al., 2009), monitoring for biodiversity (Nielsen
et al., 2009), monitoring to detect the spread of invasive species (Byers et al
.
,
2002), or monitoring of pollution or contamination levels (Wiener et al., 2012).
Monitoring for changes over time helps discern whether management actions
are needed for a vulnerable species or ecosystem and for assessing whether
management actions have been effective. For example, the Convention on
Biological Diversity, which aimed to reduce the rate of loss of biological diver-
sity, referred to indicators to assess progress toward the 2010 target (http://
www.biodiv.org/2010-target). Included in these indicators was monitoring
the changing abundance and distribution of selected species, as well as mea-
suring changes in the status of rare or threatened species.
In this chapter, we consider various methods of assessing change over
time. We use a data set of lake contamination measured by mercury con-
centrations in fish (in ppm). Fish were collected by trawls at different loca-
tions around the lake. Fish tissue was minced and then assayed for mercury
concentration. The trawls were conducted at 10 randomly chosen stations
in the lake for 12 years. The feature of this design is that the same stations
were repeatedly measured, and this in turn means that the structure of the
observation data was clustered. The other feature of the data is that they are
balanced; that is, there are equal numbers of observations (
n
i
= 12) for each of
the 10 stations, giving a total of
n
=
120 observations in the data set.
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