74
Hale and Pflaumann
N pachyderma (dextral) - (including
"pachyderma/dutertrei intergrades 'j
Globigerina quinqueloba
Globigerinoides ruber (pink)
G. ruber (white)
Globigerina rubescens
Globigerinoides trilobus trilobus
Globigerinoides trilobus sacculifer
Globorotalia scitula
Globorotalia truncatulinoides
Orbulina universa
Globigerinoides tenellus
Cluster Analysis
In order to further analyze temperatures calculated
by the MAT, a cluster analysis was performed to
examine the relationships among samples within
each core using the relative abundances of
foraminiferal species as the variables. Through this
procedure, the samples within each core were
combined into more or less homogeneous groups
according to relative abundances of planktonic
foraminiferal species within the samples. We chose
to use eight clusters for each core as the number
that would best illustrate the data and facilitate the
discussion of results. This choice was subjective
and intuitive, made after computing a number of
different cluster solutions as suggested by Hair et
al. (1984) and Fishbein and Patterson (1993). The
calculated temperatures for the samples within
each cluster were then identified to determine to
what extent samples with similar species compositions fell within the same temperature ranges. This
procedure provides some insight into the extent to
which species variability of the samples affects the
temperatures calculated by the SIMMAX equations. Classification by cluster analysis has become
rather common in the investigation of geological
problems with large numbers of observations and!
or variables, especially in the studies of numerical
taxonomy and paleoenvironments. A large variety
of hierarchical clustering techniques are available,
but unfortunately there are no widely accepted statistical guidelines available for determining which
should be employed in individual cases. Researchers generally experiment with several methods and
choose that which best represents their data. In
practice, the utility of the method is evaluated by
its performance rather than theoretical statistical
considerations (Davis 1986). Ward's clustering
method was employed here because it yielded the
most reasonable grouping of samples for our data,
and it is recommended by Fishbein and Patterson
(1993) as appropriate for paleontological faunal
data. This method attempts to create the most homogeneous clusters possible. The squared Euclidian
distance method was used to determine similarity
among the samples. Non-standardized data were
used because this resulted in fewer one-sample
clusters. This may result from the closed nature of
the data sets used, meaning that the measurements
(species percentages) for a given sample always
add up to 100%. This results in an interdependence
of the values within each observation in the sense
that an increase in one species automatically reduces the value for all other species, and vice versa.
The STATGRAPHICS PLUS For Windows program, version 1.4 was used for the cluster analyses.
Stable Oxygen Isotope Analysis
In the two Rio Grande Rise cores the white variety of Globigerinoides ruber was chosen for
oxygen isotope analysis because of its persistent
abundant presence in all samples and because its
modern habitat is in the upper photic zone (Be and
Tolderlund 1971; Hemleben eta!. 1989). Since it is
one of the least solution-resistant of the recent
planktonic foraminiferal species (Be 1967) special
care was taken to select specimens that were complete and intact. The specimens chosen for isotope
measurements were taken from the 212-315)J. size
fraction in order to insure consistency of ontogenetic developmental stage. Isotope measurements
were carried out using the FINNIGAN MAT 251
mass spectrometer at the Geosciences Department
of Bremen University. Oxygen-isotope values for
the Brazil Slope core (GeoB 2204) were measured
on G. sacculifer, and were provided by A.
Diirkoop. R. Schneider provided oxygen-isotope
values for G. ruber from the Ceara Rise core
(GeoB 1523).
Hale and Pflaumann
N pachyderma (dextral) - (including
"pachyderma/dutertrei intergrades 'j
Globigerina quinqueloba
Globigerinoides ruber (pink)
G. ruber (white)
Globigerina rubescens
Globigerinoides trilobus trilobus
Globigerinoides trilobus sacculifer
Globorotalia scitula
Globorotalia truncatulinoides
Orbulina universa
Globigerinoides tenellus
Cluster Analysis
In order to further analyze temperatures calculated
by the MAT, a cluster analysis was performed to
examine the relationships among samples within
each core using the relative abundances of
foraminiferal species as the variables. Through this
procedure, the samples within each core were
combined into more or less homogeneous groups
according to relative abundances of planktonic
foraminiferal species within the samples. We chose
to use eight clusters for each core as the number
that would best illustrate the data and facilitate the
discussion of results. This choice was subjective
and intuitive, made after computing a number of
different cluster solutions as suggested by Hair et
al. (1984) and Fishbein and Patterson (1993). The
calculated temperatures for the samples within
each cluster were then identified to determine to
what extent samples with similar species compositions fell within the same temperature ranges. This
procedure provides some insight into the extent to
which species variability of the samples affects the
temperatures calculated by the SIMMAX equations. Classification by cluster analysis has become
rather common in the investigation of geological
problems with large numbers of observations and!
or variables, especially in the studies of numerical
taxonomy and paleoenvironments. A large variety
of hierarchical clustering techniques are available,
but unfortunately there are no widely accepted statistical guidelines available for determining which
should be employed in individual cases. Researchers generally experiment with several methods and
choose that which best represents their data. In
practice, the utility of the method is evaluated by
its performance rather than theoretical statistical
considerations (Davis 1986). Ward's clustering
method was employed here because it yielded the
most reasonable grouping of samples for our data,
and it is recommended by Fishbein and Patterson
(1993) as appropriate for paleontological faunal
data. This method attempts to create the most homogeneous clusters possible. The squared Euclidian
distance method was used to determine similarity
among the samples. Non-standardized data were
used because this resulted in fewer one-sample
clusters. This may result from the closed nature of
the data sets used, meaning that the measurements
(species percentages) for a given sample always
add up to 100%. This results in an interdependence
of the values within each observation in the sense
that an increase in one species automatically reduces the value for all other species, and vice versa.
The STATGRAPHICS PLUS For Windows program, version 1.4 was used for the cluster analyses.
Stable Oxygen Isotope Analysis
In the two Rio Grande Rise cores the white variety of Globigerinoides ruber was chosen for
oxygen isotope analysis because of its persistent
abundant presence in all samples and because its
modern habitat is in the upper photic zone (Be and
Tolderlund 1971; Hemleben eta!. 1989). Since it is
one of the least solution-resistant of the recent
planktonic foraminiferal species (Be 1967) special
care was taken to select specimens that were complete and intact. The specimens chosen for isotope
measurements were taken from the 212-315)J. size
fraction in order to insure consistency of ontogenetic developmental stage. Isotope measurements
were carried out using the FINNIGAN MAT 251
mass spectrometer at the Geosciences Department
of Bremen University. Oxygen-isotope values for
the Brazil Slope core (GeoB 2204) were measured
on G. sacculifer, and were provided by A.
Diirkoop. R. Schneider provided oxygen-isotope
values for G. ruber from the Ceara Rise core
(GeoB 1523).