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Predicting strontium isotope variation and fish location with bedrock geology: Understanding the effects of geologic heterogeneity

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Abstract

Recent advances in using naturally occurring isotopes to reconstruct movement patterns have revolutionized the study of migration and spatial patterns across taxa. Isoscape approaches utilize isotopic variation in the underlying geology to quantify migration pathways. Spatial patterns in the geology can be used to predict isotopic variation, such as 87Sr/86Sr; however, previous attempts to create predictive models have had mixed results. Our primary objective was to investigate the relationship between bedrock lithology and 87Sr/86Sr ratio as a tool to extend the spatial resolution of animal migration studies. Secondly, we investigated the ability to use geologic prediction as an a priori tool for determining chemically distinct watersheds. We first developed a regression model to relate known stream water 87Sr/86Sr to rock information from geologic maps, then used model outputs to classify adult fall Chinook salmon to their juvenile rearing location from 87Sr/86Sr signatures recorded in their otoliths (ear bones). We discuss the effect of scale and geologic heterogeneity on our ability to determine 87Sr/86Sr ratios within the study area. Our results indicate that the relationship between 87Sr/86Sr values and bedrock lithology can be used to accurately determine the rearing location of fish using otolith 87Sr/86Sr signatures. The scale at which geology can be used as a predictor of 87Sr/86Sr values is constrained by geologic heterogeneity and inherent variability in 87Sr/86Sr ratios within major rock categories. Further, our results indicate that geological data alone can be used to quantitatively investigate which watersheds are likely to be distinguishable using this method within a basin. Geologic prediction also has the potential to improve the scale and resolution of isotopic studies and the development of isoscapes. By applying measures of spatial heterogeneity we will be better able to quantitatively place limits on the accuracy of geologic predictions of 87Sr/86Sr ratios.
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Predicting strontium isotope variation and sh location with bedrock
geology: Understanding the effects of geologic heterogeneity
Jens C. Hegg
a,
, Brian P. Kennedy
a,b
, Alexander K. Fremier
a,1
a
Department of Fish and Wildlife Sciences, University of Idaho, Moscow, ID 83843-1136, USA
b
Departments of Geological Sciences and Biological Sciences, University of Idaho, Moscow, ID 83843-1136, USA
abstractarticle info
Article history:
Received 17 April 2013
Received in revised form 9 October 2013
Accepted 10 October 2013
Available online 18 October 2013
Editor: David R. Hilton
Keywords:
Strontium isotopes
Isoscapes
Otolith microchemistry
Migration
Recent advances in using naturally occurring isotopes to reconstruct movement patterns haverevolutionized the
study of migration and spatial patterns across taxa. Isoscape approaches utilize isotopic variation in the
underlying geology to quantify migration pathways. Spatial patterns in the geology can be used to predict
isotopic variation, such as
87
Sr/
86
Sr; however, previous attempts to create predictive models have had mixed
results. Our primary objective was to investigate the relationship between bedrock lithology and
87
Sr/
86
Sr ratio
as a tool to extend the spatial resolution of animal migration studies. Secondly, we investigated the ability to
use geologic prediction as an aprioritool for determining chemically distinct watersheds. We rst developed a
regression model to relate known stream water
87
Sr/
86
Sr to rock information from geologic maps, then used
model outputs to classify adult fall Chinook salmon to their juvenile rearing location from
87
Sr/
86
Sr signatures
recorded in their otoliths (ear bones). We discuss the effect of scale and geologic heterogeneity on our ability
to determine
87
Sr/
86
Sr ratios within the study area. Our results indicate that the relationship between
87
Sr/
86
Sr
values and bedrock lithology can be used to accurately determine the rearing location of sh using otolith
87
Sr/
86
Sr signatures. The scale at which geology can be used as a predictor of
87
Sr/
86
Sr values is constrained
by geologic heterogeneity and inherent variability in
87
Sr/
86
Sr ratios within major rock categories. Further,
our results indicate that geological data alone can be used to quantitatively investigate which watersheds are
likely to be distinguishable using this method within a basin. Geologic prediction also has the potential to
improve the scale and resolution of isotopic studies and the development of isoscapes. By applying measures
of spatial heterogeneity we will be better able to quantitatively place limits on the accuracy of geologic
predictions of
87
Sr/
86
Sr ratios.
© 2013 Elsevier B.V. All rights reserved.
1. Introduction
Recent advances in reconstructing location and movement patterns
using naturally occurring isotopes have revolutionized the study of
migration and spatial patterns of habitat use across taxa (Hobson
et al., 2010).Isotopic methods have allowed researchers to link breeding
and overwintering grounds of butteries (Wassenaar and Hobson,
1998)andbirds(Marra et al., 1998; Wassenaar and Hobson, 2000;
Hobson et al., 2012), to quantify the natal origins and movement
patterns of sh (Harrington et al., 1998; Thorrold et al., 1998;
Kennedy et al., 2002; Hogan et al., 2007), whales and bats (Hobson,
1999), and to identify the forensic location of marijuana origin and
growing conditions (Hurley et al., 2010). Recent investigations have
reconstructed movement patterns in unprecedented temporal and
spatial detail (110 km) (Hamann and Kennedy, 2012) and at larger
regional scales (Barnett-Johnson et al., 2010) that would be impossible
using traditional tagging techniques.
The precision and power of landscape isotope, or isoscape,
approaches rely on the underlying isotopic variation in the landscape
(West et al., 2010). The ratio of strontium isotopes (
87
Sr/
86
Sr) can
exhibit ne scale environmental variation in river systems, making
it useful in studying, origin, migration and species distribution at
both large and small scales (Kennedy et al., 1997; West et al., 2009;
Barnett-Johnson et al., 2010; Hamann and Kennedy, 2012; Muhlfeld
et al., 2012). Also, in contrast to most other isotope systems,
87
Sr/
86
Sr
values are tightly linked to the underlying geology (Faure, 1977; Bain
and Bacon, 1994; Stewart et al., 1998). This signicant relationship
between bedrock geology and watershed chemistry may allow stream
water
87
Sr/
86
Sr ratios to be directly predicted from geology, potentially
leading to more accurate
87
Sr/
86
Sr isoscapes and increasing the reso-
lution and extent of research with less sampling effort. Lastly, because
biological fractionation of Sr isotopes does not occur, a precise signature
of provenance of organisms or habitat use is possible if water chemistry
can be characterized or predicted (Graustein, 1989; Kennedy et al.,
1997, 2000).
Chemical Geology 360361 (2013) 8998
Corresponding author. Tel.: +1 509 592 8867.
E-mail address: hegg1432@vandals.uidaho.edu (J.C. Hegg).
1
Present address: School of the Environment, Washington State University, Pullman
WA 99164-2812, USA.
0009-2541/$ see front matter © 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.chemgeo.2013.10.010
Contents lists available at ScienceDirect
Chemical Geology
journal homepage: www.elsevier.com/locate/chemgeo
Author's personal copy
Previous attempts to predict
87
Sr/
86
Sr using geologic variation, both
across the landscape and in surface water, have been met with varying
degrees of success (Chesson et al., 2012). Humston et al. (2006)
introduced a qualitative, a priori tool for researchers to determine the
feasibility of isotopic and elemental studies within a study reach.
Barnett-Johnson et al. (2008) reported that the majority of
87
Sr/
86
Sr
variation in the California Central Valley could be explained using felsic
and old sedimentary rock within the basin but did not extend this
predictive relationship to predict
87
Sr/
86
Sr values within the basin or
determine the location of salmon in the study. Bataille and Bowen
(2012) created large scale isoscapes of
87
Sr/
86
Sr values with landscape
geology, age, and weathering rates which explained 70% of the variation
in surface water
87
Sr/
86
Sr across the United States. They then applied
this model to Caribbean watersheds and extended it to include
additional sources of
87
Sr/
86
Sr (Bataille et al., 2012). While contributing
to our understanding of spatial variation in Sr isotope signature, prior
studies have been hampered by an inability to generalize predictions
and difculty in predicting across large differences in geologic makeup
or spatial scale.
We hypothesize that understanding how geology varies across
the landscape using metrics of landscape scale and heterogeneity will
improve our ability to generalize isotopic predictions from bedrock
geology in the future. We further hypothesize that geologic predictions
can be used to increase the resolution and extent of migration studies,
and that watershed geologic makeup alone can be used as an apriori
tool to isolate landscapes that are conducive to such studies.
The objective of this paper is to investigate the feasibility of
87
Sr/
86
Sr
prediction from bedrock as a tool to extend the spatial resolution
of animal migration studies. We rst present a regression-based
approach that relates surface water
87
Sr/
86
Sr measurements to bedrock
lithology in the Snake River basin of Idaho and Washington. We then
demonstrate that outputs from this model can be used to correctly
classify the location of juvenile salmon. Next, we apply our regression
model to unsampled watersheds within the basin and discuss the effect
of watershed scale and geologic heterogeneity in creating generalized
predictions of
87
Sr/
86
Sr prediction in the future. Finally, we analyze the
geologic differences needed to distinguish watersheds isotopically and
use geologic data alone as an a priori tool to determine the whether
watersheds are likely to be isotopically distinct.
2. Methods
Our primary goal was to develop a statistical relationship between
87
Sr/
86
Sr values within the Snake River basinand the associated bedrock
geology to test whether it could be applied to answer ecological
questions. Secondly, we examined this geologic relationship to deter-
mine under what geologic conditions and watershed scales this type
of geologic modeling could be used to improve isoscape modeling of
87
Sr/
86
Sr ratios.
To develop our geologic relationship we used water samples
collected seasonally to measure dissolved
87
Sr/
86
Sr isotope ratios from
13 sites throughout the Snake River basin by Hegg et al. (2013) as the
dependent variable to create a multiple linear regression. All samples
were analyzed using Thermal Ionization Mass Spectrometry and the
seasonal values for each site were averaged. Refer to Hegg et al.
(2013) for specic analysis methods. The primary rock types in the
watershed upstream of each sample point were quantied and used
as the independent variable (Table 1 in the Online Appendix).
This regression relationship was then applied to a recent dataset of
sh otolith
87
Sr/
86
Sr values to test whether it could be used to extend
the resolution or scale of migration studies. To do this, a linear dis-
criminate function was developed using the predicted outputs of our
regression equation with the geology of watersheds within the Snake
River basin as inputs. We used
87
Sr/
86
Sr signatures of the rearing stage
for 127 adult and juvenile salmon from Hegg et al. (2013) to test the
performance of our regression relationship as a method for determining
the rearing location of sh of sh. We used this sh dataset because
the original classication had been completed using the same water
samples as we used to create our regression relationship. Therefore,
by comparing these two approaches, we can attribute any differences
in classication accuracy to the effects of geologic prediction.
Understanding the scale at which geologic predictions can be made
is important for developing future isoscape models. Therefore, we
analyzed the ability of our regression model to determine
87
Sr/
86
Sr
ratios from geology at various scales. First we applied our original
regression model to three additional, small watersheds within the
basin to determine if the relationship can be generalized to smaller
watershed scales. Next, we created a second regression model that
includes
87
Sr/
86
Sr values for these three additional watersheds to
determine if prediction accuracy can be improved. We then quantied
the effects of watershed scale and heterogeneity on the accuracy of
regression outputs using the percentage area of rock types within
basin watersheds and the Shannon index of diversity and evenness.
Finally, the relationship between geology and
87
Sr/
86
Sr chemistry
offers the possibility that researchers could quantify whether a study
area is amendable to isotopic research before valuable time and
resources are expended in sample analysis. We tested our ability
to use geologic maps directly, without water sampling, to determine
whether watersheds are distinguishable, and thus amendable to
isotopic study. We used watershed geologic data as the independent
variable in a linear discriminate function with major watersheds
as the dependent variable. Our ability to distinguish watersheds using
this method was then compared with the results based on water
sampling. Finally, we analyzed the geologic differences required for
two watersheds to be distinguishable using logistic regression on the
pairwise comparisons of the major Snake River watersheds.
All statistical analyses were conducted in R statistical package
(versions 2.10.1 and 2.15.1, http://www.r-project.org/).
2.1. Study site
The Snake River, the largest tributary to the Columbia River, drains
an area of 280,000 km
2
encompassing six states (Fig. 1). Fall Chinook
salmon, which spawn in the lower reaches of the major tributaries in
the basin, are listed as endangered under the Endangered Species Act
(April 22 1992, Federal Register, Vol 57, No 78, p 14653). Fall Chinook
salmon in the Snake River inhabit a river system that has been
signicantly altered by hydropower construction, blocking upstream
access to the majority of fall Chinook salmon spawning grounds and
impounding a large portion of the downstream habitat behind eight
hydropower dams.
The Snake River tributaries can be grouped broadly by geology
(Fig. 1). The Clearwater and Salmon Rivers ow over felsic rocks of the
Idaho batholith, with the Clearwater being inuenced most heavily by
the older metamorphic rock (Foster and Fanning, 1997). The Tucannon,
Grande Ronde and Imnaha Rivers ow primarily over the Columbia
River Basalts (Hooper et al., 2007), with the Grande Ronde and Imnaha
Rivers being inuenced in their headwaters by the more diverse
Wallowa terrane (Hales et al., 2005). The upper Snake River begins
in the geologically more diverse and older Teton Range (Love et al.,
1978), and the basalt and rhyolites of the Snake River Plain (Leeman,
1982). The unique geologic conditions through which each group of
rivers ows lead to detectable differences in geochemical ngerprints
between rivers in the Columbia River Basin.
Geochemical variationamong basin tributaries has allowedprevious
classication of salmon spawning and rearing areas based upon
geochemical signature (Hegg et al., 2013). Hegg et al. (2013) classied
the main tributaries and Upper and Lower Snake River into four groups
based upon
87
Sr/
86
Sr ratio in stream water using a linear discriminate
function. Otoliths from returning adult fall Chinook salmon were then
analyzed and the
87
Sr/
86
Sr signatures from their natal, rearing and
overwintering stages were recovered using laser ablation inductively
90 J.C. Hegg et al. / Chemical Geology 360361 (2013) 8998
Author's personal copy
coupled plasma mass spectrometry. The location of each sh at these
life history points was then determined by classifying the
87
Sr/
86
Sr
signatures using the linear discriminate function developed from
water sampling across major basins.
In the research presented here, we aimed to determine the location
of these sh using geologic predictions of streamwater
87
Sr/
86
Sr ratio
developed from a regression of known
87
Sr/
86
Sr samples and geologic
data, then examine whether the spatial scale or resolution of sh
location could be increased using prediction. Therefore, we used the
stream water
87
Sr/
86
Sr signatures and the juvenile rearing phase of
the above otolith dataset to test our ability to determine sh origin
using predictions of
87
Sr/
86
Sr values from bedrock geology.
2.2. Quantifying bedrock geology
Our geological analyses were based upon current bedrock geologic
maps from the Preliminary Integrated Geologic Map Database of the
United States (Ludington et al., 2005). These maps detail the bedrock
geology of the Snake River basin at 1:500,000 scale with consistent
lithology across the region. The primary rock type within each map
N
Salmon
Palouse
Grande
Ronde
Clearwater
Imnaha
Tucannon
Snake
0240120
Kilometers
Snake basin geology
Mafic
Felsic
Carbonates
Metamorphic
Sedimentary/other
Water
Fall Chinook salmon
spawning range
Montana
Utah
Idaho
California Nevada
Oregon
Washington
Legend
River Courses
Water Sampling Points
Prediction Watersheds
Upper
Snake R.
Salmon R.
Upper
Clearwater R.
Lower
Clearwater R.
Bear Cr.
Big Cr.
Palouse R.
Imnaha R.
Tucannon R.
Grande
Ronde R.
Upper
Snake R.
Lapwai Cr.
A
B
Fig. 1. The location (A) of the Snake River basin and the watershed boundaries and water sample points used to predict
87
Sr/
86
Sr ratios are shown. Watersheds are nested; downstream
watersheds include all upstream watersheds. Lithology of the Snake River watershed (B) shows rock type categories with strong impacts on
87
Sr/
86
Sr ratio based primarily on protolithic
composition (Ludington et al., 2005; Stoeser et al., 2006).
91J.C. Hegg et al. / Chemical Geology 360361 (2013) 8998
Author's personal copy
polygon is recorded in the attribute table of the map layer according to
LithClass 6.1 standard (http://www.nadm-geo.org).
While quantifying geologic variability within our study area we
focused our analyses on percent abundance of rock types within
a basin rather than rock age. Rock age has an effect on
87
Sr/
86
Sr due
to the evolution of radiogenic
87
Sr from
87
Rb over time (half life
of 48.8 billion years); however, quantifying this relationship is
complicated for two reasons. First, the covariation of rock age with
rock type within the Snake River basin would not allow us to distinguish
causality. For example, the Idaho Batholith, a granitic structure that
wouldbeexpectedtohavehigh
87
Sr/
86
Sr, is also generally older
and associated with extremely old, high
87
Sr/
86
Sr, metasedimentary
deposits, making it difcult to determine the relative contribution of
age and rock type in the
87
Sr/
86
Sr values. Conversely, the Columbia
River basalts are relatively young, but would also be expected to have
low
87
Sr/
86
Sr based upon their mac composition. Secondly, acquiring
reliable and comparable geologic ages for watersheds across the large
Snake River basin proved challenging. There can be large variation in
the range of ages reported for a given rock type polygon and rock age
varies in its precision between different map units. The addition of age
did not signicantly improve our predictive ability, likely due to the
factors mentioned above, and therefore we only used geologic type in
this analysis.
Our aim in reclassifying rock types was to capture the geologic
variation relevant to
87
Sr/
86
Sr differences in stream water. Our rock
type classication was primarily based upon distinguishing between
mac and felsic rock types since these broad rock types typically display
different strontium isotopic chemistry based upon the composition of
their magma source (Faure and Mensing, 2004). Thus, all igneous
rocks were classied by either macorfelsicrocktype.Wedistinguished
all non-igneous rocks by their protolithic rock type when the protolith
was obvious from the map entry. Many non-igneous rock types have
no obvious protolithic composition. When no obvious protolith could
be determined the rock types were then classied into categories of
metamorphic, carbonate, or sedimentary/other.
The potentially high rates of weathering in carbonate rocks can have
large impacts on
87
Sr/
86
Sr ratios within a watershed, so carbonate rocks
weregiventheirownclassication (Blum et al., 1998). We designated
a metamorphic rock category based on prior knowledge that high
87
Sr/
86
Sr values might be present in very old metamorphic systems
associated with the Idaho batholith (Martignole et al., 2010; Jansen,
2011). The sedimentary/other classication included rocks and uncon-
solidated sedimentary deposits of indeterminate origin as well as
chemical and biogenic deposits other than carbonates. The details of
rock reclassication are listed in Table 2 of the online Appendix.
2.3. Surface area calculation
Surface area may be important when calculating the relative
contributions of geologic types. Differential weathering and the
propensity for more resistant rock types to form vertical faces may
bias the at map area toward the least resistant rock types. We
used 3-dimensional (3D) surface area alongside the conventional
2-dimensional (2D) map area to determine whether 3D area might
be a better predictor of
87
Sr/
86
Sr.
Three-dimensional surface area was calculated for the entire Snake
River basin using 90meter elevation rasters available from the National
Elevation Dataset (Gesch et al., 2009) and the DEM surface tools
package from Jenness Enterprises (Jenness, 2012). The total 2D and 3D
surface area of each rock type within each sample watershed was then
calculated using the Zonal Statistics tool available in the Spatial Analyst
toolbox in ArcMap. Thus, two geologic datasets were produced, one
recording the at 2D area of each rock type within the basin and another
which recorded the calculated 3D surface area.
The watershed above each water sample point was delineated
using the ArcHydro extension for ArcMap 9.3 (ESRI). In ArcMap, the
intersection between the watershed boundaries and the geologic map
layer was used to calculate the 2D and 3D area of each rock type within
the watershed above each sample point. The percent area of each rock
type for both 2D and 3D maps was then calculated from the attribute
table of the intersected map.
2.4. Model selection and prediction of
87
Sr/
86
Sr from geology
Multiple linear regression was used to develop a relationship
between
87
Sr/
86
Sr watershed geology within the spawning area of
Snake River Fall Chinook salmon. To develop this regression, percent
geologic area was the independent variable, while the
87
Sr/
86
Sr values
from 13 watersheds in the Snake River from Hegg et al. (2013)
were used as the dependent variable. Percent rock area followed an
exponential relationship with
87
Sr/
86
Sr and was transformed using
log(x+ 1) to meet the assumption of linearity and account for real
zero values within the data (Bartlett, 1947).
The most likely candidate models were compared (Table 3 online
Appendix) using AICc, a version of Akaike's Information Criterion modi-
ed for small datasets (Burnham and Anderson, 2002). This statistical
technique selects the model that best explains variation in the data
while rewarding parsimony by penalizing over-parameterization.
Candidate models were constructed using rock types that were well
represented in the basin, and rock types that were expected to have
asignicant inuence on dissolved
87
Sr/
86
Sr values within the study
area. Based upon the large areas of mac and felsic rock within the
basin these rock types were considered good candidate variables.
Similarly, the age and high
87
Sr/
86
Sr composition of metamorphic rock
in the study area indicated that it might be an important variable.
All other rock types were considered to have a representation that
was either of minor signicance or too variable in composition to be
effective predictors.
Our ultimate aim was to re-classify the sh from (Hegg et al., 2013)
using a linear discriminate function and training set based on
87
Sr/
86
Sr
predictions from bedrock geology. To do this, we digitized prediction
points at 10 river-kilometer (10-rkm) intervals (Fig. 3) within the
spawning area of Fall Chinook based on spawning site surveys (Garcia
et al., 2008). The watershed upstream of each prediction point was
then delineated using ArcHydro and the percent area of each rock
type was calculated. The
87
Sr/
86
Sr value for each point was predicted
by applying our regression equation to the geologic data at each point.
Prediction points were then grouped according to the four river
groupings (Table 1)fromHegg et al. (2013), and a linear discriminate
function was created using these points as training sets.
2.5. Rearing origins classication from otoliths
We used the regression relationship developed in the previous
section to test whether geologic predictions can be used to extend
ecological studies using
87
Sr/
86
Sr as a tracer. We used results from our
regression to classify 127 salmon otoliths to rearing location based on
the
87
Sr/
86
Sr signature of their otoliths. We then compared these
classications to prior classications from Hegg et al. (2013) who used
stream water
87
Sr/
86
Sr samples as a training set. Fish were classied to
rearing location using the linear discriminate function we developed
previously using geologic predictions as the training set. We then
calculated the Kappa statistic (Fleiss et al., 2004) to compare the
classication accuracy using geologic prediction to those of Hegg et al.
(2013).
Hegg et al. (2013) estimated an 86% classication accuracy based on a
single misclassication of six known-origin sh, with a cross validation
error rate of 0% for the original training set. The regression equation
used to create geologic predictions is based on the
87
Sr/
86
Sr values
from Hegg et al. (2013) and is thus not completely independent.
Therefore, we would expect that any classication error when comparing
92 J.C. Hegg et al. / Chemical Geology 360361 (2013) 8998
Author's personal copy
our sh geologic regression based classications to those of Hegg et al. is
due to the error in predicting
87
Sr/
86
Sr from geology.
2.6. Effects of scale and heterogeneity
To test the effect of watershed scale on our ability to predict
87
Sr/
86
Sr
ratios, we applied our regression model from Section 2.4 to three smaller
basins within the Snake River, each with varying geologic makeup
(Table 1, Online Appendix). These watersheds were chosen as a test of
scale due to their smaller size. They were not included in the original
geologic regression because they are outside the spawning range of
Snake River Fall Chinook salmon. They were also chosen due to the
existence of
87
Sr/
86
Sr values for their tributaries, allowing additional
analysis of the relationship of
87
Sr/
86
Sr to geologyat these smaller scales.
GPS locations and
87
Sr/
86
Sr values for 19 sites within the Big Creek
watershed, a tributary of the Middle Fork Salmon River, were obtained
from Hamann and Kennedy (2012) (Fig. 1, Online Appendix). Six
87
Sr/
86
Sr values and GPS locations were collected from Lapwai Creek,
a tributary to the Clearwater River (Fig. 2, Online Appendix). Twelve
87
Sr/
86
Sr water samples and GPS coordinates were also used from Bear
Valley Creek, in the headwaters of the Middle Fork Salmon River, as
part of a prior feasibility study in cooperation with the US Forest Service
(Kennedy, unpublished data) (Fig. 3, Online Appendix). All
87
Sr/
86
Sr
values were determined using Thermal Ionization Mass Spectrometry
(TIMS) except Lapwai Creek, which was analyzed using Multi-Collector
Inductively Coupled Plasma Mass spectrometry (MC-ICPMS).
The geologic makeup of these additional watersheds was deter-
mined using the same techniques as for the larger Snake River basin
in the preceding sections. Then,
87
Sr/
86
Sr ratios were predicted using
the regression model created in Section 2.4 to test the extent to which
this regression was scale independent. We then t a second regression
model to the combined
87
Sr/
86
Sr data for all water samples (Snake
River, Lapwai Creek, Bear Valley Creek and Big Creek) to test whether
a predictive model could be created which encompassed a larger
range of watershed scales. Candidate models using the combined data
were constructed using the same independent variable combinations
of 2D mac, felsic and metamorphic rock and selected using AICc.
To analyze how the varying representation rock types within
watersheds affected our ability to predict
87
Sr/
86
Sr ratios, we calculated
the Shannon index of diversity for rock types within each sampled
watershed (Shannon and Weaver, 1949). In this case the Shannon
diversity index (H) is used to describe the variability of rock types
present within a watershed, in contrast to its more familiar application
to biodiversity.
H¼X
s
i¼1
pilnpi
ðÞ ð1Þ
Htakes into account the relative abundance (Pi)ofanindividual
rock type and the number of rock types (S) to calculate the relative
evenness and diversity of rock types within a basin. The metric varies
between 0 and ln(S) with low values indicating low diversity and
uneven representation of rock types.
2.7. Exploring a priori prediction from geology
We tested the ability of geology alone to be used as an a priori
classier of location, without rst predicting
87
Sr/
86
Sr values using
linear regression. This was done with the intent of providing a
quantitative method for determining whether
87
Sr/
86
Sr ratio may be
useful as a tracer, before
87
Sr/
86
Sr values are known within the system
or before a research project is undertaken. We used the percent area
of mac and metamorphic rock types from the watershed upstream of
each 10-rkm point predictions as the explanatory variable to create a
linear discriminate function. We used the four chemically distinct
river groups from Hegg et al. (2013) as the classication variable in
this discriminate function. In this way we were able to test the ability
of geologic data alone to determine which watersheds are likely to be
distinguishable within a basin. We then calculated the cross-validation
error rate to determine whether geology alone could distinguish rivers
within the basin.
We examined the change in
87
Sr/
86
Sr ratio for a given amount of
change in geology within a watershed, and the probability that two
watersheds can be distinguished by
87
Sr/
86
Sr ratio given the difference
in their geologic makeup. To do this we rst calculated the pairwise
differences in
87
Sr/
86
Sr values, geologic diversity, mac, metamorphic
and felsic rock for all combinations of the watersheds used in the original
13 watersheds from Hegg et al. (2013). Then the difference in
87
Sr/
86
Sr
value was regressed against each geologic variable to understand
thechangein
87
Sr/
86
Sr value for a given change in
87
Sr/
86
Sr. Finally,
each pairwise watershed comparison was assigned as distinguishable
or indistinguishable based on whether the watersheds were part of the
same or distinguishable river groups in Hegg et al. (2013).Wethen
used logistic regression to determine the probability that two watersheds
are distinguishable given their difference in each geologic variable. Error
was estimated for both linear and logistic regression as a 95% condence
interval using the standard error output of the regression.
3. Results
3.1. Model selection for prediction of
87
Sr/
86
Sr from geology
Model t for multiple linear regression of the Snake River water
samples and bedrock geology was assessed using AICc weights
(Table 3, online appendix). All models were signicant (p N0.05, α=
0.05) and accounted for greater than 70% of the variation in the data.
Models containing predictors calculated using 3D area outperformed
the same models using 2D area. The model with the highest AICc weight
was constructed using 3D area,
87Sr=86 Sr ¼0:07100500:005571log %Mafic þ1ðÞ
þ0:015923 log %Metamorphic þ1ðÞþεð2Þ
followed closely by the same model,
87Sr=86 Sr ¼0:07101310:005723log %Mafic þ1ðÞ
þ0:015871log %Metamorphic þ1ðÞþεð3Þ
Table 1
Comparison of classicationaccuracy to classify sh to theirjuvenile rearing location based upon
87
Sr/
86
Sr signatures in their otoliths.Linear discriminatefunctions were developed using
training sets of
87
Sr/
86
Sr ratios predicted from bedrock geology using the regression equation in Section 2.4 (rows) and from water samples (columns) collected by Hegg et al. (2013).
Classication using water samples
(Hegg et al., 2013)
Tucannon, Grande Ronde,
Imnaha Rivers
Clearwater
River
Lower Snake
River
Upper Snake
River
User accuracy
Classication using geologic regression Tucannon, Grande Ronde, Imnaha Rivers 1 0 0 0 100%
Clearwater River 0 37 1 0 97%
Lower Snake River 0 3 83 0 97%
Upper Snake River 0 0 0 2 100%
Producer accuracy 100% 93% 99% 100%
93J.C. Hegg et al. / Chemical Geology 360361 (2013) 8998
Author's personal copy
using 2D area. Both of the top models explained 97% of the variation in
the data. While the 3D models had higher AICc scores, the difference
in prediction accuracy between 2D and 3D was less than 1%. Since our
goal was to create a relationship between
87
Sr/
86
Sr and geology which
can be easily utilized by researchers, this slight increase in accuracy
did not justify the extra calculations involved in determining 3D area.
Therefore, we used the 2D model for subsequent analyses. The results
of geologic reclassication and watershed delineation are described in
Table 1 of the online Appendix.
3.2. Rearing location classication from otoliths
Developing a linear discriminate function using
87
Sr/
86
Sr calculated
at 10-rkm intervals using the geologic regression from Section 2.4
resulted in a 3% classication error rate (3 misclassied out of 93 total
prediction points) using leave-one-out cross validation. This same
discriminate function, when used to classify sh, classied 97% (124 of
127) of sh to the same rearing location as Hegg et al. (2013) with a
Cohen's Kappa of 0.93 (st. error = 0.03, C.I. = 0.861) indicating high
agreement between methods when accounting for random error
(Table 1,Fig. 2). Proportions of sh classied to each source group are
not signicantly different between methods (Monte Carlo Chi-Square,
α= 0.05) indicating that predictions of
87
Sr/
86
Sr are capable of
predicting fall Chinook natal origins.
The three misclassied sh had a signature intermediate between
the Clearwater and Lower Snake River, similar to the single known-
origin juvenile misclassied in Hegg et al. (2013). This known-origin
juvenile originated in the Clearwater, but was captured in the Lower
Snake River during the rearing period. Hegg et al. (2013) speculated
that this misclassication may have been due to incomplete equili-
bration of the otolith signature to the Lower Snake environment,
potentially due to the rate at which juveniles outmigrate from their
natal streams.
3.3. Effects of scale and heterogeneity
Geologic diversity, as a function of both the representation and
evenness of the lithology within a watershed, was greatest for the
Snake River watershed. As expected, the largest watersheds displayed
the highest overall diversity of rock types and geologic diversity
decreased with watershed size. The three small watersheds used to
test the effects of scale had the lowest geologic diversity (Fig. 3A).
Error increased signicantly when predicting
87
Sr/
86
Sr within the
three smallest watersheds using the regression developed in Section 2.4
relating
87
Sr/
86
Sr from water samples to watershed geology. This is
expected when extrapolating to ner scales than the data originally
used to create the regression. While residuals for the Snake River
watershed samples were quite small and centered on zero (mean =
6.9 × 10
8
± 0.000457 1-st. dev.), the combined residuals for the three
small watersheds were much higher (Mean = 0.001439 ± 0.002259
1-st. dev.) and tended to be positively skewed, indicating that the
relationship of
87
Sr/
86
Sr to geologic makeup does not follow the same
relationship at smaller scales. Of the small watersheds, Lapwai Creek
best t the model, followed by Big Creek and Bear Valley Creek.
When dissolved
87
Sr/
86
Sr samples and geologic results from the
Snake River, Big Creek, Lapwai Creek and Bear Valley Creek were
combined to create a comprehensive linear regression, the model with
the highest AICc weight included mac and felsic rock as independent
variables (Table 4, online Appendix). The model was signicant
(p b0.0001, α= 0.05), however variance explained by the model
(R
2
= 0.64) was less than the original regression model.
3.4. Exploring a priori prediction from geology
The discriminate functiondeveloped using percent area of macand
metamorphic geology as explanatory variables, and river groups as the
dependent variable, resulted in a 3% error rate using leave-one-out
cross validation. This error rate was identical to the discriminate
function from Section 2.4 which was based upon the regression
relationship between
87
Sr/
86
Sr and watershed geology.
Analysis of pairwise differences between watersheds showed that
increasing differences in watershed geology could be used to determine
whether two watersheds were likely to be distinguishable. Regression
of the difference in
87
Sr/
86
Sr for a given difference in watershed geology
showed a signicant positive relationship between
87
Sr/
86
Sr and
the difference in mac, felsic, and metamorphic geology between
watersheds (Fig. 4A). Geologic diversity, as measured by Shannon
diversity, also showed a signicant positive relationship (Fig. 4B).
Rearing Classification
From Water Samples
Rearing Classification
From Geologic Prediction
0.706
0.708
0.710
0.712
0.714
Tucannon
G. Ronde
Imnaha
Clearwater
Salmon
Lower
Snake
Upper
Snake
0.706
0.708
0.710
0.712
0.714
Clearwater
Salmon
Lower
Snake
Upper
Snake
Tucannon
G. Ronde
Imnaha
Classification
Clearwater,
Salmon
Lower-
Snake
Upper-
Snake
Tucannon,
Grande Ronde,
Imnaha
AB
87Sr / 86Sr
Misclassified
Misclassified
Fig. 2. Classication of adult sh to their juvenile rearing location based on
87
Sr/
86
Sr signatures in their otoliths is shown. Classication using a linear discriminate function with water
samples as the training set ( A) from Hegg et al. (2013) resulted in one misclassied sh, a juvenile of known origin. Classication using a linear discriminate function based on
87
Sr/
86
Sr
ratios calculated from geology using the regression equation in Section 2.4 (B) misclassied four sh to the Clearwater group, including the sh originally misclassied in Hegg et al.
(2013). Points are coded by color and shape according to statistical classication to river groups. Misclassied sh appear as a different color and shape from the classication column.
Lighter colored points indicate juvenile sh of known origin. Points are jittered on the x-axis to avoid overplotting.
94 J.C. Hegg et al. / Chemical Geology 360361 (2013) 8998
Author's personal copy
Logistic regression of the pairwise differences between watersheds
showed a signicant relationship between difference in watershed
geology and the probability that two watersheds were distinguishable
using
87
Sr/
86
Sr (Fig. 5A). Geologic diversity also showed a signicant
relationship with the probability that watersheds are distinguishable
(Fig. 5B). Results from the pairwise comparisons of watersheds are
shown in Table 2.
4. Discussion
Naturally occurring chemical and isotopic tracers are proving to
be useful and powerful methods for studying ecological questions at
multiple scales (Harrington et al., 1998; Hobson, 1999; Kennedy et al.,
2000; Hamann and Kennedy, 2012). Strontium isotope ratios can
provide a powerful tracer of animal movement at varying scales, but
baseline isoscapes are not well developed, hindering its widespread
use (Hobson et al., 2010). Isoscapes for other isotope systems such as
hydrogen and oxygen, which are based on large scale precipitation
trends, are well developed but useful only at regional and continental
scales (Bowen, 2010). Because
87
Sr/
86
Sr can be used to track animal
movement at local, regional and continental scales,
87
Sr/
86
Sr isoscapes
can be used link ecological processes across scales, a major challenge
of traditional ecological studies (Hobbs, 2003). Much work is still
needed to create a generalizable model of
87
Sr/
86
Sr variation that
accounts for a majority of
87
Sr/
86
Sr variation across a broad range of
geologies and scales. Our method for classifying bedrock geology by
mac or felsic protolith may help to standardize future models by
providing a repeatable method that accounts for the major geologic
drivers of
87
Sr/
86
Sr variation across geologic settings.
This study shows that the relationship between
87
Sr/
86
Sr and
bedrock geology can be used to accurately reconstruct the location of
aquatic organisms and extend the resolution of strontium isotopic
studies beyond baselinewater sampling points. This work also provides
a relatively simple method by which investigators can determine a
priori the feasibility of
87
Sr/
86
Sr ratio as an investigative tool within
a given population or watershed. By creating a linear discriminate
function with the important reaches as the grouping variable and
the mac and felsic geology as the explanatory variables, the cross
validation error rate can be used to give an indication of how well
87
Sr/
86
Sr might distinguish between important reaches. Thus, it is
possible to quantify the degree to which unsampled watersheds are
likely to be isotopically distinct using geology alone. Further, analysis
of the differences between watersheds provides relationships between
geology and
87
Sr/
86
Sr, which may be useful to parameterize future
predictive models of
87
Sr/
86
Sr variation across the landscape.
4.1. Effects of scale and heterogeneity
The regression model between geologic and strontium ratio was
constructed with data from a regional watershed (Snake River Basin)
and performed well at that scale. However, our results indicate that
the ability to predict
87
Sr/
86
Sr from bedrock geology decreases when
extrapolated to watersheds below 1000 km
2
. Two factors may play
a role in this loss of predictive ability. Further, creating a second
regression model incorporating
87
Sr/
86
Sr water samples from these
smaller watersheds did not improve the predictive ability at smaller
scales.
One factor may be that rock type classications are broad, and
can potentially obscure large underlying variation in signature. Any
generalizable model predicting
87
Sr/
86
Sr from bedrock must create
broad classications of rock types, effectively forcing rocks of variable,
but similar,
87
Sr/
86
Sr isotope chemistry to be modeled as a unit. This
variation in
87
Sr/
86
Sr values within a rock type classication can be
signicant, particularly for felsic rocks whose geochemical makeup,
age and origin can lead to large variations in
87
Sr/
86
Sr isotope signature
(Faure and Mensing, 2004).
Second, as the size of watersheds decreases, they are increasingly
dominated by single rock units rather than an average of upstream
inputs (Fig. 3A), exposing the variation in
87
Sr/
86
Sr within the felsic
rock type classication. At coarse scales the model can make accurate
predictions based upon broad rock types because each river is an
average of the diverse signatures of the upstream watershed. Smaller
watersheds however (Fig. 6A), and typically dominated by a single
rock type (Fig. 6B), and therefore prediction accuracy decreases.
Further, the more a watershed is dominated by felsic rock the lower
the prediction accuracy of the model (Fig. 6C). This is expected since
individual felsic rock units should vary widely from the mean
87
Sr/
86
Sr
of the basin based on their age and chemical makeup. Thus, as scale
decreases, local variations in
87
Sr/
86
Sr values become increasingly
important for accurate prediction, and rock types containing large
Watershed
Snake
River
Big
Creek
Bear Valley
Creek
Lapwai
Creek
% of Dominant Rock Type
40%
50%
60%
70%
80%
90%
Shannon Diversity
0.2
0.4
0.6
0.8
1.0
1.2
Watershed Area (km2)
102103104105
A
B
Fig. 3. (A) Geologic diversity increases with watershed scale. (B) The percentage area of
the dominant rock type within a watershed decreases with watershed scale. These
relationships illustrate that individual rock types begin to dominate as scale decreases,
making the unique
87
Sr/
86
Sr ratio of a given geologic formation more important at smaller
scales. Dotted lines are tted linear models to indicate the direction of the trend.
95J.C. Hegg et al. / Chemical Geology 360361 (2013) 8998
Author's personal copy
variation in
87
Sr/
86
Sr signatures begin to be particularly poorly
predicted. Therefore, we would expect that generalized models would
perform best at the largest scales, where stream water
87
Sr/
86
Sr
signatures are an average of many rock units throughout a basin and
effectively integrate the overall variation within each rock type
classication. It is possible, however, that at smaller scales the difference
in a given rock type could provide an indication that watersheds are
distinguishable, even when the absolute
87
Sr/
86
Sr cannot be predicted.
Results from our analysis of pairwise differences between watersheds
give an indication of how this could be determined.
The scale and geologic makeup at which predictions of
87
Sr/
86
Sr
ratios can be made from bedrock will be different for every watershed.
Our study indicates, however, that in order to effectively apply
predictions from bedrock geology or produce generalizable isoscape
models, it is important to constrain the scale and geologic heterogeneity
at which predictions are made. Measures of heterogeneity such as
Shannon diversity and the percentage area of the dominant rock type
are independent of scale and geologic makeup, and can be applied to
any watershed. These metrics couldpotentially be used to quantitatively
determine, based on the geologic heterogeneity of the watershed, a
lower spatial threshold above which predictions are appropriate. In
the case of the Snake River, with more than 55% of the watershed
dominated by a single rock type and geologic Shannon diversity below
1.0 (H), prediction accuracy begins to decrease substantially (Fig. 6).
Spatially this corresponds to watersheds of 1000 km
2
or smaller. Further
work is needed to understand if heterogeneity measures can be
generalized across differing watersheds with differing geologies, and
to develop quantitative methods for applying these metrics across
watersheds.
4.2. Exploring a priori prediction from geology
One difculty for researchers planning to use
87
Sr/
86
Sr isotope
ratios as a tracer is determining whether a study system contains
enough isotopic variation between the important watersheds to
provide meaningful results. Our results indicate that it is possible
to use geologic variation as inputs to a linear discriminate function
to determine a priori whether important watersheds are likely to
be isotopically distinct. This provides a feasible a priori method
that requires minimal time input or prior knowledge. The data
requirements are minimal, only geology and watershed layers are
needed. Using GIS, a researcher can then reclassify the geologic map,
dene the relevant watersheds, and intersect the layers. Calculating
the percentage area of each rock type is then a simple calculation.
Using the cross-validation error rate of a discriminate function to
determine likely isotopic differentiation is not, however, a denitive
test. It assumes that the major rock types within a study area are
isotopically distinct but it is possible for rocks to be isotopically similar
regardless of their rock type classication, which would confound the
results. Therefore a more mechanistic understanding of the isotopic
Logistic Regression
% Felsic Rock
% Mafic Rock
% Metamorphic Rock
Shannon Diversity
0 0.25 0.50 0.75 1.0
B
Difference in Shannon Diversity
0.00
0.25
0.50
0.75
1.00
0% 10% 20% 30% 40% 50%
Difference in % Rock Type
Probability of Distinguishable
Watersheds
A
Fig. 5. As the difference in geologic makeup between two watersheds increases, the probability that they can be distinguished using
87
Sr/
86
Sr values increases (A). Small differences in
metamorphic rock in particular increase the probability that watersheds are isotopically distinct, as do mac and felsic geology. The difference in geologic heterogeneity between two
watersheds, as measured usingShannon diversity,is also a good predictor of thatwatersheds are isotopically distinct (B). Shaded area is the95% condence intervalaround the tted line.
Regression
% Felsic Rock
% Mafic Rock
% Metamorphic Rock
Shannon Diversity
0 0.25 0.50 0.75 1.0
Difference in Shannon Diversity
B
A
0.000
0.002
0.004
0.006
0.008
0% 25% 50% 75%
Difference in % Rock Type
Difference in 87Sr / 86 Sr
Fig. 4. The pairwise difference in
87
Sr/
86
Sr between watersheds of the Snake River varies predictably with the difference in geologic makeup. The absolute difference in
87
Sr/
86
Sr ratio
between two watersheds shows a positive relationship with the difference in mac, felsic and metamorphic makeup of the watersheds (A). The absolute difference in
87
Sr/
86
Sr ratio
betweenwatersheds alsofollows a positive relationship with the absolutedifferencein geologic diversityas measured by Shannondiversity (B). Shadedarea is the 95% condence interval
around the tted line.
96 J.C. Hegg et al. / Chemical Geology 360361 (2013) 8998
Author's personal copy
variation within rock types is needed to provide a truly predictive a
priori method.
Our regression results provide a more quantitative method of
determining whether watersheds might be distinct. In the Snake
River, watersheds with a difference of 3540% of macorfelsicrock
type have a 95% probability of being isotopically distinct (Fig. 5A). Linear
regression shows a positive relationship between the difference in
percentage of rock type and the change expected in
87
Sr/
86
Sr values,
which gives a measure of the difference in
87
Sr/
86
Sr ratios between
distinguishable watersheds (Fig. 4A).
The logistic regression of metamorphic rock type provides insight
into how a single, relatively rare, geology can exert an important
impact on watershed differentiability. A difference of only 10% in meta-
morphic rock within a watershed provides an 85% probability that
the watersheds are distinguishable and only 15% difference results in a
95% probability (Fig. 5A). This is an important consideration when
creating future generalized models, as some rock types may exert
a larger inuence than their representation on the landscape would
indicate.
Interestingly, our results show that a metric of geologic heteroge-
neity can be used to relate watershed geology to variation in
87
Sr/
86
Sr
isotopic values. A difference in Shannon diversity of 0.56 indicates a
95% probability that two watersheds are distinguishable and the linear
regression shows a signicant positive relationship between diversity
and
87
Sr/
86
Sr ratios (Figs. 4Band5B). This provides additional evidence
that metrics of geologic diversity may provide a means to improve
87
Sr/
86
Sr isoscape methods.
This study shows that the relationship between
87
Sr/
86
Sr and
bedrock geology has the potential to be a useful ecological tool for the
study of migration and distribution of organisms across a landscape.
Though more work is needed to generalize these results outside the
Snake River, they provide some insight into what might be expected
in similar watersheds. Applying these methods to additional watersheds
may uncover patterns in geologic heterogeneity which could place
bounds on the scale and predictive ability of future models. Additionally,
these analyses provide a starting point for understanding the isotopic
differences we expect for a given change in geologic makeup, which
could be used to parameterize future isoscape models.
Our study highlights two areas in which methods must improve
for
87
Sr/
86
Sr isoscape predictions to be generalizable. First, geologic
age should be included as a variable in future models in order to
explain smaller scale variation in
87
Sr/
86
Sr, especially within felsic
rocks. Second, geologic heterogeneity should be explored as a method
to guide future modeling efforts, particularly as a tool to determine
the lower threshold of prediction accuracy. Past efforts at determining
stream water
87
Sr/
86
Sr values using geology (Barnett-Johnson et al.,
2008; Bataille and Bowen, 2012; Bataille et al., 2012; Chesson et al.,
2012) have focused on intrinsic characteristics of rock types. This
study shows that this approach is valid, but limited by our under-
standing of how
87
Sr/
86
Sr signatures vary in relation to the distribution
of geologic features within watersheds and at varying scales. By
applying tools of landscape ecology to understand how the spatial
occurrence of geologic features affects our ability to predict
87
Sr/
86
Sr
ratios we may be able to improve predictions and better constrain the
spatial limits of future models.
Acknowledgments
Thanks to members of the CIFEES lab at University of Idaho,
including E. Hamann, J. Reader and S. Bourret for help in otolith
collection, analysis, and method development. Thank you to R. Lewis
with the Idaho Geological Survey for discussions of Snake River geology
and critique of the rock type classications. Thanks to B. Connor with U.
S. Fish andWildlife, B. Arnsberg from Nez Perce Tribal Fisheries,D. Milks
and staff at Lyons Ferry Hatchery, and the Washington Department of
Fish and Wildlife for sh sample collection. Thanks to the Washington
State University Geoanalytical Lab, J. Vervoort, C. Knaack, and G. Hart
for help with isotopic analysis and feedback on the model. This work
was funded by grants to R. Zabel and B. Kennedy from the USACE and
to B. Kennedy from NMFSNWFSC. Additional funding came from an
NSF GK-12 award, #0841199, and by the NSF Idaho EPSCoR program,
Table 2
Results of regression analysisfor pairwise watershedcomparisons from Hegget al. (2013)
show signicant positive relationships between the difference in mac, felsic and
metamorphic geology and the difference in
87
Sr/
86
Sr ratio using linear regression. All
models and coefcients were signicant (pb0.05). Error is reported a ± 95% condence
interval.
Linear regression Intercept Coefcient
Model
87
Sr/
86
Sr = % mac+ε0.0012 ± 0.0006 0.0064 ± 0.0016
87
Sr/
86
Sr = % felsic + ε0.0006 ± 0.0005 0.0101 ± 0.0016
87
Sr/
86
Sr = % metamorphic + ε0.0009 ± 0.0004 0.0167 ± 0.0020
87
Sr/
86
Sr = Shannon diversity+ ε0.0023 ± 0.0008 0.0023± 0.0018
Logistic regression Log odds
Model Intercept Coefcient
87
Sr/
86
Sr = % mac+ε1.2488 ± 1.1430 13.0494± 6.8689
87
Sr/
86
Sr = % felsic + ε1.3093 ± 1.0953 15.1571± 7.1456
87
Sr/
86
Sr = % metamorphic + ε0.4771 ± 0.8750 22.7080 ± 14.8427
87
Sr/
86
Sr = Shannon diversity+ ε0.4835 ± 0.9639 6.1581± 3.6998
0.2
0.4
0.6
0.8
1.0
1.2
Geologic
Heterogeneity
(Shannon Diversity)
Snake River
Lapwai Creek
Big Creek
Bear Valley Creek
Watershed
Area of Dominant Rock Type
40% 50% 60% 70% 80% 90%
B
Watershed Area (km2)
102103104105
A
87Sr / 86Sr Residual
-0.006
-0.004
-0.002
0.000
0.002
0.004
0.006
0.008
0% 20% 40% 60% 80%
Felsic Rock
C
Fig. 6. The ability to predict
87
Sr/
86
Sr ratio using bedrock lithology increaseswith watershed size(A). As watersheds decrease in size andare increasingly dominated by a singlerock type,
prediction accuracy decreases (B). As the percentage of felsic rock increaseswithin a watershed,prediction ability decreases (C)showing that the lossof prediction ability is largely driven
by felsicgeology. Valuesfor each watershedare based on watersampling and analysis using TIMS,except Lapwai creekwhich was analyzed using MC-ICPMS. Values forthe Snake River are
seasonal averages from Hegg et al. (2013), all others are single water samples.
97J.C. Hegg et al. / Chemical Geology 360361 (2013) 8998
Author's personal copy
award number EPS-0814387. Thanks also to the anonymous reviewers
who helped improve the focus and scope of the manuscript.
Appendix A. Supplementary data
Supplementary data to this article can be found online at http://dx.
doi.org/10.1016/j.chemgeo.2013.10.010.
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98 J.C. Hegg et al. / Chemical Geology 360361 (2013) 8998
... During the last few decades, strontium isotope ratios ( 87 Sr/ 86 Sr) have proven to be a powerful tracer of provenance not only for geological applications but also in a wide variety of studies including archaeology (e.g., Bentley et al., 2003;Evans et al., 2006;Montgomery, 2010;Rich et al., 2015;Szczepanek et al., 2018), hydrology (e.g., Christian et al., 2011;Hogan et al., 2000;Négrel et al., 2004;Zieliński et al., 2018), forensics (Beard and Johnson, 2000;West et al., 2009), ecology (e.g., Chamberlain et al., 1996;Hegg et al., 2013;Hoppe and Koch, 2007;Sillen et al., 1998), water supply (Chesson et al., 2012;Leung and Jiao, 2006), and food authenticity (e.g., Crittenden et al., 2007;Rodrigues et al., 2011;Rossmann et al., 2000;Voerkelius et al., 2010). Regardless of the purpose of research, the usage of Sr isotopes as a provenance tracer requires knowledge of spatial variations in 87 Sr/ 86 Sr values within the environment at a local and regional scale, preferably in the form of accurate reference maps. ...
... Maps describing isotopic variations are usually called isoscapes or isotopic landscapes. Isoscape models created by using geostatistical methods (e.g., Bataille et al., 2018;Beard and Johnson, 2000;Willmes et al., 2018) constitute an interesting research challenge but their accuracy is still not satisfactory (Chesson et al., 2012;Hegg et al., 2013). Due to the large spatial scale and thus their low resolution, they are of little use for local migration and provenance studies. ...
... This was necessary since the 87 Sr/ 86 Sr data of rocks and sediments in Poland are relatively sparse and mostly concentrated in two areas, the Sudetes and the Holy Cross Mountains. According to Hegg et al. (2013), the geological prediction has the critical potential to improve the scale and resolution of isotopic studies and the development of isoscapes. The Sr isotope composition of rocks and sediments depends mainly on their type and, to a lesser extent, on their age. ...
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This study presents first isoscape maps of strontium isotope signatures and their spatial variation in Poland, based on ~900 samples of rocks, sediments, surface water, and flora. This dataset is supplemented by ⁸⁷Sr/⁸⁶Sr ratios predicted for several carbonate rock units. High, radiogenic Sr isotope ratios (>0.72), related to the Pleistocene glacial deposits, are omnipresent throughout the country and are also found in the Sudetes and the Holy Cross Mountains, where igneous and clastic Palaeozoic rocks are widely exposed. The lowest Sr signatures (<0.71) occur predominantly in the Silesian-Małopolska and Lublin uplands and are related to exposures of Palaeozoic, Mesozoic, and Neogene carbonate rocks. The large variation of ⁸⁷Sr/⁸⁶Sr ratios in the environment across the country is chiefly driven by the diversity in the geological substrate, and locally, it is also influenced by anthropogenic contamination. Strontium isoscapes for the geological substrate and surface waters differ from each other, in terms of the range of ⁸⁷Sr/⁸⁶Sr values and their distributional pattern. The differences result primarily from mixing processes in the geosphere (weathering), hydrosphere, and biosphere that control Sr inputs from various natural sources present in the environment. On the other side, they are also created by anthropogenic contamination of surface water and presumably of soils. This situation has important implications for future archaeological provenance and migration studies, as isoscapes for surface water and vegetation cannot be directly used to estimate the local ⁸⁷Sr/⁸⁶Sr baselines for past human populations. Therefore, caution is required when modern Sr data of surface water and plants are used in archaeological research. ⁸⁷Sr/⁸⁶Sr values of the geological substrate, which may be affected by anthropogenic contamination to a lesser extent than water, soil, and vegetation, are favoured for the baseline estimation for historical times.
... Although differences in water chemical signatures between locations can sometimes be explained by geomorphology (Hegg, Kennedy & Fremier, 2013), temporal variations in the elemental signatures are generally not well understood and certainly not accurately predictable (Brennan et al., 2015). As suggested by Gillanders (2002), the use of otolith microchemistry as a tool for reconstructing the environmental history of fish requires constituting a library of elemental fingerprints over several seasons or years, depending on the scales of the studies to obtain the most accurate interpretations. ...
... Examination of otolith Sr:Ca signatures of fishes within freshwater systems allows assessments of habitat shift at micro-scales (Muhlfeld et al., 2012;Teichert et al., 2018) owing to groundwater hydrology and underlying geological conditions leading to local environmental strontium isotopic ratios that are reflected in otolith composition (Hegg, Kennedy & Fremier, 2013;Brennan et al., 2015). ...
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... Spatial distinction of water is dependent on concentrations of unique microelements within the water (Campana, 1999;West, Bowen, & Dawson, 2010). At a landscape level, elemental concentrations are influenced by bedrock and surficial geology (Gibbs, 1970;Hegg, Kennedy, & Fremier, 2013;Pracheil, Hogan, Lyons, & McIntyre, 2014). Additionally, water residency times may influence the elements present in water. ...
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... The geology of the major spawning tributaries in this watershed is diverse both in age and in rock type, creating significant differences in water chemistry between the major spawning areas (Hegg et al. 2013b). Ongoing water sampling throughout the basin has shown that 87 Sr/ 86 Sr signatures in the four main spawning areas of the basin are distinct and that discriminate function analysis using 87 Sr/ 86 Sr can be used to determine the locations of juvenile and adult fish using otolith chemistry (Hegg et al. 2013a(Hegg et al. , 2018. ...
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Ecological patterns are often fundamentally chronological. However, generalization of data is necessarily accompanied by a loss of detail or resolution. Temporal data in particular contain information not only in data values but in the temporal structure, which is lost when these values are aggregated to provide point estimates. Dynamic time warping (DTW) is a time series comparison method that is capable of efficiently comparing series despite temporal offsets that confound other methods. The DTW method is both efficient and remarkably flexible, capable of efficiently matching not only time series but also any sequentially structured data set, which has made it a popular technique in machine learning, artificial intelligence, and big data analytical tasks. DTW is rarely used in ecology despite the ubiquity of temporally structured data. As technological advances have increased the richness of small‐scale ecological data, DTW may be an attractive analysis technique because it is able to utilize the additional information contained in the temporal structure of many ecological data sets. In this study, we use an example data set of high‐resolution fish movement records obtained from otolith microchemistry to compare traditional analysis techniques with DTW clustering. Our results suggest that DTW is capable of detecting subtle behavioral patterns within otolith data sets which traditional data aggregation techniques cannot. These results provide evidence that the DTW method may be useful across many of the temporal data types commonly collected in ecology, as well other sequentially ordered “pseudo time series” data such as classification of species by shape.
... Further, numerous studies in anadromous, catadromous, coastal and estuarine species utilize a suite of these elements and isotopes to determine provenance. These include tracing the provenance of reef fish to natal seagrass beds, the natal origin of American shad across the Atlantic seaboard, nursery areas of menhaden in Chesapeake Bay, the entry of juvenile salmon into the ocean and facultative oligohaline habitat use in Atlantic tarpon (Chittaro et al., 2006;Walther & Thorrold, 2008;Hegg, Kennedy & Fremier, 2013;Schaffler, Miller & Jones, 2014;Woodcock & Walther, 2014). ...
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• The ecology of endangered and rare species can be difficult to study owing to their low abundances and legal limits on scientist’s ability to catch, sample, and track them. This is particularly true of sawfish (family Pristidae), whose numbers have declined precipitously, placing all five species on the IUCN Red List of Threatened Species worldwide. Best known for their distinctive, toothed rostrum, the ecology, movement and life-history of sawfish are poorly understood. • Sawfish rostral teeth are modified placoid scales, which grow continuously throughout the life of the fish. This continuous growth, combined with their stable calcified makeup, makes sawfish rostral teeth a potential source of temporal records of chemical and isotopic changes through the life of the fish. • Rostral teeth are often preserved in museums and as curios, potentially providing a source of life-history data to inform conservation actions without the need for field study, or as an important compliment to it. This is the first study to recover temporally explicit chemical data from sawfish rostral teeth. • Using archived samples of largetooth sawfish (Pristis pristis) we show that multiple chemical tracers can be recovered from sawfish rostral teeth, and that these tracers can be used to understand movement across salinity gradients. We further show that sawfish rostral teeth contain repeated structures and indistinct banding which could potentially be used for ageing or growth analysis of fish.
... Strontium isotope studies have proven especially useful in the study of the mobility of past human populations (e.g., Grupe et al. 1997;Bentley et al. 2003;Price et al. 2004;Montgomery 2010;Szczepanek et al. 2018;Walser et al. 2020). They also constitute reliable tools for tracking the migration of fauna or identifying their local or non-local character (e.g., Chamberlain et al. 1996;Hoppe and Koch 2007;Hegg, Kennedy, and Fremier 2013). More recently, Woodward and colleagues (2015) also applied Sr isotope data in order to document changes in environmental conditions in the Nile Valley during the Holocene. ...
Article
Archaeological sites at Affad (Sudan) are the only ones in northeastern Africa providing ostological remains of both African aurochs (Bos primigenius), dated to 50 kya, and domestic cattle, dated to 7–6 kya. The evidence enables studies of behavioral diversity between taurids. Strontium isotope analyses of the tooth enamel of both Pleistocene and Holocene ruminants suggest the local origin of these animals. The archaeozoological analysis reveals the temporal variability of environmental conditions was linked to a humid climate during the Marine Isotope Stage 3 (MIS3), which was more humid than the dry fluctuations during the African Humid Period. In addition, changes in the phenotype of cattle indicate that humans influenced domesticated animal behavior in the sub-Saharan region.
... Oncorhynchus tshawytscha in the Snake River of Idaho, a major tributary to the Columbia River The geology of the major spawning tributaries in this watershed is diverse both in age 138 and rock type, creating significant differences in water chemistry between the major spawning 139 areas (Hegg et al. 2013b). Ongoing water sampling throughout the basin has shown that 87 Sr/ 86 Sr 140 signatures in the four main spawning areas of the basin are distinct, and that discriminate 141 function analysis using 87 Sr/ 86 Sr can be used to determine the locations of juvenile and adult fish 142 using otolith chemistry (Hegg et al. 2013a(Hegg et al. , 2018. ...
Preprint
Full-text available
Ecological patterns are often fundamentally chronological. However, generalization of data is necessarily accompanied by a loss of detail or resolution. Temporal data in particular contains information not only in data values but in the temporal structure, which is lost when these values are aggregated to provide point estimates. Dynamic Time Warping (DTW) is a time series comparison method that is capable of efficiently comparing series despite temporal offsets that confound other methods. The DTW method is both efficient and remarkably flexible, capable of efficiently matching not only time series but any sequentially structured dataset, which has made it a popular technique in machine learning, artificial intelligence, and big data analytical tasks. DTW is rarely used in ecology despite the ubiquity of temporally structured data. As technological advances have increased the richness of small-scale ecological data, DTW may be an attractive analysis technique because it is able to utilize the additional information contained in the temporal structure of many ecological datasets. In this study we use an example dataset of high-resolution fish movement records obtained from otolith microchemistry to compare traditional analysis techniques with DTW clustering. Our results suggest that DTW is capable of detecting subtle behavioral patterns within otolith datasets which traditional data aggregation techniques cannot. These results provide evidence that the DTW method may be useful across many of the temporal data types commonly collected in ecology, as well other sequentially ordered "pseudo time series" data such as classification of species by shape.
Article
Effective species management often requires understanding patterns of movement and habitat use. A common approach in identifying where individuals reside relies upon chemical tracers from the environment that are incorporated into an individual's tissues. For fish, isotopes in their otoliths, specifically the portion of their otolith formed during their larval stage, have been used to identify the natal origin. Complicating this work, however, is the fact that during this life stage, there is a shift in the source of isotopes deposited onto the growing otolith from maternally to environmentally derived. The objective of this study was to identify the portion of the otolith representing this transition to environmentally derived isotopes so as to accurately investigate questions of natal origin for a threatened population of fall Chinook salmon (Oncorhynchus tshawytscha). We exposed developing larvae to four treatments that differed in terms of their water strontium isotope ratio (87Sr/86Sr) and used change‐point analysis of otolith 87Sr/86Sr and strontium to calcium ratio (Sr/Ca) to identify the otolith radius corresponding to the transition to environmentally derived isotopes. Our results indicated this transition occurred, on average, at 132 μm (87Sr/86Sr; ±50 μm standard deviation) and 127 μm (Sr/Ca; ±29 μm) from the otolith core, which corresponded to the developmental time between hatching and exogenous feeding. A substantial proportion of our otoliths (i.e., 61%) did not show convergence between otolith and water 87Sr/86Sr by the end of the 113‐day experiment, which was likely due to the dietary contribution of marine‐based feed. Therefore, we were unable to recommend an otolith radius to target for the purposes of reconstructing natal origin apart from being beyond approximately 130 μm.
Preprint
The focus of this study was to assess the potential of otolith microchemistry as a fishery management tool for different European freshwater fish species in an Alpine foreland with a diverse range of different water bodies but low geological variation. ⁸⁷ Sr/ ⁸⁶ Sr isotope and Sr/Ca ratios in water samples from 26 habitat sites in a pre-alpine catchment region around lake Chiemsee, Germany, an important region for recreational and economic fisheries, were analysed. ⁸⁷ Sr/ ⁸⁶ Sr isotope ratios and the Sr mass fractions in otoliths of 246 fish out of 16 species were determined using (laser ablation) inductively coupled plasma mass spectrometry ((LA)-ICP-MS). Habitats could be discriminated into three distinct strontium isotope regions (SIGs) and seven clusters with characteristic ⁸⁷ Sr/ ⁸⁶ Sr isotope and Sr/Ca ratios. The direct comparison of ⁸⁷ Sr/ ⁸⁶ Sr isotope ratios in water and otolith samples allowed to identify fish that might have been a) migrating b) transferred from other water bodies or c) stocked from fish farms. Sr/Ca ratios in water and the Sr mass fraction in otoliths were highly correlated, although significant differences between species from the same environment could be documented. Sr mass fractions in sagittae of Perca fluviatilis were about 60 % of those in sagittae of Coregonus spp and of lapilli of roach Rutilus rutilus from the same habitats. Different partition factors for water to otolith Sr/Ca mass fractions were determined for different species. Discrimination of fish otoliths by ⁸⁷ Sr/ ⁸⁶ Sr isotope ratios and Sr mass fractions according to habitat clusters was possible with success rates ranging from 92 % to 100 % for cyprinids, European perch Perca fluviatilis , whitefish Coregonus spp . and European grayling Thymallus thymallus, and was 74 % for salmonids. Otolith microchemistry proved to have great potential to serve as a fishery management tool at smaller spatial scales such as in the studied Alpine foreland when considering the limited variation of ⁸⁷ Sr/ ⁸⁶ Sr isotope and Sr/Ca ratios, the type and spatial distribution of habitats, and the species and question under investigation. Highlights Otolith microchemistry applied in in area with limited geological variability Fish transferred, stocked or migrated were identified Regressions between Sr/Ca ratios in water predict Sr mass fractions in otoliths Species specific Sr discrimination from water into otoliths European freshwater fish species assigned to habitat clusters of origin
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Quantifying the scale of offspring dispersal is essential for understanding demographic connectivity across landscapes and rates of population spread. However, characterizing natal dispersal in fishes is complicated by the difficulties of tracking origins and movement during early life-history stages. We combined direct observation of natal dispersal based on otolith chemistry with indirect estimates of dispersal from population genetics to quantify intergenerational dispersal of smallmouth bass inhabiting a river network. Average parent-offspring dispersal was estimated as 7.7 km from genetic isolation-by-distance and demographic population data. Otolith chemistry indicated that adults were captured an average of 8.3 km from their natal tributary, supporting the genetics-based estimate. Our estimate of intergenerational dispersal is higher than previous estimates for lotic fishes and considerably higher than estimates for smallmouth bass in lake systems. Differences in availability of seasonal habitats for smallmouth bass may account for the contrasting scales of dispersal between lake and river populations. The large intergenerational dispersal distance of riverine smallmouth bass should be considered in conservation of fisheries or efforts to control invasive populations in river networks.
Technical Report
Full-text available
The growth in the use of Geographic Information Systems (GIS) has highlighted the need for regional and national digital geologic maps that have been attributed with information about age and lithology. Such maps can be conveniently used to generate derivative maps for manifold special purposes such as mineral-resource assessment, metallogenic studies, tectonic studies, and environmental research. This report is part of a series of integrated geologic map databases that cover the entire United States. In the conterminous United States (CONUS), state geologic maps that range in scale from 1:100,000 to 1:1,000,000 are available for most of the country, and digital versions of these state maps are the basis of this product. In a few cases, new digital compilations were made, based on other sources, or existing paper maps were digitized. For Alaska and Hawaii, new maps are being compiled. The digital geologic maps are presented in standardized formats as ARC/INFO export files and as ArcView shapefiles. Five data tables that relate the map units to detailed lithologic and age information accompany these GIS files. The maps for the CONUS have been fitted to a common set of state boundaries based on the 1:100,000 topographic map series of the United States Geological Survey (USGS). When the maps are merged, the combined attribute tables can be used directly with the merged maps to make derivative maps. No attempt has been made to reconcile differences in mapped geology across state lines. The various digital geologic maps that form the basis for this product have been produced in a wide variety of formats. Although most of them were available as ArcGIS coverages or shapefiles, the items and formats in the polygon attribute tables (PATs) and arc attribute tables (AATs) vary dramatically. To unify these disparate maps, it was necessary to create a set of standard formats, and then to convert the state digital geologic maps to conform to those standards. The details of those standards are presented in the accompanying documentation. The creation of a unique map unit name called unit_link allows the different State maps to be merged. (Database field names are in italics). Unit_link consists of a two-letter State code, concatenated with the original map unit name, sometimes slightly modified, followed by a semicolon, and an integer that designates geographic regions (provinces) within the map, if they were used. This variable, unit_link, can then be used as a key field to relate the tables that contain age and lithologic information to the spatial database.
Book
Stable isotope ratio variation in natural systems reflects the dynamics of Earth systems processes and imparts isotope labels to Earth materials. Carbon isotope ratios of atmospheric CO2 record exchange of carbon between the biosphere and the atmosphere; the incredible journeys of migrating monarchs is documented by hydrogen isotopes in their wings; and water carries an isotopic record of its source and history as it traverses the atmosphere and land surface. Through these and many other examples, improved understanding of spatio-temporal isotopic variation in Earth systems is leading to innovative new approaches to scientific problem-solving. This volume provides a comprehensive overview of the theory, methods, and applications that are enabling new disciplinary and cross-disciplinary advances through the study of "isoscapes": isotopic landscapes. "This impressive new volume shows scientists deciphering and using the natural isotope landscapes that subtly adorn our spaceship Earth." Brian Fry, Coastal Ecology Institute, Louisiana State University, USA "An excellent timely must read and must-have reference book for anybody interested or engaged in applying stable isotope signatures to questions in e.g. Anthropology, Biogeochemistry, Ecology, or Forensic Science regarding chronological and spatial movement, changes, or distribution relating to animals, humans, plants, or water." Wolfram Meier-Augenstein, Centre for Anatomy & Human Identification, University of Dundee, UK "Natural resources are being affected by global change, but exactly where, how, and at what pace? Isoscapes provide new and remarkably precise answers." John Hayes, Woods Hole Oceanographic Institution, USA "This exciting volume is shaping a new landscape in environmental sciences that is utilizing the remarkable advances in isotope research to enhance and extend the capabilities of the field." Dan Yakir, Weizmann Institute of Science, Israel.
Article
We investigated the potential of using stable-carbon (δ 13C) and hydrogen (δD) isotope ratios in feathers of Red-winged Blackbirds (Agelaius phoeniceus) to delineate geographic origins where feathers were grown. We used outer primary feathers from territorial male blackbirds along a broad latitudinal transect from Louisiana, USA to Saskatchewan, Canada. Feather δD values showed an expected depletion with latitude, and were correlated strongly (r 2 = 0.83) with the mean growing season δD for precipitation at collection sites, Feather δ 13C values revealed that blackbirds fed on both C 3 and C 4 based foodwebs. Inputs of C 4-based carbon likely related to consumption of agricultural crops such as corn and sorghum. Overall, our dual isotope approach showed great potential as a means of delineating breeding origins of blackbirds throughout the continental Midwest, and supports previous findings that δD measurements of feathers are strongly correlated with precipitation and latitude throughout the central region of the continent.
Article
The elemental composition of fish otoliths may represent a permanent record of the environmental conditions an individual has experienced as trace elements, incorporated into the growing surface of the otolith, reflect the physical and chemical characteristics of the ambient water. We tested the utility of trace element signatures in otoliths as natural tags of the river of origin of juvenile American shad (Alosa sapidissima) collected from the Connecticut, Hudson and Delaware Rivers in August and October 1994. Four elements (K, Mn, Sr, and Ba) showed significant variability among sites within rivers in August, although only Mg showed a significant site effect by October. Four elements (Mg, Mn, St, and Ba) differed significantly among rivers in both months. Linear discriminant functions based on the trace element signatures classified fish to their natal river with ~90% accuracy in both August and October collections. The discriminant function generated from the August data was able to classify fish collected in October successfully with better than 80% accuracy. On the basis of our findings, the river of origin of adult fish could be accurately determined by quantifying the trace element composition of the juvenile portion of their otoliths.
Chapter
The measurable variations in the isotopic composition of strontium in ecosystems, unlike those of the lighter elements discussed in this volume, are entirely caused by the mixing of strontium derived from different geologic regimes of differing isotopic composition and are not due to fractionation by biological processes. The values and variation of strontium isotope ratios within an ecosystem can therefore yield information about the sources of strontium to and the patterns of strontium flow within the ecosystem. The lack of measurable isotopic fractionation of strontium means that information about processes is not obtainable directly, but must be inferred from mixing calculations. The lack of measurable isotopic fractionation also means that there must be variations in isotopic composition between various sources of strontium to an ecosystem in order for there to be any internal variation in isotopic composition.
Article
Strontium isotope analysis has proven useful in geo-location investigations of organic and inorganic materials and may complement the region-of-origin information provided by hydrogen and oxygen stable isotope analysis. In this study, we analyzed 99 drinking (tap) water samples collected from 95 municipal water systems across the USA to investigate the potential that Sr-87/Sr-86 can be used to provenance samples from managed hydrological systems. Results from a leaching and exchange experiment demonstrated that non-ideal storage conditions did not prohibit Sr isotope analysis of previously archived water samples stored in glass. Tap water samples were analyzed via multi-collector inductively coupled plasma mass spectrometry, which was preceded by a novel, automated, in-line Sr purification method. Measured tap water Sr-87/Sr-86 was compared to expected Sr-87/Sr-86 for collection location, which was predicted using four published isotope landscape (isoscape) models: age of bedrock (bedrock model), age plus major and minor lithology of bedrock (major bedrock model), weathering of Sr from rock (local water model), and surface fluxes within watershed (catchment model). The geologic history of the geographic regions represented by collected tap waters was diverse and we therefore expected significant covariation in measured and modeled Sr-87/Sr-86 values. Tap water exhibited large ranges in both Sr concentration (0-1.9 mg/L) and Sr-87/Sr-86 (0.7037-0.7320). Measured tap water Sr-87/Sr-86 ratios were significantly and positively correlated with predictions based on bedrock and catchment models. However, these bedrock and catchment models explained relatively little of the tap water Sr isotopic variation (similar to 10% and 17%, respectively), suggesting that the factors affecting drinking water Sr-87/Sr-86 are complex and more numerous than the variables included in current water models. This could be due to the reliance of some municipal water systems on groundwater, rather than surficial water sources; the natural movement of water across distinct geologic gradients; and/or the managed transport of water from source to point-of-use. Although published isoscape models for predicting Sr isotopic variation within the continental USA are reasonable approaches for estimating surface water Sr-87/Sr-86, additional efforts are needed to develop a prediction model specifically for tap water Sr-87/Sr-86.
Article
This chapter presents analytic methods for matched studies with multiple risk factors of interest. We consider matched sample designs of two types, prospective (cohort or randomized) and retrospective (case-control) studies. We discuss direct and indirect parametric modeling of matched sample data and then focus on conditional logistic regression in matched case-control studies. Next, we describe the general case for matched samples including polytomous outcomes. An illustration of matched sample case-control analysis is presented. A problem solving section appears at the end of the chapter.