Lab 1_Bald Eagle_Data Use in Excel
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WFA 3133 – Applied Ecology
Spring 2022
Lab 1: Data Use in Excel & Hypothesis Testing (30 points)
Exploring the population dynamics of wintering bald eagles through long-term data
This data set explores factors affecting the population numbers of bald eagles (
Haliaeetus
leucocephalus
; Figure 1) surrounding Lake Coeur d’Alene, Idaho. The bald eagle is a large bird
of prey that demands our attention by its physical features, its history of near extinction, and its
dynamic population seen today.
Background Information:
The population trend of the bald eagle during the past 70 years provides a history with several
important lessons. After World War II, the insecticide, dichlorobiphenyl-trichloroethane (DDT),
was allowed for widespread agricultural use. Despite its effectiveness in killing insect pests on
crops, the chemical accumulated in the body tissues of bald eagles (through bioaccumulation),
making the birds unhealthy and causing them to lay thin-shelled eggs that broke as soon as the
parents sat on them to begin incubation. The numbers of bald eagles in the contiguous United
States, which were already declining due to hunting, plummeted as a result. The bald eagle was
listed as endangered under the Endangered Species Act of 1973, and this protection, combined
with the national ban of DDT in 1972, is credited with leading to the recovery of these
magnificent birds.
Bald eagle numbers not only vary over historical time, but they also vary across the landscape
with changes in the seasons. Like many birds, most bald eagles migrate in the winter in search of
food. The primary food source for bald eagles is fish, and the eagles need open water to access
the fish, which in many locations consists of spawning salmon at the shallow edges of lakes and
streams. Once the lakes and streams freeze over, the eagles have to use an alternative food source
(e.g., carrion, such as dead deer or elk) or go elsewhere. Bald eagles will also feed on ducks,
although not as frequently as fish. During the migration, the eagles follow a route with several
stopovers at lakes and
streams along a southward
corridor. The bald eagles
travel individually, and
although a given eagle may
spend only a week or two at
a stopover, collectively the
eagles may be present for
several months. Although
the birds travel as
individuals, once at a
stopover, they will roost
together in the evening (i.e.,
location were eagles gather
to sleep for the night) and
perch together in the same
or adjacent trees.
1
Figure 1.
Adult bald eagle (left) with distinctive physical features
perched in a cottonwood tree and an immature bald eagle (right)
with a mixture of brown and right plumage in the winter
environment. Photos by Tom Michalski.
WFA 3133 – Applied Ecology
Spring 2022
Because of its endangered status in the early 1970s, several agencies and biologists initiated
long-term surveys. Some of the surveys are ongoing nationwide surveys, such as the Midwinter
Bald Eagle Survey, and others are local surveys such as the data set that is the focus of this
activity. Since 1974, just two years after the ban on DDT, the Bureau of Land Management in
Northern Idaho has counted migrating bald eagles every winter.
The bald eagle counts are taken on a weekly basis at eleven sites around Wolf Lodge Bay on
Lake Coeur d’Alene in the Pacific Northwest (Figure 2). The eagles stop at Lake Coeur d’Alene
because of the availability of kokanee salmon, which is a land-locked strain of sockeye salmon
(
Oncorhynchus nerka
). The salmon live to about three years of age and then spawn in November
or December, dying immediately after spawning and leaving a large number of carcasses in the
shallow water for the eagles to feed on. The biologists go out by car and count the number of
eagles on perch trees or flying at these sites. The adult and immature eagles are counted
separately. The sites are usually visited once per week in the morning from mid-November to the
beginning of February with the highest numbers of eagles usually being present during
December. In addition, the biologists record weather conditions, human activity at each site,
salmon abundance, and various other factors that could influence the counts of migrating eagles.
Summary Statistics in Science
With every scientific investigation or study, a lot of data are collected and/or generated. One of
the most common and important steps in data processing is the generation of summary statistics.
A statistic is a number that scientists use to estimate a certain characteristic of an entire
population. For example, characteristics could include height, weight, crop yields, or plant
densities. Statistics could provide answers to differences in height, average weights, variability
between crop yields, and similarity in plant densities.
2
Figure 2.
Map of the study area in the Pacific Northwest (United States) and the bald eagle
winter survey sites along Lake Coeur d’Alene, Idaho.
WFA 3133 – Applied Ecology
Spring 2022
To determine the exact statistic of any one of the above mentioned characteristics, a scientist
would need to measure every individual in the entire population – this is an extremely rare
occurrence, and normally logistically impossible to do. As a result, scientists generate estimates
by randomly
sub-sampling from a population.
Using the provided dataset on bald eagle counts at Lake Coeur d’Alene in northern Idaho (Lab
1_Bald Eagle Dataset_2022.xlsx on Canvas), we are going to examine 3 commonly used types of
summary statistics:
1.
Central Tendency: Sample Mean and Sample Median
2.
Variation: Range, Variance, and Standard Deviation
1. Central Tendency: Sample Mean
Sample mean is the most common and useful statistic; it is used to generate an average value for
a population. Means must always be reported with units of measurement
(e.g., cm, kg, L).
We will never know the true population mean without sampling all the individuals, but this
statistic will produce a sample mean:
1. Central Tendency: Sample
Median
Although the sample mean is one of
the most common and useful
summary statistics, it is not always
the most appropriate statistic for a
particular situation. One of the
assumptions of the sample statistic is
that observations (i.e. bald eagle,
salmon numbers, December
temperatures) are drawn from
populations with a normal
distribution (Figure 3).
However, when a population
deviates from a normal distribution
and becomes non-normal (Figure 4)
it is necessary to use another
estimate of central tendency. An
alternate statistic is the sample
median. The sample median is the
3
Number of standard deviations from mean
Figure 3.
Normal distribution.
Figure 4.
Negatively and positively skewed distributions.
In negatively skewed distribution, mean < median. In
positively skewed distribution, mean > median.
WFA 3133 – Applied Ecology
Spring 2022
middle value
in a group of observations. Median must always be reported with units of
measurement
.
2. Variation: Range
The third important summary statistic to account for is variation, that is, how much variation is
around the mean or median? Understanding variation is important, because two populations with
the same mean might have very different amounts of variation among the observations.
Understanding means and variations is vital to compare populations statistically later on.
The simplest index of variation is the
range
. Range is defined as the
difference between the
largest and smallest observations
. Variation must always be reported with units of measurement.
2. Variation: Variance
The range does not report variation between samples very well, as different data sets can have
the same range but with very different observations. A better representative is variation of all
samples related to the sample mean. The
variance
is calculated by squaring the differences
between sample mean and each observation and adding them up to provide a sum of squares,
then dividing by the total sample size minus one:
2. Variation: Standard Deviation
Notice that the units of the sample variance are in squared units. This doesn’t make sense in our
case of bald eagle and salmon numbers, as we can’t have squared bald eagles or salmon. To fix
this, take the square root of the sample variance, which gives us the
standard deviation
:
3. Scatterplots and Linear Regression
Scatterplots depict the independent variable on the x-axis, and the dependent variable on the y-
axis. When we want to determine the relationship between the
dependent variable (y) and the independent variable (x), we
may use linear regression to observe how the two variables are
correlated (positive or negative correlation, see “Glossary for
the scientific process”).
Figure 5.
Scatterplot with linear regression line showing
positive correlation.
Linear equation:
y = mx + b
4
X
Y
WFA 3133 – Applied Ecology
Spring 2022
m
= slope;
b
= y-intercept
5
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