Biology 357 – Ecology
Name:
.
Ecology Laboratory #3
“Density Estimation and Analysis”
(30 points - due in two weeks)
INTRODUCTION
Ecologists study populations and the factors that affect them. The Lincoln-Peterson Index
(census) method used widely to estimate population abundance and density. In today’s lab, you
will work together in groups to estimate the population abundance of a hunted species (Tubulus
gradulosa fischerii) occupying four (4) boxes. By using the Lincoln-Peterson Index (Census)
method, you will arrive at your best estimate of the number of Tubulus in 2 boxes. You will
work in groups, selected at random, of course. Your group will have to determine the
methods, do the calculations, and arrive at your best estimate. I will attempt to help,
within reason, and to guide you. However, you must do the work and provide the estimates.
Thus, your objectives today are to obtain a better understanding of this method and how this
relates to our study and understanding of wildlife populations.
Here’s the general Lincoln-Peterson formula:
N= n x M .
m
Where:
N = your estimate of population density (per box).
M = the number of individuals captured, marked, and released during the first
capture session.
n = the number of individuals you capture in the 2nd capture session.
m = the number of marked individuals you caught in the 2nd capture session.
The questions before you are:
1.
How does your group propose to obtain an accurate estimation of
the abundance of Tubulus in each of the 2 boxes before you?
2.
What are your methods?
3.
Is just 1 sample enough? If so, you are betting an awful lot of lab
points on just 1 sample!
Here’s a hint: you may have to repeat you Lincoln-Peterson Index (census) methods
several times to arrive at your group’s best estimate. Also, you will have to design your methods
so that they are exactly the same from box to box and from sample to sample. This is called
precision: the repeatability of exact measurements. When you have completed your work,
you will submit me a written estimate of both box’s in your group. How close will you be? If
you are the closest, then you are the most accurate. Accuracy is how close your estimates are
to the real population abundance/density.
Precision and accuracy are NOT the same.
High Accuracy and High Precision
Low Accuracy, but High Precision
High Accuracy and Low Precision
Low Accuracy and Low Precision
Remember, you will have to record all your data to receive full credit for your estimates. In
other words, every member of your group must complete their own lab sheets and do their own
calculations in order for the group to submit their estimates and receive a chance for the 15
points. For the sake of simplicity, you might want to work on the small box first, just to refine
your group’s sampling technique. Then attempt to tackle the larger box second. Good luck.
Biology 357 – Ecology
Ecology Lab Worksheet
A.
#
Box _____:
Lincoln-Peterson Estimate #1 - Box #_____
1st attempt:
2nd attempt:
2nd attempt:
how many Tubulus did you capture?
how many Tubulus did you capture?
how many of those Tubulus were “recaptures’?
(M)
(n)
(m)
Here’s the formula again. Fill out the values and calculate your estimate:
N=
nxM
m
N=
?
#
Lincoln-Peterson Estimate #2 - Box _____
1st attempt:
2nd attempt:
2nd attempt:
how many Tubulus did you capture?
how many Tubulus did you capture?
how many of those Tubulus were “recaptures’?
N=
nxM
m
N=
?
(M)
(n)
(m)
Lincoln-Peterson Estimate #3 - Box #_____
1st attempt:
2nd attempt:
2nd attempt:
how many Tubulus did you capture?
how many Tubulus did you capture?
how many of those Tubulus were “recaptures’?
N=
N=
Now you have to work on another box:
nxM
m
?
(M)
(n)
(m)
B.
Box #_____:
Lincoln-Peterson Estimate #1 - Box #_____
1st attempt::
2nd attempt::
2nd attempt:
how many Tubulus did you capture?
how many Tubulus did you capture?
how many of those Tubulus were “recaptures’?
(M)
(n)
(m)
Here’s the formula again. Fill out the values and calculate your estimate:
N=
nxM
m
N=
?
Lincoln-Peterson Estimate #2 - Box #_____
1st attempt::
2nd attempt::
2nd attempt:
how many Tubulus did you capture?
how many Tubulus did you capture?
how many of those Tubulus were “recaptures’?
(M)
(n)
(m)
Here’s the formula again. Fill out the values and calculate your estimate:
N=
nxM
m
N=
?
Lincoln-Peterson Estimate #3 - Box #_____
1st attempt::
2nd attempt::
2nd attempt:
how many Tubulus did you capture?
how many Tubulus did you capture?
how many of those Tubulus were “recaptures’?
(M)
(n)
(m)
Here’s the formula again. Fill out the values and calculate your estimate:
N=
nxM
m
N=
?
Now you have to provide your estimates for both boxes. To do this, fill in the blanks on the next
page:
Biology 357 – Ecology
Box #_____.
A.
Sample
Number
Lincoln-Peterson
Index Estimate
Difference from the
mean estimate
Multiply this difference by 2 and
sum below
1
2
3
Sum
?
Sum:
(called the variance)
Divide
by 3
(mean)
?
Square root of sum:
(called the standard deviation)
Your group’s mean estimate is:
The standard deviation from your estimate is:
Thus, your formal estimate is stated as:
Tubulus.
.
+
Now, complete the formula again for the second box on the next page.
Tubulus.
Box #_____.
B.
Sample
Number
Lincoln-Peterson
Index Estimate
Difference from the
mean estimate
Multiply this difference by 2 and
sum below
1
2
3
?
Sum:
Sum
(called the variance)
Divide
by 3
(mean)
?
Square root of sum:
(called the standard deviation)
Your group’s mean estimate is:
The standard deviation from your estimate is:
Thus, your formal estimate is stated as:
Tubulus.
.
+
Tubulus.
Please wait until everyone has completed their work before reporting your results. Extra
points may be awarded based on the accuracy and precision of your work.
Questions to ponder when writing your lab report:
1.
How close were your estimates to the actual number? Did you have issues with accuracy,
precision, or both?
2.
Which group had the highest estimate? Which group had the highest standard deviation?
What factors would/could account for this variation?
3.
What factors would account for any differences in estimates. Would different
models/formulas provide different estimates given similar methods?
4.
Speculate in your report (the discussion section) what would have to your estimates if a
group of marked individuals died between samples?
Please follow the same formatting standards as the previous two lab exercises. Further,
see me early if you have any questions.