Download Lincoln-Peterson Population Lab: Mark and Recapture Technique

Lincoln-Peterson Population Lab: Mark and Recapture Technique
THIS IS A CLASS COPY. Do all work in your lab notebook.
Introduction
Unlike plants, animals are often secretive and usually mobile. Consequently, simple counts or
plot sampling techniques are useless for determining population size. However, for several
reasons, including understanding population dynamics and setting harvest limits, it is important to
estimate animal abundance. Therefore, several techniques have been developed to accomplish
this task. Of the numerous possibilities that exist, mark-recapture methods are frequently
employed. The general procedure involves capturing and marking animals (this phase is referred
to as the marking period). Different animals often require unique capture and marking
techniques. The marked animals are then released. After a certain period of time (long enough for
the animals to redistribute themselves within the habitat) individuals in the mobile population are
again captured and counted. The second cohort of individuals is called the census population.
Within the census population a certain number of individuals will carry the mark applied earlier
and others will be unmarked. Those individuals carrying the mark belong to the marked cohort.
It is important to keep track of the number of marked and unmarked individuals in the census
population. This general procedure may be applied either short term or long term and applies to
both open and closed populations. Accordingly, the mark recapture model that is used will
depend on the population type and the duration of the study (table one).
Table One
Mark-Recapture Model
Model type
Description
Lincoln-Peterson Method
Closed population
One marking period
Schnabel Method
Closed population
Multiple marking periods
Jolly-Seber Model
Open population
Multiple marking periods
Objectives
In today’s lab you will
1. Take part in estimating the population size of a wild bean population
2. Learn the basic assumptions underlying the Lincoln Peterson Model
3. Learn the potential errors and strengths in sampling populations
Assumptions of Lincoln-Peterson Method
1. All individuals have the same chance of getting caught in the first sample.
2. Marking individuals does not affect their behavior making them more likely to be caught or
predated.
3. The population is “closed,” so N is constant.
4. Emigration and mortality must be absent or equal for marked and unmarked individuals.
Lincoln-Peterson Population Lab: Mark and Recapture Technique
5. Individuals must retain their markings indicating capture throughout the study.
Where:
M= number of animals captured and marked in 1st sample
C= number of animals captured in 2nd sample (marked +unmarked; census population)
R= number of marked animals captured in 2nd sample (marked cohort)
N= estimate of population size
The size of M represents the marking effort and the size of C represents the sampling effort.
The unknown population size (N) may be estimated by rearranging the above formula:
Population =
# Initially Captured & Marked x Total Captured Second Sample
# of Marked Individuals Recaptured
In the example below 50 turtles were caught and marked, 100 were then captured later of
which, 14 had been caught and marked in the original sample of 50.
Population = 50 X 100 = 35 estimated population
14
While this formula provides an estimate of the population size, it tends to over estimate N
because of a failure to meet one or more of the assumptions (listed above). However, we can
correct for the bias by using the following formula:
You have data from each year of the study, beginning with 2005. To do estimates of population
you can look at our data in a few ways. You could look at all the years collectively and get
something like this.
(Total # turtles found 2005-2010 +1) (Total number captured in 2011 +1)
(# of marked recaptures 2011 – 1)
You could use just a couple of years and then compare them to two other years or more.
(Total number of turtles found in 2010 +1) (Total number captured in 2011 + 1)
(# of marked recaptures 2011 – 1)
Materials
• 500 Kidney Beans
• 1 Flat Tray or brown bag
• 1 Marker
Lincoln-Peterson Population Lab: Mark and Recapture Technique
Procedure
We will be estimating the population size of beans rather than live animals so that you can
examine the effect of marking and sampling effort on the final population estimate. You will
mark a small number of beans to simulate low marking effort and a large number of beans to
simulate high marking effort. Sample effort depends on the size of the census population.
1. Mark 25 beans (5% Marked) on both sides and mix them in with the rest
2. Without looking sample the beans by taking out 10 beans (2% population) repeat 3 times
and record data {Low marking and sampling effort}
3. Now draw out 50 beans (10% population) repeat three times and record data {Low
marking and high sampling effort}
4. Now remove and mark another 25 beans (10% Marked)
5. Without looking sample the beans by taking out 10 beans (2% population) and record
data {High marking and low sampling effort}
6. Without looking sample the beans by taking out 100 beans (20% population) and record
data {High marking and high sampling effort}
7. Compare your estimates of “N” under low marking and sampling effort, low marking and
high sampling effort, high marking and low sampling effort, and high marking and high
sampling effort.
Sample
Number
5% Marked
2% Captured
M
C
R
N
5% Marked
10% Captured
M
C
R
N
10% Marked
2% Captured
M
C
R
N
10% Marked
20% Captured
M
C
R
One
Two
Three
Mean
% Error
1 SD
Mean
% Error
1 SD
Mean
% Error
1 SD
Calculations
1. Calculate the variance and standard deviation (See attached handout for instructions)
2. Calculate percent error
% Error = (Actual – Calculated) x 100%
Actual
Mean
% Error
1 SD
N
Lincoln-Peterson Population Lab: Mark and Recapture Technique
DISCUSSION QUESTIONS
Assume all questions and thus answers are about the box turtle study.
1. Recall Assumption 1: Each animal is equally likely to be captured. This assumption is
almost never true. Explain how the likelihood of capture is not the same for all individuals at
the first marking effort. How would you minimize this problem?
2. Recall Assumption 2: Marking does not influence an individual animal’s probability of
recaptured. Describe how being initially captured and marked could (a) increase and (b)
decrease an individual’s probability of recapture.
3. Recall Assumption 3: Births and immigration do not occur between the marking and
recapture efforts. Can we assume a closed or open population at Lovett for box turtles?
4. Recall Assumption 4: If mortality & emigration occur between capture and recapture,
marked animals have the same combined mortality-emigration rate as unmarked
animals. If the assumption is violated, is it more likely because marked animals have a higher
rate of mortality + emigration than unmarked animals, or a lower rate? (Explain why) How
can a researcher attempt to insure that the assumption is met?
5. Recall assumption 5: Marks should not be lost between capture and recapture. How can
a researcher attempt to insure that the assumption is met? What would happen to the estimate
if marks were lost?
6. Do not answer this question unless we did standard deviation in the lab - Assume that you are
given the job of determining the size of the population of Coast Horned Lizards (a threatened
species in Southern California coastal sage scrub habitat) in an area being considered for
development. Your supervisor requires that your estimate be made with 95% confidence
limits of ± 15% or better, but also that you invest the smallest possible amount of manpower,
time and money. You decide to use the Lincoln-Petersen method to minimize handling and
disturbance of the animals. Your review of the literature reveals population densities in
similar habitats that lead you to guess that your study area might contain ~ 800 animals. In
planning your mark-release- recapture study, how large a sample size would you need?
Lincoln-Peterson Population Lab: Mark and Recapture Technique
Standard Deviation and Variance
Deviation just means how far from the normal
Standard Deviation
The Standard Deviation is a measure of how spread out numbers are.
Its symbol is σ (the greek letter sigma)
The formula is easy: it is the square root of the Variance. So now you ask, "What is the Variance?"
Variance
The Variance is defined as:
The average of the squared differences from the Mean.
To calculate the variance follow these steps:
• Work out the Mean (the simple average of the numbers)
• Then for each number: subtract the Mean and square the result (the squared
difference).
• Then work out the average of those squared differences.
Example
You and your friends have just measured the heights of your dogs (in millimeters):
The heights (at the shoulders) are: 600mm, 470mm, 170mm, 430mm and 300mm.
Find out the Mean, the Variance, and the Standard Deviation.
Your first step is to find the Mean:
Answer:
600 + 470 + 170 + 430 + 300
Mean =
1970
=
5
= 394
5
Lincoln-Peterson Population Lab: Mark and Recapture Technique
so the mean (average) height is 394 mm. Let's plot this on the chart:
Now, we calculate each dogs difference from the Mean:
To calculate the Variance, take each difference, square it, and then average the result:
So, the Variance is 21,704.
And the Standard Deviation is just the square root of Variance, so:
Standard Deviation: σ = √21,704 = 147.32... = 147 (to the nearest mm)
Lincoln-Peterson Population Lab: Mark and Recapture Technique
And the good thing about the Standard Deviation is that it is useful. Now we can show which heights are
within one Standard Deviation (147mm) of the Mean:
So, using the Standard Deviation we have a "standard" way of knowing what is normal, and what is extra
large or extra small.
Rottweilers are tall dogs. And Dachshunds are a bit short ... but don't tell them!
But ... there is a small change with Sample Data
Our example was for a Population (the 5 dogs were the only dogs we were interested in).
But if the data is a Sample (a selection taken from a bigger Population), then the calculation changes!
When you have "N" data values that are:
• The Population: divide by N when calculating Variance (like we did)
• A Sample: divide by N-1 when calculating Variance
All other calculations stay the same, including how we calculated the mean.
Example: if our 5 dogs were just a sample of a bigger population of dogs, we would divide by 4 instead of
5 like this:
Sample Variance = 108,520 / 4 = 27,130
Sample Standard Deviation = √27,130 = 164 (to the nearest mm)
Think of it as a "correction" when your data is only a sample.
Formulas
Here are the two formulas
The "Population Standard Deviation":
Lincoln-Peterson Population Lab: Mark and Recapture Technique
The "Sample Standard Deviation":
Looks complicated, but the important change is to
divide by N-1 (instead of N) when calculating a Sample Variance.