Biology 357 - Ecology
Name:
.
Ecology Laboratory #2
“Survivorship Analysis”
(30 points - due in two weeks)
INTRODUCTION
During lectures, we will discuss human population growth and population dynamics as significant
factors affecting the structure and function of the world’s ecosystems. Population dynamics is the study of
changes in the abundance (size), distribution and composition of a population over time. These changes in
the abundance and composition determines how populations respond to external (ecological) and internal
(within population) factors. The factors that most affect a population are:
A.
B.
C.
D.
E.
Birth rates
Death rates
Immigration rates
Emigration rates
Age Structure
The simplified formula for estimating population abundance is:
Abundance = B - D + I - E
The opposite of death is survival (technically known as survivorship); studying survival
patterns can yield insights into a species’ general traits. Moreover, the age structure can have a profound
effect on a populations’ ability to absorb catastrophic events (volcanoes, earthquakes, etc.) and remain
stable, decrease or increase. All species exhibit some form of survivorship patterns. In general there are
three (3) types: I, II, and III. Each represents a unique strategy for reproduction and survival. Thus,
studying various aspects of survival age structure can reveal important population attributes which can be
used to project a species’ ability to persist over a time period and their likely effect. Today, we are going to
use the cemetery data to investigate an aspect of age structure: survivorship. With these samples, we will
investigate and develop survivorship “curves” for humans living in the United States before and after 1900.
When studying age structure, populations have to be divided into groups of similar ages, or “age
classes.” For this assignment, we will divide the data into 22 “age classes” and develop the survivorship
curves for 4 groups:
1.
Females born before 1900
2.
Females born after 1900.
3.
Males born before 1900.
4.
Males born after 1900.
The information for each group will come from the data that you collected, and from previous
classes. From the summarized data, we will build “life tables” that give us information about the age
structure of the population. Then, we will produce graphs for each group and analyze the results. Because
we are working with specific age classes, we will calculate age-specific life tables.
A.
Today’s Objectives:
1.
2.
B.
To learn population age structure by studying survivorship curves.
To graph survivorship curves based on our cemetery data.
Our Hypotheses (Example):
1. Null Hypothesis: No differences between male and females born before and after 1900.
Alternate Hypothesis: There is a difference between male and females born before and after 1900.
2.
3
METHODS
First, we need to define “age classes.” Individuals can die at any age, and individuals of the same
age (or group of similar ages) belong to the same cohort, age interval, or age class. Biologists build
survivorship curves that are composed of age intervals. Moreover, an age interval is associated with an age
class (see table below). For our purposes today, the individuals living and dying from age 0 - 4 will be
called “age class 1.” Age class 2 will be for those individuals dying from age 5 - 9. Age class 3 will be for
those individuals dying from age 10 - 14. The sequence will be completed for all 22 age classes below.
Keep in mind that the additional age intervals/age classes can be added to include those individuals living
past 100 years.
Age
Interval
Equals
Age
Class
Age
Interval
Equals
Age
Class
Age
Interval
Equals
Age
Class
Age
Interval
Equals
Age
Class
0-4
1
25 - 29
6
50 - 54
11
75 - 79
16
5-9
2
30 - 34
7
55 - 59
12
80 - 84
17
10 - 14
3
35 - 39
8
60 - 64
13
85 - 89
18
15 - 19
4
40 - 44
9
65 - 69
14
90 - 94
19
20 - 24
5
45 - 49
10
70 - 74
15
95 - 99
20
1
Next, we have to summarize the data according to the hypotheses we wish to test. I summarized
the data into the 4 groups previously listed (females before 1900, after 1900, etc.). Here’s how the data for
females, post-1900 looks:
Age
Class
f (x)
d (x)
l (x)
1
121
Y
1000
2
q (x)
Age
Class
f (x)
12
22
16
13
31
3
16
14
32
4
26
15
19
5
24
16
23
6
20
17
18
7
29
18
8
8
26
19
0
9
21
20
0
10
10
21
0
11
19
22
0
Total
X
d (x)
l (x)
q (x)
Z
W
0.0
4
We will work each column, moving from left to right. The first thing we need to do is sum the
total number of females that lived and died for this group and place it the box with an “X” at the bottom of
the f(x) column. This is the total number of individuals in our sample. Do this now! Next, you will
probably wonder what the number 1000 is for at the top of the l (x) column. Well, it’s used to standardize all
the information to 1000 individuals. This information will be expressed as a per capita rate (per 1000
individuals) and will make them comparable. But how do you fill in the d (x), l (x), and q (x) columns?
Next, we have to fill in the d (x) column. To fill in the d (x) for the first age class (where the Y is),
called d (1), take the f (1) and divide it by the total number of individuals (where the arrow points). In this
case you would divide 121 by 481 to get 0.252. Repeat the process with the other age classes to complete
the d (x) column. At this time, ask me to review your work because errors made in this column will creep
into the remaining 2 columns ruin your calculations. When are finished, add every number in the d (x)
column and place this number at the bottom where the “Z” is. If you have done it correctly, the sum total of
this column should be close to 1.0000. This d (x) column represents the number of individuals dying within
a certain time interval.
Next, you have to fill out the l (x) column. This is easier than the d (x) column. The first l (x)
number is calculated by multiplying 0.252 (from the d (x) column) by 1,000 (= 252); it represents our effort
to standardize the data to 1,000 individuals (per capita population). To fill in the next box - l (2) - for age
class 2, take l (2) and multiply by 1,000, placing the result in the box In effect, we are calculating the
number of individuals surviving to age class 2. I will help you complete the rest of the columns. When
you have finished all the l (x) calculations, add them up and place the total where the “W” is. The total
should be close to 1,000. If it is not within 2 points of 1,000, then review your calculations; you likely have
a calculation error. I’ll help you find it.
We’re almost finished! Yes, that’s right. However, we have to finish the q (x) first. This column
represents the mortality rate for each age class and it is a bit tricky to calculate. To calculate q (x), first write
the number 1,000 above the q (x) column. Next, take the number in l (1) and subtract it from 1,000. Place
the result in the q (1) box. Subtract the number in l (2) from q (1). Place the result in q (2). The process is
similar to going down a flight of “stairs” - each “step” is created by subtracting an l (x) value from the
preceding q (x) value. Fill in the rest of the l (x) column and total the values. Your total should be close to
zero. Remember, if your total is within 2 individuals from zero you should be okay. Please ask me to
review it. Now we are ready for the last step. To draw the survivorship curve for this age class, you have
to put age class on the x-axis, and each corresponding q (x) value on the y-axis. I will show you how to
graph this on graph paper. Once this is completed, you are done! . . . . . . .
Well, not quite. I have a homework assignment for you. You have the data for all 4 categories in
the following pages. I would like you to complete the calculations for each group and graph each of their
survivorship curves. After you have finished making the 4 graphs answer the following 2 questions on a
separate piece of paper and hand it and the completed graphs into me at the beginning of the next
laboratory period.
Questions:
1.
2.
Based on the material presented to you in the lecture and the analysis in today’s laboratory
exercise, what type of survivorship curves have you drawn? Are they Type I, II, or III curves?
What external factors would account for any differences among your 4 graphs?
5
Males born before 1900.
Age Class
f (x)
d (x)
l (x)
1
34
Y
1000
2
10
3
14
4
13
5
24
6
16
7
35
8
28
9
33
10
39
11
61
12
66
13
68
14
110
15
125
16
143
17
135
18
69
19
59
20
28
21
7
22
2
Total
q (x)
6
Males born after 1900.
Age Class
f (x)
d (x)
l (x)
1
211
Y
1000
2
37
3
25
4
45
5
45
6
47
7
41
8
37
9
43
10
40
11
45
12
40
13
61
14
66
15
59
16
56
17
46
18
21
19
6
20
2
21
0
22
0
Total
q (x)
7
Females born before 1900.
Age Class
f (x)
d (x)
l (x)
1
28
Y
1000
2
4
3
5
4
17
5
25
6
24
7
29
8
20
9
24
10
36
11
50
12
45
13
65
14
76
15
105
16
133
17
113
18
103
19
63
20
29
21
13
22
5
Total
q (x)
8
Females born after 1900.
Age Class
f (x)
d (x)
l (x)
1
6
Y
1000
2
3
3
2
4
3
5
2
6
4
7
2
8
8
9
13
10
14
11
14
12
13
13
13
14
23
15
46
16
46
17
34
18
48
19
31
20
13
21
3
22
0
Total
q (x)
9
Name:
Location:
.
Survivorship Lab
“Cemetery Data”
Gender
Sample
(M or F)
Year
of
Birth
Year
of
Death
Age
Gender
Sample
(years)
(M or F)
1.
26.
2.
27.
3.
28.
4.
29.
5.
30.
6.
31.
7
32.
8
33.
9.
34.
10.
35.
11.
36.
12.
37.
13.
38.
14.
39.
15.
40.
16.
41.
17.
42.
18.
43.
19.
44.
20.
45.
21.
46.
22.
47.
23.
48.
24.
49.
25.
50.
Year
of
Birth
Year
of
Death
Age
(years)
10
Name:
Location:
.
Survivorship Lab
“Cemetery Data”
Gender
Sample
(M or F)
Year
of
Birth
Year
of
Death
Age
Gender
Sample
(years)
(M or F)
1.
26.
2.
27.
3.
28.
4.
29.
5.
30.
6.
31.
7
32.
8
33.
9.
34.
10.
35.
11.
36.
12.
37.
13.
38.
14.
39.
15.
40.
16.
41.
17.
42.
18.
43.
19.
44.
20.
45.
21.
46.
22.
47.
23.
48.
24.
49.
25.
50.
Year
of
Birth
Year
of
Death
Age
(years)
11
Name:
Location:
.
Survivorship Lab
“Cemetery Data”
Gender
Sample
(M or F)
Year
of
Birth
Year
of
Death
Age
Gender
Sample
(years)
(M or F)
1.
26.
2.
27.
3.
28.
4.
29.
5.
30.
6.
31.
7
32.
8
33.
9.
34.
10.
35.
11.
36.
12.
37.
13.
38.
14.
39.
15.
40.
16.
41.
17.
42.
18.
43.
19.
44.
20.
45.
21.
46.
22.
47.
23.
48.
24.
49.
25.
50.
Year
of
Birth
Year
of
Death
Age
(years)