Life Tables - MIT OpenCourseWare
[Pages:2]MIT Department of Biology 7.014 Introductory Biology, Spring 2005
Recitation Section 21 Answer Key
April 27-28, 2005
Life Tables
A. Cohort life table
You are studying the life of the common tribble. In a large tribble colony, you mark 1000 newborn tribbles and observe them for the next 5 years. You find the following:
1. Derive formulas for and calculate the remaining values in the table, based on the following definitions.
lx survivorship in year x = survival of individuals to age x mx mortality rate in year x = proportion of individuals of age x dying by age x+1 Lx age units lived in year x = mean # of individuals alive between year x and x+1 ex remaining life expectancy at age x = expectation of further life for individuals of age x
5
Li
ex
=
i =x
n x
s x
=
n (x+1) nx
lx
=
n x n0
mx = 1- sx
Lx
=
n x + n (x+1) 2
Year (age)
x 0 1 2 3 4 5
# tribbles alive at start of
year nx 1000 900 700 200 50 0
Survivorship
lx 1 0.9 0.7 0.2 0.05 0
Mortality rate
mx 0.1 0.22 0.71 0.75 1.00
Mean # tribbles alive in
year Lx 950 800 450 125 25
avg. life expectancy = x + e x
Average Remaining
Life Expectancy
ex 2.35 1.55 0.86 0.75 0.50 0.00
Average life expectancy
for individuals of
age x
2.35 2.55 2.86 3.75 4.50
2
2. Sketch the survivorship curve for tribbles: 3. Describe this curve in words. Speculate on what could cause the qualitative shape of the curve.
1.0
l x 0.5
Tribbles su rv iv e w ell u n til age 2, w h en su rv iv orsh ip decreases sh arply. Perh aps at age 2, th ey reach old age, or becom e old
en o u gh to be p r eyed u p o n .
0
0
1 2 3 4 5
age
4. What other types of curves are there? Describe qualitative conditions that produce these curves. The immediate exponential decay curve applies to organisms that have a lot of offspring that die
very young, such as frogs, fish, or trees.
The linear decay curve applies to organisms whose probability of dying is not dependent on age.
The very slow decay followed by the exponential decay curve applies to organisms that have very
few offspring, and take great care to protect those offspring, such as humans.
B. Replacement rates You also collected data on the tribbles born to the cohort you are studying. This is summarized below:
YEAR (age)
x 0 1 2 3 4 5
# tribbles alive at start of year
nx
1000 900 700 200 50 0
# individuals born to members of
cohort during year x 0
1200 100 50
5 0
Fecundity
bx 0 1.33 0.14 0.25 0.10 0
lxbx 0 1.2
0.10 0.05 0.01*
0
for question
3 0 0 2 0 0 0
for question
4 0 0 0 4 0 0
1. Calculate the fecundity and realized fecundity (lxbx) for each age group.
i = 5
2. Calculate the net reproductive rate, R0 = libi . Is this population stable (R0=1), growing i = 0 (R0>1), or shrinking (R0 ................
................
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