Transcript Attachment 4

How do biologists use math to understand
the natural world?
First, what is population biology?
• Population biologists study how groups of the same
species living in the same place at the same time interact
with each other and their surroundings.
• Scientists are concerned with how populations respond to
changes. Some questions a population biologist might
ask are:
1. When will elephants in Africa go extinct if illegal
poaching continues at the current rate?
2. How fast will Zika virus spread through Mosquito
populations in Florida?
3. Will bird populations be able to migrate fast enough
under expected climate change conditions?
How do biologists answer these
questions?
They go into the field and collect data on their
population(s) of interest!
• For example, they might count the number of
elephants in an area, place tags on them, and return
to count them next year.
• Then they use their data and math to answer their
questions.
• Now it’s your turn to be a population biologist.
How do they use math?
• If we return to our elephant
example, a biologist will go
to Africa and count all of
the elephants they see in a
given area.
• In addition to counting
them, they might assess
how old the elephant is
based on its teeth. You
can tell about how old an
elephant is based on the
number of molars in its
mouth.
How do they use math?
• Next, a biologist can construct a life table.
• A life table is a table that shows the probability of
survivorship and reproduction for different age classes in
a population.
• This is an example of the column headings in a life table.
Age class
Number
Proportion Number of
alive at the alive at the
deaths
start of the
state of
during the
year
the year
year
Average
number of
offspring
per
individual
Death rate
Average
life
expectanc
y (years)
How do they use math?
• Here is a life table. What columns did the biologist collect
in the field and what columns did they calculate when they
got to their computer?
Age class
(years)
Number alive
at the start of
the year
Number of
deaths during
the year
Average
number of
offspring per
individual
Death rate
0-1
337
207
0
=207/337
0.61
1-2
252
125
2.5
=125/252
0.50
2-3
127
60
4
=60/127
0.47
3-4
67
32
2
=32/67
0.48
How do they use math?
• Good, death rate is calculated on the computer. They
count the number alive and number that have died in the
field.
Age class
(years)
Number alive
at the start of
the year
Number of
deaths during
the year
Average
number of
offspring per
individual
Death rate
0-1
337
207
0
=207/337
0.61
1-2
252
125
2.5
=125/252
0.50
2-3
127
60
4
=60/127
0.47
3-4
67
32
2
=32/67
0.48
How do they use math?
• Next, the use simple statistics to find out more about this
population.
Age class
(years)
Number alive
at the start of
the year
Number of
deaths during
the year
Average
number of
offspring per
individual
Death rate
0-1
337
207
0
=207/337
0.61
1-2
252
125
2.5
=125/252
0.50
2-3
127
60
4
=60/127
0.47
3-4
67
32
2
=32/67
0.48
Data collected in the field:
Symbol
Name
x
Age interval
S(x)
b(x)
Definition
Age of an individual in a
population
Units
Time
Cohort
survival
The total number of
individuals that are alive at the
beginning of age interval x
Number of
individuals
Fecundity
schedule
Average number of female
offspring born per unity time to
an individual female of a
particular age
Number of
individuals
Data calculated on the computer:
Symbol
l(x)
g(x)
Name
Definition
Proportion of the
original cohort that
survives to the start
Survivorship of age x or the
schedule probability that an
individual survives
from birth to the
beginning of age x.
Probability that an
Survival
individual survives
probability from age x to age
x+1
Formula
Units
Proportion
No units,
probability
Data calculated on the computer:
Symbol
G
Name
Definition
Average age of the
parents of all the
Generation
offspring produced
time
by a single cohort
(Caughley, 1977)
Formula
Units
Time
Data calculated on the computer:
Symbol
R0
Name
Definition
The mean number
Net
of female offspring
reproductive
produced per female
rate
over her lifetime
Formula
Units
Number of
offspring
Data calculated on the computer:
Symbol
R0
Name
Definition
The mean number
Net
of female offspring
reproductive
produced per female
rate
over her lifetime
Formula
Units
Number of
offspring
Data calculated on the computer:
Symbol
r
Name
Definition
The rate at which a
population increases in
Intrinsic rate of size if there is no
increase
competition
for
resources with other
animals
Formula
Data calculated on the computer:
Symbol
r
Name
Definition
The rate at which a
population increases in
Intrinsic rate of size if there is no
increase
competition
for
resources with other
animals
Formula
This seems confusing!
• Although there are a lot of new topics introduced, once
you have a chance to be the biologist this will become
easier.
• Today, you are going to calculate life table statistics for
non-human primates. You are going to use a real dataset
collected by biologists around the world.
• Begin by opening your Microsoft Excel spreadsheet.
The dataset
1. Name the species in this dataset.
2. Click on each tab and determine which species has the
3.
4.
5.
6.
longest life (species that has the largest age interval).
Click on the “metadata” tab. What information is in this
tab?
Find a partner and pick one of the seven species. Make
sure all statistics are calculated for each species as a
class.
Using the formulas in the Excel sheet, fill in the boxes in
yellow for your chosen species.
Complete the assessment after you finish the in-class
activity.