Educational material integrating math and biology for middle school, high school, and
introductory college sciences classes: Population dynamics and physiology of Drosophila.
PHILIP H.
REBECCA M.
SUSAN
DIANE
2,3
1
1
ZEIDLER-WATTERS , RICHARD COOPER and ROBIN L. COOPER .
% of flies on dish
10
5
0
0
10
15
10
5
0
10
5
0
0
10
20
20
15
10
5
0
20
Cumulative Sum
40
300
Determining pupation rates:
Adults at one of two ratios (one male to one female or one male to three females) were placed into food
containing vials. They were allowed to lay eggs and were monitored daily. Once larvae began pupating, they
were circled and numbered on the exterior of the vial. Each pupa was then documented with the time at which
it was first seen. This continued as pupa continued to form.
150
10
20
Time (min)
50
1000
0
0
Determining eclosion rates:
Using the same vials used for calculation pupation rates, they were monitored for the emergence of new
adults. When the first fly eclosed in a vial, it was documented, and all adult flies were removed. The vials were
then monitored daily for newly eclosed flies. Adults were continuously removed, and records were kept as to
how many flies were removed in each session. This continued until no new flies eclosed in a given vial.
Trial 4
Trial 5
10
80
60
40
20
0
Food choices and effects in quality of food:
Adults laid eggs on apple juice containing agar. The eggs were taken off and placed in the various
environments containing sugar or a corn meal diet at different developmental times. The developmental
growth was examined every 12 hours. The shapes of the mouth hooks were used to determine the larvae
stages. To conduct this part of experiments, mouth hooks had to be removed from the larvae and placed on
microscope slides to be viewed with a compound microscope at 100x. The adults were tested for various
behavioral assays based on sensory function. The 3rd instar larvae were tested for behaviors.
Body Wall Movements (BWM) for larvae
Early 3rd instar larvae were used for behavioral assays after they fed on sugar water for 2, 4 and 6 days.
Feeding and locomotory behavior were performed as described in Neckameyer (1996) and Li et al., (2001). In
brief, single animals were placed on a 2% agar surface and the number of body wall contractions counted for
1 min. The 1st instar larvae were placed in sugar water and examined after the set number of days.
10
20
Time (min)
EGGS
SUCCESSFUL
FEMALES
LARVAE
PUPAE
FEMALES
MATED
FEMALES
OTHER
MALES
Now one can start to express the
population dynamics in a flow chart.
And even graph the data gathered
and construct mathematical
expressions.
Students collaborate on developing
a flow diagram expressing these
ideas. This should start simple
(e.g. the four boxes linked
horizontally in the diagram below)
and then take on more realistic
detail. The result should be
something approximating the figure
on the left.
144
168
144
168
144
168
10
8
6
4
168
96
192
120
12
2
6 Days Sugar Water
10
8
6
4
2
100
48
(2)
72
(3)
96
(4)
120
(5)
144
(6)
168
(7)
192
(8)
Time (hours)
80
96
120
(4)
(5)
(6)
Time to pupation and then the time for the pupa to become an adult with larvae raised on
2, 4 or 6 days on sugar water before being placed in corn meal.
60
40
20
0
0
10
20
0
10
20
Time (min)
Righting response after being vortexed. This type of test
is used in adult Drosophila to examine if the brain and
sensory neurons are functioning well. The results did not
show any difference in the adults from the larvae fed
sugar water 2, 4, or 6 days. All the flies quickly got up
after being vortexed. They were all able to do this in less
than 10 seconds.
50
100
80
60
40
20
0
Time (min)
50
12
cm
24
cm
70
60
40
30
10
0
4
6
Days Fed Sugar Water
Trial 1
Trial 2
Trial 3
Trial 4
Banana
Egg laying
Many pupa
& adults
Larvae died
Many pupa
& adults
1st instar
28 pupa
All larvae died
25 adults (fungus)
30 pupa
28 adults
Corn meal
5 days
All died as larvae Day 10 15%
The 3 pupa died Day 11 78%
Day 12 98%
The adult test with
light responses with
larvae fed sugar water
for various days.
Trial 5
Lemon
Sugar water
15 days (3/60)
(14 day larvae
but sick)
CONCLUSIONS
1. Modules examining population dynamics can be successfully
implemented in biology classes by altering several factors. Sex ratios in
the parental generation and food availability measurably affects how to
population grows.
2. Students can use mathematical modeling, along with an
understanding of the fruit fly life cycle, to describe how the population
changes. This can be accomplished by using a flow diagram or with the
aid of computer modeling software.
3. Lemon was the fruit that fruit flies liked the most to lay their eggs, but it
turned out that lemon was the worst fruit for the larvae to grow on.
Peach
5 days
Banana
5 days
18%
81%
98%
23%
77%
98%
4. Sugar water alone was one of the foods that increased their life span
by nearly 2 weeks. Behavioral tests showed no huge changes in larvae
fed only sugar water. Only mouth hook movements and body wall
movements showed some minor decreases then the ones fed normal
food.
In the future it would be interesting to test the effects of different types of
amino acids on larval development and behavior.
100
250
200
150
100
50
References
80
60
40
20
0
0
2 days
4 days
6 days
(7)
Time (Hours)
50
Body Wall Movement per Min
Behaviors for the newly elcosed adults
A plastic tube on a wooden stick with a small flashlight on top of the tube was used. The light was placed on
the top of the tube to examine the locomotive ability of the flies to go to the top of the tube. The time it took
flies to reach the 12 and 24 cm marks was measured. A righting response of the adults was also tested after
they were shaken for 20 seconds. This was done by placing the flies in a plastic vial and vortexed and then
quickly examined . Animals that had 2, 4, or 6 days in sugar water as a larvae and then placed in cornmeal for
pupation were the experimental conditions for this set of experiments.
MALES
144
6 Days Sugar Water
24
(1)
Peach
Adults:
120
12
50
Banana
Peach
Lemon
300
Mouth Hook Movement per Min
Mouth Hook Movements (MHM) for larvae
Larvae were placed in a 2% yeast solution on an agar plate after they fed on sugar water for 2, 4 and 6 days.
In this condition, Drosophila larvae immediately fed, causing a pattern of repetitive mouth hook movements.
The number of full mouth hook contractions in 1 minute was counted (Li et al., 2001).
The results of these behaviors are plotted as body wall contractions or mouth hook movements per minute.
The three fruits, cornmeal, and
sugar water diets all in their
containers.
120
4
TABLE 2: These are showing the survival rate of the different diets.
Closed system 1 male: 1 female but each container with different
amounts of food. Let the chamber go until populations die out
and then count total number of adults.
96
0
Survival:
Form Pupa:
72
6
TABLE 1:
Egg Lying
In this experiment around 100 adults were placed in a glass cage, adult taste preference and egg laying were
examined together in this assay. 3 Petri dishes containing lemon, peach and banana as food were placed
inside the cage. These foods were also used to test survival of the larvae. After the adults have had 4 hours
on these dishes they were removed and how many eggs were laid on each dish were counted. This showed
egg laying preference. Then every day larva developed and formation of pupa in the different foods were
examined.
48
8
The number of eggs on each dish for the five trails. Since there was not an equal number of
eggs in each trial, calculate a percent of eggs on each dish related to counting the number of
eggs on the banana as 100%.
Closed system adult counts:
Three large containers were setup with ample water and a different amounts of food. A male and female fruit
fly were placed in each. They were set aside and allowed to grow indefinitely. The population continued to
thrive until the food ran out. Once all of the flies had died, the containers were opened and adults counted.
96
192
2
2
Trial 3
4
4 Days Sugar Water
20
2000
Trial 2
168
2
50
4000
3000
100
Trial 1
144
4
12
c
200
6
4 Days Sugar Water
24
Time (sec)
METHODS
% of eggs
250
120
0
100
4500
96
6
0
5000
Banana
Peach
Lemon
72
8
Number of eggs
350
48
10
20
50
Time (min)
50
24
m
10
Time (min)
60
50
Time (min)
20
80
0
15
10
100
50
Time (min)
20
0
These large vials one can
keep the adults which
form and count
continuously the number
of pupa which form until it
become too crowded.
20
8
2
24
Another example of 2
sets of conditions,
repeated 3 times.
1 female :1 male vs
3 females :1 male
10
12
0
0
20
2
20
50
Time (min)
% of flies on dish
1 female :1 male
20
4
0
0
15
6
10
40
50
Time (min)
20
0
These graphs are showing the
number of flies that landed on
each fruit. The left panel is the
raw data of the total number of
flies for the 5, 10, 20 and 50 min
time points for the five different
trials. The right side panel is
the converted data set when
transferred to percent of total
number of flies.
20
% of flies on dish
Ever 5 minutes count the number of adults
on the various food s. Repeat trails
at various time intervals. Graph data (left)
10
8
Cumulative Sum
0
2 Days Sugar Water
Cumulative Sum
5
60
2 Days Sugar Water
12
cm
24
cm
10
80
Time pupation to eclosion
12
10
Cumulative Sum
15
The aquarium and the fruits under them.
Peach, lemon, and banana .
Mark each pupa as they
form. Take out adults at a
particular day before pups
elcose. Then count the
rate of eclosion by
releasing the flies each
day.
3 females :1 male
Banana
Lemon
Peach
100
% of flies on dish
3 females :1 male
% of flies on dish
# of flies on dish
Module 1: Rate of population growth depending on #of females and elclosin rate
1 female :1 male
20
0
An example of 2 sets of
conditions, repeated 3
times.
1 female :1 male vs
3 females :1 male
Time to pupation
12
Module 2: Food choice of adults and
effects on larvae
KIM
Module 3: Pupa and adult behaviors in response to diet as a larvae .
Math and Science Outreach Unit of PIMSER.
# of flies on dish
Before starting the modules a pretest will given to examine the
knowledge base of the students on population dynamics and thoughts
on the effect of nutrition and amount of resources on the population
survival.
3P-12
# of flies on dish
The driving principle is to develop educational material which integrates math, biology and
environmental factors for middle and high school sciences classes as well as introductory college
courses. Here we outline an approach to modeling the life cycle and its implications for population
growth in laboratory Drosophila populations. The goal is to develop a viable example of
methodology that can be implemented in high schools and middle schools to introduce modeling
that links with empirical studies in a way that is accessible to students. The approach is intended
to encourage conceptual thinking and open a range of student-driven explorations at the
intersection of biology and mathematics.
Activity without understanding opposes what we know about effective science teaching
(Windschitl, Thompson, & Braaten, 2008a,b). In addition, the lack of cross disciplinary training in
K-20 grades compartmentalizes learning and hampers educational integration. This is even
evident within the sciences such as with math and biology. We are developing modules which
will be cross-disciplinary and can be used for middle school through college level courses. We
are developing modules for measuring fecundity with various numbers of females and
males, various environmental factors such as temperature and types of food. With the data
collected we will develop a means for teachers and students to use mathematical models to
explain the collected observations. The mathematical models can be used to predict the impact of
environmental disturbances which could influence fecundity (egg laying). Then experiments can
be performed to test if the predictions in the mathematical model hold or if adjustments in the
model need to be performed. The module begins with students observing Drosophila from
nymphs through the adult stage. In time we plan to have students use the parameters and data
collected from their studies and use Simulink (The MathWorks, Natick, MA) to simulate the
population dynamics over time.
In this study we also examined how diet can effect larval development and behavior as
well as adult behaviors. The food choices were lemon, banana, and peaches as well as corn meal
and sugar water. Adult flies did not show any real difference for food type to eat but tended to lay
more eggs on the lemon; however, all the larvae died in lemon due to mold/fungal growth more
common on lemon than the other food choices.
Larvae only fed sugar water delayed pupation for up to 14 days as compared to 4 days
with a healthy diet. The nutrient deprived larvae were smaller in body length for the same instar
stage. Behavioral assays in these larvae were carried out as a measure of health.
of STEM, Univ. of KY and
# of eggs
INTRODUCTION
of Biol., Univ. of KY.;
2Dept.
# of flies on dish
1Dept.
3
JOHNSON ,
Cumulative Sum
3
MAYO ,
cm
2
KRALL ,
Cumulative Sum
1
CROWLEY ,
# of flies on dish
SAMUEL
1
POTTER ,
Corn
food
2 days
4 days
6 days
These graphs show the body wall and the mouth hook movement results with the different days of larvae eating sugar water.
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Websites: Larva Food http://flystocks.boi.indiana.edu/german-food.htm