Footprints of bees are fractals, complexity of bee training
23
On Training Trigona biroi : Behavioral Complexity and Apparent Patterns Jomar F. Rabajante 1 , Alejandro C. Fajardo, Jr. 2 1 Institute of Mathematical Sciences and Physics, University of the Philippines Los Baños, College, Laguna 4031, Philippines 2 Institute of Biological Sciences, University of the Philippines Los Baños, College, Laguna 4031, Philippines
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stingless bees, Trigona biroi, footprints, fractals, complexity, training, learningCitation: J.F. Rabajante and A.C. Fajardo, Jr., On Training Trigona biroi : Behavioral Complexity and Apparent Patterns, 15th BEENET Conference and Techno-fora, Hotel Agripino, Salagdoong, Maria, Siquijor, 23-25 July 2009.
Transcript of Footprints of bees are fractals, complexity of bee training
On Training Trigona biroi :Behavioral Complexity
and Apparent Patterns
Jomar F. Rabajante1, Alejandro C. Fajardo, Jr.2
1 Institute of Mathematical Sciences and
Physics, University of the Philippines Los
Baños, College, Laguna 4031, Philippines2 Institute of Biological Sciences, University of the
Philippines Los Baños, College, Laguna
4031, Philippines
Objectives
• Determine the complex behaviors of
Trigona biroi
• Determine a near-optimal way of training
the bees to learn a new food-type
• Determine the behavioral patterns of
Trigona biroi during
– Scouting
– Recruitment
– Foraging
Complex Systems
• Complex systems are composed of
interacting components that show dynamic
behaviors. Usually, such systems have
sophisticated structures, which make their
designs hard to comprehend.
• However, even though complex systems
are complex, they still work-out for
stability, and recognizable behavioral
patterns may exist (attractor and edge-of-
chaos).
Characteristics of a
Complex System
Adaptable
Related Experiment 1
• Open Field
Related Experiment 2
• Closed
room
• No direct
sunlight
Related Experiment 3
• Closed
room
• With direct
sunlight
Related Experiment 3
• Closed
room
• With direct
sunlight
Related Experiment 4
Independent Experiment 1
• Room with
direct
sunlight
• Open
Windows
Independent Experiment 2
• Semi-
enclosed
area (semi-
open field)
COMPLEXITY OF
BEE COLONIES
There are many factors to consider in training the
bees:
• The food itself (e.g. sucrose concentration)
• Sunlight / light
• Direction of sunlight
• Open space
• Food location
• Weather
• Etc…
APPARENT PATTERNS
Successful Scouting
0
10
20
30
40
50
60
70
80
90
100
429
433
440
442
445
447
449
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468
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475
477
Du
rati
on
in
seco
nd
s
Time of Day in Seconds
Scout Behavior Per Patch
Successful Scouting
0
10
20
30
40
50
60
70
80
90
100573
575
577
580
584
586
589
592
595
598
601
603
605
607
609
611
613
615
617
619
Du
rati
on
in
S
eco
nd
s
Time of Day in Seconds
Scout Behavior Per Patch
Successful Foraging (Outside)
y = 7E-09x5 - 3E-06x4 + 0.000x3 - 0.020x2 + 0.468x - 1.507R² = 0.980
-50
0
50
100
150
200
250
300
350
6:5
0
7:1
4
7:3
3
7:4
6
8:2
9
8:4
2
8:5
0
8:5
9
9:0
8
9:1
7
9:2
5
9:3
3
9:4
1
9:4
9
9:5
7
10:0
5
10:1
3
10:2
1
10:2
9
10:3
7
10:4
5
10:5
3
11:1
0
11:3
0
11:5
0
12:2
0
13:0
5
Nu
mb
er
of
bees
Time of day in seconds
Number of Foragers per Patch
Successful Foraging (Outside)
y = 3E-09x5 - 1E-06x4 + 0.000x3 -0.008x2 + 0.159x + 0.277
R² = 0.967
0
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40
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100
120
140
160
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6:5
0
7:3
1
7:5
7
8:4
7
9:0
4
9:2
0
9:3
5
9:5
0
10:0
5
10:2
0
10:3
5
10:5
0
11:2
0
11:5
8
13:1
5
y = 8E-11x6 - 4E-08x5 + 7E-06x4 -0.000x3 + 0.026x2 - 0.448x + 2.694
R² = 0.959
0
20
40
60
80
100
120
140
160
6:5
07:2
27:4
28:3
18:4
68:5
89:1
09:2
29:3
39:4
49:5
510:0
610:1
710:2
810:3
910:5
0
Successful Foraging (Inside)
y = 0.330x - 7.280R² = 0.902
y = -3E-10x6 + 1E-07x5 - 2E-05x4 + 0.001x3 - 0.049x2 + 0.592x - 0.671R² = 0.963
-10
0
10
20
30
40
50751
761
771
781
791
801
823
829
843
856
862
867
872
877
882
887
892
898
903
908
915
922
930
938
944
954
Nu
mb
er
of
Bees
Time of Day in Seconds
Number of Foragers per Patch
Outside VS Inside Training
Inside a room
Outside semi-enclosed area
Using Two-Sample Kolmogorov-Smirnov Test
(Nonparametric), at 95% confidence level, the two
population have significant difference.
Geometry of Footprints
Get Footprints
Geometry of Footprints
Geometry of Footprints
Get Fractal Dimension
Binarize
Geometry of Footprints
Get Fractal Dimension
On Training Trigona biroi :Behavioral Complexity
and Apparent Patterns
Jomar F. Rabajante1, Alejandro C. Fajardo, Jr.2
1 Institute of Mathematical Sciences and
Physics, University of the Philippines Los
Baños, College, Laguna 4031, Philippines2 Institute of Biological Sciences, University of the
Philippines Los Baños, College, Laguna
4031, Philippines
