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, Philippines 2 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-ofchaos).

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 • Semienclosed area (semiopen 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

Time of Day in Seconds 477

475

473

471

470

468

466

464

462

461

459

457

456

454

453

451

449

447

445

442

440

433

429

Duration in seconds

Successful Scouting

Scout Behavior Per Patch

100

90

80

70

60

50

40

30

20

10

0

Successful Scouting Scout Behavior Per Patch 100 90 80

60 50 40

30 20 10

Time of Day in Seconds

619

617

615

613

611

609

607

605

603

601

598

595

592

589

586

584

580

577

575

0 573

Duration in Seconds

70

Successful Foraging (Outside) Number of Foragers per Patch 350 300

200 150 100

50 0 -50

6:50 7:14 7:33 7:46 8:29 8:42 8:50 8:59 9:08 9:17 9:25 9:33 9:41 9:49 9:57 10:05 10:13 10:21 10:29 10:37 10:45 10:53 11:10 11:30 11:50 12:20 13:05

Number of bees

250

y = 7E-09x5 - 3E-06x4 + 0.000x3 - 0.020x2 + 0.468x - 1.507 R² = 0.980

Time of day in seconds

Successful Foraging (Outside) y = 3E-09x5 - 1E-06x4 + 0.000x3 0.008x2 + 0.159x + 0.277 R² = 0.967

160 y = 8E-11x6 - 4E-08x5 + 7E-06x4 0.000x3 + 0.026x2 - 0.448x + 2.694 R² = 0.959

140 120 100

6:50 7:31 7:57 8:47 9:04 9:20 9:35 9:50 10:05 10:20 10:35 10:50 11:20 11:58 13:15

80 60 40 20 0

6:50 7:22 7:42 8:31 8:46 8:58 9:10 9:22 9:33 9:44 9:55 10:06 10:17 10:28 10:39 10:50

180 160 140 120 100 80 60 40 20 0

Successful Foraging (Inside) Number of Foragers per Patch 50

40

y = -3E-10x6 + 1E-07x5 - 2E-05x4 + 0.001x3 - 0.049x2 + 0.592x - 0.671 R² = 0.963

20

y = 0.330x - 7.280 R² = 0.902

10 0 751 761 771 781 791 801 823 829 843 856 862 867 872 877 882 887 892 898 903 908 915 922 930 938 944 954

Number of Bees

30

-10

Time of Day in Seconds

Outside VS Inside Training Using Two-Sample Kolmogorov-Smirnov Test (Nonparametric), at 95% confidence level, the two population have significant difference.

Inside a room Outside semi-enclosed area

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, Philippines 2 Institute of Biological Sciences, University of the Philippines Los Baños, College, Laguna 4031, Philippines