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Modeling the Area RestrictSearching Strategy of StinglessBees, Trigona biroi, as aQuasi-Random Walk Process

9th Annual National ConventionPhilippine Society for the Study of Nature (PSSN)12-15 November 2009Mindanao State University Iligan Institue of Technology

(MSU-IIT) Ilagan City, Lanao del Norte, Philippines

Jomar F. RabajanteMath Division, Institute of Mathematical Sciences andPhysics

University of the Philippines Los BaosRoberto B. Figueroa Jr.Institute of Computer ScienceUniversity of the Philippines LosBaos

Arian J. JacildoInstitute of Computer Science

University of the Philippines Los Baos

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Outline

Outline

Introduction

Model Formulation

Optimal Foraging Theory Biroi Preference Algorithm

Area Restrict Searching strategy

Visualization using Netlogo (demo) Conclusions and Recommendations

References

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Outline

Introduction

Interdisciplinary research collaboration

Mathematics

Mathematical Modeling

Computer Science

Computer Visualization

Biological Science

Tool for teaching UPLB Bee Program

Aid in planning for beekeeping

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Outline

Introduction: Pollination

If the bees disappeared off the surface of the globe, thenman would only have four years of life left. No more bees,

no more pollination, no more plants, no more animals, no

more man- Eistein

Bees are good natural cross-pollinators

Pollination helps provide adequate food

supply for human (Can increase cropproduction by 40%)

Pollination helps sustain biodiversity of

plant species 2009 University of the Philippines at Los

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Outline

Introduction: Pollination

2009 University of the Philippines at Los

Why study bees foraging behavior? Pollination usually happens during the

foraging activity of bees.

Trigona biroiFriese stingless (Meliponini) native in the Philippines better pollinator than the honeybees (Apis)

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Outline

Introduction: Pollination

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OutlineModel Formulation

Foraging Behavior of bees

Optimal Foraging Theory

Bees are maximizing the benefits that can beobtained from the food vis--vis the costs needed

in foraging

Marginal Value Theorem

Bees find another food source when the

profitability of the food is diminishing

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OutlineModel Formulation

Foraging Behavior of bees

Patch hopping

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OutlineModel Formulation

Foraging Behavior of bees

Determining the

paths throughexperiments:

Compare the

skewness of the

distributions of

time visitation

of bees 2009 University of the Philippines at Los

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OutlineModel Formulation

Stochastic Process

Probabilities

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OutlineModel Formulation

Stochastic Process

Not Purely Random - the chances of

going to certain feeders are not allequal

Bees have preferences (following the

Optimal Foraging Theory)

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i i f l i h

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OutlineBiroi Preference Algorithm(AHP)

2009 University of the Philippines at Los

CRITERIA Height SucroseConcentration

Distance

Height 1 5 1/3

SucroseConcentration

1/5 1 1/9

Distance 3 9 1

0.267399

0.063736

0.668864

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Outline

2009 University of the Philippines at Los

Food1

Values for Food1

Distance = 5m

Height = 6m

Sucrose% = 40%

Hive

Values for Food2

Distance = 6m

Height = 6m

Sucrose% = 50%

Food2

Values for Food3

Distance = 7m

Height = 3m

Sucrose% = 60%

Food3

AHP

Height Sucrose% Distance

Height 1 5 1/3

Sucrose% 1/5 1 1/9

Distance 3 9 1

?

Biroi Preference

Algorithm

Probabilities

??

Biroi Preference Algorithm

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OutlineArea Restrict Searching

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OutlineNetLogo Simulation

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Scouts

Randomly

Search Food

Sources

Foragers Select Food

Source via Biroi

Preference Algorithm

plus

Area Restrict Searching

Use simulation than exhaustive

enumeration of possibilities

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OutlineNetLogo Simulation (demo)

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OutlineConclusions

We have improved our model for bee

foraging behavior by incorporating area

restrict searching.

We have implemented a software to

visualize our model using Netlogo, anagent based simulation tool.

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OutlineRecommendations

Incorporateother

parameters (e.g.

environmental

factors)

Improve the

multi-agent

design (e.g. 3Dview)

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OutlineAcknowledgement

UPLB Bee Program

Institute of Mathematical Sciences and

Physics

Institute of Computer Science

College of Arts and Sciences

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OutlineResearch Team

2009 University of the Philippines at Los

Arian J. Jacildo

Jomar F. Rabajante

Roberto B. Figueroa

Jr.

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OutlineSelected References

Biroi Preference Algorithm

Rabajante, et al. (2009)

Bee Behavior

Nieh, et al. (2000) Roubik, et al. (1995)

AHP

Taha, H. A. (2007)

Netlogo Wilensky, U. (1999)

http://ccl.northwestern.edu/netlogo

2009 University of the Philippines at Los