CMPS272, Winter 2007, Section 01: BeesnFlowers

Game Theory Project Status Report:

Title: BEES n FLOWERS Contributors: Corrie Scalisi (Computer Scientist) Mark Deckert (Computer Scientist) Robert Clark (Biologist)

General Description: This project is testing hypotheses about the evolution of bee preference to flower types and learning. We examine a threefold progression of proposed evolutionary steps to explore solitary bee behavior and how that behavior affects the flowers they visit. We are using a cellular automata framework where bees visit flowers to gain nectar payouts and flowers obtain payout based on visitation.

Specifics: Our project was inspired by a recent paper outlining the effect of sympatric flower species composition, population size, and reproductive self-assurance on the evolution of self-pollination in Clarkia xantania (Moeller and Geber 2005). Moeller and Geber observed that Clarkia populations that were isolated and small contained significantly larger corollas (petals). To explain this increase in corolla size it was suggested that bees might be more discriminating for large petaled flowers when competition between bees for flower resources was low. Our project tests the validity of this idea and asks the following general questions: 1) What kinds of bee behaviors will be favored under high and low competition regimes? 2) What affect does bee behavior have on the morphology of the flowers they visit?

Approach: We are using game theory principles and a cellular automaton to include a spatial component to the analysis. We have constructed two payoff matrixes to reflect both a bee game and a flower game and allow the two games to influence each other to capture the interaction seen in nature. To parameterize the game we are using the Clarkia xantania (flower)/ Diadasia angusticeps (solitary bee) interaction used in the Moeller and Geber paper. The cellular automata will be represented as a grid containing flowers of two types, placed randomly at the initiation of the game. The initial ratio of flower types will be a parameter under investigation in this study. The percentage of cells filled will vary and be investigated for spatial patterns that may arise during the game. We will place bees of two comparison types (described later) onto the array and monitor feeding performance and visitation to each flower. Each bee will move to a new flower at each time step within a day. At the end of each day the bee returns to its original position and begins feeding the next day. Flowers are replenished between days. After a defined number of days (generation time) the array is updated in the following manner. Bees of a particular type are compared using the average payout per individual normalized over the total per individual payout (replicator equation). The frequency of each bee type in the next generation will reflect their relative fitness in the past generation and will be randomly distributed on the array in the next generation. The ratio of flower types will be updated using a replicator equation to reflect relative fitness, measured by bee visitation, and will be randomly distributed on the array in the next generation. The bee game will consist of three comparisons between behaviors with varying competition regimes. We will compare: 1) Randomly Traveling Bees vs. Defined path Bees (updated queue learning) 2) Randomly Traveling Bees vs. Defined path Bees with discrimination (makes flower type switch) 3) Defined path Bees (updated queue learning) vs. Defined path Bees with discrimination (makes flower type switch) Testing these comparisons under varying competition regimes will enable us to test whether the hypothesis proposed by Moeller and Geber is explanatory and will enable us to investigate the hypothetical stepwise evolution of foraging behavior in solitary bees.

Works Cited: Moeller, D.A., Geber, M.A. (2005) Ecological Context of the Evolution of Self-Pollination in Clarkia xantiana: Population Size, Plant Communities, and Reproductive Assurance Evolution, 59(4) pp. 786-799

-- RobertClark? - 27 Feb 2007